Effective Porosity Detection in Laser-Based Additive Manufacturing Using Shallow Learning and Physics-Informed Pyrometer Features

Effective Porosity Detection in Laser-Based Additive Manufacturing Using Shallow Learning and Physics-Informed Pyrometer Features | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Effective Porosity Detection in Laser-Based Additive Manufacturing Using Shallow Learning and Physics-Informed Pyrometer Features RAJESH KUMAR BALARAMAN, Mehdi Jafary-Zadeh, Farzam Farbiz, Nagarajan Raghavan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7042984/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Laser-based additive manufacturing (LBAM) has transformed the production of complex metallic components through precise, layer-by-layer deposition. However, porosity defects can compromise the mechanical integrity of printed parts, necessitating effective real-time monitoring and defect detection methods. This study utilizes dual-wavelength pyrometer data to classify melt pool thermal profiles into no-porosity, micro-porosity, and macro-porosity categories, labelled based on X-ray Computed Tomography (CT) scans. Temperature profiles across four orientations (0°, 90°, + 45°, and − 45°) relative to the laser scanning direction were processed through shallow learning models, enhanced with signal processing and physics-informed features, including melt pool distance (MPD) and aspect ratio of maximum temperature to MPD (ARTM). Our approach achieved classification accuracy (up to 95%), precision (96%), and recall (95%) in defect classification. To address challenges in predicting minority classes, we introduce a classification deviation error (CDE) metric. This work demonstrates that shallow learning models, combined with strategically engineered features, provide an efficient and reliable alternative to computationally expensive deep learning methods for in situ defect detection and quality assurance in LBAM. Laser-Based Additive Manufacturing (LBAM) In Situ Monitoring Pyrometer Sensor Porosity Detection Physics-Informed Shallow Learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Laser-based additive manufacturing (LBAM) is transforming the production of complex three-dimensional (3D) metallic components by offering high precision, minimal material waste, and reduced production time. Widely utilized in aerospace, automotive, and medical industries, LBAM converts computer-aided design (CAD) models into functional parts through powder melting techniques such as direct laser deposition (DLD) [ 1 ], laser metal deposition (LMD) [ 2 ], laser cladding, laser powder bed fusion (LPBF) [ 3 ], selective laser melting (SLM) [ 4 ], and selective laser sintering (SLS) [ 5 ]. These processes involve critical machine parameters, including laser power, scanning speed, hatch spacing, layer thickness, and environmental conditions [ 4 ]. After manufacturing, components are detached from the substrate and subjected to post-processing methods such as hot isostatic pressing, polishing, and coating to enhance surface finish, dimensional accuracy, and mechanical properties [ 6 , 7 ]. Quality assurance (QA) plays a vital role in ensuring the structural integrity of LBAM components, identifying defects like cracks, porosity, and surface irregularities. Traditional ex situ inspection techniques, including X-ray computed tomography (CT), ultrasonic testing, and optical methods [ 6 , 8 , 9 ], are effective but time-intensive and expensive. To overcome these limitations, in situ monitoring (ISM) [ 10 – 14 ] leverages integrated sensors for real-time defect detection, capturing insights into melt pool dynamics [ 15 – 17 ], temperature distribution [ 18 , 19 ], cooling behaviour [ 20 ], and spatter formation [ 21 ]. While ISM enhances defect detection, predictive modelling is critical for understanding process-structure-property (p-s-p) relationships in additive manufacturing (AM) [ 10 , 22 ]. Physics-based simulations employ thermal and fluid dynamics models to predict defects such as porosity, warping, lack of fusion, cracks, as well as microstructure, mechanical properties, fatigue behaviour, and residual stress [ 23 – 25 ]. However, these simulations are computationally expensive, require complex calibration, and rely on theoretical simplifications, such as uniform material property assumptions, limiting their accuracy in real-world applications. Consequently, they are not suited for ISM that requires real-time accounting for localized variations in heat distribution and material interactions. Conversely, data-driven methods leverage sensor data and machine learning (ML) models to predict defects efficiently could enable ISM and adaptive control for consistent quality [ 26 – 28 ]. In data-driven approaches, ML models are employed to correlate signal features with metallurgical defects that reduce reliance on costly simulation and experimental trials, offering a scalable and efficient solution for quality assurance in AM. These models can be mainly classified into shallow learning (SL) and deep learning (DL) based on their architecture, complexity, and hierarchical data representation [ 29 , 30 ]. DL models, including Convolutional Neural Networks (CNN) [ 31 – 33 ], Recurrent Neural Networks (RNN) [ 34 ], Generative Adversarial Networks (GAN) [ 35 ], Autoencoders, and Transformers, can learn complex features from raw sensor data but require large datasets and high computational power to train these models. DL models often struggle with small datasets, leading to overfitting and poor prediction rates for minority class defects. In contrast, SL models, such as Linear/Logistic Regression (LR), Random Forest (RF), Decision Tree (DT), Support Vector Machine (SVM), and K-Nearest Neighbors (KNN), have simpler architecture; hence, they are computationally more effective, and ideal to deal with smaller datasets [ 36 – 38 ]. These models mitigate overfitting and class imbalance through regularization and Synthetic Minority Oversampling Technique (SMOTE) [ 39 , 40 ] to enhance accuracy in determining minority classes. Optimizing the appropriate architectures of SL models can achieve comparable performance metrics such as accuracy and error rates to DL models while offering significantly lower space–time complexity, making them an efficient choice for limited datasets and resource-constrained AM applications [ 30 , 41 ]. However, SL models rely heavily on feature extraction from sensor data. As a result, feature engineering, which involves extracting relevant statistical and physics-informed features from raw sensor data, is critical for establishing correlations between sensor data and defects like porosity, thereby enhancing model performance in predictive quality control [ 42 – 44 ]. Several studies have investigated the relationship between melt pool dynamics and defect formation using various in-situ sensing techniques, with pyrometers playing a key role in capturing real-time thermal profiles. Dual-wavelength pyrometers and high-speed co-axial infrared cameras are frequently used to collect thermal data across layers, enabling the analysis of melt pool characteristics and material-specific properties such as optical emissivity and absorptivity [ 1 , 45 , 46 ]. The pyrometry signal, i.e. , measured emission intensity, is directly influenced by laser energy density, which is governed by process parameters including laser power and scanning speed. These thermal signatures have shown strong correlations with melt pool instabilities and defects such as keyhole-induced porosity [ 47 , 48 ]. Therefore, by extracting features from pyrometer signals and correlating them with X-ray CT scan data labeled by pore size and location, it becomes feasible to link thermal anomalies to porosity defects, offering a robust basis for predictive quality control in metal AM [ 36 , 49 – 54 ]. In this work, we introduce a new approach for classifying porosity defects in LBAM by integrating ISM with SL models. Using a high-resolution pyrometer sensor, we capture detailed melt pool thermal profiles as the foundation of our analysis. The Methodology section outlines our process, including the experimental setup, thermal data processing, and classification of porosity defects into three distinct classes based on pore sizes. We also address class imbalance issues and describe our feature extraction and selection strategies from various thermal profile orientations to enhance predictive performance. Our SL models are employed for porosity classification and validated using both traditional evaluation metrics and our classification deviation error (CDE) metric, specifically designed to predict minority classes—an essential aspect of multi-class defect detection. In the Results and Discussion section, we compare model performance using traditional metrics and the CDE metric, demonstrating the effectiveness of our approach in reducing misclassification rates. Finally, the Summary highlights the significance of the extracted features from melt pool dynamics, emphasizing how domain knowledge contributes to improved model accuracy and robustness. 2. Methodology This study utilizes open-access datasets from the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University (MSU), where thin-walled Ti-6Al-4V structures were fabricated using LBAM techniques, specifically Direct Laser Deposition (DLD) [ 1 , 34 ]. The primary focus is on analysing thermal data collected during fabrication to detect and classify porosity defects using shallow learning models. This section outlines the experimental setup, data processing, and feature engineering steps undertaken in our analysis. 2.1. Experimental Setup A thin-walled structure (47.81×27.56×1.78 mm) was fabricated on a Ti-6Al-4V substrate (150×153×3.3 mm) using an OPTOMEC Laser Engineering Net Shaping (LENS™) 750 system, integrated with a Stratonics Dual-wavelength Pyrometer for thermal monitoring [ 1 , 34 ]. The substrate was mounted on a CNC-controlled platform, and Ti-6Al-4V powder was continuously injected through an angled nozzle aligned with a laser beam of 1.016 mm diameter. The build chamber was maintained at room temperature with an argon flow rate of 4L/min to ensure a controlled environment. The process parameters are a laser power of 290 W, a scan speed of 12.7 mm/s, and powder feed rate of 0.32 g/s. A single-track deposition length of 50.8 mm was repeated with an increment height of 0.508 mm across 60 layers, resulting in a structure height of 27.56 mm. To streamline melt pool data analysis, the system was configured to match the hatch spacing with the nozzle diameter, enabling each layer to be completed in a single-pass track configuration while thermal data was continuously recorded. 2.2. Data Processing The dual-wavelength pyrometer captured melt pool thermal readings with a resolution of 752 × 480 pixels, a pixel pitch of 6.45 µm, a temperature detection range of 1000–2500°C, and an exposure time of 2.0274 ms, at a data collection rate of 6.4 Hz. The coordination system was defined as follows: X-axis : Corresponds to the laser's orthogonal direction, measuring the part's width. Y-axis : Aligns with the laser's scan path, measuring the part's length. Z-axis : Represents the nozzle's upward movement, measuring the part's height. 2.2.1. Data Cleaning and Preparation Thermal data were saved as CSV files, labelled with time stamps, XYZ coordinates, and layer numbers. Data corresponding to non-active melting phases – such as nozzle movements when the laser was off – were excluded. In some layers, minor inconsistencies in pyrometer readings at specific Y-locations occurred due to sensor issues. However, these missing data points were sparse and did not significantly affect overall analysis accuracy. 2.2.2. Melt Pool Images Thermal readings captured during the AM process were transformed into two-dimensional (2D) images for each melt pool, providing critical insights into temperature distribution, geometry, cooling rate, flow dynamics, thermal gradients, and phase transitions. These thermal characteristics critically influence the material's microstructure and mechanical properties. To isolate the relevant melt pool zone, minimize thermal noise, and reduce input data dimensionality, a region of interest (ROI) was defined around the active melt pool. Each thermal image was cropped to a 150 x 150 pixel area, centered near the melt pool region, focusing on temperatures around the reference melting point of Ti-6Al-4V (T M = 1636℃) [ 31 , 34 , 36 , 55 ]. The melt pool profile, typically circular or elliptical, was analyzed along four key orientations, as represented in Fig. 1 (a) : Laser Path (Y-Axis, 0°) : Captures the laser’s direct impact on melting powder and is used to measure melt pool length. Orthogonal (X-Axis, 90°) : Analyzes lateral heat transfer to determine melt pool width. Oblique (U-V Axes, + 45° and − 45°) : Examines temperature gradients along diagonal axes, capturing combined thermal behaviour and flow dynamics across the melt pool region. Key thermal features extracted from each melt pool image included, as shown in Fig. 1 (b) : Maximum Temperature (MAX) : Peak thermal intensity above the melting point. Minimum Temperature (MIN) : Reference melting temperature (T M ). Melt Pool Distance (MPD) : Distance over which the temperature exceeds T M , calculated along each orientation (0°, 90°, + 45°, -45°) to evaluate anisotropic thermal behaviour. Thermal profiles frequently exhibited fluctuations, indicating non-uniform heating and cooling rates that can affect solidification and defect formation, indicated in Fig. 1 (b) . These fluctuations can cause thermal instabilities, leading to deviations in melt pool formation. As a result, some melt pools may develop pores, while others may lack a consistent melt pool structure, indicating potential anomalies. By analyzing these thermal profiles, we can correlate and validate the presence of defects with pore size data obtained from CT scans. 2.2.3. Porosity Classification Porosity levels for each melt pool were quantified using X-ray CT scans with a 1 µm resolution, capable of detecting pore from 0.05 mm to 1 mm in diameter. Each pore’s spatial coordinate was matched with the corresponding melt pool image. Given that an average melt pool occupied fewer than 40 pixels in the 150 x 150 ROI, accurate alignment was ensured, and no blind spots were observed. However, the limited number of thermal images with detectable pores greater than 0.05 mm introduced a significant class imbalance, and complicating defect severity analysis. To address this, porosity was stratified into three distinct categories based on pore size measured: No Porosity : No detectable pores. Micro-Porosity : Pores between 0.05 mm and 0.5 mm in diameter. Macro-Porosity : Pores larger than 0.5 mm in diameter. Thermal features (MAX, MPD) were analyzed across all four orientations and three porosity classes. Figure 2 (a) represents thermal images of each class, while Fig. 2 (b) shows corresponding temperature profiles along the laser path (Y-axis). Layer-wise distribution of porosity across the laser path (Y-axis) and build height (Z-axis), as presented in Fig. 3 . The highlighted melt pool regions, shown using thermal images, help distinguish between different porosity levels. Key observations from Fig. 3 indicate: Macro-Porosity localised near build edges due to uneven cooling rates and thermal gradients, promoting larger pore formation. Micro-Porosity concentrated at the bottom layers due to unstable thermal conditions during initial substrate deposition, leading to uneven heat distribution. No Porosity distributed uniformly in the middle sections, where thermal conditions remain relatively stable. Understanding these spatial distributions of porosity is crucial for optimizing process parameters and ensuring part quality. By correlating thermal profiles with porosity, we can identify patterns and develop predictive models to minimize defects in real-time. 2.2.4. Class Imbalance The dataset comprised 1557 thermal images categorized into three classes based on pore size: 1485 images with no porosity, 46 with micro-porosity, and 26 with macro-porosity. This significant imbalance in class distribution (illustrated in Fig. 3 ) poses a challenge for classification models, as ML algorithms can be biased towards the majority class (no porosity) and may underperform on the minority classes (micro- and macro-porosity). Such bias can result in low recall for defect-prone melt pools, increasing the risk of undetected flaws. To address this issue, we applied the SMOTE during preprocessing to balance the dataset [ 39 ]. SMOTE generates synthetic samples for the minority classes by interpolating between existing instances, increasing their representation in the dataset. This approach helps the model learn the underlying patterns of all classes more effectively. Following SMOTE, the dataset was balanced and split into training and testing sets using stratified sampling, preserving class proportions. We allocated 75% of the data for training and 25% for testing, ensuring an equal ratio of the three classes in both subsets. This method enhances the model's ability to generalize and accurately predict porosity levels across all classes. 2.3. Feature Engineering Feature engineering was performed on melt pool images derived from pyrometer data, focusing on data points above the reference melting point (T M ) of Ti-6Al-4V. This process aimed to capture the thermal features within the melt pool that influence porosity formation. Extracted features were categorized into two sets: Statistical Features : Quantitative descriptors derived from the temperature data. Physics-Informed Features : Features informed by the physical principles governing melt pool dynamics. 2.3.1. Statistical Features Thermal profiles were extracted from the pyrometer readings at each melt pool location along four orientations: laser path (0°), orthogonal (90°), and oblique (+ 45°, -45°), as described in Section 2.2.2 and illustrated in Fig. 1 . These directional profiles reflect temperature variation along the melt pool’s spatial extent, capturing information about thermal gradients and solidification patterns, which are closely linked to defect formation. Statistical features were grouped into: Independent Features : Directly computed from raw temperature profile, capturing fundamental statistical properties. Derived Features : Computed from combinations of independent features, providing higher-order statistical thermal characteristics. The features were calculated using standard statistical formulas (provided in Table 1 ) and are defined as follows: Independent Features (p 1 to p 9 ): Mean Temperature (MEAN, p 1 ) : Average temperature across the melt pool profile. Standard Deviation (STD, p 2 ) : Variation in temperatures. Root Mean Square (RMS, p 3 ) : Square root of the mean of squared temperatures. Square Mean Rooted Absolute (SMRA, p 4 ) : Squared mean of absolute temperatures. Maximum Temperature (MAX, p 5 ) : Highest temperature recorded in the profile. Total Harmonic Distortion + Noise (THD + N, p 6 ) : Quantifies signal distortion and noise in the temperature profile. Skewness (SKEW, p 7 ) : Indicates the asymmetry of the temperature distribution. Kurtosis (KURT, p 8 ) : Measures the "tailedness" of the temperature distribution. Derived Features (p 10 to p 15 ): Signal-to-Noise Ratio (SNR, p 9 ): Ratio of mean temperature of standard deviation. Waveform Factor (p 10 ): Ratio of RMS value to mean temperature. Crest Factor (p 11 ): Ratio of peak temperature to RMS temperature. Clearance Factor (p 12 ): Ratio of peak temperature to SMRA temperature. Impulse Factor (p 13 ): Ratio of peak temperature to mean temperature. Peak-to-Peak Value (p 14 ): Difference between maximum and minimum temperatures. These statistical features describe various aspects of thermal behavior, such as central tendency, dispersion, shape, and harmonic distortions, and serve as key inputs for shallow learning (SL) models in porosity classification. 2.3.2. Physics-Informed Features While statistical features offer valuable quantitative insights, they may not fully capture the complex thermal phenomena influencing porosity formation. To incorporate domain-specific knowledge, we introduced physics-informed features derived from melt pool temperature profiles, as provided in Table 1 : Melt Pool Distance (MPD, p 15 ) : The spatial distance along a specific orientation, where the temperature exceeds the melting temperature (T M ) of the alloy. Aspect Ratio of Maximum Temperature to Melt Pool Distance (ARTM, p 16 ) : A thermal-based ratio relating the peak temperature to the extend distance of melt pool. This thermally derived metric captures in-process melt pool behaviour that cannot be observed from post-process geometrical measurements alone, using Eq. ( 1 ): $$\:ARTM=\frac{Maximum\:Temperature\:\left(MAX\right)}{Melt\:Pool\:Distance\:\left(MPD\right)}$$ 1 ARTM provides insight into the concentration and distribution of thermal energy within the melt pool. A higher ARTM value indicates a sharper temperature gradient over a shorter melt pool distance, which is associated with rapid heating and cooling rates. By incorporating ARTM and MPD physics-informed features, we aim to bridge the gap between sensor-based thermal data and physical melt pool dynamics. These features enhance the input space dimensions for SL models and contributed to improved porosity classification performance. These physics-informed features are particularly valuable for identifying subtle variations in melt pool behaviour that contribute to porosity formation. Figure 4 (a) illustrates the spatial temperature distribution along the MPD for the three porosity categories: Macro-Porosity : Occurs at higher maximum temperatures (~ 2000°C) with shorter MPDs. This suggests rapid melting and solidification, leading to larger pores, possibly, due to gas entrapment or keyholing effects. No Porosity : Falls between these two extremes, representing optimal thermal conditions with a balanced MPD and temperature. Micro-Porosity : Occurs at lower maximum temperatures with longer MPDs. This indicates insufficient energy input, resulting in incomplete melting and small pores, possibly due to lack of fusion. Table 1 Feature Extraction from melt pool images: statistical features (p 1 to p 14 ) and proposed physics-informed features (p 15 and p 16 ) STATISTICAL FEATURES Independent Features Derived Features Mean Value \(\:{\text{p}}_{1}=\frac{1}{k}{\sum\:}_{i=1}^{k}s\left(i\right)\) Signal to Noise Ratio (SNR) \(\:{\text{p}}_{9}=\:\frac{{\text{p}}_{1}}{{\text{p}}_{2}}\) Standard Deviation (STD) \(\:{\text{p}}_{2}={\left(\frac{1}{k-1}{\sum\:}_{i=1}^{k}{\left(s\left(i\right)-{\text{p}}_{1}\right)}^{2}\right)}^{\frac{1}{2}}\) Waveform Factor \(\:{\text{p}}_{10}=\:\frac{{\text{p}}_{3}}{{\text{p}}_{1}}\) Root Mean Square (RMS) \(\:{\text{p}}_{3}={\left(\frac{1}{k}{\sum\:}_{i=1}^{k}{s\left(i\right)}^{2}\right)}^{\frac{1}{2}}\) Crest Factor \(\:{\text{p}}_{11}=\:\frac{\left|{\text{p}}_{5}\right|}{{\text{p}}_{3}}\) Square Mean Rooted Absolute (SMRA) \(\:{\text{p}}_{4}={\left(\frac{1}{k}{\sum\:}_{i=1}^{k}\sqrt{\left|s\left(i\right)\right|}\right)}^{2}\) Clearance Factor \(\:{\text{p}}_{12}=\:\frac{\left|{\text{p}}_{5}\right|}{{\text{p}}_{4}}\) Max Value \(\:{\text{p}}_{5}=\text{m}\text{a}\text{x}\left(\left|s\left(i\right)\right|\right)\) Impulse Factor \(\:{\text{p}}_{13}=\:\frac{\left|{\text{p}}_{5}\right|}{{\text{p}}_{1}}\) Total Harmonic Distortion + Noise (THD + N) \(\:{\text{p}}_{6}=100\:\frac{\sqrt{{\sum\:}_{i=2}^{k}{H}_{i}^{2}}}{{H}_{i}}\) Peak-to-Peak \(\:{\text{p}}_{14}=\:{\text{p}}_{5}-{\text{T}}_{M}\) Skewness Coefficient \(\:{\text{p}}_{7}={\left(\frac{1}{\left(k-1\right){\left({\text{p}}_{2}\right)}^{3}}{\sum\:}_{i=1}^{k}{\left(s\left(i\right)-{\text{p}}_{1}\right)}^{2}\right)}^{3}\) Kurtosis Coefficient \(\:{\text{p}}_{8}={\left(\frac{1}{\left(k-1\right){\left({\text{p}}_{2}\right)}^{4}}{\sum\:}_{i=1}^{k}{(s\left(i\right)-{\text{p}}_{1})}^{2}\right)}^{4}\) PHYSICS-INFORMED FEATURES Melt-Pool Distance (MPD) \(\:{\text{p}}_{15}=|{\text{w}}_{2}\:-\:{\text{w}}_{1}|\) Aspect Ratio (ARTM) \(\:{\text{p}}_{16}=\:\frac{{|\text{p}}_{5}|}{{\text{p}}_{15}}\) \(\:s\left(i\right)\) is the \(\:{i}^{th}\) sample of the data; k is length of the data; \(\:{H}_{i}\) is the \(\:{i}^{th}\) harmonic of the data; \(\:{w}_{1}\) and \(\:{w}_{2}\) are the minimum and maximum pixel above melting temperature respectively T M is the reference melting temperature of Ti-6Al-4V Figure 4(b) shows the relationship between MPD and ARTM across different porosity levels. The plot demonstrates a non-linear correlation, where ARTM decreases as MPD increases. This relationship is characterized as follows: Macro-Porosity : High ARTM and short MPD. Micro-Porosity : Low ARTM and long MPD. No Porosity : Intermediate ARTM and MPD values. This trend suggests that high thermal concentration (high ARTM) with insufficient melt pool distance could lead to macro-porosity, while overly dispersed thermal energy (low ARTM) with extended melt pool distance leads to micro-porosity. An optimal balance between thermal concentration and melt pool distance minimizes porosity. By integrating both statistical and physics-informed features, we enhance the model's ability to capture the complex interplay between thermal dynamics and porosity formation. This comprehensive feature set provides a robust foundation for shallow learning models to accurately classify porosity levels in additive manufacturing. 2.4. Feature Selection Selecting the most influential features from the extracted set is crucial for enhancing the performance of shallow learning (SL) models. Our feature set consisted of 17 features, including 15 statistical and 2 physics-informed features (MPD and ARTM). Effective feature selection helps in reducing dimensionality, avoiding overfitting, shortening training time, and improving model accuracy. To identify the most significant features, we computed pairwise Pearson correlation coefficients (r) among all features, forming a feature correlation matrix [ 38 ]. The Pearson correlation coefficient, defined in Eq. ( 2 ), quantifies the linear relationship between two variables and ranges from − 1 to 1. A coefficient close to 1 or -1 indicates a strong positive or negative linear correlation, respectively [ 56 ]: $$\:\text{r}=\frac{{\sum\:}_{i=1}^{n}({x}_{i}-\widehat{x}\left)\right({y}_{i}-\widehat{y})}{\sqrt{{\sum\:}_{i=1}^{n}{{(x}_{i}-\widehat{x})}^{2}}\sqrt{{\sum\:}_{i=1}^{n}{{(y}_{i}-\widehat{y})}^{2}}}$$ 2 where x i and y i are feature values, and x̅ and y̅ are their respective mean values. To prevent multicollinearity and improve model interpretability [ 57 ], we selected only one feature from each pair of highly correlated features (|r| >0.9). This step reduces redundancy in the feature set and ensures that the model learns from independent information. Figure 5 (a) displays the selected features, which are weakly correlated with each other (|r| < 0.9). The selected features are: MPD (Melt Pool Distance), ARTM (Aspect Ratio of Maximum Temperature to MPL), MAX (Maximum Temperature), SKEW (Skewness), KURT (Kurtosis), WAVE (Waveform), SNR (Signal-to-Noise Ratio), and THD + N (Total Harmonic Distortion plus Noise). As expected, most derived features were excluded because they are computed from the independent features and are highly correlated with them. To further evaluate the importance of the selected features, we employed a model ensemble-based approach with the Random Forest (RF) algorithm. Feature importance scores were calculated based on the mean decrease in impurity across all trees in the ensemble. We considered all four orientations of the thermal profiles in this analysis. Figure 5 (b) ranks the features in descending order of importance based on the RF model's output. Notably, our proposed physics-informed features, ARTM and MPD , ranked among the top three, underscoring their significant contribution in classifying porosity levels based on melt pool thermal profiles. This result highlights the effectiveness of incorporating physics-informed features alongside statistical features, further improving model performance. 2.5. Case Assessments We evaluated the top eight selected features (see Section 2.4 ), extracted from four orientations relative to the laser scanning direction (0°, 90°, + 45°, and − 45°), across nine distinct analysis cases using five shallow learning models. These cases included uni-directional, bi-directional, and multi-directional feature combinations, providing a unique perspective on the melt pool’s thermal profile. Because the melt pool’s shape—whether conical, elliptical, or irregular—significantly influences the quality and mechanical properties of additive manufacturing (AM) components, examining temperature distributions from multiple directions offers deeper insights into melt pool dynamics. This broader viewpoint aids in optimizing process parameters, reducing porosity defects, and ensuring consistent material properties. Accordingly, we defined nine cases, each characterized by different orientation-based feature combinations, as summarized in Table 2 . 2.6. Shallow Learning Models In this study, shallow learning (SL) models are employed to predict porosity in laser-based additive manufacturing (AM) components. These models are particularly suitable for scenarios with limited data and where feature engineering is critical. Unlike deep learning (DL) methods, which typically require large datasets to generalize effectively, SL approaches can achieve comparable or superior performance with fewer data points by relying on carefully engineered features and simpler model architectures [ 58 , 59 ]. Table 2 Feature configurations for nine distinct analysis cases, defined by thermal profile orientations (0°, 90°, + 45°, -45°) and multi-directional temperature distributions around the melt pool. Cases Laser Orientation Temperature Distribution Relative to Laser Feature Representation Number of Features Case 1 Laser Scan Parallel Y 8 Case 2 Orthogonal Perpendicular X 8 Case 3 Oblique – 1 Inclined Toward U 8 Case 4 Oblique – 2 Inclined Away V 8 Case 5 Directional Mean Average of four orientations Mean (YXUV) 8 Case 6 Bi-Directional Parallel and Perpendicular YX 16 Case 7 Bi-Directional Parallel and Inclined Toward YU 16 Case 8 Multi-Directional Comprehensive across orientations YXUV 32 Case 9 Multi-Directional Physics-informed features of all orientations YXUV 8 The pyrometer sensor data were first transformed into thermal images of the melt pool region, cropped to a size of 150 × 150 pixels, to isolate the area influenced by temperature gradients. Porosity measurements, obtained from CT-scan data, were used to label each melt pool instance as having no porosity, micro-porosity, or macro-porosity. Feature engineering and selection (as described in Section 2.4 ) resulted in eight key features (including the physics-informed MPD and ARTM) derived from temperature profiles across four orientations relative to the laser scanning direction (0°, 90°, + 45°, -45°). Table 3 Shallow learning models for porosity classification and their hyperparameters S.No. Models Description Hyperparameters 1 Logistic Regression A computationally efficient classifier, suitable for multi-class problems, offering insights into feature importance but less effective for non-linear data. Solver: newton-cg; Regularization; l1 or l2; C: 0.001-100; iterations: 1000; Multi-class option: multinomial 2 Random Forest An ensemble model adaptable to high-dimensional and complex multi-class problems, but computationally intensive. Number of trees: 10–500; Max-depth: <500; Max-features:sqrt; Min samples to split 3 Support Vector Machine A robust classifier for complex multi-class problems that identifies optimal boundaries, but higher processing time. Kernel: RBF; Regularization: <1000; Kernel coefficient: optimized; degree: 3; gamma: scale 4 K-Nearest Neighbour A distance-based model for non-linear features, though sensitive to outliers and irrelevant features. Number of neighbors: optimized; Distance metrics: Euclidean; Algorithms: Ball Tree, KD Tree 5 Decision Tree A tree-based classifier that splits data recursively and requires tuning to prevent overfitting. Max-depth: optimized; Criteria: Gini/Entrophy; Min Samples per node: tuned To address the class imbalance issue, we applied the SMOTE technique to augment minority classes, ensuring a balanced dataset for training and testing. Nine distinct analysis cases were defined, encompassing uni-directional, bi-directional, and multi-directional feature combinations (as detailed in Table 2 ), capturing different perspectives of the melt pool’s thermal behavior. Each of these cases was used as input to five shallow learning classifiers—Logistic Regression (Log-C), Random Forest (RFC), Support Vector Machine (SVC), K-Nearest Neighbor (KNN), and Decision Tree (DTC). Hyperparameter optimization was performed using randomized search cross-validation (CV), and model performance was evaluated using traditional classification metrics (see Table 3 for details). All computations were implemented in Python using the Scikit-learn (sklearn) library on an Apple MacBook Air (M1 chip, 16 GB RAM). This approach represents an early attempt to integrate multi-directional temperature features from melt pool imaging into shallow learning pipelines for porosity prediction, which could inform process parameter optimization and contribution to improved quality control in AM components. 2.7. Performance Metrics To evaluate the performance of the models across various case studies, traditional classification metrics—Accuracy, Precision, Recall, F1-score, and Confusion Matrix analysis—were used. While these metrics are well-known and commonly used in ML, they may not fully capture the performance nuances in imbalanced classification scenarios, as they tend to prioritize the majority class [ 60 ]. 2.7.1. Proposed Classification Deviation Error Metric Given the limitations of conventional metrics in imbalance classification, we introduce a metric, i.e., classification deviation error (CDE). The CDE measures the deviation of a model’s predictions from an ideal classifier across all classes. It compares the normalized confusion matrix, CM Normalized , to the identity matrix I , as expressed in Eq. ( 3 ): $$\:CDE=\left|\right|I-{CM}_{Normalized}{\left|\right|}_{2}=\:\sqrt{{\sum\:}_{i=1}^{n}{\sum\:}_{j=1}^{n}{({\delta\:}_{ij}-{CM}_{Normalized}(i,j\left)\right)}^{2}}$$ 3 Where: I is the n×n identity matrix, n is the number of classes, CM Normalized is the normalized confusion matrix, δ ij ​ is the Kronecker delta (1 if i = j , and 0 otherwise), ∥⋅∥ 2 denotes the Euclidean norm for matrices. A perfect classifier would yield CM Normalized = I , resulting in a CDE of zero. Higher CDE values indicate a greater deviation from ideal performance, which can help identifying areas where the model struggles, particularly in predicting minority classes. By providing a single scalar value that reflects the overall misclassification severity, the CDE metric offers a more nuanced and informative assessment of model performance than traditional metrics alone. 3. Results and Discussion This section evaluates the performance of five shallow learning classifiers—Logistic Regression (Log-C), Random Forest Classifier (RFC), Support Vector Classifier (SVC), K-Nearest Neighbor (KNN), and Decision Tree Classifier (DTC)—for predicting porosity levels (no porosity, micro-porosity, macro-porosity) from pyrometer-derived thermal profiles of the melt pool region. The thermal data were processed, and eight key features were selected (as detailed in Section 2.4 ). Nine distinct case studies were defined to incorporate different orientations relative to the laser scanning direction. Both traditional classification metrics and the proposed CDE metric were used to assess model effectiveness and performance across these case studies. 3.1. Shallow Learning with Traditional Classification Metrics After standardizing the balanced dataset and optimizing hyperparameters via randomized search and cross-validation approach, we used Accuracy, Precision, Recall, and F1-score to evaluate model performance across the nine case studies. The accuracy trends for each model are shown in Fig. 6 : RFC : Consistently outperformed other models, achieving a peak accuracy of 94% in Case 7, which involved a bi-directional feature combination (parallel and oblique orientations with 16 features). SVC, DTC : Both models maintained high accuracy across most cases, with a peak of 95% in Case 6 (a combination of parallel and perpendicular orientations with 16 features). KNN : Displayed variable accuracy but performed best in Case 5, with an accuracy of 91%, where features were averaged across all orientations (8 features). Log-C : Showed relatively lower accuracies but peaked at 95% in Case 6 and 91% in Case 8, where all orientations (32 features) were considered. Case 2 , which involved an orthogonal laser direction (Y-Axis), resulted in lowest accuracies (~ 83%) across all models. While RFC and SVC achieved high accuracy, they also required longer training times. Although Log-C scored lower accuracy, it excelled in precision (0.94–0.96) across all cases, demonstrating that a single metric like accuracy can be misleading. Relying solely on accuracy, or any other traditional metric is insufficient to capture the nuanced performance, especially for minority classes. 3.2. Shallow Learning with CDE Metric To address the limitations of traditional metrics in handling class imbalance, we introduced the CDE metric ( Section 2.7.1 ). Table 4 and Fig. 7 present the CDE values across the nine case studies. Unlike accuracy, which can be inflated by correctly classifying majority classes, the CDE highlights discrepancies in predicting minority classes: Log-C : Achieved notably low CDE values (0.08–0.09 in Case 7), despite moderate accuracy, indicating its superior handling of minority class predictions. RFC : Showed a low CDE of 0.18 in Case 7, confirming a well-balanced performance across all classes. SVC : Despite reaching 95% accuracy in some cases, its CDE was significantly higher (4), revealing poor predictive performance on minority classes. KNN and DTC : Produced lower CDE values than SVC, but did not outperform Log-C or RFC in terms of balanced error distribution. The CDE metric effectively revealed weaknesses that were hidden by traditional metrics. While some models appeared strong based on accuracy alone, CDE highlighted that Log-C and RFC provided more reliable predictions for minority classes. To further illustrate these misclassifications, Table 5 includes a normalized confusion matrix for Case 7, highlighting the challenges in predicting minority classes (micro- and macro-porosity). Complexities such as substrate interaction at early layers and boundary effects at the part edges (as shown in Fig. 3 and Fig. 4 ) contributed to these classification challenges. Despite appearing strong in traditional metrics, RFC and SVC were less effective for minority class predictions compared to Log-C, which maintained lower CDE values and a faster inference time of 0.001 ms. Table 4 Comparison of case assessment and shallow learning models with traditional classification metrics and proposed Classification Deviation Error (CDE) metric. Metrics Traditional Metrics (%) Proposed Cases Models Accuracy Precision Recall F1-Score CDE Case 1 Log-C 84 96 84 88 0.28 RFC 93 96 93 94 0.19 SVC 94 95 94 94 1.24 KNN 90 95 90 92 0.29 DTC 91 96 91 93 0.19 Case 2 Log-C 83 95 83 88 0.15 RFC 91 94 91 92 1.12 SVC 91 93 91 92 2.28 KNN 86 92 86 89 1.92 DTC 86 93 86 89 1.26 Case 3 Log-C 88 96 88 91 0.13 RFC 93 96 93 94 0.19 SVC 93 95 93 94 1.02 KNN 90 95 90 92 0.80 DTC 91 95 91 93 0.73 Case 4 Log-C 83 96 83 88 0.16 RFC 94 96 94 95 0.28 SVC 93 93 93 93 2.50 KNN 86 95 86 89 0.32 DTC 90 96 90 92 0.17 Case 5 Log-C 85 96 85 89 0.27 RFC 94 96 94 94 0.28 SVC 91 94 91 92 2.35 KNN 90 95 92 93 0.85 DTC 90 95 90 92 0.41 Case 6 Log-C 95 95 1 98 4.0 RFC 93 96 95 96 2.07 SVC 95 95 1 98 4.0 KNN 83 94 83 88 3.84 DTC 95 95 1 98 4.0 Case 7 Log-C 86 96 86 90 0.09 RFC 94 96 94 95 0.18 SVC 93 94 93 93 2.50 KNN 87 95 87 90 0.32 DTC 91 95 91 93 0.86 Case 8 Log-C 90 94 90 92 0.90 RFC 94 95 94 94 0.95 SVC 94 92 94 93 2.85 KNN 87 96 87 90 0.14 DTC 89 94 89 91 1.01 Case 9 Log-C 85 96 85 89 0.27 RFC 93 96 93 94 0.28 SVC 91 94 91 92 2.35 KNN 86 95 86 89 0.64 DTC 91 95 91 92 0.41 Table 5 Normalized confusion matrix and CDE analysis of five shallow learning models for Case 7. Pore No Micro Macro No 0.86 0.10 0.04 Micro 0.00 1.00 0.00 Macro 0.00 0.17 0.83 (a) Logistic Regression (CDE = 0.09) Pore No Micro Macro No 0.95 0.04 0.01 Micro 0.25 0.75 0.00 Macro 0.17 0.00 0.83 (b) Random Forest (CDE = 0.18) Pore No Micro Macro No 0.96 0.02 0.02 Micro 0.50 0.50 0.00 Macro 1.00 0.00 0.00 (c) Support Vector Machine (CDE = 2.5) Pore No Micro Macro No 0.87 0.07 0.05 Micro 0.25 0.75 0.00 Macro 0.17 0.17 0.67 (d) K-Nearest Neighbour (CDE = 0.32) Pore No Micro Macro No 0.93 0.04 0.04 Micro 0.25 0.75 0.00 Macro 0.50 0.17 0.33 (e) Decision Tree (CDE = 0.86) 3.3. Comparative Assessment Conventional in situ monitoring methods often rely on deep learning models, which require large training datasets, substantial computational resources, and extensive preprocessing. For example, studies utilizing functional PCA or multilinear PCA [ 38 ] can effectively capture certain aspects of melt pool morphology for binary classification. However, these methods may fail to reflect the full complexity of thermal dynamics and spatial variations. Although some deep learning approaches have achieved high accuracies, their computational cost, large dataset demands, and focus on single-direction thermal profiles limit their suitability for multi-class porosity prediction [ 26 , 37 ]. In contrast, our approach leverages multi-directional thermal profiles and physics-informed features to produce robust, computationally low cost predictions. For instance, Log-C and RFC classification achieved accurate results with low CDE values, along with short inference times (0.001 ms). This makes our method suitable for real-time inference, especially given the pyrometer’s 2.027 ms exposure time at a 6.4 Hz collection rate [ 1 ], while also predicting minority classes. This strategy not only meets or exceeds the accuracy levels reported in the literature [ 31 , 34 , 36 , 55 ] but also utilizes a comprehensive dataset of 1,557 melt pool images spanning multiple orientations. By integrating the CDE metric into the evaluation process, we gain a more complete understanding of each model’s strengths and weaknesses, ensuring more reliable and informative porosity predictions in LBAM. 4. Summary In this work, we presented a reliable and effective approach for defect detection in laser-based additive manufacturing (LBAM) through a data-driven shallow learning (SL) model utilizing enhanced pyrometer sensor features. Our study highlights the advanced capabilities of ISM to detect defects, such as porosity, which could comprise the mechanical integrity of manufactured components. By leveraging dual-wavelength pyrometer data, we classified melt pool thermal profiles into distinct porosity categories, which were correlated with CT scans, ultimately optimizing defect detection in LBAM processes. In addressing the challenges of 2D thermal imaging analysis, particularly issues related to data scarcity and the computational demands of deep learning (DL) approaches, we proposed a methodology that extracts one-dimensional (1D) temperature profiles from multiple orientations relative to the laser movement. These 1D profiles allow for effective featurization using signal processing techniques to analyse the thermal dynamics influencing porosity formation. Additionally, our method introduces physics-informed features such as melt pool distance (MPD) and the aspect ratio of maximum temperature to MPD (ARTM), alongside fifteen statistical signal features identified as highly predictive through ensemble-based feature selection. The shallow learning models implemented in this study demonstrated high performance, achieving up to 95% accuracy, 96% precision, and 95% recall. However, predicting minority classes remained a significant challenge. To address this, we introduced a CDE metric, which quantitatively evaluates how far a model’s predictions deviate from an ideal classifier across all classes. By highlighting discrepancies in class-wise prediction accuracy, particularly for minority classes, CDE complements conventional metrics and supports model refinement aimed at identifying misclassification of minority classes. Our approach demonstrates that shallow learning models, when combined with strategically engineered features, offer a reliable and efficient alternative to more complex deep learning methods. These models provide rapid and accurate defect prediction with reduced computational demands, making them particularly suited for real-time quality assurance in additive manufacturing. This research not only advances the understanding of melt pool dynamics through innovative sensor data utilization and machine learning but also proposes new metrics and standards for predictive accuracy in the field of additive manufacturing. Declarations CRediT statement Conceptualization: RK, MJ, FF Data curation: RK Formal analysis: RK, FF Investigation: RK Methodology: RK, MJ, FF Project Administration: MJ, NR Software: RK Supervision: MJ, FF, NR Validation: RK, MJ, FF, NR Visualization: RK Writing – original draft: RK, MJ Writing – review & editing:RK, MJ, FF, NR Disclosure of Interest No potential conflict of interest was reported by the author(s). Data Availability The data that support the findings of this study are openly available in Thermal-Porosity Characterization Data of Additively Manufactured Ti-6Al-4V Thin-walled Structure via Laser Engineered Net Shaping (Original Data) (Dataverse), reference number [1]. Acknowledgments The authors gratefully acknowledge the logistical and technical support as well as infrastructure provided by the Digital Manufacturing and Design (DManD) Centre at the Singapore University of Technology and Design (SUTD). The authors also acknowledge the Ministry of Education (MOE), Singapore, for providing a research student scholarship (RSS) for 2021–2025. This research is supported by the Agency for Science, Technology and Research (A*STAR), under the Industry Alignment Fund Pre-Positioning Programme (IAF-PP) project “Metal Additive Manufacturing Powders: Reusability, Rejuvenation, Cost, Quality & Performance (RRAMP)” [Award No. M22K7a0047]. References Marshall, G.J., S.M. Thompson, and N. Shamsaei, Data indicating temperature response of Ti–6Al–4V thin-walled structure during its additive manufacture via Laser Engineered Net Shaping. Data in brief, 2016. 7 : p. 697-703. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7042984","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":483702773,"identity":"6ff3822d-5e8a-49fc-9229-29b6b4db167c","order_by":0,"name":"RAJESH KUMAR BALARAMAN","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-4580-7188","institution":"Singapore University of Technology and Design Engineering Product Development","correspondingAuthor":true,"prefix":"","firstName":"RAJESH","middleName":"KUMAR","lastName":"BALARAMAN","suffix":""},{"id":483702774,"identity":"682fd60a-2560-4604-9f2f-b868ae66519b","order_by":1,"name":"Mehdi Jafary-Zadeh","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Mehdi","middleName":"","lastName":"Jafary-Zadeh","suffix":""},{"id":483702775,"identity":"ce0bb653-02ce-48d7-a5b3-4ca859d81209","order_by":2,"name":"Farzam Farbiz","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Farzam","middleName":"","lastName":"Farbiz","suffix":""},{"id":483702776,"identity":"b350713b-e2ac-47fe-87bd-1890fb4bac12","order_by":3,"name":"Nagarajan Raghavan","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Nagarajan","middleName":"","lastName":"Raghavan","suffix":""}],"badges":[],"createdAt":"2025-07-04 04:47:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7042984/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7042984/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86778472,"identity":"de2c109f-2d7a-4733-92bf-380d3f945229","added_by":"auto","created_at":"2025-07-15 12:55:51","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":171433,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Thermal image of a No-Porosity melt pool with four orientation axes: Laser Scan (Y), Orthogonal (X), Oblique-1 (U), and Oblique-2 (V), highlighting the melt pool boundary (brown contour); \u003cstrong\u003e(b)\u003c/strong\u003e Temperature profiles along the four orientations, with the melting temperature (1636°C) indicated as a reference line.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/85029a8f0e04d4717315fcdb.png"},{"id":86777004,"identity":"2edd0c1e-a297-4fdd-930f-a6adfeb81478","added_by":"auto","created_at":"2025-07-15 12:47:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":234960,"visible":true,"origin":"","legend":"\u003cp\u003ePorosity levels along laser scan direction (Y-axis) \u003cstrong\u003e(a)\u003c/strong\u003e Thermal images illustrating the variation of temperature range and melt pool shape. \u003cstrong\u003e(b)\u003c/strong\u003e Temperature profiles demonstrate decreasing MPD and increasing MAX with higher porosity levels above melting temperature (T\u003csub\u003eM\u003c/sub\u003e) (1636℃)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/4a6fd6b325ba9ce4e1d60fe1.png"},{"id":86777006,"identity":"3a21ef7a-819b-4443-bb8c-e5974e4f56fd","added_by":"auto","created_at":"2025-07-15 12:47:51","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":346464,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of No-Porosity, Micro-Porosity, and Macro-Porosity classes of melt pool along the laser path (Y-axis) and build height (Z-axis). Arrows indicate the locations of representative thermal images for each porosity level within the layers.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/a3ca955a3a9a331c52ea92d3.png"},{"id":86778747,"identity":"7103fb09-3fcb-4c83-94b1-df87d7a4924c","added_by":"auto","created_at":"2025-07-15 13:03:51","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":84875,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Relationship between Maximum Temperature (MAX) and Melt Pool Distance (MPD) across the three porosity categories (No Porosity, Micro-Porosity, Macro-Porosity); \u003cstrong\u003e(b)\u003c/strong\u003e Plot of the Aspect Ratio of MAX to MPD (ARTM) versus MPD, illustrating thermal distribution patterns for each porosity class.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/f970163536eb7b8265f53312.png"},{"id":86778473,"identity":"cdabb26d-d0fc-4c60-aaeb-d77d2047482e","added_by":"auto","created_at":"2025-07-15 12:55:51","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":101079,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)\u003c/strong\u003e Pearson correlation heat map for the eight selected features, each with pairwise correlation coefficients below 0.90. \u003cstrong\u003e(b) \u003c/strong\u003eEnsemble-based feature importance indicating each feature’s relative significance across four orientation cases.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/dfb8b4ef1d5b1b532872a92d.png"},{"id":86777008,"identity":"5e487203-62de-4dfd-8108-7b2e776b4110","added_by":"auto","created_at":"2025-07-15 12:47:51","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":98714,"visible":true,"origin":"","legend":"\u003cp\u003eTraditional classification accuracy metric of the shallow learning models across nine case studies, (C\u003csub\u003e1\u003c/sub\u003e to C\u003csub\u003e9\u003c/sub\u003e), in multi-class porosity prediction.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/2d0b855738e3c8ed293ab866.png"},{"id":86777015,"identity":"1535796d-285a-4e20-82b2-ac55b79d465d","added_by":"auto","created_at":"2025-07-15 12:47:51","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":79270,"visible":true,"origin":"","legend":"\u003cp\u003eCDE metric of the shallow learning models across nine case studies (C\u003csub\u003e1\u003c/sub\u003e to C\u003csub\u003e9\u003c/sub\u003e), in multi-class porosity prediction.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/dbe85268cdf8d8bbef5b5500.png"},{"id":86780367,"identity":"15080e83-07e9-42b6-8db9-a93876556e7c","added_by":"auto","created_at":"2025-07-15 13:19:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3120676,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7042984/v1/192153f0-d16f-4cfc-9889-a060fdec250f.pdf"}],"financialInterests":"","formattedTitle":"Effective Porosity Detection in Laser-Based Additive Manufacturing Using Shallow Learning and Physics-Informed Pyrometer Features","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eLaser-based additive manufacturing (LBAM) is transforming the production of complex three-dimensional (3D) metallic components by offering high precision, minimal material waste, and reduced production time. Widely utilized in aerospace, automotive, and medical industries, LBAM converts computer-aided design (CAD) models into functional parts through powder melting techniques such as direct laser deposition (DLD) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], laser metal deposition (LMD) [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], laser cladding, laser powder bed fusion (LPBF) [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], selective laser melting (SLM) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and selective laser sintering (SLS) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. These processes involve critical machine parameters, including laser power, scanning speed, hatch spacing, layer thickness, and environmental conditions [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. After manufacturing, components are detached from the substrate and subjected to post-processing methods such as hot isostatic pressing, polishing, and coating to enhance surface finish, dimensional accuracy, and mechanical properties [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eQuality assurance (QA) plays a vital role in ensuring the structural integrity of LBAM components, identifying defects like cracks, porosity, and surface irregularities. Traditional \u003cem\u003eex situ\u003c/em\u003e inspection techniques, including X-ray computed tomography (CT), ultrasonic testing, and optical methods [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], are effective but time-intensive and expensive. To overcome these limitations, \u003cem\u003ein situ\u003c/em\u003e monitoring (ISM) [\u003cspan additionalcitationids=\"CR11 CR12 CR13\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] leverages integrated sensors for real-time defect detection, capturing insights into melt pool dynamics [\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], temperature distribution [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], cooling behaviour [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], and spatter formation [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. While ISM enhances defect detection, predictive modelling is critical for understanding process-structure-property (p-s-p) relationships in additive manufacturing (AM) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\u003cp\u003ePhysics-based simulations employ thermal and fluid dynamics models to predict defects such as porosity, warping, lack of fusion, cracks, as well as microstructure, mechanical properties, fatigue behaviour, and residual stress [\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. However, these simulations are computationally expensive, require complex calibration, and rely on theoretical simplifications, such as uniform material property assumptions, limiting their accuracy in real-world applications. Consequently, they are not suited for ISM that requires real-time accounting for localized variations in heat distribution and material interactions. Conversely, data-driven methods leverage sensor data and machine learning (ML) models to predict defects efficiently could enable ISM and adaptive control for consistent quality [\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn data-driven approaches, ML models are employed to correlate signal features with metallurgical defects that reduce reliance on costly simulation and experimental trials, offering a scalable and efficient solution for quality assurance in AM. These models can be mainly classified into shallow learning (SL) and deep learning (DL) based on their architecture, complexity, and hierarchical data representation [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. DL models, including Convolutional Neural Networks (CNN) [\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], Recurrent Neural Networks (RNN) [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], Generative Adversarial Networks (GAN) [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], Autoencoders, and Transformers, can learn complex features from raw sensor data but require large datasets and high computational power to train these models. DL models often struggle with small datasets, leading to overfitting and poor prediction rates for minority class defects.\u003c/p\u003e\u003cp\u003eIn contrast, SL models, such as Linear/Logistic Regression (LR), Random Forest (RF), Decision Tree (DT), Support Vector Machine (SVM), and K-Nearest Neighbors (KNN), have simpler architecture; hence, they are computationally more effective, and ideal to deal with smaller datasets [\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. These models mitigate overfitting and class imbalance through regularization and Synthetic Minority Oversampling Technique (SMOTE) [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] to enhance accuracy in determining minority classes. Optimizing the appropriate architectures of SL models can achieve comparable performance metrics such as accuracy and error rates to DL models while offering significantly lower space\u0026ndash;time complexity, making them an efficient choice for limited datasets and resource-constrained AM applications [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. However, SL models rely heavily on feature extraction from sensor data. As a result, feature engineering, which involves extracting relevant statistical and physics-informed features from raw sensor data, is critical for establishing correlations between sensor data and defects like porosity, thereby enhancing model performance in predictive quality control [\u003cspan additionalcitationids=\"CR43\" citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eSeveral studies have investigated the relationship between melt pool dynamics and defect formation using various in-situ sensing techniques, with pyrometers playing a key role in capturing real-time thermal profiles. Dual-wavelength pyrometers and high-speed co-axial infrared cameras are frequently used to collect thermal data across layers, enabling the analysis of melt pool characteristics and material-specific properties such as optical emissivity and absorptivity [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The pyrometry signal, \u003cem\u003ei.e.\u003c/em\u003e, measured emission intensity, is directly influenced by laser energy density, which is governed by process parameters including laser power and scanning speed. These thermal signatures have shown strong correlations with melt pool instabilities and defects such as keyhole-induced porosity [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. Therefore, by extracting features from pyrometer signals and correlating them with X-ray CT scan data labeled by pore size and location, it becomes feasible to link thermal anomalies to porosity defects, offering a robust basis for predictive quality control in metal AM [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan additionalcitationids=\"CR50 CR51 CR52 CR53\" citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn this work, we introduce a new approach for classifying porosity defects in LBAM by integrating ISM with SL models. Using a high-resolution pyrometer sensor, we capture detailed melt pool thermal profiles as the foundation of our analysis. The \u003cb\u003eMethodology\u003c/b\u003e section outlines our process, including the experimental setup, thermal data processing, and classification of porosity defects into three distinct classes based on pore sizes. We also address class imbalance issues and describe our feature extraction and selection strategies from various thermal profile orientations to enhance predictive performance.\u003c/p\u003e\u003cp\u003eOur SL models are employed for porosity classification and validated using both traditional evaluation metrics and our classification deviation error (CDE) metric, specifically designed to predict minority classes\u0026mdash;an essential aspect of multi-class defect detection. In the \u003cb\u003eResults and Discussion\u003c/b\u003e section, we compare model performance using traditional metrics and the CDE metric, demonstrating the effectiveness of our approach in reducing misclassification rates. Finally, the \u003cb\u003eSummary\u003c/b\u003e highlights the significance of the extracted features from melt pool dynamics, emphasizing how domain knowledge contributes to improved model accuracy and robustness.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003eThis study utilizes open-access datasets from the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University (MSU), where thin-walled Ti-6Al-4V structures were fabricated using LBAM techniques, specifically Direct Laser Deposition (DLD) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The primary focus is on analysing thermal data collected during fabrication to detect and classify porosity defects using shallow learning models. This section outlines the experimental setup, data processing, and feature engineering steps undertaken in our analysis.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Experimental Setup\u003c/h2\u003e\u003cp\u003eA thin-walled structure (47.81\u0026times;27.56\u0026times;1.78 mm) was fabricated on a Ti-6Al-4V substrate (150\u0026times;153\u0026times;3.3 mm) using an OPTOMEC Laser Engineering Net Shaping (LENS\u0026trade;) 750 system, integrated with a Stratonics Dual-wavelength Pyrometer for thermal monitoring [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The substrate was mounted on a CNC-controlled platform, and Ti-6Al-4V powder was continuously injected through an angled nozzle aligned with a laser beam of 1.016 mm diameter. The build chamber was maintained at room temperature with an argon flow rate of 4L/min to ensure a controlled environment. The process parameters are a laser power of 290 W, a scan speed of 12.7 mm/s, and powder feed rate of 0.32 g/s. A single-track deposition length of 50.8 mm was repeated with an increment height of 0.508 mm across 60 layers, resulting in a structure height of 27.56 mm. To streamline melt pool data analysis, the system was configured to match the hatch spacing with the nozzle diameter, enabling each layer to be completed in a single-pass track configuration while thermal data was continuously recorded.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Data Processing\u003c/h2\u003e\u003cp\u003eThe dual-wavelength pyrometer captured melt pool thermal readings with a resolution of 752 \u0026times; 480 pixels, a pixel pitch of 6.45 \u0026micro;m, a temperature detection range of 1000\u0026ndash;2500\u0026deg;C, and an exposure time of 2.0274 ms, at a data collection rate of 6.4 Hz. The coordination system was defined as follows:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eX-axis\u003c/b\u003e: Corresponds to the laser's orthogonal direction, measuring the part's width.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eY-axis\u003c/b\u003e: Aligns with the laser's scan path, measuring the part's length.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eZ-axis\u003c/b\u003e: Represents the nozzle's upward movement, measuring the part's height.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e2.2.1. Data Cleaning and Preparation\u003c/h2\u003e\u003cp\u003eThermal data were saved as CSV files, labelled with time stamps, XYZ coordinates, and layer numbers. Data corresponding to non-active melting phases \u0026ndash; such as nozzle movements when the laser was off \u0026ndash; were excluded. In some layers, minor inconsistencies in pyrometer readings at specific Y-locations occurred due to sensor issues. However, these missing data points were sparse and did not significantly affect overall analysis accuracy.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e2.2.2. Melt Pool Images\u003c/h2\u003e\u003cp\u003eThermal readings captured during the AM process were transformed into two-dimensional (2D) images for each melt pool, providing critical insights into temperature distribution, geometry, cooling rate, flow dynamics, thermal gradients, and phase transitions. These thermal characteristics critically influence the material's microstructure and mechanical properties. To isolate the relevant melt pool zone, minimize thermal noise, and reduce input data dimensionality, a region of interest (ROI) was defined around the active melt pool. Each thermal image was cropped to a 150 x 150 pixel area, centered near the melt pool region, focusing on temperatures around the reference melting point of Ti-6Al-4V (T\u003csub\u003eM\u003c/sub\u003e = 1636℃) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe melt pool profile, typically circular or elliptical, was analyzed along four key orientations, as represented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eLaser Path (Y-Axis, 0\u0026deg;)\u003c/b\u003e: Captures the laser\u0026rsquo;s direct impact on melting powder and is used to measure melt pool length.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eOrthogonal (X-Axis, 90\u0026deg;)\u003c/b\u003e: Analyzes lateral heat transfer to determine melt pool width.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eOblique (U-V Axes, +\u0026thinsp;45\u0026deg; and \u0026minus;\u0026thinsp;45\u0026deg;)\u003c/b\u003e: Examines temperature gradients along diagonal axes, capturing combined thermal behaviour and flow dynamics across the melt pool region.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eKey thermal features extracted from each melt pool image included, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMaximum Temperature (MAX)\u003c/b\u003e: Peak thermal intensity above the melting point.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMinimum Temperature (MIN)\u003c/b\u003e: Reference melting temperature (T\u003csub\u003eM\u003c/sub\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMelt Pool Distance (MPD)\u003c/b\u003e: Distance over which the temperature exceeds T\u003csub\u003eM\u003c/sub\u003e, calculated along each orientation (0\u0026deg;, 90\u0026deg;, +\u0026thinsp;45\u0026deg;, -45\u0026deg;) to evaluate anisotropic thermal behaviour.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThermal profiles frequently exhibited fluctuations, indicating non-uniform heating and cooling rates that can affect solidification and defect formation, indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e. These fluctuations can cause thermal instabilities, leading to deviations in melt pool formation. As a result, some melt pools may develop pores, while others may lack a consistent melt pool structure, indicating potential anomalies. By analyzing these thermal profiles, we can correlate and validate the presence of defects with pore size data obtained from CT scans.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.2.3. Porosity Classification\u003c/h2\u003e\u003cp\u003ePorosity levels for each melt pool were quantified using X-ray CT scans with a 1 \u0026micro;m resolution, capable of detecting pore from 0.05 mm to 1 mm in diameter. Each pore\u0026rsquo;s spatial coordinate was matched with the corresponding melt pool image. Given that an average melt pool occupied fewer than 40 pixels in the 150 x 150 ROI, accurate alignment was ensured, and no blind spots were observed. However, the limited number of thermal images with detectable pores greater than 0.05 mm introduced a significant class imbalance, and complicating defect severity analysis. To address this, porosity was stratified into three distinct categories based on pore size measured:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eNo Porosity\u003c/b\u003e: No detectable pores.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMicro-Porosity\u003c/b\u003e: Pores between 0.05 mm and 0.5 mm in diameter.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMacro-Porosity\u003c/b\u003e: Pores larger than 0.5 mm in diameter.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThermal features (MAX, MPD) were analyzed across all four orientations and three porosity classes. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e represents thermal images of each class, while Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e shows corresponding temperature profiles along the laser path (Y-axis). Layer-wise distribution of porosity across the laser path (Y-axis) and build height (Z-axis), as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The highlighted melt pool regions, shown using thermal images, help distinguish between different porosity levels. Key observations from Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e indicate:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMacro-Porosity\u003c/b\u003e localised near build edges due to uneven cooling rates and thermal gradients, promoting larger pore formation.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMicro-Porosity\u003c/b\u003e concentrated at the bottom layers due to unstable thermal conditions during initial substrate deposition, leading to uneven heat distribution.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eNo Porosity\u003c/b\u003e distributed uniformly in the middle sections, where thermal conditions remain relatively stable.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eUnderstanding these spatial distributions of porosity is crucial for optimizing process parameters and ensuring part quality. By correlating thermal profiles with porosity, we can identify patterns and develop predictive models to minimize defects in real-time.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e2.2.4. Class Imbalance\u003c/h2\u003e\u003cp\u003eThe dataset comprised 1557 thermal images categorized into three classes based on pore size: 1485 images with no porosity, 46 with micro-porosity, and 26 with macro-porosity. This significant imbalance in class distribution (illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) poses a challenge for classification models, as ML algorithms can be biased towards the majority class (no porosity) and may underperform on the minority classes (micro- and macro-porosity). Such bias can result in low recall for defect-prone melt pools, increasing the risk of undetected flaws.\u003c/p\u003e\u003cp\u003eTo address this issue, we applied the SMOTE during preprocessing to balance the dataset [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. SMOTE generates synthetic samples for the minority classes by interpolating between existing instances, increasing their representation in the dataset. This approach helps the model learn the underlying patterns of all classes more effectively. Following SMOTE, the dataset was balanced and split into training and testing sets using stratified sampling, preserving class proportions. We allocated 75% of the data for training and 25% for testing, ensuring an equal ratio of the three classes in both subsets. This method enhances the model's ability to generalize and accurately predict porosity levels across all classes.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Feature Engineering\u003c/h2\u003e\u003cp\u003eFeature engineering was performed on melt pool images derived from pyrometer data, focusing on data points above the reference melting point (T\u003csub\u003eM\u003c/sub\u003e) of Ti-6Al-4V. This process aimed to capture the thermal features within the melt pool that influence porosity formation. Extracted features were categorized into two sets:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eStatistical Features\u003c/b\u003e: Quantitative descriptors derived from the temperature data.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePhysics-Informed Features\u003c/b\u003e: Features informed by the physical principles governing melt pool dynamics.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\u003ch2\u003e2.3.1. Statistical Features\u003c/h2\u003e\u003cp\u003eThermal profiles were extracted from the pyrometer readings at each melt pool location along four orientations: laser path (0\u0026deg;), orthogonal (90\u0026deg;), and oblique (+\u0026thinsp;45\u0026deg;, -45\u0026deg;), as described in \u003cb\u003eSection 2.2.2\u003c/b\u003e and illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. These directional profiles reflect temperature variation along the melt pool\u0026rsquo;s spatial extent, capturing information about thermal gradients and solidification patterns, which are closely linked to defect formation. Statistical features were grouped into:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eIndependent Features\u003c/b\u003e: Directly computed from raw temperature profile, capturing fundamental statistical properties.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eDerived Features\u003c/b\u003e: Computed from combinations of independent features, providing higher-order statistical thermal characteristics.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe features were calculated using standard statistical formulas (provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and are defined as follows:\u003c/p\u003e\u003cp\u003eIndependent Features (p\u003csub\u003e1\u003c/sub\u003e to p\u003csub\u003e9\u003c/sub\u003e):\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMean Temperature (MEAN, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e1\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Average temperature across the melt pool profile.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eStandard Deviation (STD, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Variation in temperatures.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eRoot Mean Square (RMS, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e3\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Square root of the mean of squared temperatures.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSquare Mean Rooted Absolute (SMRA, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e4\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Squared mean of absolute temperatures.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMaximum Temperature (MAX, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e5\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Highest temperature recorded in the profile.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eTotal Harmonic Distortion\u0026thinsp;+\u0026thinsp;Noise (THD\u0026thinsp;+\u0026thinsp;N, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e6\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Quantifies signal distortion and noise in the temperature profile.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSkewness (SKEW, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e7\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Indicates the asymmetry of the temperature distribution.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eKurtosis (KURT, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e8\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: Measures the \"tailedness\" of the temperature distribution.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eDerived Features (p\u003csub\u003e10\u003c/sub\u003e to p\u003csub\u003e15\u003c/sub\u003e):\u003c/p\u003e\u003col start=\"9\"\u003e\n \u003cli\u003e\u003cstrong\u003eSignal-to-Noise Ratio (SNR, p\u003csub\u003e9\u003c/sub\u003e):\u0026nbsp;\u003c/strong\u003eRatio of mean temperature of standard deviation.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eWaveform Factor (p\u003csub\u003e10\u003c/sub\u003e):\u003c/strong\u003e Ratio of RMS value to mean temperature.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eCrest Factor (p\u003csub\u003e11\u003c/sub\u003e):\u0026nbsp;\u003c/strong\u003eRatio of peak temperature to RMS temperature.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eClearance Factor (p\u003csub\u003e12\u003c/sub\u003e):\u0026nbsp;\u003c/strong\u003eRatio of peak temperature to SMRA temperature.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eImpulse Factor (p\u003csub\u003e13\u003c/sub\u003e):\u0026nbsp;\u003c/strong\u003eRatio of peak temperature to mean temperature.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003ePeak-to-Peak Value (p\u003csub\u003e14\u003c/sub\u003e):\u003c/strong\u003e Difference between maximum and minimum temperatures.\u003c/li\u003e\n\u003c/ol\u003e\u003cp\u003eThese statistical features describe various aspects of thermal behavior, such as central tendency, dispersion, shape, and harmonic distortions, and serve as key inputs for shallow learning (SL) models in porosity classification.\u003c/p\u003e\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\u003cdiv class=\"Heading\"\u003e2.3.2. Physics-Informed Features\u003c/div\u003e\u003cp\u003eWhile statistical features offer valuable quantitative insights, they may not fully capture the complex thermal phenomena influencing porosity formation. To incorporate domain-specific knowledge, we introduced physics-informed features derived from melt pool temperature profiles, as provided in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMelt Pool Distance (MPD, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e15\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: The spatial distance along a specific orientation, where the temperature exceeds the melting temperature (T\u003csub\u003eM\u003c/sub\u003e) of the alloy.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eAspect Ratio of Maximum Temperature to Melt Pool Distance (ARTM, p\u003c/b\u003e\u003csub\u003e\u003cb\u003e16\u003c/b\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e: A thermal-based ratio relating the peak temperature to the extend distance of melt pool. This thermally derived metric captures in-process melt pool behaviour that cannot be observed from post-process geometrical measurements alone, using Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e):\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:ARTM=\\frac{Maximum\\:Temperature\\:\\left(MAX\\right)}{Melt\\:Pool\\:Distance\\:\\left(MPD\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eARTM provides insight into the concentration and distribution of thermal energy within the melt pool. A higher ARTM value indicates a sharper temperature gradient over a shorter melt pool distance, which is associated with rapid heating and cooling rates. By incorporating ARTM and MPD physics-informed features, we aim to bridge the gap between sensor-based thermal data and physical melt pool dynamics. These features enhance the input space dimensions for SL models and contributed to improved porosity classification performance.\u003c/p\u003e\u003cp\u003eThese physics-informed features are particularly valuable for identifying subtle variations in melt pool behaviour that contribute to porosity formation. Figure\u0026nbsp;4\u003cb\u003e(a)\u003c/b\u003e illustrates the spatial temperature distribution along the MPD for the three porosity categories:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMacro-Porosity\u003c/b\u003e: Occurs at higher maximum temperatures (~\u0026thinsp;2000\u0026deg;C) with shorter MPDs. This suggests rapid melting and solidification, leading to larger pores, possibly, due to gas entrapment or keyholing effects.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eNo Porosity\u003c/b\u003e: Falls between these two extremes, representing optimal thermal conditions with a balanced MPD and temperature.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMicro-Porosity\u003c/b\u003e: Occurs at lower maximum temperatures with longer MPDs. This indicates insufficient energy input, resulting in incomplete melting and small pores, possibly due to lack of fusion.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFeature Extraction from melt pool images: statistical features (p\u003csub\u003e1\u003c/sub\u003e to p\u003csub\u003e14\u003c/sub\u003e) and proposed physics-informed features (p\u003csub\u003e15\u003c/sub\u003e and p\u003csub\u003e16\u003c/sub\u003e)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003eSTATISTICAL FEATURES\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003eIndependent Features\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003eDerived Features\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMean Value\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{1}=\\frac{1}{k}{\\sum\\:}_{i=1}^{k}s\\left(i\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSignal to Noise Ratio (SNR)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{9}=\\:\\frac{{\\text{p}}_{1}}{{\\text{p}}_{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStandard Deviation (STD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{2}={\\left(\\frac{1}{k-1}{\\sum\\:}_{i=1}^{k}{\\left(s\\left(i\\right)-{\\text{p}}_{1}\\right)}^{2}\\right)}^{\\frac{1}{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eWaveform Factor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{10}=\\:\\frac{{\\text{p}}_{3}}{{\\text{p}}_{1}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRoot Mean Square (RMS)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{3}={\\left(\\frac{1}{k}{\\sum\\:}_{i=1}^{k}{s\\left(i\\right)}^{2}\\right)}^{\\frac{1}{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCrest Factor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{11}=\\:\\frac{\\left|{\\text{p}}_{5}\\right|}{{\\text{p}}_{3}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSquare Mean Rooted Absolute (SMRA)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{4}={\\left(\\frac{1}{k}{\\sum\\:}_{i=1}^{k}\\sqrt{\\left|s\\left(i\\right)\\right|}\\right)}^{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eClearance Factor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{12}=\\:\\frac{\\left|{\\text{p}}_{5}\\right|}{{\\text{p}}_{4}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMax Value\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{5}=\\text{m}\\text{a}\\text{x}\\left(\\left|s\\left(i\\right)\\right|\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eImpulse Factor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{13}=\\:\\frac{\\left|{\\text{p}}_{5}\\right|}{{\\text{p}}_{1}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTotal Harmonic Distortion\u0026thinsp;+\u0026thinsp;Noise (THD\u0026thinsp;+\u0026thinsp;N)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{6}=100\\:\\frac{\\sqrt{{\\sum\\:}_{i=2}^{k}{H}_{i}^{2}}}{{H}_{i}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePeak-to-Peak\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{14}=\\:{\\text{p}}_{5}-{\\text{T}}_{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSkewness Coefficient\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{7}={\\left(\\frac{1}{\\left(k-1\\right){\\left({\\text{p}}_{2}\\right)}^{3}}{\\sum\\:}_{i=1}^{k}{\\left(s\\left(i\\right)-{\\text{p}}_{1}\\right)}^{2}\\right)}^{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKurtosis Coefficient\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{8}={\\left(\\frac{1}{\\left(k-1\\right){\\left({\\text{p}}_{2}\\right)}^{4}}{\\sum\\:}_{i=1}^{k}{(s\\left(i\\right)-{\\text{p}}_{1})}^{2}\\right)}^{4}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003ePHYSICS-INFORMED FEATURES\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMelt-Pool Distance (MPD)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{15}=|{\\text{w}}_{2}\\:-\\:{\\text{w}}_{1}|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAspect Ratio (ARTM)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{p}}_{16}=\\:\\frac{{|\\text{p}}_{5}|}{{\\text{p}}_{15}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:s\\left(i\\right)\\)\u003c/span\u003e\u003c/span\u003eis the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e sample of the data; k is length of the data; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{H}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{i}^{th}\\)\u003c/span\u003e\u003c/span\u003e harmonic of the data;\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{2}\\)\u003c/span\u003e\u003c/span\u003e are the minimum and maximum pixel above melting temperature respectively\u003c/p\u003e\u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eM\u003c/em\u003e\u003c/sub\u003e is the reference melting temperature of Ti-6Al-4V\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure 4(b)\u003c/b\u003e shows the relationship between MPD and ARTM across different porosity levels. The plot demonstrates a non-linear correlation, where ARTM decreases as MPD increases. This relationship is characterized as follows:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMacro-Porosity\u003c/b\u003e: High ARTM and short MPD.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eMicro-Porosity\u003c/b\u003e: Low ARTM and long MPD.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eNo Porosity\u003c/b\u003e: Intermediate ARTM and MPD values.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThis trend suggests that high thermal concentration (high ARTM) with insufficient melt pool distance could lead to macro-porosity, while overly dispersed thermal energy (low ARTM) with extended melt pool distance leads to micro-porosity. An optimal balance between thermal concentration and melt pool distance minimizes porosity.\u003c/p\u003e\u003cp\u003eBy integrating both statistical and physics-informed features, we enhance the model's ability to capture the complex interplay between thermal dynamics and porosity formation. This comprehensive feature set provides a robust foundation for shallow learning models to accurately classify porosity levels in additive manufacturing.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Feature Selection\u003c/h2\u003e\u003cp\u003eSelecting the most influential features from the extracted set is crucial for enhancing the performance of shallow learning (SL) models. Our feature set consisted of 17 features, including 15 statistical and 2 physics-informed features (MPD and ARTM). Effective feature selection helps in reducing dimensionality, avoiding overfitting, shortening training time, and improving model accuracy. To identify the most significant features, we computed pairwise Pearson correlation coefficients (r) among all features, forming a feature correlation matrix [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The Pearson correlation coefficient, defined in Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), quantifies the linear relationship between two variables and ranges from \u0026minus;\u0026thinsp;1 to 1. A coefficient close to 1 or -1 indicates a strong positive or negative linear correlation, respectively [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\text{r}=\\frac{{\\sum\\:}_{i=1}^{n}({x}_{i}-\\widehat{x}\\left)\\right({y}_{i}-\\widehat{y})}{\\sqrt{{\\sum\\:}_{i=1}^{n}{{(x}_{i}-\\widehat{x})}^{2}}\\sqrt{{\\sum\\:}_{i=1}^{n}{{(y}_{i}-\\widehat{y})}^{2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere x\u003csub\u003ei\u003c/sub\u003e and y\u003csub\u003ei\u003c/sub\u003e are feature values, and x̅ and y̅ are their respective mean values.\u003c/p\u003e\u003cp\u003eTo prevent multicollinearity and improve model interpretability [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e], we selected only one feature from each pair of highly correlated features (|r| \u0026gt;0.9). This step reduces redundancy in the feature set and ensures that the model learns from independent information. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e displays the selected features, which are weakly correlated with each other (|r| \u0026lt; 0.9). The selected features are: \u003cb\u003eMPD\u003c/b\u003e (Melt Pool Distance), \u003cb\u003eARTM\u003c/b\u003e (Aspect Ratio of Maximum Temperature to MPL), \u003cb\u003eMAX\u003c/b\u003e (Maximum Temperature), \u003cb\u003eSKEW\u003c/b\u003e (Skewness), \u003cb\u003eKURT\u003c/b\u003e (Kurtosis), \u003cb\u003eWAVE\u003c/b\u003e (Waveform), \u003cb\u003eSNR\u003c/b\u003e (Signal-to-Noise Ratio), and \u003cb\u003eTHD\u0026thinsp;+\u0026thinsp;N\u003c/b\u003e (Total Harmonic Distortion plus Noise). As expected, most derived features were excluded because they are computed from the independent features and are highly correlated with them.\u003c/p\u003e\u003cp\u003eTo further evaluate the importance of the selected features, we employed a model ensemble-based approach with the Random Forest (RF) algorithm. Feature importance scores were calculated based on the mean decrease in impurity across all trees in the ensemble. We considered all four orientations of the thermal profiles in this analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e ranks the features in descending order of importance based on the RF model's output. Notably, our proposed physics-informed features, \u003cb\u003eARTM\u003c/b\u003e and \u003cb\u003eMPD\u003c/b\u003e, ranked among the top three, underscoring their significant contribution in classifying porosity levels based on melt pool thermal profiles. This result highlights the effectiveness of incorporating physics-informed features alongside statistical features, further improving model performance.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003e2.5. Case Assessments\u003c/h2\u003e\u003cp\u003eWe evaluated the top eight selected features (see \u003cb\u003eSection 2.4\u003c/b\u003e), extracted from four orientations relative to the laser scanning direction (0\u0026deg;, 90\u0026deg;, +\u0026thinsp;45\u0026deg;, and \u0026minus;\u0026thinsp;45\u0026deg;), across nine distinct analysis cases using five shallow learning models. These cases included uni-directional, bi-directional, and multi-directional feature combinations, providing a unique perspective on the melt pool\u0026rsquo;s thermal profile. Because the melt pool\u0026rsquo;s shape\u0026mdash;whether conical, elliptical, or irregular\u0026mdash;significantly influences the quality and mechanical properties of additive manufacturing (AM) components, examining temperature distributions from multiple directions offers deeper insights into melt pool dynamics. This broader viewpoint aids in optimizing process parameters, reducing porosity defects, and ensuring consistent material properties. Accordingly, we defined nine cases, each characterized by different orientation-based feature combinations, as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e2.6. Shallow Learning Models\u003c/h2\u003e\u003cp\u003eIn this study, shallow learning (SL) models are employed to predict porosity in laser-based additive manufacturing (AM) components. These models are particularly suitable for scenarios with limited data and where feature engineering is critical. Unlike deep learning (DL) methods, which typically require large datasets to generalize effectively, SL approaches can achieve comparable or superior performance with fewer data points by relying on carefully engineered features and simpler model architectures [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFeature configurations for nine distinct analysis cases, defined by thermal profile orientations (0\u0026deg;, 90\u0026deg;, +\u0026thinsp;45\u0026deg;, -45\u0026deg;) and multi-directional temperature distributions around the melt pool.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCases\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLaser Orientation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTemperature Distribution Relative to Laser\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eFeature Representation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNumber of Features\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLaser Scan\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eParallel\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eY\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOrthogonal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePerpendicular\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eX\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOblique \u0026ndash; 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInclined Toward\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eU\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOblique \u0026ndash; 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInclined Away\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eV\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDirectional Mean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAverage of four orientations\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMean (YXUV)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBi-Directional\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eParallel and Perpendicular\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eYX\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBi-Directional\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eParallel and Inclined Toward\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eYU\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMulti-Directional\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eComprehensive across orientations\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eYXUV\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e32\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCase 9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMulti-Directional\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003ePhysics-informed features of all orientations\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eYXUV\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe pyrometer sensor data were first transformed into thermal images of the melt pool region, cropped to a size of 150 \u0026times; 150 pixels, to isolate the area influenced by temperature gradients. Porosity measurements, obtained from CT-scan data, were used to label each melt pool instance as having no porosity, micro-porosity, or macro-porosity. Feature engineering and selection (as described in \u003cb\u003eSection 2.4\u003c/b\u003e) resulted in eight key features (including the physics-informed MPD and ARTM) derived from temperature profiles across four orientations relative to the laser scanning direction (0\u0026deg;, 90\u0026deg;, +\u0026thinsp;45\u0026deg;, -45\u0026deg;).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eShallow learning models for porosity classification and their hyperparameters\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS.No.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModels\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDescription\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eHyperparameters\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLogistic Regression\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eA computationally efficient classifier, suitable for multi-class problems, offering insights into feature importance but less effective for non-linear data.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSolver: newton-cg;\u003c/p\u003e\u003cp\u003eRegularization; l1 or l2;\u003c/p\u003e\u003cp\u003eC: 0.001-100; iterations: 1000;\u003c/p\u003e\u003cp\u003eMulti-class option: multinomial\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRandom Forest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAn ensemble model adaptable to high-dimensional and complex multi-class problems, but computationally intensive.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNumber of trees: 10\u0026ndash;500;\u003c/p\u003e\u003cp\u003eMax-depth: \u0026lt;500;\u003c/p\u003e\u003cp\u003eMax-features:sqrt;\u003c/p\u003e\u003cp\u003eMin samples to split\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSupport Vector Machine\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eA robust classifier for complex multi-class problems that identifies optimal boundaries, but higher processing time.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eKernel: RBF;\u003c/p\u003e\u003cp\u003eRegularization: \u0026lt;1000;\u003c/p\u003e\u003cp\u003eKernel coefficient: optimized;\u003c/p\u003e\u003cp\u003edegree: 3; gamma: scale\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eK-Nearest Neighbour\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eA distance-based model for non-linear features, though sensitive to outliers and irrelevant features.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNumber of neighbors: optimized;\u003c/p\u003e\u003cp\u003eDistance metrics: Euclidean;\u003c/p\u003e\u003cp\u003eAlgorithms: Ball Tree, KD Tree\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDecision Tree\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eA tree-based classifier that splits data recursively and requires tuning to prevent overfitting.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMax-depth: optimized;\u003c/p\u003e\u003cp\u003eCriteria: Gini/Entrophy;\u003c/p\u003e\u003cp\u003eMin Samples per node: tuned\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTo address the class imbalance issue, we applied the SMOTE technique to augment minority classes, ensuring a balanced dataset for training and testing. Nine distinct analysis cases were defined, encompassing uni-directional, bi-directional, and multi-directional feature combinations (as detailed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e), capturing different perspectives of the melt pool\u0026rsquo;s thermal behavior. Each of these cases was used as input to five shallow learning classifiers\u0026mdash;Logistic Regression (Log-C), Random Forest (RFC), Support Vector Machine (SVC), K-Nearest Neighbor (KNN), and Decision Tree (DTC). Hyperparameter optimization was performed using randomized search cross-validation (CV), and model performance was evaluated using traditional classification metrics (see Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3\u003c/span\u003e for details). All computations were implemented in Python using the Scikit-learn (sklearn) library on an Apple MacBook Air (M1 chip, 16 GB RAM).\u003c/p\u003e\u003cp\u003eThis approach represents an early attempt to integrate multi-directional temperature features from melt pool imaging into shallow learning pipelines for porosity prediction, which could inform process parameter optimization and contribution to improved quality control in AM components.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003e2.7. Performance Metrics\u003c/h2\u003e\u003cp\u003eTo evaluate the performance of the models across various case studies, traditional classification metrics\u0026mdash;Accuracy, Precision, Recall, F1-score, and Confusion Matrix analysis\u0026mdash;were used. While these metrics are well-known and commonly used in ML, they may not fully capture the performance nuances in imbalanced classification scenarios, as they tend to prioritize the majority class [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e].\u003c/p\u003e\u003cdiv id=\"Sec19\" class=\"Section3\"\u003e\u003ch2\u003e2.7.1. Proposed Classification Deviation Error Metric\u003c/h2\u003e\u003cp\u003eGiven the limitations of conventional metrics in imbalance classification, we introduce a metric, i.e., classification deviation error (CDE). The CDE measures the deviation of a model\u0026rsquo;s predictions from an ideal classifier across all classes. It compares the normalized confusion matrix, CM\u003csub\u003eNormalized\u003c/sub\u003e, to the identity matrix \u003cem\u003eI\u003c/em\u003e, as expressed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e):\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:CDE=\\left|\\right|I-{CM}_{Normalized}{\\left|\\right|}_{2}=\\:\\sqrt{{\\sum\\:}_{i=1}^{n}{\\sum\\:}_{j=1}^{n}{({\\delta\\:}_{ij}-{CM}_{Normalized}(i,j\\left)\\right)}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cem\u003eI\u003c/em\u003e is the n\u0026times;n identity matrix,\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003en is the number of classes,\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCM\u003csub\u003eNormalized\u003c/sub\u003e is the normalized confusion matrix,\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eδ\u003csub\u003eij\u003c/sub\u003e ​ is the Kronecker delta (1 if \u003cem\u003ei\u0026thinsp;=\u0026thinsp;j\u003c/em\u003e, and 0 otherwise),\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e∥\u0026sdot;∥\u003csub\u003e2\u003c/sub\u003e denotes the Euclidean norm for matrices.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eA perfect classifier would yield CM\u003csub\u003eNormalized\u003c/sub\u003e = \u003cem\u003eI\u003c/em\u003e, resulting in a CDE of zero. Higher CDE values indicate a greater deviation from ideal performance, which can help identifying areas where the model struggles, particularly in predicting minority classes. By providing a single scalar value that reflects the overall misclassification severity, the CDE metric offers a more nuanced and informative assessment of model performance than traditional metrics alone.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eThis section evaluates the performance of five shallow learning classifiers\u0026mdash;Logistic Regression (Log-C), Random Forest Classifier (RFC), Support Vector Classifier (SVC), K-Nearest Neighbor (KNN), and Decision Tree Classifier (DTC)\u0026mdash;for predicting porosity levels (no porosity, micro-porosity, macro-porosity) from pyrometer-derived thermal profiles of the melt pool region. The thermal data were processed, and eight key features were selected (as detailed in \u003cb\u003eSection 2.4\u003c/b\u003e). Nine distinct case studies were defined to incorporate different orientations relative to the laser scanning direction. Both traditional classification metrics and the proposed CDE metric were used to assess model effectiveness and performance across these case studies.\u003c/p\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Shallow Learning with Traditional Classification Metrics\u003c/h2\u003e\u003cp\u003eAfter standardizing the balanced dataset and optimizing hyperparameters via randomized search and cross-validation approach, we used Accuracy, Precision, Recall, and F1-score to evaluate model performance across the nine case studies. The accuracy trends for each model are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eRFC\u003c/b\u003e: Consistently outperformed other models, achieving a peak accuracy of 94% in Case 7, which involved a bi-directional feature combination (parallel and oblique orientations with 16 features).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSVC, DTC\u003c/b\u003e: Both models maintained high accuracy across most cases, with a peak of 95% in Case 6 (a combination of parallel and perpendicular orientations with 16 features).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eKNN\u003c/b\u003e: Displayed variable accuracy but performed best in Case 5, with an accuracy of 91%, where features were averaged across all orientations (8 features).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eLog-C\u003c/b\u003e: Showed relatively lower accuracies but peaked at 95% in Case 6 and 91% in Case 8, where all orientations (32 features) were considered.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eCase 2\u003c/strong\u003e, which involved an orthogonal laser direction (Y-Axis), resulted in lowest accuracies (~\u0026thinsp;83%) across all models. While RFC and SVC achieved high accuracy, they also required longer training times. Although Log-C scored lower accuracy, it excelled in precision (0.94\u0026ndash;0.96) across all cases, demonstrating that a single metric like accuracy can be misleading. Relying solely on accuracy, or any other traditional metric is insufficient to capture the nuanced performance, especially for minority classes.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Shallow Learning with CDE Metric\u003c/h2\u003e\u003cp\u003eTo address the limitations of traditional metrics in handling class imbalance, we introduced the CDE metric (\u003cb\u003eSection 2.7.1\u003c/b\u003e). Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e present the CDE values across the nine case studies. Unlike accuracy, which can be inflated by correctly classifying majority classes, the CDE highlights discrepancies in predicting minority classes:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eLog-C\u003c/b\u003e: Achieved notably low CDE values (0.08\u0026ndash;0.09 in Case 7), despite moderate accuracy, indicating its superior handling of minority class predictions.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eRFC\u003c/b\u003e: Showed a low CDE of 0.18 in Case 7, confirming a well-balanced performance across all classes.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSVC\u003c/b\u003e: Despite reaching 95% accuracy in some cases, its CDE was significantly higher (4), revealing poor predictive performance on minority classes.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eKNN and DTC\u003c/b\u003e: Produced lower CDE values than SVC, but did not outperform Log-C or RFC in terms of balanced error distribution.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe CDE metric effectively revealed weaknesses that were hidden by traditional metrics. While some models appeared strong based on accuracy alone, CDE highlighted that Log-C and RFC provided more reliable predictions for minority classes.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo further illustrate these misclassifications, Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e5\u003c/span\u003e includes a normalized confusion matrix for Case 7, highlighting the challenges in predicting minority classes (micro- and macro-porosity). Complexities such as substrate interaction at early layers and boundary effects at the part edges (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cb\u003eFig.\u0026nbsp;4\u003c/b\u003e) contributed to these classification challenges. Despite appearing strong in traditional metrics, RFC and SVC were less effective for minority class predictions compared to Log-C, which maintained lower CDE values and a faster inference time of 0.001 ms.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of case assessment and shallow learning models with traditional classification metrics and proposed Classification Deviation Error (CDE) metric.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003eMetrics\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003eTraditional Metrics (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eProposed\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCases\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModels\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAccuracy\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePrecision\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRecall\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eF1-Score\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eCDE\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCase 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLog-C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRFC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.19\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSVC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.24\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKNN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.29\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDTC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCase 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLog-C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRFC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSVC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e2.28\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKNN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.92\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDTC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.26\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCase 3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLog-C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.13\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRFC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSVC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.02\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKNN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDTC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCase 4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLog-C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" 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colname=\"c7\"\u003e\u003cp\u003e0.32\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDTC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCase 8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLog-C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRFC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSVC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e2.85\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKNN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.14\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDTC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.01\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCase 9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLog-C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e0.27\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eRFC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSVC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e2.35\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eKNN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.64\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDTC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eNormalized confusion matrix and CDE analysis of five shallow learning models for Case 7.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(a) Logistic Regression (CDE\u0026thinsp;=\u0026thinsp;0.09)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.25\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(b) Random Forest (CDE\u0026thinsp;=\u0026thinsp;0.18)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.02\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.02\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(c) Support Vector Machine (CDE\u0026thinsp;=\u0026thinsp;2.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.25\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.67\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(d) K-Nearest Neighbour (CDE\u0026thinsp;=\u0026thinsp;0.32)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePore\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMicro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.25\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMacro\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e(e) Decision Tree (CDE\u0026thinsp;=\u0026thinsp;0.86)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec23\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Comparative Assessment\u003c/h2\u003e\u003cp\u003eConventional \u003cem\u003ein situ\u003c/em\u003e monitoring methods often rely on deep learning models, which require large training datasets, substantial computational resources, and extensive preprocessing. For example, studies utilizing functional PCA or multilinear PCA [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] can effectively capture certain aspects of melt pool morphology for binary classification. However, these methods may fail to reflect the full complexity of thermal dynamics and spatial variations. Although some deep learning approaches have achieved high accuracies, their computational cost, large dataset demands, and focus on single-direction thermal profiles limit their suitability for multi-class porosity prediction [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn contrast, our approach leverages multi-directional thermal profiles and physics-informed features to produce robust, computationally low cost predictions. For instance, Log-C and RFC classification achieved accurate results with low CDE values, along with short inference times (0.001 ms). This makes our method suitable for real-time inference, especially given the pyrometer\u0026rsquo;s 2.027 ms exposure time at a 6.4 Hz collection rate [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], while also predicting minority classes. This strategy not only meets or exceeds the accuracy levels reported in the literature [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e] but also utilizes a comprehensive dataset of 1,557 melt pool images spanning multiple orientations. By integrating the CDE metric into the evaluation process, we gain a more complete understanding of each model\u0026rsquo;s strengths and weaknesses, ensuring more reliable and informative porosity predictions in LBAM.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Summary","content":"\u003cp\u003eIn this work, we presented a reliable and effective approach for defect detection in laser-based additive manufacturing (LBAM) through a data-driven shallow learning (SL) model utilizing enhanced pyrometer sensor features. Our study highlights the advanced capabilities of ISM to detect defects, such as porosity, which could comprise the mechanical integrity of manufactured components. By leveraging dual-wavelength pyrometer data, we classified melt pool thermal profiles into distinct porosity categories, which were correlated with CT scans, ultimately optimizing defect detection in LBAM processes.\u003c/p\u003e\u003cp\u003eIn addressing the challenges of 2D thermal imaging analysis, particularly issues related to data scarcity and the computational demands of deep learning (DL) approaches, we proposed a methodology that extracts one-dimensional (1D) temperature profiles from multiple orientations relative to the laser movement. These 1D profiles allow for effective featurization using signal processing techniques to analyse the thermal dynamics influencing porosity formation. Additionally, our method introduces physics-informed features such as melt pool distance (MPD) and the aspect ratio of maximum temperature to MPD (ARTM), alongside fifteen statistical signal features identified as highly predictive through ensemble-based feature selection.\u003c/p\u003e\u003cp\u003eThe shallow learning models implemented in this study demonstrated high performance, achieving up to 95% accuracy, 96% precision, and 95% recall. However, predicting minority classes remained a significant challenge. To address this, we introduced a CDE metric, which quantitatively evaluates how far a model\u0026rsquo;s predictions deviate from an ideal classifier across all classes. By highlighting discrepancies in class-wise prediction accuracy, particularly for minority classes, CDE complements conventional metrics and supports model refinement aimed at identifying misclassification of minority classes.\u003c/p\u003e\u003cp\u003eOur approach demonstrates that shallow learning models, when combined with strategically engineered features, offer a reliable and efficient alternative to more complex deep learning methods. These models provide rapid and accurate defect prediction with reduced computational demands, making them particularly suited for real-time quality assurance in additive manufacturing. This research not only advances the understanding of melt pool dynamics through innovative sensor data utilization and machine learning but also proposes new metrics and standards for predictive accuracy in the field of additive manufacturing.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCRediT statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization: RK, MJ, FF\u003c/p\u003e\n\u003cp\u003eData curation: RK\u003c/p\u003e\n\u003cp\u003eFormal analysis: RK, FF\u003c/p\u003e\n\u003cp\u003eInvestigation: RK\u003c/p\u003e\n\u003cp\u003eMethodology: RK, MJ, FF\u003c/p\u003e\n\u003cp\u003eProject Administration: MJ, NR\u003c/p\u003e\n\u003cp\u003eSoftware: RK\u003c/p\u003e\n\u003cp\u003eSupervision: MJ, FF, NR\u003c/p\u003e\n\u003cp\u003eValidation: RK, MJ, FF, NR\u003c/p\u003e\n\u003cp\u003eVisualization: RK\u003c/p\u003e\n\u003cp\u003eWriting \u0026ndash; original draft: RK, MJ\u003c/p\u003e\n\u003cp\u003eWriting \u0026ndash; review \u0026amp; editing:RK, MJ, FF, NR\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDisclosure of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo potential conflict of interest was reported by the author(s).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are openly available in Thermal-Porosity Characterization Data of Additively Manufactured Ti-6Al-4V Thin-walled Structure via Laser Engineered Net Shaping (Original Data) (Dataverse), reference number [1].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors gratefully acknowledge the logistical and technical support as well as infrastructure provided by the Digital Manufacturing and Design (DManD) Centre at the Singapore University of Technology and Design (SUTD). The authors also acknowledge the Ministry of Education (MOE), Singapore, for providing a research student scholarship (RSS) for 2021\u0026ndash;2025. This research is supported by the Agency for Science, Technology and Research (A*STAR), under the Industry Alignment Fund Pre-Positioning Programme (IAF-PP) project \u0026ldquo;Metal Additive Manufacturing Powders: Reusability, Rejuvenation, Cost, Quality \u0026amp; Performance (RRAMP)\u0026rdquo; [Award No. M22K7a0047].\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMarshall, G.J., S.M. Thompson, and N. 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Russo, \u003cem\u003ePerformance of evaluation metrics for classification in imbalanced data.\u003c/em\u003e Computational Statistics, 2024: p. 1-27.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Laser-Based Additive Manufacturing (LBAM), In Situ Monitoring, Pyrometer Sensor, Porosity Detection, Physics-Informed Shallow Learning","lastPublishedDoi":"10.21203/rs.3.rs-7042984/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7042984/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLaser-based additive manufacturing (LBAM) has transformed the production of complex metallic components through precise, layer-by-layer deposition. However, porosity defects can compromise the mechanical integrity of printed parts, necessitating effective real-time monitoring and defect detection methods. This study utilizes dual-wavelength pyrometer data to classify melt pool thermal profiles into no-porosity, micro-porosity, and macro-porosity categories, labelled based on X-ray Computed Tomography (CT) scans. Temperature profiles across four orientations (0\u0026deg;, 90\u0026deg;, +\u0026thinsp;45\u0026deg;, and \u0026minus;\u0026thinsp;45\u0026deg;) relative to the laser scanning direction were processed through shallow learning models, enhanced with signal processing and physics-informed features, including melt pool distance (MPD) and aspect ratio of maximum temperature to MPD (ARTM). Our approach achieved classification accuracy (up to 95%), precision (96%), and recall (95%) in defect classification. To address challenges in predicting minority classes, we introduce a classification deviation error (CDE) metric. This work demonstrates that shallow learning models, combined with strategically engineered features, provide an efficient and reliable alternative to computationally expensive deep learning methods for in situ defect detection and quality assurance in LBAM.\u003c/p\u003e","manuscriptTitle":"Effective Porosity Detection in Laser-Based Additive Manufacturing Using Shallow Learning and Physics-Informed Pyrometer Features","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-15 12:47:46","doi":"10.21203/rs.3.rs-7042984/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2025-09-17T12:31:50+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-07-10T23:03:04+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-10T21:01:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-07T01:12:31+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2025-07-04T00:47:11+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"7808c25a-2aee-4c3e-9fce-947113d097d7","owner":[],"postedDate":"July 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-21T15:20:42+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-15 12:47:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7042984","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7042984","identity":"rs-7042984","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}