Development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) System Using Vibration Data in CNC Vertical Machining

Development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) System Using Vibration Data in CNC Vertical Machining | 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 Development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) System Using Vibration Data in CNC Vertical Machining Maximiliano Agustin Gomez Montero, Joseph Chen, Ye Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8117293/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents the development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) system aimed at enhancing quality monitoring in CNC milling and drilling operations. Vibration signals were captured using a tri-axial accelerometer during drilling and end- milling processes on aluminum 6061 workpieces. To reflect physical inspection strategies, the raw signals were segmented to match surface roughness measurement areas, while upper- and lower- hole regions were analyzed separately to represent perpendicularity. Twelve time- and frequency- domain features were extracted per axis and processed to reduce the dimension to the top five most relevant for each target output. Predictive models were developed using Multiple Linear Regression and Artificial Neural Networks (ANN), with linear regression achieving testing accuracy of 96.06% for surface roughness and 92.22% for perpendicularity, while the ANN improved performance to 99.67% and 95.98%, respectively. The results demonstrate that integrating vibration-based sensing with machine learning enables accurate online prediction of surface roughness and perpendicularity, contributing to more autonomous and data-driven decision-making in advanced manufacturing environments. CNC Milling Surface Roughness Perpendicularity Artificial Neural Networks Online Quality Control Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction In the context of modern industrial processes, CNC (Computer Numerical Control) milling is widely utilized in manufacturing, enabling the production of complex geometries with precision and repeatability. The process involves the removal of material using rotating cutting tools guided by CNC systems. Two common operations in CNC milling machines, end milling and drilling, are employed across industries for their ability to achieve quality surface finishes and precise geometric tolerances [ 1 – 2 ]. End milling is used for creating flat surfaces and intricate contours, while drilling is essential for producing accurate holes for assembly. These operations are integral to sectors such as aerospace, automotive, medical devices, and consumer electronics, where precision and efficiency are important. As global manufacturing demands continue to grow, CNC milling remains an important process, driving innovation in both hardware and software solutions [ 3 ]. The demand for CNC milling machines is projected to grow at a compound annual growth rate of 12% during the 2023–2030 period, driven by the increasing emphasis on industrial automation and advanced technologies such as artificial intelligence, machine learning, and robotics. These advancements have transformed milling machines into intelligent tools capable of performing intricate tasks with accuracy and efficiency [ 4 ]. Despite its importance, achieving consistent surface quality and geometric accuracy remains challenging, often requiring extensive manual inspections. Surface roughness affects both the functionality and aesthetics of machined parts, while perpendicularity, a geometric orientation feature, ensures proper alignment and assembly. Advances in sensor technologies and data analytics offer opportunities to address quality monitoring and control challenges in CNC machining. Machine vibrations, an inherent characteristic of milling and drilling processes, serve as a dynamic source of information about performance [ 5 , 6 ]. This study proposes the development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) system based on vibration data for evaluating surface roughness and perpendicularity in CNC milling and drilling, intending to reduce manual inspections and enhance efficiency. This study aims to develop such a system to simultaneously evaluate these key output features. By leveraging vibration analysis, transforming the data into useful information and utilizing machine learning techniques, this research seeks to establish a unified predictive framework in the subject. The remainder of this paper is structured as follows: Section 2 reviews the relevant literature on surface roughness and perpendicularity prediction in CNC milling and drilling, focusing on sensor-based monitoring and machine learning applications. Section 3 details the methodology, including the experimental setup, data processing, feature extraction, and the development of the predictive model. Section 4 presents the results, evaluating the system’s performance. Finally, Section 5 concludes the study, summarizing key findings and outlining potential directions for future research. 2. Literature Review CNC milling and drilling have been extensively studied due to its versatility and precision in machining complex geometries. The growing demand for higher quality and automation in manufacturing has driven research toward optimization techniques, predictive modeling, and data-driven approaches. Literature review was conducted to identify trends and approaches in CNC milling and drilling studies. This analysis revealed a growing body of literature focusing on surface quality prediction and process optimization. However, few studies simultaneously work with both surface roughness and geometric tolerances, such as perpendicularity, using vibration data, emphasizing the need for further investigation. Studies have explored the influence of cutting parameters, such as spindle speed, feed rate, and depth of cut, on surface roughness. For instance, Sahare et al. (2024) conducted experiments using the Taguchi method to optimize machining parameters in the milling of aluminum AI2023. They employed an L27 orthogonal array to analyze the effects of spindle speed, feed rate, depth of cut, and tool diameter on surface roughness. Their findings indicated that spindle speed and feed rate significantly affect surface roughness, with higher speeds and lower feed rates leading to improved finishes [ 7 ]. Similarly, Ahmad et al. (2017) applied the Taguchi methodology to optimize end milling process parameters for EN8 steel. Utilizing an L9 orthogonal array, the study examined the impact of spindle speed, feed rate, and depth of cut on surface finish. The study underscored the importance of feed rate and spindle speed in achieving optimal surface quality. Despite the effectiveness of the Taguchi method in parameter optimization, the study did not incorporate real-time data acquisition or predictive modeling, underscoring the potential benefits of integrating such approaches for enhanced machining performance [ 8 ]. Geometric tolerances, including perpendicularity, are critical for ensuring the dimensional accuracy and proper assembly of machined components. Saha et al. (2022) investigated the effects of CNC milling parameters on the cylindricity and perpendicularity of milled circular pockets in AISI 304H stainless steel. The study employed Taguchi’s L9 orthogonal array to analyze the impact of spindle speed and feed rate on these geometric characteristics. Perpendicularity measurements were conducted using a Coordinate Measuring Machine (CMM), revealing that spindle speed significantly influenced perpendicularity, while feed rate showed a lesser but notable effect. Additionally, response surface methodology (RSM) was used to develop mathematical models correlating input parameters with output responses [ 9 ]. Ibrahim et al. (2020) analyzed the effects of drilling parameters on surface roughness, cylindricity, and perpendicularity in machining magnesium AZ31 alloy. Using the Taguchi method (L18 orthogonal array), they evaluated the influence of spindle speed, feed rate, drill point angle, and lubricant. Their results showed that perpendicularity was significantly affected by the feed rate [ 10 ]. These findings emphasize the importance of optimizing machining parameters to achieve geometric accuracy in CNC milling applications Drilling process has been researched in CNC machining due to its impact on geometric tolerances, particularly perpendicularity and cylindricity. Patel et al. (2014) analyzed the effects of spindle speed, feed rate, and coolant ratio on perpendicularity in materials such as EN8, EN24, and EN31. Using a cobalt alloy steel drill with a point angle of 135° and a helix angle of 30°, their study employed Design of Experiments (DOE) and Analysis of Variance (ANOVA) to identify optimal cutting conditions. Results demonstrated that feed rate and spindle speed significantly influence perpendicularity, with DOE methodology proving effective for minimizing defects [ 11 ]. Similarly, Sheth et al. (2014) investigated the influence of machining parameters on cylindricity and perpendicularity in components produced by VMC machines. Their study highlighted the importance of achieving geometric tolerances for assembly-critical features such as holes for nuts, bolts, or pins. By applying DOE techniques and regression modeling, they demonstrated the potential to predict and optimize machining parameters for improved geometric outcomes [ 12 ]. These findings underscore the value of integrating drilling parameter data into predictive models to enhance machining accuracy and assembly reliability. A dynamic characteristic in these processes, machine vibrations, are an inherent aspect of machining and have been investigated for their impact on surface quality and geometric tolerances. Möhring et al. (2020) conducted a comprehensive investigation into the correlation between acceleration data from a sensor-integrated milling tool and resulting surface properties. Their study demonstrated that acceleration data is a reliable indicator of surface quality, enabling real-time adjustments to spindle speed and feed rate for improved machining outcomes [ 13 ]. Similarly, Rao and Ramesh (2020) analyzed the effects of tool vibrations on roundness and surface roughness in helical milling of Inconel 718. They developed predictive models that highlighted how vibration amplitude and frequency in the X- and Y-directions significantly influence machining accuracy. Their experiments demonstrated that reducing cutter orbital speeds can improve both surface finishes and roundness, underscoring the critical role of vibration control in optimizing machining processes [ 14 ]. However, despite these advancements, the specific relationship between vibrations and perpendicularity remains underexplored and this research aims to investigate that. To measure vibrations, accelerometer sensors have been utilized, which measure the rate of change of velocity of an object. Accelerometers data have been examined using different approaches to create meaningful information. Kirby et al. (2004) focused on predicting surface roughness during machining by processing vibration signals captured via accelerometers. The signals were transformed into absolute amplitudes, and their mean values were calculated over an equivalent range of 30 spindle revolutions. These mean amplitudes, along with feed rate, were used as inputs for a multiple regression model, while spindle speed and depth of cut were excluded based on their negligible impact on surface roughness as determined through Pearson correlation and ANOVA. The resulting regression model achieved a high coefficient of determination (R² = 0.96) [ 15 ]. Krishnakumar et al. (2015) adopted a more advanced approach by analyzing vibration signals in the frequency domain using a Fast Fourier Transform analyzer. Statistical features such as standard error, kurtosis, and median were extracted, and a J48 decision tree algorithm was used to identify the most significant features based on information gain. These features were then utilized in machine learning models, including artificial neural networks (ANNs) and decision trees, to predict tool wear during high-speed machining of titanium alloys. The ANN model outperformed the decision tree with a classification efficiency of 95.4%, highlighting the potential of integrating frequency-domain features and machine learning techniques for tool condition monitoring [ 16 ]. The integration of machine learning into machining processes has shown substantial promise in predictive accuracy for critical outcomes such as surface roughness and machining stability. Raju et al. (2024) extended this approach by incorporating spindle bearing vibrations into predictive models for CNC milling, utilizing machine learning techniques such as polynomial regression and artificial neural networks (ANNs). Their study demonstrated near-perfect prediction accuracy, showcasing the potential of vibration data for surface quality optimization [ 17 ]. Similarly, Lin et al. (2020) employed multiple regression and ANN approaches to model surface roughness using cutting parameters and machining vibrations in end milling, achieving a prediction accuracy of 93.14% [ 18 ]. Despite these advancements, the application of machine learning to predict geometric orientation, such as perpendicularity, remains an open challenge, offering significant opportunities for future exploration. Guleria et al. (2022) investigated the classification of surface roughness in CNC turning of forged EN8 steel using vibration signal processing and Support Vector Machine (SVM). They extracted features from time-domain, frequency-domain, and Fast Fourier Transform (FFT) image analysis, including mean, standard deviation, kurtosis, skewness, and entropy. A Bayesian-optimized SVM was employed, achieving 91.9% accuracy using frequency-domain features and demonstrating the potential of vibration-based monitoring for real-time quality assessment [ 19 ]. Arendra and Herianto (2020) developed a vibration-based tool wear detection system for CNC milling using MMA 7361 accelerometers and NI DAQ USB-6008 for real-time data acquisition [ 20 ]. They extracted key vibration features, including standard deviation, skewness, kurtosis, and range, from both time-domain and order-domain analyses. Feature selection using a Linear Discriminant Classifier (LDC) identified the most relevant predictors, which were then classified using a Multi-Layer Perceptron (MLP), achieving 96.4% accuracy. Their findings demonstrate how machine learning and vibration analysis can effectively monitor machining conditions, a methodology that could be adapted for predicting geometric deviations in drilling and milling processes. Building on these findings, the integration of vibration signals has proven to be a transformative approach for understanding machining dynamics and enhancing predictive capabilities. While significant advancements have been made in predictive modeling, existing research often isolates surface roughness and perpendicularity as independent phenomena. This fragmented approach fails to capture the interconnected nature of these metrics in ensuring dimensional accuracy and assembly-critical tolerances. This study addresses these critical subjects by developing a vibration-based predictive system that simultaneously evaluates surface roughness and perpendicularity in CNC milling. By leveraging signal processing techniques, such as calculating frequency and time-domain features in a structured process, and employing Multi Linear Regression and Artificial Neural Networks, provides a comprehensive approach for prediction. The proposed system aligns with the increasing demand for intelligent manufacturing solutions, enabling real-time monitoring and improving the precision and efficiency of processes. 3. Methodology 3.1 Architecture of the System The architecture of the proposed Online Surface Roughness and Perpendicularity Prediction (OSRPP) System is illustrated in Fig. 1 . To achieve the desired workpiece surface roughness and perpendicularity, the process begins by entering optimized values for parameters and the workpiece in the machine. Once these parameters are set, vibration data is collected from the controller when the process is taking place. \(\:{A}_{x}\) , \(\:{A}_{y}\) and \(\:{A}_{z}\) represent the online accelerometer data stored for further processing. These datasets are analyzed and engineered with the hypothesis that can represent the relation between vibration and both surface roughness and perpendicularity. The prediction model is part of an integrated system that predicts surface roughness and perpendicularity. The model alone, as a mathematical construct, requires inputs and outputs. The complete system uses online data to make predictions. If the predicted surface roughness and perpendicularity are within specifications, the process continues being monitored. If any of them are out of the specification range, the system alerts the operator, who can pause or adjust the machine as needed. This study proposes a Multi-Linear Regression and ANN-based system and tests its performance. The experimental setup is designed to collect data for the development of the OSRPP system. The experiments are conducted on a (HAAS VF-5/40XT) CNC machine, using 6061 aluminum due to its machinability and its ability to highlight surface finish variations. The process includes a drilling operation followed by an end-milling operation. The tool for drilling is a carbide drill with 0.375 in diameter, chosen to reduce deflection and eliminate the need for a center drill. The tool for end-milling is a High-Speed-Steel end mill with 0.375 in diameter and 2 flutes, selected for its efficiency in cutting aluminum and preventing material buildup [ 21 – 22 ]. This setup was based on optimized machining parameters previously obtained through experimental design. Although the optimization phase is not detailed here, it was carried out in a separate study by the author. For surface roughness, the optimized end milling parameters were set to a feed rate of 8 in/min , spindle speed of 4500 rpm , depth of cut of 0.008 in , and coolant enabled, resulting in an average surface roughness of 0.215 µm . For perpendicularity, the optimized drilling parameters included a feed rate of 13 in/min , spindle speed of 5000 rpm , coolant enabled, and adherence to the drill-mill sequence. The proposed workpiece, shown in Fig. 2 , was designed to facilitate data collection for both drilling and end-milling processes. A three-axis accelerometer was mounted on the machine table to minimize noise and external vibrations. To protect it from coolant sprays and debris, the sensor was enclosed in a protective box, as shown in Fig. 3 . During machining, vibration data was collected using (Kistler) acquisition software and stored for subsequent analysis. Surface roughness (Ra) is measured using a profilometer at consistent points, in the range between 0.2 in and 0.6 in where 0 in is the start point of the cut. Perpendicularity is assessed using a (Mitutoyo) Coordinate Measuring Machine (CMM), providing precise geometric measurements across different sections of the workpiece. Figure 4 a and Fig. 4 b show measurement set up for each output variable. 3.2 Design of Experiments to collect data Given the complexity of variable interactions in machining, it is essential to collect representative process data. To achieve this, a Design of Experiments (DOE) was implemented using a full factorial approach to analyze the combined effects of spindle speed, feed rate, and depth of cut on machining outcomes. To account for natural process variability, experimental parameters were slightly adjusted across multiple trials. Vibration data was captured online using a three-axis accelerometer connected to a data acquisition system. Key output features, surface roughness and perpendicularity, were subsequently measured. These measurements, along with the processed vibration data, formed the dataset used for training the predictive model. The experimental design factors and levels are summarized in Table 1 . The End Milling process followed a \(\:{3}^{3}\) full factorial design while drilling experiments were accoupled to the previous one resulting in a total of 81 experiments. Table 1 DOE Factors and Levels for End Milling Process End Milling Parameters Variable Unit Level 1 Level 2 Level 3 Feed Rate in/min 7.9 8 8.1 Spindle speed rpm 4480 4500 4520 Depth of Cut in 0.0078 0.008 0.0082 Drilling Parameters Variable Unit Level 1 Level 2 Level 3 Feed Rate in/min 12.9 13 13.1 Spindle speed rpm 4980 5000 5020 3.3 Data Engineering and Processing The vibration signals during machining comes from the sensor as series of values of aceeleration in units of g that sensor has collected. The sampling frequency of the vibration data is 25 kHz (25,000 Hz). This indicates that the accelerometer captures 25,000 samples per second during the acquisition. Table 2 shows an example of how the vibration data is presented as outcome of the data acquisition system. Table 2 Example of Vibration Data Collected Time Channel1 [g] Channel2 [g] Channel3 [g] 0.00000 -0.014862 -0.024284 -0.011239 0.00004 -0.014862 -0.017381 -0.015685 0.00008 -0.012841 -0.017258 -0.019513 0.00012 -0.008442 -0.022928 -0.018772 0.00016 -0.008323 -0.02034 -0.01445 0.00020 -0.010463 -0.022435 -0.008398 These resulted in 81 files with hundreds of thousands of datapoints for each of the processes. Thus, it was necessary to select the desired range of interested data. To do that, each dataset collected in the operation was processed to extract the relevant data range as follows. For end milling, the range where the surface roughness of the workpiece was measured consistently was defined as 0.2 in to 0.6 in from the start point of the cut. Then, the first peak of the average force was identified in each vibration dataset. From this point, the next 0.2 inches were excluded from analysis (equivalent to 37,500 data points, given a feed rate of 8 in/min). Subsequently, data from the following 0.4 inches was retained, representing the study range for the milling process on the workpiece. Figure 5 a and Fig. 5 b illustrate the data cleaning process for the milling operation. For the drilling process, the selected vibration data focused on capturing representative segments from both the upper and lower portions of the cut. This segmentation enables a comparative analysis between the two regions, which is essential for evaluating the influence of drilling on geometric orientation. Figure 6 illustrates the data selection approach. To characterize the vibration signals collected during machining, a set of statistical time-domain features was extracted. These features are widely used in condition monitoring and signal analysis due to their ability to capture different characteristics of the signal: Root Mean Square (RMS) and Total Energy quantify the energy content and intensity of the signal. Standard Deviation and Absolute Mean measure the variability and average magnitude, respectively. Skewness and Kurtosis describe the asymmetry and sharpness of the signal distribution, often associated with abnormalities or transient events. Crest Factor captures the relationship between the peak amplitude and the overall signal level, highlighting impulsive behavior. Each of these features provides unique insights into the dynamic behavior of the machining process. Detailed formulas for each metric are provided in Appendix A . In addition to the time-domain analysis, frequency-domain features were computed to better understand how vibration energy is distributed across different frequency components. These metrics are essential for identifying dominant vibration modes and resonance behaviors that are not easily visible in the time domain. To analyze the frequency content of the vibration signals, the Fast Fourier Transform (FFT) was applied. The discrete Fourier transform (DFT), computed efficiently via the FFT algorithm, is given by Eq. 1 : $$\:{X}_{k}={\sum\:}_{n=0}^{N-1}{x}_{n}{e}^{-j2\pi\:kn/N}$$ 1 Where \(\:{x}_{n}\) 𝑖𝑠 𝑡he value of the signal at the \(\:{n}^{th}\) time sample, N total number of samples in the signal, 𝑘 is the index of frequency bins and 𝑗 is the imaginary unit. This transformation decomposes the signal into its constituent frequencies, allowing the identification of dominant frequencies and amplitudes that correlate with machining dynamics as shown in Fig. 7 [ 23 ]. After applying the Fast Fourier Transform (FFT) to convert the vibration signals into the frequency domain, five key features were extracted to characterize the spectral properties: Dominant Frequency : Identifies the frequency bin with the highest energy concentration, typically associated with the most energetically significant vibration mode during machining. Peak Frequency : Indicates the frequency corresponding to the highest amplitude component in the spectrum, often linked to resonance or periodic tool–workpiece interactions. Peak Value : Represents the maximum magnitude observed in the frequency spectrum, indicating the highest vibration intensity. Bandwidth : Measures the spread of energy around the spectral centroid, quantifying how concentrated or dispersed the vibration energy is, and aiding in the assessment of process stability. Spectral Centroid : Acts as the center of mass of the frequency spectrum, providing a weighted average of the frequency components and indicating where the majority of the energy is concentrated. These spectral features complement the time-domain descriptors by highlighting periodicities, harmonics, and high-frequency patterns related to machining dynamics. The mathematical definitions of each feature are included in Appendix B [ 24 ]. Due to the complexity of these calculations, the metrics were computed using scripts to ensure accuracy and consistency in the data analysis process. 3.4 Dimensionality Reduction and Variable Selection A total of 36 input variables were extracted per workpiece, corresponding to 12 features calculated for each of the three accelerometer channels. While these variables provide a comprehensive description of the signal, processing all 36 in a real-time application can be computationally expensive. This may delay prediction to the point that the machining process is already complete before a result is generated. To address this limitation, a dimensionality reduction strategy was implemented to retain only the most informative features. The K-Best feature selection method was applied, which ranks all input variables according to their relevance to the output variable using statistical correlation. Specifically, the f_regression scoring function was used, which evaluates the linear dependency between each feature and the target variable using ANOVA F-values. This score compares the variance explained by each input feature to the variance within groups, according to the Eq. 2 : $$\:F=\frac{Variance\:between\:groups}{Variance\:within\:groups}$$ 2 The full table of F-values for the 36 extracted features is provided in Appendix C . The features with the highest F-scores were selected as inputs to the prediction models. For surface roughness prediction, five features were selected based on their statistical significance, as summarized in Table 3 . These include three time-domain variables and two frequency-domain variables. Similarly, for perpendicularity, the top five selected features are presented in Table 4 . Table 3 Top 5 ANOVA F-values for Surface Roughness Feature Name Domain F-Value Denoted as RMS 1 Time 34.16 \(\:{x}_{1}\) FFT Peak Value 1 Frequency 20.09 \(\:{x}_{2}\) Std Dev 2 Time 14.47 \(\:{x}_{3}\) Kurtosis 3 Time 8.07 \(\:{x}_{4}\) FFT Peak Freq 1 Frequency 2.58 \(\:{x}_{5}\) Table 4 Top 5 ANOVA F-values for Perpendicularity Feature Name Domain F-Value Denoted as Std Dev 1 Time 121.26 \(\:{x}_{6}\) RMS 1 Time 74.63 \(\:{x}_{7}\) Skewness 2 Time 23.46 \(\:{x}_{8}\) FFT Peak Val 1 Frequency 13.67 \(\:{x}_{9}\) Dominant Frequency 1 Frequency 10.59 \(\:{x}_{10}\) These selected features formed the input vector \(\:X\:\) for each predictive model. The combination of time and frequency domain characteristics helped capture both the transient and harmonic components of the vibration signals, enabling accurate prediction of quality metrics. Once the selected features were prepared for modeling, the next subsections detail the development of each prediction model. 3.5 Multi Linear Regression Model To establish a baseline predictive model, a Multiple Linear Regression (MLR) approach was implemented. MLR was selected due to its simplicity, interpretability, and well-established performance in modeling linear relationships between input features and output variables. It provides a useful benchmark for evaluating the effectiveness of more complex models such as artificial neural networks. In this context, the MLR model estimates the output variable, either surface roughness or perpendicularity, as a linear combination of the five selected features. The regression coefficients were optimized to minimize the mean squared error between predicted and actual values in the training dataset. The equations obtained for each of the outputs are given in Eq. 3 and Eq. 4 : \(\:{y}_{1\:}\left(Ra\right)=0.2612-0.0298{x}_{1}+0.0278{x}_{2}-0.0226{x}_{3}-0.0105{x}_{4}-0.0124{x}_{5}\) (3) \(\:{y}_{2\:}\left(Penp\right)=0.0296+0.0069{x}_{6}-0.0102{x}_{7}-0.0013{x}_{8}-0.0027{x}_{9}-0.0180{x}_{10}\) (4) where \(\:{x}_{i}\) are the selected input features. The MLR model serves not only as a baseline but also provides valuable insight into the linear contribution of each variable, which can be used for physical interpretation and engineering validation. 3.5 Artificial Neural Networks Model To enhance the system’s ability to capture non-linear patterns in the vibration data, an Artificial Neural Network (ANN) model was developed. ANNs are well-suited for complex regression problems in manufacturing applications due to their capacity to learn intricate relationships between input features and output responses. In contrast to linear models such as MLR, neural networks can model non-linear interactions, making them ideal for predicting variables like surface roughness and perpendicularity, which often depend on combined effects across multiple signal characteristics. The architecture of the proposed ANN model is shown in Fig. 8 . The network was structured with five input neurons, each corresponding to one of the selected variables after feature selection. This input layer was followed by three hidden layers, consisting of 64, 32, and 16 neurons, respectively. Each hidden layer used the ReLU (Rectified Linear Unit) activation function to introduce non-linearity while maintaining computational efficiency. The output layer contained a single neuron with a linear activation function to predict the target value for each case. The model was trained using a backpropagation algorithm with the Adam optimizer and mean squared error (MSE) as the loss function. A validation set was used to monitor performance and prevent overfitting through early stopping. Separate models were trained for surface roughness and perpendicularity using the top five features identified for each case via KBest. 4. Results and Discussion The performance of the predictive models was evaluated on a testing dataset composed of 16 samples not used during training or validation. Both Multiple Linear Regression (MLR) and Artificial Neural Network (ANN) models were tested independently for each of the two target variables. Table 5 presents the comparison between real and predicted surface roughness values for both the MLR and ANN models. The ANN predictions closely follow the real values with higher precision across the full range of observations. Table 6 shows the prediction results for perpendicularity deviation. As with surface roughness, the ANN model consistently provides estimates closer to the actual measured values than MLR. Table 5 Surface Roughness Prediction Testing Results \(\:{x}_{1}\) … \(\:{x}_{5}\) \(\:{y}_{1}\) MLR \(\:{y{\prime\:}}_{1}\) MLR Accuracy (%) ANN \(\:{y{\prime\:}}_{1}\) ANN Accuracy (%) 0.0165 … 0.7473 0.4923 0.492399 99.98 0.491690 99.87 0.0157 … 0.6607 0.3045 0.293924 96.52 0.303323 99.61 0.0318 … 0.2738 0.2090 0.214430 97.40 0.208600 99.80 0.0787 … 0.6997 0.1833 0.179322 97.81 0.182481 99.54 0.0272 … 0.6628 0.235 0.236558 99.33 0.233960 99.55 0.0195 … 0.3702 0.2753 0.275543 99.92 0.273351 99.28 0.0265 … 1.5171 0.1860 0.174101 93.60 0.185013 99.46 0.0281 … 0.8378 0.2133 0.211772 99.26 0.212668 99.68 0.0281 … 5.0556 0.1721 0.183778 93.22 0.171646 99.72 0.0235 … -0.4124 0.2166 0.229180 94.22 0.215140 99.29 0.0157 … 1.1857 0.2840 0.273569 96.32 0.283810 99.93 0.0211 … 0.9107 0.2674 0.255587 95.56 0.266943 99.81 0.0264 … 1.9398 0.3345 0.337170 99.20 0.333679 99.75 0.0273 … 2.1372 0.2470 0.255105 96.75 0.246573 99.78 0.0190 … 0.9995 0.2938 0.277366 94.38 0.293357 99.82 0.0302 … 0.1563 0.2096 0.244144 83.55 0.209345 99.84 Table 6 Perpendicularity Prediction Testing Results \(\:{x}_{6}\) … \(\:{x}_{10}\) \(\:{y}_{2}\) MLR \(\:{y{\prime\:}}_{2}\) MLR Accuracy (%) ANN \(\:{y{\prime\:}}_{2}\) ANN Accuracy (%) 0.0028 … 8.5428 0.002 0.002027 98.65 0.001833 91.65 0.0174 … 24.290 0.0125 0.01182 94.56 0.012107 96.85 0.0616 … 3.0849 0.0438 0.042431 96.87 0.042469 96.96 0.0212 … 24.506 0.0146 0.014649 99.66 0.014955 97.57 0.0527 … 59.814 0.0377 0.0365 96.81 0.036979 98.08 0.0375 … 69.815 0.0261 0.028263 91.71 0.026128 99.89 0.0206 … 39.444 0.0142 0.013561 95.50 0.014403 98.56 0.0275 … 91.295 0.0184 0.014045 76.32 0.017332 94.19 0.0060 … 62.052 0.0045 0.005151 85.54 0.004259 94.64 0.0495 … 88.615 0.0366 0.035035 95.72 0.033675 92.00 0.0351 … 36.369 0.0253 0.028313 88.09 0.024913 98.46 0.0077 … 93.166 0.0054 0.004844 89.70 0.005273 97.65 0.0849 … 97.905 0.0625 0.061786 98.85 0.060334 96.53 0.0176 … 27.776 0.0124 0.011831 95.41 0.01119 90.24 0.0882 … 96.634 0.0614 0.071549 83.47 0.056963 92.77 0.0388 … 13.640 0.0277 0.024574 88.71 0.027784 99.69 Table 7 summarizes the prediction performance of both systems in terms of Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Testing Accuracy (%). Table 7 Results Summary of System’s Metrics Output Model base MAE RMSE Accuracy (%) Surface Roughness MLR 0.00899 0.01225 96.06 ANN 0.00070 0.00084 99.67 Perpendicularity Deviation MLR 0.00236 0.00397 92.22 ANN 0.00112 0.00163 95.98 5. Conclusions This study presents a robust and efficient predictive system to predict surface roughness and perpendicularity, two critical output quality characteristics, based on vibration signals collected during the CNC milling and drilling processes. The combination of advanced signal processing, feature selection, and machine learning models demonstrated highly accurate results on independent test data. Figure 9 a and Fig. 9 b illustrate the real and predicted values for surface roughness and perpendicularity, respectively. The ANN model demonstrated a closer alignment with the actual values throughout the entire test range, particularly in regions where the signal exhibited greater variability. The results presented here have significant implications for modern manufacturing systems, particularly in the era of Industry 4.0 and smart machining. This study shows that vibration data, when properly processed and modeled, can be transformed into a powerful source of predictive insight. Instead of relying solely on post-process inspections or expensive metrology systems, manufacturers could predict in real time whether a part will meet dimensional and surface quality requirements. With accuracy as high as 99.67% for surface roughness and 95.98% for perpendicularity deviation, the proposed ANN model opens the door to autonomous decision-making in production lines. This means determining in-process if a part is likely to be accepted or rejected, and taking immediate corrective actions before additional waste or cost is generated. By reducing the predictive process down to just five well-selected variables per target output, the system also becomes computationally lightweight facilitating the way for deployment on edge devices or PLCs directly on the shop floor. This approach embodies the future of intelligent manufacturing, where sensor-driven, AI-enhanced quality prediction becomes the new standard for close to zero-defect production. Future work will focus on expanding the dataset to include a broader range of materials, cutting parameters, and tool geometries, enabling greater model generalization. Additionally, efforts may be directed toward implementing the system in real-time CNC environments, allowing live signal acquisition and prediction during machining. Future developments may also explore unified multi-output models, hybrid data and physics-informed architectures, and direct integration into industrial control systems to validate the approach under full production conditions. Declarations Conflict of interest: The authors declare no competing interests. References Milling CNC A Comprehensive Guide to Understanding and Mastering the Technology. Retrieved from https://www.wevolver.com/article/cnc-milling-a-comprehensive-guide-to-understanding-and-mastering-the-technology Zhang P System Interfaces for Industrial Control https://doi.org/10.1016/B978-081551571-5.50004-9 All About End Milling Retrieved from https://shop.machinemfg.com/all-about-end-milling/ Grand View Research (2023) Computer Numerical Control Machines Market Size, Share & Trends Analysis Report By Type (Lathe Machines, Milling Machines, Laser Machines), By End-use (Automotive, Industrial, Construction Equipment), By Region, And Segment Forecasts, 2023–2030 Wang Y, Zhang P, Lee S (2021) Predictive modeling of surface finish in CNC milling using vibration signals. Procedia CIRP 99:305–310. https://doi.org/10.1016/j.procir.2021.05.045 Adam Jablonski Vibrations as a Source of Information. 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Wiley, Chichester, UK NIST/SEMATECH (2012) e-Handbook of Statistical Methods . Retrieved from https://www.itl.nist.gov/div898/handbook/ Haykin S (2009) Neural networks and learning machines (3rd ed.). Pearson Supplementary Files Appendices.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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09:00:43","extension":"xml","order_by":51,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":147304,"visible":true,"origin":"","legend":"","description":"","filename":"JAMTD25065710structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/87220d4bcf336db081cb92b7.xml"},{"id":96889549,"identity":"57fde7ce-bd02-4182-9bc4-f61811822ca1","added_by":"auto","created_at":"2025-11-27 09:00:40","extension":"html","order_by":52,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":160775,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/290979260d1d5d9a55fbd912.html"},{"id":96920464,"identity":"6aa3d59f-ce1a-4b4a-981c-fd7105377daf","added_by":"auto","created_at":"2025-11-27 14:15:11","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":104161,"visible":true,"origin":"","legend":"\u003cp\u003eCNC Milling OSRPP System Architecture\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/d22cc1b5a7d4a50fbbd5d694.jpg"},{"id":96920792,"identity":"32de7f5a-cf19-4ae1-8478-06d4366a12e1","added_by":"auto","created_at":"2025-11-27 14:15:26","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":28820,"visible":true,"origin":"","legend":"\u003cp\u003eWorkpiece Design for Vibration Data Collection during Drilling and Milling\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/f713cd23d5cca26ba299719b.jpg"},{"id":96889538,"identity":"687fe03d-56d7-4397-a15d-794310b67548","added_by":"auto","created_at":"2025-11-27 09:00:39","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":49060,"visible":true,"origin":"","legend":"\u003cp\u003eThree-Axis Accelerometer Setup for Vibration Data Acquisition\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/4be397bc105a5d6925479581.jpg"},{"id":96889536,"identity":"b49fbde6-dadf-4c6d-8a8b-c1a2969e4294","added_by":"auto","created_at":"2025-11-27 09:00:39","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":103190,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea-b\u003c/strong\u003e. Measurement Setup for Surface Roughness using Profilometer and Perpendicularity Deviation using CMM\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/5dd5f24c0f60130147f2fa02.jpg"},{"id":96889540,"identity":"699e61eb-53b9-477c-93e6-ae6b9ac9669d","added_by":"auto","created_at":"2025-11-27 09:00:39","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":77377,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea-b\u003c/strong\u003e. Data Selection Process for Milling Vibration Signals\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/937a12d3f7eaa76b907bf5f9.jpg"},{"id":96889542,"identity":"1857ded3-2960-4765-8cda-03f0e61c34b3","added_by":"auto","created_at":"2025-11-27 09:00:39","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":32685,"visible":true,"origin":"","legend":"\u003cp\u003eData Selection Process for Drilling Vibration Signals\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/4fba8756d4d17202f59632a0.jpg"},{"id":96889545,"identity":"d3a12446-aed7-463f-bec5-f688ad248935","added_by":"auto","created_at":"2025-11-27 09:00:40","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":52543,"visible":true,"origin":"","legend":"\u003cp\u003eTransformation of Vibration Signals from Time- to Frequency-Domain via FFT by MHM Lab\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/b37d1942b417208be985c5f1.jpg"},{"id":96918711,"identity":"e79c3a92-33ee-4c2c-9d03-1a96ab730ecf","added_by":"auto","created_at":"2025-11-27 14:12:23","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":86552,"visible":true,"origin":"","legend":"\u003cp\u003eArchitecture of the Artificial Neural Network Model for Prediction\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/0361399fae10ae321f117839.jpg"},{"id":96889546,"identity":"e8ea78fb-835a-4b23-af83-b763487ddd56","added_by":"auto","created_at":"2025-11-27 09:00:40","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":140690,"visible":true,"origin":"","legend":"\u003cp\u003ea. Comparison of Predicted vs Actual Values for Surface Roughness\u003c/p\u003e\n\u003cp\u003eb. Comparison of Predicted vs Actual Values for Perpendicularity Deviation\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/e7aa8b46d59e070c83e4ffaf.jpg"},{"id":99317686,"identity":"e25f2c4a-413e-42bd-8df7-30b0713a6f17","added_by":"auto","created_at":"2025-12-31 16:30:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1793205,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/25e098db-a7d7-4e7b-9bf5-81a364b5774d.pdf"},{"id":96889535,"identity":"86b6fe58-79dd-4676-8fc8-c2fa47b323d5","added_by":"auto","created_at":"2025-11-27 09:00:39","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":26033,"visible":true,"origin":"","legend":"","description":"","filename":"Appendices.docx","url":"https://assets-eu.researchsquare.com/files/rs-8117293/v1/905ca67202225241f5616e9d.docx"}],"financialInterests":"","formattedTitle":"Development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) System Using Vibration Data in CNC Vertical Machining","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the context of modern industrial processes, CNC (Computer Numerical Control) milling is widely utilized in manufacturing, enabling the production of complex geometries with precision and repeatability. The process involves the removal of material using rotating cutting tools guided by CNC systems. Two common operations in CNC milling machines, end milling and drilling, are employed across industries for their ability to achieve quality surface finishes and precise geometric tolerances [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eEnd milling is used for creating flat surfaces and intricate contours, while drilling is essential for producing accurate holes for assembly. These operations are integral to sectors such as aerospace, automotive, medical devices, and consumer electronics, where precision and efficiency are important. As global manufacturing demands continue to grow, CNC milling remains an important process, driving innovation in both hardware and software solutions [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe demand for CNC milling machines is projected to grow at a compound annual growth rate of 12% during the 2023\u0026ndash;2030 period, driven by the increasing emphasis on industrial automation and advanced technologies such as artificial intelligence, machine learning, and robotics. These advancements have transformed milling machines into intelligent tools capable of performing intricate tasks with accuracy and efficiency [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eDespite its importance, achieving consistent surface quality and geometric accuracy remains challenging, often requiring extensive manual inspections. Surface roughness affects both the functionality and aesthetics of machined parts, while perpendicularity, a geometric orientation feature, ensures proper alignment and assembly.\u003c/p\u003e\u003cp\u003eAdvances in sensor technologies and data analytics offer opportunities to address quality monitoring and control challenges in CNC machining. Machine vibrations, an inherent characteristic of milling and drilling processes, serve as a dynamic source of information about performance [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis study proposes the development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) system based on vibration data for evaluating surface roughness and perpendicularity in CNC milling and drilling, intending to reduce manual inspections and enhance efficiency.\u003c/p\u003e\u003cp\u003eThis study aims to develop such a system to simultaneously evaluate these key output features. By leveraging vibration analysis, transforming the data into useful information and utilizing machine learning techniques, this research seeks to establish a unified predictive framework in the subject.\u003c/p\u003e\u003cp\u003eThe remainder of this paper is structured as follows: \u003cb\u003eSection 2\u003c/b\u003e reviews the relevant literature on surface roughness and perpendicularity prediction in CNC milling and drilling, focusing on sensor-based monitoring and machine learning applications. \u003cb\u003eSection 3\u003c/b\u003e details the methodology, including the experimental setup, data processing, feature extraction, and the development of the predictive model. \u003cb\u003eSection 4\u003c/b\u003e presents the results, evaluating the system\u0026rsquo;s performance. Finally, Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e5\u003c/span\u003e concludes the study, summarizing key findings and outlining potential directions for future research.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cp\u003eCNC milling and drilling have been extensively studied due to its versatility and precision in machining complex geometries. The growing demand for higher quality and automation in manufacturing has driven research toward optimization techniques, predictive modeling, and data-driven approaches.\u003c/p\u003e\u003cp\u003eLiterature review was conducted to identify trends and approaches in CNC milling and drilling studies. This analysis revealed a growing body of literature focusing on surface quality prediction and process optimization. However, few studies simultaneously work with both surface roughness and geometric tolerances, such as perpendicularity, using vibration data, emphasizing the need for further investigation.\u003c/p\u003e\u003cp\u003eStudies have explored the influence of cutting parameters, such as spindle speed, feed rate, and depth of cut, on surface roughness. For instance, \u003cb\u003eSahare et al. (2024)\u003c/b\u003e conducted experiments using the Taguchi method to optimize machining parameters in the milling of aluminum AI2023. They employed an L27 orthogonal array to analyze the effects of spindle speed, feed rate, depth of cut, and tool diameter on surface roughness. Their findings indicated that spindle speed and feed rate significantly affect surface roughness, with higher speeds and lower feed rates leading to improved finishes [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Similarly, \u003cb\u003eAhmad et al. (2017)\u003c/b\u003e applied the Taguchi methodology to optimize end milling process parameters for EN8 steel. Utilizing an L9 orthogonal array, the study examined the impact of spindle speed, feed rate, and depth of cut on surface finish. The study underscored the importance of feed rate and spindle speed in achieving optimal surface quality. Despite the effectiveness of the Taguchi method in parameter optimization, the study did not incorporate real-time data acquisition or predictive modeling, underscoring the potential benefits of integrating such approaches for enhanced machining performance [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eGeometric tolerances, including perpendicularity, are critical for ensuring the dimensional accuracy and proper assembly of machined components. \u003cb\u003eSaha et al. (2022)\u003c/b\u003e investigated the effects of CNC milling parameters on the cylindricity and perpendicularity of milled circular pockets in AISI 304H stainless steel. The study employed Taguchi\u0026rsquo;s L9 orthogonal array to analyze the impact of spindle speed and feed rate on these geometric characteristics. Perpendicularity measurements were conducted using a Coordinate Measuring Machine (CMM), revealing that spindle speed significantly influenced perpendicularity, while feed rate showed a lesser but notable effect. Additionally, response surface methodology (RSM) was used to develop mathematical models correlating input parameters with output responses [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. \u003cb\u003eIbrahim et al. (2020)\u003c/b\u003e analyzed the effects of drilling parameters on surface roughness, cylindricity, and perpendicularity in machining magnesium AZ31 alloy. Using the Taguchi method (L18 orthogonal array), they evaluated the influence of spindle speed, feed rate, drill point angle, and lubricant. Their results showed that perpendicularity was significantly affected by the feed rate [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. These findings emphasize the importance of optimizing machining parameters to achieve geometric accuracy in CNC milling applications\u003c/p\u003e\u003cp\u003eDrilling process has been researched in CNC machining due to its impact on geometric tolerances, particularly perpendicularity and cylindricity. Patel et al. (2014) analyzed the effects of spindle speed, feed rate, and coolant ratio on perpendicularity in materials such as EN8, EN24, and EN31. Using a cobalt alloy steel drill with a point angle of 135\u0026deg; and a helix angle of 30\u0026deg;, their study employed Design of Experiments (DOE) and Analysis of Variance (ANOVA) to identify optimal cutting conditions. Results demonstrated that feed rate and spindle speed significantly influence perpendicularity, with DOE methodology proving effective for minimizing defects [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Similarly, Sheth et al. (2014) investigated the influence of machining parameters on cylindricity and perpendicularity in components produced by VMC machines. Their study highlighted the importance of achieving geometric tolerances for assembly-critical features such as holes for nuts, bolts, or pins. By applying DOE techniques and regression modeling, they demonstrated the potential to predict and optimize machining parameters for improved geometric outcomes [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. These findings underscore the value of integrating drilling parameter data into predictive models to enhance machining accuracy and assembly reliability.\u003c/p\u003e\u003cp\u003eA dynamic characteristic in these processes, machine vibrations, are an inherent aspect of machining and have been investigated for their impact on surface quality and geometric tolerances. \u003cb\u003eM\u0026ouml;hring et al. (2020)\u003c/b\u003e conducted a comprehensive investigation into the correlation between acceleration data from a sensor-integrated milling tool and resulting surface properties. Their study demonstrated that acceleration data is a reliable indicator of surface quality, enabling real-time adjustments to spindle speed and feed rate for improved machining outcomes [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Similarly, \u003cb\u003eRao and Ramesh (2020)\u003c/b\u003e analyzed the effects of tool vibrations on roundness and surface roughness in helical milling of Inconel 718. They developed predictive models that highlighted how vibration amplitude and frequency in the X- and Y-directions significantly influence machining accuracy. Their experiments demonstrated that reducing cutter orbital speeds can improve both surface finishes and roundness, underscoring the critical role of vibration control in optimizing machining processes [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. However, despite these advancements, the specific relationship between vibrations and perpendicularity remains underexplored and this research aims to investigate that.\u003c/p\u003e\u003cp\u003eTo measure vibrations, accelerometer sensors have been utilized, which measure the rate of change of velocity of an object. Accelerometers data have been examined using different approaches to create meaningful information. \u003cb\u003eKirby et al. (2004)\u003c/b\u003e focused on predicting surface roughness during machining by processing vibration signals captured via accelerometers. The signals were transformed into absolute amplitudes, and their mean values were calculated over an equivalent range of 30 spindle revolutions. These mean amplitudes, along with feed rate, were used as inputs for a multiple regression model, while spindle speed and depth of cut were excluded based on their negligible impact on surface roughness as determined through Pearson correlation and ANOVA. The resulting regression model achieved a high coefficient of determination (R\u0026sup2; = 0.96) [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003cb\u003eKrishnakumar et al. (2015)\u003c/b\u003e adopted a more advanced approach by analyzing vibration signals in the frequency domain using a Fast Fourier Transform analyzer. Statistical features such as standard error, kurtosis, and median were extracted, and a J48 decision tree algorithm was used to identify the most significant features based on information gain. These features were then utilized in machine learning models, including artificial neural networks (ANNs) and decision trees, to predict tool wear during high-speed machining of titanium alloys. The ANN model outperformed the decision tree with a classification efficiency of 95.4%, highlighting the potential of integrating frequency-domain features and machine learning techniques for tool condition monitoring [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe integration of machine learning into machining processes has shown substantial promise in predictive accuracy for critical outcomes such as surface roughness and machining stability. Raju et al. (2024) extended this approach by incorporating spindle bearing vibrations into predictive models for CNC milling, utilizing machine learning techniques such as polynomial regression and artificial neural networks (ANNs). Their study demonstrated near-perfect prediction accuracy, showcasing the potential of vibration data for surface quality optimization [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Similarly, Lin et al. (2020) employed multiple regression and ANN approaches to model surface roughness using cutting parameters and machining vibrations in end milling, achieving a prediction accuracy of 93.14% [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Despite these advancements, the application of machine learning to predict geometric orientation, such as perpendicularity, remains an open challenge, offering significant opportunities for future exploration.\u003c/p\u003e\u003cp\u003e\u003cb\u003eGuleria et al. (2022)\u003c/b\u003e investigated the classification of surface roughness in CNC turning of forged EN8 steel using vibration signal processing and Support Vector Machine (SVM). They extracted features from time-domain, frequency-domain, and Fast Fourier Transform (FFT) image analysis, including mean, standard deviation, kurtosis, skewness, and entropy. A Bayesian-optimized SVM was employed, achieving 91.9% accuracy using frequency-domain features and demonstrating the potential of vibration-based monitoring for real-time quality assessment [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. \u003cb\u003eArendra and Herianto (2020)\u003c/b\u003e developed a vibration-based tool wear detection system for CNC milling using MMA 7361 accelerometers and NI DAQ USB-6008 for real-time data acquisition [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. They extracted key vibration features, including standard deviation, skewness, kurtosis, and range, from both time-domain and order-domain analyses. Feature selection using a Linear Discriminant Classifier (LDC) identified the most relevant predictors, which were then classified using a Multi-Layer Perceptron (MLP), achieving 96.4% accuracy. Their findings demonstrate how machine learning and vibration analysis can effectively monitor machining conditions, a methodology that could be adapted for predicting geometric deviations in drilling and milling processes.\u003c/p\u003e\u003cp\u003eBuilding on these findings, the integration of vibration signals has proven to be a transformative approach for understanding machining dynamics and enhancing predictive capabilities. While significant advancements have been made in predictive modeling, existing research often isolates surface roughness and perpendicularity as independent phenomena. This fragmented approach fails to capture the interconnected nature of these metrics in ensuring dimensional accuracy and assembly-critical tolerances.\u003c/p\u003e\u003cp\u003eThis study addresses these critical subjects by developing a vibration-based predictive system that simultaneously evaluates surface roughness and perpendicularity in CNC milling. By leveraging signal processing techniques, such as calculating frequency and time-domain features in a structured process, and employing Multi Linear Regression and Artificial Neural Networks, provides a comprehensive approach for prediction. The proposed system aligns with the increasing demand for intelligent manufacturing solutions, enabling real-time monitoring and improving the precision and efficiency of processes.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Architecture of the System\u003c/h2\u003e\u003cp\u003eThe architecture of the proposed Online Surface Roughness and Perpendicularity Prediction (OSRPP) System is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. To achieve the desired workpiece surface roughness and perpendicularity, the process begins by entering optimized values for parameters and the workpiece in the machine. Once these parameters are set, vibration data is collected from the controller when the process is taking place. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{x}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{y}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{z}\\)\u003c/span\u003e\u003c/span\u003e represent the online accelerometer data stored for further processing. These datasets are analyzed and engineered with the hypothesis that can represent the relation between vibration and both surface roughness and perpendicularity.\u003c/p\u003e\u003cp\u003eThe prediction model is part of an integrated system that predicts surface roughness and perpendicularity. The model alone, as a mathematical construct, requires inputs and outputs. The complete system uses online data to make predictions. If the predicted surface roughness and perpendicularity are within specifications, the process continues being monitored. If any of them are out of the specification range, the system alerts the operator, who can pause or adjust the machine as needed. This study proposes a Multi-Linear Regression and ANN-based system and tests its performance.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe experimental setup is designed to collect data for the development of the OSRPP system. The experiments are conducted on a (HAAS VF-5/40XT) CNC machine, using 6061 aluminum due to its machinability and its ability to highlight surface finish variations. The process includes a drilling operation followed by an end-milling operation. The tool for drilling is a carbide drill with 0.375 \u003cem\u003ein\u003c/em\u003e diameter, chosen to reduce deflection and eliminate the need for a center drill. The tool for end-milling is a High-Speed-Steel end mill with 0.375 \u003cem\u003ein\u003c/em\u003e diameter and 2 flutes, selected for its efficiency in cutting aluminum and preventing material buildup [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis setup was based on optimized machining parameters previously obtained through experimental design. Although the optimization phase is not detailed here, it was carried out in a separate study by the author. For surface roughness, the optimized end milling parameters were set to a feed rate of 8 \u003cem\u003ein/min\u003c/em\u003e, spindle speed of 4500 \u003cem\u003erpm\u003c/em\u003e, depth of cut of 0.008 \u003cem\u003ein\u003c/em\u003e, and coolant enabled, resulting in an average surface roughness of 0.215 \u003cem\u003e\u0026micro;m\u003c/em\u003e. For perpendicularity, the optimized drilling parameters included a feed rate of 13 \u003cem\u003ein/min\u003c/em\u003e, spindle speed of 5000 \u003cem\u003erpm\u003c/em\u003e, coolant enabled, and adherence to the drill-mill sequence.\u003c/p\u003e\u003cp\u003eThe proposed workpiece, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, was designed to facilitate data collection for both drilling and end-milling processes.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eA three-axis accelerometer was mounted on the machine table to minimize noise and external vibrations. To protect it from coolant sprays and debris, the sensor was enclosed in a protective box, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. During machining, vibration data was collected using (Kistler) acquisition software and stored for subsequent analysis.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSurface roughness (Ra) is measured using a profilometer at consistent points, in the range between 0.2 \u003cem\u003ein\u003c/em\u003e and 0.6 \u003cem\u003ein\u003c/em\u003e where 0 \u003cem\u003ein\u003c/em\u003e is the start point of the cut. Perpendicularity is assessed using a (Mitutoyo) Coordinate Measuring Machine (CMM), providing precise geometric measurements across different sections of the workpiece. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb show measurement set up for each output variable.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Design of Experiments to collect data\u003c/h2\u003e\u003cp\u003eGiven the complexity of variable interactions in machining, it is essential to collect representative process data. To achieve this, a Design of Experiments (DOE) was implemented using a full factorial approach to analyze the combined effects of spindle speed, feed rate, and depth of cut on machining outcomes. To account for natural process variability, experimental parameters were slightly adjusted across multiple trials. Vibration data was captured online using a three-axis accelerometer connected to a data acquisition system. Key output features, surface roughness and perpendicularity, were subsequently measured. These measurements, along with the processed vibration data, formed the dataset used for training the predictive model.\u003c/p\u003e\u003cp\u003eThe experimental design factors and levels are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The End Milling process followed a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{3}^{3}\\)\u003c/span\u003e\u003c/span\u003e full factorial design while drilling experiments were accoupled to the previous one resulting in a total of 81 experiments.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDOE Factors and Levels for End Milling Process\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=\"7\" nameend=\"c7\" namest=\"c1\"\u003e\u003cp\u003eEnd Milling Parameters\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eUnit\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLevel 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eLevel 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u003cp\u003eLevel 3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFeed Rate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ein/min\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e7.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e8.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpindle speed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003erpm\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e4480\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e4500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e4520\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDepth of Cut\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ein\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e0.0078\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e0.008\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.0082\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDrilling Parameters\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eUnit\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003eLevel 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003eLevel 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eLevel 3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFeed Rate\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ein/min\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e12.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e13.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpindle speed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003erpm\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e4980\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e5000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e5020\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Data Engineering and Processing\u003c/h2\u003e\u003cp\u003eThe vibration signals during machining comes from the sensor as series of values of aceeleration in units of \u003cem\u003eg\u003c/em\u003e that sensor has collected. The sampling frequency of the vibration data is 25 kHz (25,000 Hz). This indicates that the accelerometer captures 25,000 samples per second during the acquisition. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows an example of how the vibration data is presented as outcome of the data acquisition system.\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 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eExample of Vibration Data Collected\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\u003eTime\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eChannel1 [g]\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eChannel2 [g]\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eChannel3 [g]\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.014862\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.024284\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.011239\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.014862\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.017381\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.015685\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00008\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.012841\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.017258\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.019513\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00012\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.008442\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.022928\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.018772\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00016\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.008323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.02034\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.01445\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.00020\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-0.010463\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.022435\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.008398\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\u003eThese resulted in 81 files with hundreds of thousands of datapoints for each of the processes. Thus, it was necessary to select the desired range of interested data. To do that, each dataset collected in the operation was processed to extract the relevant data range as follows.\u003c/p\u003e\u003cp\u003eFor end milling, the range where the surface roughness of the workpiece was measured consistently was defined as 0.2 \u003cem\u003ein\u003c/em\u003e to 0.6 \u003cem\u003ein\u003c/em\u003e from the start point of the cut. Then, the first peak of the average force was identified in each vibration dataset. From this point, the next 0.2 inches were excluded from analysis (equivalent to 37,500 data points, given a feed rate of 8 in/min). Subsequently, data from the following 0.4 inches was retained, representing the study range for the milling process on the workpiece. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb illustrate the data cleaning process for the milling operation.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFor the drilling process, the selected vibration data focused on capturing representative segments from both the upper and lower portions of the cut. This segmentation enables a comparative analysis between the two regions, which is essential for evaluating the influence of drilling on geometric orientation. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the data selection approach.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo characterize the vibration signals collected during machining, a set of statistical time-domain features was extracted. These features are widely used in condition monitoring and signal analysis due to their ability to capture different characteristics of the signal:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eRoot Mean Square (RMS)\u003c/b\u003e and \u003cb\u003eTotal Energy\u003c/b\u003e quantify the energy content and intensity of the signal.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eStandard Deviation\u003c/b\u003e and \u003cb\u003eAbsolute Mean\u003c/b\u003e measure the variability and average magnitude, respectively.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSkewness\u003c/b\u003e and \u003cb\u003eKurtosis\u003c/b\u003e describe the asymmetry and sharpness of the signal distribution, often associated with abnormalities or transient events.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eCrest Factor\u003c/b\u003e captures the relationship between the peak amplitude and the overall signal level, highlighting impulsive behavior.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eEach of these features provides unique insights into the dynamic behavior of the machining process. Detailed formulas for each metric are provided in \u003cb\u003eAppendix A\u003c/b\u003e.\u003c/p\u003e\u003cp\u003eIn addition to the time-domain analysis, frequency-domain features were computed to better understand how vibration energy is distributed across different frequency components. These metrics are essential for identifying dominant vibration modes and resonance behaviors that are not easily visible in the time domain.\u003c/p\u003e\u003cp\u003eTo analyze the frequency content of the vibration signals, the Fast Fourier Transform (FFT) was applied. The discrete Fourier transform (DFT), computed efficiently via the FFT algorithm, is given by Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{X}_{k}={\\sum\\:}_{n=0}^{N-1}{x}_{n}{e}^{-j2\\pi\\:kn/N}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{n}\\)\u003c/span\u003e\u003c/span\u003e \u0026#119894;\u0026#119904; \u0026#119905;he value of the signal at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{n}^{th}\\)\u003c/span\u003e\u003c/span\u003e time sample, N total number of samples in the signal, \u0026#119896; is the index of frequency bins and \u0026#119895; is the imaginary unit. This transformation decomposes the signal into its constituent frequencies, allowing the identification of dominant frequencies and amplitudes that correlate with machining dynamics as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAfter applying the Fast Fourier Transform (FFT) to convert the vibration signals into the frequency domain, five key features were extracted to characterize the spectral properties:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eDominant Frequency\u003c/b\u003e: Identifies the frequency bin with the highest energy concentration, typically associated with the most energetically significant vibration mode during machining.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePeak Frequency\u003c/b\u003e: Indicates the frequency corresponding to the highest amplitude component in the spectrum, often linked to resonance or periodic tool\u0026ndash;workpiece interactions.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003ePeak Value\u003c/b\u003e: Represents the maximum magnitude observed in the frequency spectrum, indicating the highest vibration intensity.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eBandwidth\u003c/b\u003e: Measures the spread of energy around the spectral centroid, quantifying how concentrated or dispersed the vibration energy is, and aiding in the assessment of process stability.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eSpectral Centroid\u003c/b\u003e: Acts as the center of mass of the frequency spectrum, providing a weighted average of the frequency components and indicating where the majority of the energy is concentrated.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eThese spectral features complement the time-domain descriptors by highlighting periodicities, harmonics, and high-frequency patterns related to machining dynamics. The mathematical definitions of each feature are included in \u003cb\u003eAppendix B\u003c/b\u003e [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eDue to the complexity of these calculations, the metrics were computed using scripts to ensure accuracy and consistency in the data analysis process.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Dimensionality Reduction and Variable Selection\u003c/h2\u003e\u003cp\u003eA total of 36 input variables were extracted per workpiece, corresponding to 12 features calculated for each of the three accelerometer channels. While these variables provide a comprehensive description of the signal, processing all 36 in a real-time application can be computationally expensive. This may delay prediction to the point that the machining process is already complete before a result is generated.\u003c/p\u003e\u003cp\u003eTo address this limitation, a dimensionality reduction strategy was implemented to retain only the most informative features. The K-Best feature selection method was applied, which ranks all input variables according to their relevance to the output variable using statistical correlation.\u003c/p\u003e\u003cp\u003eSpecifically, the f_regression scoring function was used, which evaluates the linear dependency between each feature and the target variable using ANOVA F-values. This score compares the variance explained by each input feature to the variance within groups, according to the Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:F=\\frac{Variance\\:between\\:groups}{Variance\\:within\\:groups}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe full table of F-values for the 36 extracted features is provided in \u003cb\u003eAppendix C\u003c/b\u003e. The features with the highest F-scores were selected as inputs to the prediction models. For surface roughness prediction, five features were selected based on their statistical significance, as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. These include three time-domain variables and two frequency-domain variables. Similarly, for perpendicularity, the top five selected features are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\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 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTop 5 ANOVA F-values for Surface Roughness\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\u003eFeature Name\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDomain\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF-Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDenoted as\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRMS 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e34.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{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\u003eFFT Peak Value 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFrequency\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e20.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{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\u003eStd Dev 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e14.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{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 3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{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\u003eFFT Peak Freq \u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFrequency\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{5}\\)\u003c/span\u003e\u003c/span\u003e\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=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTop 5 ANOVA F-values for Perpendicularity\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\u003eFeature Name\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDomain\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF-Value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDenoted as\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStd Dev 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e121.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{6}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRMS 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e74.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{7}\\)\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 2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e23.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{8}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFFT Peak Val 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFrequency\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e13.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{9}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDominant Frequency 1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eFrequency\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e10.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{10}\\)\u003c/span\u003e\u003c/span\u003e\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\u003eThese selected features formed the input vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\:\\)\u003c/span\u003e\u003c/span\u003efor each predictive model. The combination of time and frequency domain characteristics helped capture both the transient and harmonic components of the vibration signals, enabling accurate prediction of quality metrics.\u003c/p\u003e\u003cp\u003eOnce the selected features were prepared for modeling, the next subsections detail the development of each prediction model.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Multi Linear Regression Model\u003c/h2\u003e\u003cp\u003eTo establish a baseline predictive model, a Multiple Linear Regression (MLR) approach was implemented. MLR was selected due to its simplicity, interpretability, and well-established performance in modeling linear relationships between input features and output variables. It provides a useful benchmark for evaluating the effectiveness of more complex models such as artificial neural networks.\u003c/p\u003e\u003cp\u003eIn this context, the MLR model estimates the output variable, either surface roughness or perpendicularity, as a linear combination of the five selected features. The regression coefficients were optimized to minimize the mean squared error between predicted and actual values in the training dataset.\u003c/p\u003e\u003cp\u003eThe equations obtained for each of the outputs are given in \u003cb\u003eEq.\u0026nbsp;3\u003c/b\u003e and \u003cb\u003eEq.\u0026nbsp;4\u003c/b\u003e:\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{1\\:}\\left(Ra\\right)=0.2612-0.0298{x}_{1}+0.0278{x}_{2}-0.0226{x}_{3}-0.0105{x}_{4}-0.0124{x}_{5}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(3)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{2\\:}\\left(Penp\\right)=0.0296+0.0069{x}_{6}-0.0102{x}_{7}-0.0013{x}_{8}-0.0027{x}_{9}-0.0180{x}_{10}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(4)\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\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i}\\)\u003c/span\u003e\u003c/span\u003e are the selected input features.\u003c/p\u003e\u003cp\u003eThe MLR model serves not only as a baseline but also provides valuable insight into the linear contribution of each variable, which can be used for physical interpretation and engineering validation.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Artificial Neural Networks Model\u003c/h2\u003e\u003cp\u003eTo enhance the system\u0026rsquo;s ability to capture non-linear patterns in the vibration data, an Artificial Neural Network (ANN) model was developed. ANNs are well-suited for complex regression problems in manufacturing applications due to their capacity to learn intricate relationships between input features and output responses. In contrast to linear models such as MLR, neural networks can model non-linear interactions, making them ideal for predicting variables like surface roughness and perpendicularity, which often depend on combined effects across multiple signal characteristics.\u003c/p\u003e\u003cp\u003eThe architecture of the proposed ANN model is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. The network was structured with five input neurons, each corresponding to one of the selected variables after feature selection. This input layer was followed by three hidden layers, consisting of 64, 32, and 16 neurons, respectively. Each hidden layer used the ReLU (Rectified Linear Unit) activation function to introduce non-linearity while maintaining computational efficiency. The output layer contained a single neuron with a linear activation function to predict the target value for each case.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe model was trained using a backpropagation algorithm with the Adam optimizer and mean squared error (MSE) as the loss function. A validation set was used to monitor performance and prevent overfitting through early stopping. Separate models were trained for surface roughness and perpendicularity using the top five features identified for each case via KBest.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Results and Discussion","content":"\u003cp\u003eThe performance of the predictive models was evaluated on a testing dataset composed of 16 samples not used during training or validation. Both Multiple Linear Regression (MLR) and Artificial Neural Network (ANN) models were tested independently for each of the two target variables.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the comparison between real and predicted surface roughness values for both the MLR and ANN models. The ANN predictions closely follow the real values with higher precision across the full range of observations. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the prediction results for perpendicularity deviation. As with surface roughness, the ANN model consistently provides estimates closer to the actual measured values than MLR.\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 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSurface Roughness Prediction Testing Results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\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\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{5}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMLR \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y{\\prime\\:}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMLR Accuracy (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eANN \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y{\\prime\\:}}_{1}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u003cp\u003eANN Accuracy (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0165\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.7473\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.4923\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.492399\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e99.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.491690\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0157\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.6607\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.3045\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.293924\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e96.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.303323\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2738\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2090\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.214430\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e97.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.208600\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0787\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.6997\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.1833\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.179322\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e97.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.182481\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0272\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.6628\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.236558\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e99.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.233960\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0195\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.3702\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2753\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.275543\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e99.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.273351\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0265\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.5171\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.1860\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.174101\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e93.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.185013\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0281\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.8378\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2133\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.211772\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e99.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.212668\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0281\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5.0556\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.1721\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.183778\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e93.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.171646\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0235\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.4124\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2166\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.229180\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.215140\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0157\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.1857\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2840\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.273569\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e96.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.283810\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0211\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.9107\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2674\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.255587\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e95.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.266943\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0264\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.9398\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.3345\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.337170\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e99.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.333679\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0273\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.1372\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2470\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.255105\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e96.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.246573\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0190\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.9995\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2938\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.277366\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.293357\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0302\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.1563\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2096\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.244144\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e83.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.209345\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\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 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePerpendicularity Prediction Testing Results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\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\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{6}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{10}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMLR \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y{\\prime\\:}}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMLR Accuracy (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eANN \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y{\\prime\\:}}_{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u003cp\u003eANN Accuracy (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0028\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.5428\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.002027\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e98.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.001833\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e91.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0174\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e24.290\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0125\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.01182\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e94.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.012107\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e96.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0616\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.0849\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0438\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.042431\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e96.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.042469\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e96.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0212\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e24.506\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0146\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.014649\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e99.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.014955\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e97.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0527\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e59.814\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0377\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0365\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e96.81\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.036979\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e98.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0375\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e69.815\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0261\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.028263\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e91.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.026128\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0206\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e39.444\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0142\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.013561\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e95.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.014403\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e98.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0275\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e91.295\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0184\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.014045\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e76.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.017332\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e94.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0060\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e62.052\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0045\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.005151\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e85.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.004259\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e94.64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0495\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e88.615\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0366\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.035035\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e95.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.033675\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e92.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0351\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e36.369\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0253\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.028313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e88.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.024913\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e98.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0077\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e93.166\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0054\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.004844\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e89.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.005273\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e97.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0849\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e97.905\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0625\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.061786\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e98.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.060334\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e96.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0176\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e27.776\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0124\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.011831\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e95.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.01119\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e90.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0882\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e96.634\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0614\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.071549\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e83.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.056963\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e92.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0.0388\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026hellip;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e13.640\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0277\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.024574\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e88.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.027784\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e99.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e summarizes the prediction performance of both systems in terms of Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Testing Accuracy (%).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults Summary of System\u0026rsquo;s Metrics\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\u003eOutput\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModel base\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMAE\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRMSE\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eAccuracy (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cb\u003eSurface Roughness\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMLR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00899\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.01225\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e96.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eANN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00070\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00084\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e99.67\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cb\u003ePerpendicularity Deviation\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMLR\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00236\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00397\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e92.22\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eANN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00112\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.00163\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e95.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study presents a robust and efficient predictive system to predict surface roughness and perpendicularity, two critical output quality characteristics, based on vibration signals collected during the CNC milling and drilling processes. The combination of advanced signal processing, feature selection, and machine learning models demonstrated highly accurate results on independent test data.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e9\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e9\u003c/span\u003eb illustrate the real and predicted values for surface roughness and perpendicularity, respectively. The ANN model demonstrated a closer alignment with the actual values throughout the entire test range, particularly in regions where the signal exhibited greater variability.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe results presented here have significant implications for modern manufacturing systems, particularly in the era of Industry 4.0 and smart machining. This study shows that vibration data, when properly processed and modeled, can be transformed into a powerful source of predictive insight. Instead of relying solely on post-process inspections or expensive metrology systems, manufacturers could predict in real time whether a part will meet dimensional and surface quality requirements.\u003c/p\u003e\u003cp\u003eWith accuracy as high as 99.67% for surface roughness and 95.98% for perpendicularity deviation, the proposed ANN model opens the door to autonomous decision-making in production lines. This means determining in-process if a part is likely to be accepted or rejected, and taking immediate corrective actions before additional waste or cost is generated.\u003c/p\u003e\u003cp\u003eBy reducing the predictive process down to just five well-selected variables per target output, the system also becomes computationally lightweight facilitating the way for deployment on edge devices or PLCs directly on the shop floor.\u003c/p\u003e\u003cp\u003eThis approach embodies the future of intelligent manufacturing, where sensor-driven, AI-enhanced quality prediction becomes the new standard for close to zero-defect production.\u003c/p\u003e\u003cp\u003eFuture work will focus on expanding the dataset to include a broader range of materials, cutting parameters, and tool geometries, enabling greater model generalization. Additionally, efforts may be directed toward implementing the system in real-time CNC environments, allowing live signal acquisition and prediction during machining. Future developments may also explore unified multi-output models, hybrid data and physics-informed architectures, and direct integration into industrial control systems to validate the approach under full production conditions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest:\u003c/strong\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMilling CNC A Comprehensive Guide to Understanding and Mastering the Technology. 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Prentice Hall\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRandall RB (2011) Vibration-based condition monitoring: Industrial, aerospace and automotive applications. Wiley, Chichester, UK\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNIST/SEMATECH (2012) \u003cem\u003ee-Handbook of Statistical Methods\u003c/em\u003e. Retrieved from \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.itl.nist.gov/div898/handbook/\u003c/span\u003e\u003cspan address=\"https://www.itl.nist.gov/div898/handbook/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHaykin S (2009) Neural networks and learning machines (3rd ed.). Pearson\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"CNC Milling, Surface Roughness, Perpendicularity, Artificial Neural Networks, Online Quality Control","lastPublishedDoi":"10.21203/rs.3.rs-8117293/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8117293/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents the development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) system aimed at enhancing quality monitoring in CNC milling and drilling operations. Vibration signals were captured using a tri-axial accelerometer during drilling and end- milling processes on aluminum 6061 workpieces. To reflect physical inspection strategies, the raw signals were segmented to match surface roughness measurement areas, while upper- and lower- hole regions were analyzed separately to represent perpendicularity. Twelve time- and frequency- domain features were extracted per axis and processed to reduce the dimension to the top five most relevant for each target output. Predictive models were developed using Multiple Linear Regression and Artificial Neural Networks (ANN), with linear regression achieving testing accuracy of 96.06% for surface roughness and 92.22% for perpendicularity, while the ANN improved performance to 99.67% and 95.98%, respectively. The results demonstrate that integrating vibration-based sensing with machine learning enables accurate online prediction of surface roughness and perpendicularity, contributing to more autonomous and data-driven decision-making in advanced manufacturing environments.\u0026nbsp;\u003c/p\u003e","manuscriptTitle":"Development of an Online Surface Roughness and Perpendicularity Prediction (OSRPP) System Using Vibration Data in CNC Vertical Machining","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-27 09:00:34","doi":"10.21203/rs.3.rs-8117293/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"edf44906-e54b-4a2e-8cca-4d5fc267c031","owner":[],"postedDate":"November 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-30T14:14:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-27 09:00:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8117293","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8117293","identity":"rs-8117293","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}