{"paper_id":"30cabb3d-adcc-42eb-9ae7-b8a8d0898a6a","body_text":"Stability estimation of Mount St. Helens using Scoops3D and ensemble learning paradigms | 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 Stability estimation of Mount St. Helens using Scoops3D and ensemble learning paradigms Sumit Kumar, Sudeep Kumar, Subodh Kumar Suman, Amit Kumar, Abidhan Bardhan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4417103/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 research investigates the application of ensemble-based computational paradigms to estimate the stability of Mount St. Helens. Scoops3D was initially utilized for conducting slope stability investigation, followed by computational modelling of the factor of safety (FOS) employing various influencing parameters. Four base models including AdaBoost regressor, decision tree regressor, extra tree regressor, and gradient boosting regressor, and a bagging-based ensemble learning (BG-ENSM) framework, were used for this purpose. In both seismic and non-seismic conditions, the effect of pore-pressure ratio (r u ) on the stability of Mount St. Helens was investigated in three different combinations (i.e., Cases-1, 2, and 3) with r u = 0, r u = 0.3, and r u = 0 and 0.3. Post computational modelling, the outcomes of the implemented paradigms were evaluated based on several indicators. Experimental outcomes exhibit that the proposed BG-ENSM framework achieved the most desired estimation of FOS with R 2 of 0.9968, 0.9959, and 0.9985 against Cases-1, 2, and 3, respectively. Based on the overall results and the outcomes of parametric study, the employed BG-ENSM framework can be considered as a viable tool for stability estimation of Mount St. Helens considering the effect of r u in seismic and non-seismic conditions. 3D slope stability Rock slope stability Geological engineering Artificial intelligence Ensemble learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction The assessment of slope stability inside volcanic structures is one of the important studies in the domain of geological-geological investigation, essential for understanding the complex processes of these distinct natural formations. Volcanic structures, which include cone-shaped or composite edifices, are formed as a consequence of volcanic processes and are distributed over the Earth's surface, frequently occurring in areas associated with tectonic plate boundaries. These structures exhibit a diverse array of inclines, and their stability is critical because it impacts the security of adjacent communities, infrastructure, and the natural surroundings. Thus, the stability of these slopes should be evaluated to comprehend the risks of volcanic eruptions, including landslides, pyroclastic flows, and lava flows, which can cause damage to nearby and distant regions. In the domain of volcanic study, a wide range of slope failures observed in volcanic structures, which span from small-scale rock falls to more substantial collapses. Monumental flank slides, with a volume above 0.1 km 3 , have caused significant modifications in stratovolcanoes worldwide (Siebert 1984 ; Siebert et al. 1987 ). These occurrences are considered to be among the most abrupt, devastating, and hazardous processes. Due to catastrophic flank collapse, significant alterations have been observed in many composite volcanic or stratovolcano structures worldwide (Ui 1983 ; McGuire 1996 ). Furthermore, the most notable volcanic collapses in history, exemplified by occurrences like the eruptions of Mount St. Helens in the U.S., Bandai in Japan, and Bezymianny in Russia, were all triggered by the displacement along profound and curved failure surfaces (Voight and Elsworth 1997 ). An illustrative example of a catastrophic collapse is the event that took place at Mount St. Helens in the U.S. in 1980, which might be seen as a compelling case study (Voight et al. 1983 ). These significant collapses, often involving a volume of material exceeding 0.1 km 3 , possess the capacity to initiate debris avalanches that can subsequently develop into calamitous events related to debris, posing substantial risks not only to the structure itself but also to regions located at lower elevations or downstream. Furthermore, stratovolcanoes provide risks to populations living in developing nations, emphasizing the urgent need for quick and affordable hazard assessments. Tragically, almost 20,000 people have perished due to flank collapses in the past (Siebert et al. 1987 ; Sparks et al. 2013 ). The instability of structures can be attributed to a variety of volcano-specific factors like magma intrusion, hydrothermal alteration and slope instability due to increased pore fluid pressures (Reid 1994 ; Day 1996 ; Voight and Elsworth 1997 ). The stratovolcano structure of Mount St. Helens whose flanks have collapsed many times, is an ideal location to try and validate methodology. Traditionally, slope stability is carried out in two dimensions assuming plane strain conditions are valid even though all slopes are in general, 3D structures. Slope stability studies have attracted a lot of attention since 1930s (Bishop 1955b ; Zhang and Wang 2019 ). In many cases, it would be more appropriate to adopt a 3D assessment when there is a considerable variation in the geometry of the slope, resulting in violation of the applicability of 2D plane strain assumptions (Kalatehjari et al. 2015 ). The findings of 2D slope stability analyses often show lower factor of safety (FOS) than 3D methods for simple hillslope shapes, but the deviation between the 2D and 3D is generally between 10% and 20% (Hovland 1977 ; Xing 1988 ; Duncan 1996 ). Researchers have explored slope stability in three dimensions very recent past (Huang et al. 2002 ; Hajiazizi and Tavana 2013 ; Sun et al. 2017 ; Kumar et al. 2023a ). Using 2D Bishop’s method (1955a), Hungr ( 1987 ) proposed an approach for determining 3D FOS. Lam and Fredlund ( 1993 ) proposed a 3D method derived from general limit equilibrium methodology (Fredlund and Krahn 1977 ). Recently, Kumar et al. ( 2023a ) conducted a review of recent advances in 3D slope analysis. However, there are several methods that have been developed to analyses slope stability. Amongst them, strength reduction method (SRM) (Sun et al. 2017 ), limit analysis method (LAM) (Gao et al. 2013 ), and the limit equilibrium method (LEM) (Cavounidis 1988 ) are frequently used techniques. The LEM and SRM approaches are deterministic among them, and they rely on set values for various soil parameters to determine a soil slope’s stability using the FOS. Despite giving a conservative result, FOS-based techniques have been proved to be unproductive on multiple occasions (Zhao 2008 ). One of the limitations of FOS-based techniques is that the uncertainties in soil parameters are not expressed explicitly. Also, the calculated values of FOS are often used for a particular purpose, such as long-term slope stability. But it would not appropriate to use the same FOS for all situations with different levels of uncertainty. The soil materials’ non-linear stress-strain associations, elasto-plastic behavior, and stress-strain time-conditioning response make them quite complex (Safa et al. 2019 ). So, a full analysis of geotechnical properties is needed to take into consideration the uncertainty that comes with slope stability computations. Earthquakes can trigger numerous earth and rock slides, some of which can result in significant damage to critical structures, including dams, hills, vital hill highways, railways, and other infrastructure. In general, slope geometry and soil properties have a substantial influence on its stability. Damage to buildings, roads, railroads, infrastructures, and foundations can result from slope failures due to the resulting ground deformation. Due to their geodynamic and morphological nature, unprecedented rainfall, urbanization, and other influences, hilly terrains are typically at danger for instability. These hilly regions urgently require high-quality roads and highways to improve connectivity, increase tourism, and allow for development activities that are safe. It is needless to say that slope stability assessment considering the spatial variation of related geotechnical parameters of a major volcanic edifice like Mount St. Helen is of paramount importance. AI/ML approaches have previously been employed by numerous researchers for 2D slope stability analysis. The authors Wang et al. ( 2020 ) and Zhou et al. ( 2019 ) proposed the extreme gradient boosting approach. Another relevant machine learning technique is the relevance vector machine. The study conducted by Zhao et al. ( 2012 ) focused on Gaussian process regression. The study conducted by Huang et al. ( 2017 ) focused on the application of artificial neural networks. Ray et al. ( 2020 ) have effectively utilized machine learning techniques to demonstrate regression-based results for 2D slope stability solutions in several scenarios. Xu et al. ( 2023 ) performed a review work of conventional and machine learning (ML) methods for analyzing the stability of 2D slopes. Ray et al. ( 2022 ) used MARS, GPR, and FN to conduct a reliability analysis (RA) of a soil slope. Rao et al. ( 2023 ) also performed RA of a railway embankment considering 3D slope stability. In recent times, several studies have been conducted using ensemble learning frameworks in order to forecast desirable outcomes across several domains of engineering (Lin et al. 2022 ; Zhang et al. 2022 ). Ensemble models are particularly noteworthy for their ability to enhance the performance of unstable models by operating at a higher level (Caruana et al. 2004 ). Significantly, the performance of an ensemble model surpasses that of an individual model when it comprises two or more base models (Laradji et al. 2015 ). Due to the aforementioned considerations and as a part of ongoing research and to extend the work of Kumar et al. ( 2023b ), ensemble-based methods were utilized in this investigation to estimate the stability of Mount St. Helens. In particular, a bagging-based ensemble (BG-ENSM) framework and four base models viz., AdaBoost regressor (ABR), decision tree regressor (DTR), extra tree regressor (ETR), and gradient boosting regressor (GBR), were employed. The FOS was initially estimated using Scoops3D and slope geometries of Mount St. Helens, as per the details obtained from Reid et al. ( 2015 ). Subsequently, computational modelling was conducted utilizing a range of influencing parameters, including cohesion ( c ), angle of internal friction (ϕ), and bulk density (γ), and pore-pressure ratio ( r u ). At the end, the stability assessment was conducted in seismic and non-seismic conditions. The remaining portion of the work is organized in the following manner. Section 2 addresses the study area, whereas Section 3 presents methodological details. Section 4 offers an in-depth analysis of data processing and the intricacies of computer modelling. Section 5 provides an exposition of the findings and subsequent deliberations. Section 6 contains the summary and findings. 2. Study area The aim of this study is to analyze Mount St. Helens, which is located in the Washington District of Columbia in the USA and experienced a failure due to an eruption on May 18, 1980 (Voight et al. 1983 ). Although failure surfaces may be readily apparent in simpler geometric features of slopes (e.g., those that are polygonal or polyhedral in shape), this may not hold true for intricate geographical features like Mount St Helens. A topographical illustration of Mount St. Helen and study site are shown in Fig. 1). Prior to the disaster of Mount St. Helens, the 3D distributions of rock strength and density were unknown. Post collapse, Voight et al. ( 1983 ) and Glicken ( 1996 ) reconstructed the interior geologic structure using geologic sections given by Hopson and Melson ( 1982 ). The mountain’s core is composed of older dacite dome lavas and flank breccias, both of which have undergone hydrothermal alteration. Andesitic, basaltic, and tephra lava flows covered this unit. The domes at top and Goat Rocks have been built using relatively recent dacite. In 1980, the dacitic crypto-dome forcefully penetrated each of these elements. 3. Methodology In this section, an overview of the theoretical particulars of the deterministic analysis that is utilized in the method of computing the three-dimensional FOS is presented. This is accomplished by the implementation of Bishop's simplified technique. 3.1. FOS estimation and DEM modelling In the following section, the theoretical details of deterministic analysis are presented in order to compute the FOS by utilizing Bishop's simplified approach. This study utilizes the Scoops3D computer program to determine the factor of safety of a 3D slope. The program employs the Ordinary and Bishop simplified methods (BSM) to calculate the FOS against slope failure. The present study uses Bishop’s simplified method where the spherical failure surfaces are used for 3D slope analysis. The free-body schematic of the j, k column, in which no external force is acting and the column is subjected to every conceivable combination of forces, is illustrated in Fig. 2. In Fig. 2, W is weight of column; \\({E}_{{x}_{j,k}}, {E}_{{y}_{j,k}}\\) signify the inter-column normal force in the x and y dimensions; \\({H}_{{x}_{j,k}}, {H}_{{y}_{j,k}}\\) show the y-z plane shear force horizontally; \\({X}_{{x}_{j,k}}, {X}_{{y}_{j,k}}\\) indicate the shear force between columns in the x-z plane; \\({N}_{j,k}, {U}_{j,k}\\) signify the effective normal force and base pore water force, respectively; \\({S}_{j,k}\\) denote the mobilized shear force that acts on the base of the column; \\({\\alpha }_{j, k}\\) refer to slide angle relative to the x–y plane; \\({\\alpha }_{x},{\\alpha }_{y}\\) refer to the base inclination at the midpoint of each column in the x-z and y-z planes, respectively. After simplifying, the final FOS expression of BSM can be computed for ground water condition as shown in Eq. ( 1 ). $$FOS=\\frac{\\sum {R}_{j,k}\\left({c}_{j,k}{A}_{j,k}+{W}_{j,k}\\left(1-{r}_{uj,k}\\right){\\text{tan}\\varphi }_{j,k}\\right)/{m}_{{\\alpha }_{j,k}}}{\\sum {W}_{j,k}\\left[{R}_{j,k}{m}_{z}+{k}_{eq}{e}_{j,k}\\right]}$$ 1 where \\({m}_{{\\alpha }_{j,k}}=\\text{cos}{\\epsilon }_{j,k}+\\text{tan}{\\varphi }^{{\\prime }}d{m}_{z}\\) , and \\({m}_{z}=\\text{sin}{\\alpha }_{j,k}\\) , \\({c}_{j,k}\\) known as effective cohesion; \\({\\varphi }_{j,k}\\) known as effective internal friction angle; \\({R}_{j,k}\\) distance between the trial slip area of the j,k column to its axis of rotation, \\({A}_{j,k}\\) denote the trial surface area of column, \\({W}_{j,k}\\) known as column’s weight; \\({\\text{e}}_{j, k}\\) refer to the horizontal driving force moment arm. The sum of normal and shear forces along the columns' sides is considered to be zero along the x and y axes in 3D. A digital depiction of the elevation of the land surface, called a digital elevation model (DEM) Balasubramanian ( 2017 ), is based on any reference data. The most typical DEMs type is regular grids, which are available in a number of variations (Xu et al. 2022 ). The study of geomorphology makes extensive use of DEM. DEMs may represent many different elements of landscapes and have advantages in terms of data format and processing performance. The most crucial fundamental data sources for geographic information at the national level are DEMs. To generate a DEM, data can now be produced or taken from public data sources. Shuttle Radar Topography Mission (SRTM), GTOPO30, Terra Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER GDEM), ALOS Global Digital Surface Model (AW3D30), Digital Terrain Elevation Data (DTED-2), and EU-DEM are just a few examples of the many currents, openly accessible global DEMs. On the other hand, there are an increasing number of free GIS software programs (such as GRASS GIS, SAGA GIS, and QGIS). The type of topography, such as landforms, elevations, texture, ruggedness, and vegetation present, as well as the methods used to collect elevation data, the process used to create the DEM, the kind of grid used for the DEM, and the DEM resolution, all affect the accuracy of the DEM. (Fisher 1998 ; Schneider 1998 ; Wise 2000 ). For 3D stability studies, the U.S. Geological Survey (USGS) created the downloadable Scoops3D code. (Reid et al. 2015 ). It needs a digital elevation model as its main input (Reid et al. 2000 , 2015 ). Firstly, it is necessary to make accurate estimations regarding the topography of the ground surface. This DEM can be used to build a 3D model for slope problems because it can easily use spatial and image data from geographic information systems (GIS) (Sulebak 2000 ; Cavazzi et al. 2013 ). In addition, DEM representations are readily available due to the increasing use of satellite imagery (e.g., Google Earth) and aerial photography (e.g., drones). Based on the results of a comparative analysis conducted by Reid et al. ( 2015 ) on these DEMs using cubic convolution in the GRID program of ARC/INFO [Environmental Systems Research Institute (ESRI), 1998], the author selected 100-m resampled DEMs for the subsequent studies since this resolution is adequate for accurately computing the stability of possible failures with a volume > 0.1 km3. The digital elevation model (DEM) data used in this analysis was retrieved from Reid et al. ( 2015 ) and was created from aerial pictures obtained on May 12, 1980 (refer to Fig. 3). The DEM description of Mount St. Helens is also shown in Fig. 3. 3.2. Details of soft computing paradigms Brief details of the employed paradigms are offered in this sub-section. As sated above, four standalone models namely ABR, DTR, ETR, and GBR were used. In addition, bagging-based ensemble paradigm, called BG-ENSM was used for the estimation of FOS of Mount St. Helens. ABR is an ensemble-based algorithm and it is a modified version of the Adaboost algorithm used for regression tasks. A basic linear regression or a shallow decision tree is often used as a weak regression model in ABR. It is trained on the dataset first. The errors in the first model are then looked at, and the data points that the model had the most trouble predicting are given more attention. After that, weak regression models are trained with new sample weights, and the goal is to get better predictions for the difficult data points. The final prediction is made by adding up the predictions from each of these weak models, with the weight of each model's input based on how well it did in the iterative training process. DTR is a tree-based algorithm consisting multiple branches and nodes and used for regression tasks. In the training phase, a particular function is used to compare the input variable values. A program that takes a list of cases and turns them into a decision tree (DT) is called a DT stimulant. By reducing the fitness function, the algorithm in use tries to identify the best DTs. The dataset is partitioned into numerous split points for each input variable. At each of these division points, DTR is executed to calculate the prediction error using the fitness function discussed before. Subsequently, errors in the split points are analyzed and minimized using iteratively (Tso and Yau 2007 ). ETR is an ensemble technique that is derived from the DT regression algorithm. Ensemble algorithms aim to combine a given number of estimators in order to lower the variance of a model relative to the variance of a single tree. The proposed methodology constructs an ensemble of DTs, whereby each tree incorporates a distinctive modification to conventional DT algorithms. In contrast to conventional DTs and RF, ETR incorporates more unpredictability at two crucial stages. It starts by randomly selecting the training data subsets. Since each tree sees distinct data, overfitting is reduced. Second, instead of using the best feature in standard DTs, it randomly selects a subset of characteristics to split at each node. After building a forest of randomized DT, regression tasks are predicted by averaging their outputs. GBR is an ensemble-trained supervised ML model, boosting is the technique of creating a single composite model from several simple models. Boosting is nothing but an additive framework since it involves the sequential addition of basic models while keeping the model's trees unchanged. A better prediction can be obtained by merging more fundamental models. Gradient boosting refers to a technique that aims to minimize losses by employing gradient descent, which is an iterative optimization procedure based on first-order derivatives. Gradient boosting utilizes DTs as weak learners and trains a feeble model to establish a mapping between the inputs and the projected deviations of the weak model. Subsequently, these additions are included into the input of the existing model, so facilitating its achievement of the desired outcome. 3.3. Bagging ensemble-based modelling The bagging ensemble is an ensemble framework that consists of multiple learners trained on subsamples collected from the same set. It is employed to address the trade-offs between bias and variance and diminishes the variability of a predictive model. Bagging is a technique that prevents overfitting of data and can be applied to both regression and classification tasks. Bagging ensemble is frequently employed to enhance the accuracy of a model, mainly when introducing variations to the training set can lead to a substantial alteration in the produced prediction. Generally, bagging approach involves three steps: (a) generating numerous datasets by sampling from the original data, (b) using every dataset to train multiple learners, and (c) aggregating the predictions of all learners to get a single estimation. The final result is then derived by taking the average of the outcomes obtained from the used models in a regression study, or by utilizing a majority voting strategy for classification problems (Hernández-Lobato et al. 2011 ). An illustration of bagging ensemble technique is presented in Fig. 4. 4. Data collection and computational modelling Before its demise caused by volcanic eruptions, the geological features of Mount St. Helens seemed more uniform compared to the other stratovolcanoes. Voight et al. ( 1983 ) describe the physical features of debris resulting from the collapse of the said mountain, in which the authors found that the mean values of ∅ and c are 40° and 1000 kN/m 2 , respectively, The average specific weight for intact edifice rock, i.e., γ = 24 kN⁄m 3 . As per the study of Voight et al. ( 1983 ), slope stability analysis was conducted using r u = 0.3. In addition, the said analysis was also conducted at no pore-pressure ratio, i.e., r u = 0. A sum of 100 datasets were formed using c = 1000 kN/m 2 , ∅ = 40°, and γ = 24 kN⁄m 3 . Notably, normal distribution sampling technique was followed during data generation. The given combinations indicate one data sample that was fed as input into the Scoops3D and the slope`s FOS was determined as per 3D Bishop’s simplified method. During FOS estimation, different combinations of r u and ke were considered. Specifically, the FOS for all the 100 samples was determined for five different values of k e including 0, 0.05, 0.10, 0.15, and 0.20 (designated as Sets 1–5), with r u assigning 0 and 0.3 for each set. Therefore, total 1000 datasets (i.e., 100 × 5 × 2, five sets of k e and two sets of r u ) were generated, the particulars of which are tabulated in Table 1 . As per the table, the values of c and ∅ fall in the range of 809.77 kN/m 2 – 1195.17 kN/m 2 and 35.18° – 49.40°, respectively. The other variables, γ \\(,\\) r u , and k e are ranging from 22.02 kN/m 3 – 25.99 kN/m 3 , 0–0.3, and 0–0.20, respectively. Notably, this study simplifies the analysis by assuming consistent material qualities, the existence of groundwater, and the inclusion of seismic stress. Table 1 Descriptive details of Mount St. Helens. Parameters Min. Avg. Max. Stnd. Dev. Kurtosis c 809.77 1000 1195.17 117.31 -1.26 ϕ 35.18 40 49.40 4.21 -1.20 γ 22.02 24 25.99 1.17 -1.25 k e 0.00 - 0.20 0.08 -1.20 r u 0.00 - 0.30 - - Table 2 Details of different cases. Case Inputs Data dimension Output Case-1 c, \\(\\varnothing\\) , \\(\\gamma\\) , and k e (with r u = 0) 500 × 4 FOS Case-2 c, \\(\\varnothing\\) , \\(\\gamma\\) , and k e (with r u = 0.3) 500 × 4 FOS Case-3 c, \\(\\varnothing\\) , \\(\\gamma\\) , k e , and r u (with r u = 0 and 0.3) 1000 × 5 FOS Importantly, this study considers three distinct cases, i.e., Cases-1, 2, and 3 according to the r u values, as detailed in Table 2 . Specifically, r u = 0 was considered in Case-1 and r u = 0.30 was considered in Case-2. In Case-3, both r u values were considered. Therefore, the computational modelling was conducted for three-different combinations with r u = 0, r u = 0.30, and r u = 0 and 0.30. In each case, the dataset was partitioned into training and testing sets with 80:20 bifurcation. Notably, data normalization is an essential phase in the process of computational analysis. In the pre-processing step, it is common practice to normalize data in order to mitigate the impact of variable dimensionality. Thus, all the variables were normalized within the range of [0, 1] before model construction. This is achieved by applying the min-max technique. Following normalization, the training and testing sets were created randomly. The training set contained 80% samples (i.e., 400 datasets), whereas the testing set had the remaining 20% (i.e., 100 datasets). However, for Case-3, 1000 sets of data were taken, and the analysis was done like in Case-1. Finally, the best-obtained model was chosen as per multiple parameters viz., adjusted coefficient of determination (Adj.R 2 ), mean absolute error (MAE), performance index (PI), coefficient of determination (R 2 ), root mean squared error (RMSE), variance account factor (VAF), Willmott's Index of agreement (WI), and weighted mean absolute percentage error (WMAPE). The expressions of these indices can be expressed as: $$Adj.{R}^{2}=1-\\frac{(n-1)}{(n-p-1)}(1-{R}^{2})$$ 2 $$MAE=\\frac{1}{n}{\\sum }_{i=1}^{n}\\left|\\left({\\widehat{y}}_{i}-{y}_{i}\\right)\\right|$$ 3 $$PI=adj.{R}^{2}+0.01VAF-RMSE$$ 4 $${R}^{2}=\\frac{{\\sum }_{i=1}^{n}({y}_{i}-{y}_{mean}{)}^{2}-{\\sum }_{i=1}^{n}({y}_{i}-{\\widehat{y}}_{i}{)}^{2}}{{\\sum }_{i=1}^{n}({y}_{i}-{y}_{mean}{)}^{2}}$$ 5 $$RMSE=\\sqrt{\\frac{1}{n}{\\sum }_{i=1}^{n}({y}_{i}-{\\widehat{y}}_{i}{)}^{2}}$$ 6 $$VAF \\left(\\%\\right)=(1-\\frac{{var}({y}_{i}-{\\widehat{y}}_{i})}{{var}({y}_{i})})\\times 100$$ 7 $$WI=1- \\left[\\frac{{\\sum }_{i=1}^{n}({y}_{i}-{\\widehat{y}}_{i}{)}^{2}}{\\sum _{i=1}^{n}{\\left\\{\\left|{\\widehat{y}}_{i}-{y}_{mean}\\right|+ \\left|{y}_{i}-{y}_{mean}\\right| \\right\\}}^{2}}\\right]$$ 8 $$WMAPE=\\frac{{\\sum }_{i=1}^{n}\\left|\\frac{{y}_{i}-{\\widehat{y}}_{i}}{{y}_{i}}\\right|\\times {y}_{i}}{{\\sum }_{i=1}^{n}{y}_{i}}$$ 9 where n is the sample number, y mean specifies the mean value, and \\({y}_{i}\\) and \\({\\widehat{y}}_{i}\\) indicate the actual and estimated FOS. The values of the parameters need to match exactly with the respective ideal values (Armaghani et al. 2017 ; Duan et al. 2021 ). Below is a brief description of the above indices. Notably, when it comes to performance indicators, trends are measured by the PI, R 2 , VAF, and WI, and errors are measured by the MAE, RMSE, and WMAPE. Error measurement indices quantify the errors, while trend measurement indicators show the trend of the prediction models. The linear correlation between the actual and estimated values is indicated by the R 2 value. Furthermore, PI shows a comprehensive accuracy of a data-driven model in terms of Adj.R 2 , VAF, and RMSE, in which VAF measured the percentage variance of error. WI indicates the degree of prediction error in the model. However, the amount of associated error is frequently assessed using MAE, RMSE, and WMAPE. The MAE displays the mean size of the errors, whereas the RMSE displays the mean error in terms of square root. Furthermore, WMAPE calculates the overall weighted mean error. Note that, the predictive capacity is enhanced by higher values of PI, R 2 , VAF, and WI. A more suitable model is also indicated by lower MAE, RMSE, and WMAPE values. To identify the prediction model with the best performance, the current study thoroughly assessed the performance metrics. An illustration of FOS and estimation and computational modeling is presented in Fig. 5. 5. Results and discussions This section outlines the outcomes of the stability assessment followed by the implementation of computational approaches for determining the failure of Mount St. Helens. Subsequently, the specifics of parametric analysis (PA) are presented. 5.1. Stability analysis To perform stability analysis of Mount St. Helen, various combinations of r u and k e were taken into account for this purpose. More precisely, the FOS was calculated for 100 samples for Sets 1 to 5. The FOS determined with r u = 0 and r u = 0.3 are illustrated in Fig. 6 and Fig. 7, respectively. According to the Fig. 8, the FOS varies in the range of 1.311 to 2.864 and 0.904 to 2.022 for r u = 0 and r u = 0.3, respectively. The maximum FOS values for r u = 0 are 2.864, 2.589, 2.355, 2.152, and 1.975, while the minimum values are 1.901, 1.720, 1.565, 1.431, and 1.311. respectively, for Sets 1 to 5. Similarly, the maximum FOS values for r u = 0.3 are 2.022, 1.818, 1.644, 1.487, and 1.351, while the minimum values are 1.355, 1.219, 1.098, 0.942, and 0.904. respectively, for Sets 1 to 5. These values indicate that the FOS decreases with the increase in r u and k e values and vice versa. For better understanding, Fig. 8 can be referred to. 5.2. Model performance The performance of the employed paradigms along with their configurations are presented. Significantly, the model's performance was assessed by utilizing the training set to evaluate the correctness of the created paradigm. The testing dataset was subsequently employed to verify the model's predictive capability. However, a predictive model that demonstrated exceptional prediction accuracy throughout the validation phase was selected for evaluation. Notably, it is worthwhile to contemplate employing a data reshuffling strategy to choose an optimal framework. In this study, 5-fold cross validation technique was employed and the optimum model was selected as per testing set performance. It should also be emphasized that the selection of an optimum model requires appropriate tuning of hyper-parameters of the employed algorithms. During the training phase, it is crucial to have multiple sets of hyperparameters that have been well tuned. As stated, four standalone and one ensemble models were employed in this study, and hence, different hyper-parameters including n_estimators, n_estimators, min_samples_leaf, max_depth, etc., were tuned within a pre-specified range, as detailed in Table 3 . The optimized values of these hyper-parameters are also tabulated in Table 3 . Table 3 Details of hyper-parameters for the employed models. Models Hyper-parameters Value considered Optimum value ABR n_estimators 5 to 20 by 5 50 learning_rate 0.1 to 1.0 by 0.1 1 DTR min_samples_leaf 1 to 10 by 1 1 max_depth 5 to 50 by 5 10 ETR n_estimators 5 to 20 by 5 10 GBR learning_rate 0.1 to 1.0 by 0.1 0.1 max_depth 5 to 50 by 5 3 n_estimators 5 to 20 by 5 10 BG-ENSM learning_rate 0.1 to 1.0 by 0.1 0.1 max_depth 5 to 50 by 5 3 n_estimators 5 to 50 by 5 45 Using the details presented in Table 3 , five paradigms were finalized and their performance are outlined in Table 4 , Table 5 , and Table 6 . Herein, the performance for both training and testing sets are presented. According to the results, ETR exhibits higher precision in the training phase with R 2 of 1, 1, and 0.9999 against Cases-1, 2, and 3, respectively. However, in the testing phase, the proposed BG-ENSM realized highest precision with R 2 of 0.9968, 0.9959, and 0.9985 against Cases-1, 2, and 3, respectively. The employed ETR is the second-best paradigm with R 2 of 0.9905, 0.9892, and 0.9948 against Cases-1, 2, and 3, respectively. These results indicate that the proposed BG-ENSM paradigm is the most accurate model because a model attained higher precision during the testing phase. The employed ABR model demonstrates the lowest performance in both phases as indicated by its R 2 metric values of 0.9641 and 0.9395 against Case-1, 0.9570 and 0.9361 against Case-2, and 0.9698 and 0.9665 against Case-3 input combinations, respectively. To better demonstrate the results, scatterplot for the best performing modes is presented in Fig. 9 for both the datasets. Table 4 Performance parameters for Case-1. Indices Training Testing ABR DTR ETR GBR BG-ENSM ABR DTR ETR GBR BG-ENSM Adj.R 2 0.9638 0.9999 1.0000 0.9961 0.9989 0.9369 0.9686 0.9901 0.9880 0.9967 MAE 0.0582 0.0008 0.0001 0.0199 0.0079 0.0620 0.0416 0.0238 0.0299 0.0142 PI 1.8529 1.9969 1.9979 1.9656 1.9862 1.7910 1.8852 1.9505 1.9342 1.9745 R2 0.9641 0.9999 1.0000 0.9962 0.9989 0.9395 0.9698 0.9905 0.9884 0.9968 RMSE 0.0698 0.0030 0.0020 0.0251 0.0115 0.0786 0.0529 0.0298 0.0379 0.0185 VAF 95.89 99.99 100.00 99.46 99.89 93.27 96.96 99.02 98.42 99.63 WI 0.9886 1.0000 1.0000 0.9986 0.9997 0.9806 0.9920 0.9975 0.9957 0.9990 WMAPE 0.0292 0.0004 0.0001 0.0100 0.0039 0.0315 0.0211 0.0121 0.0152 0.0072 Table 5 Performance parameters for Case-2. Indices Training Testing ABR DTR ETR GBR BG-ENSM ABR DTR ETR GBR BG-ENSM Adj.R 2 0.9566 0.9999 1.0000 0.9957 0.9989 0.9334 0.9660 0.9888 0.9878 0.9957 MAE 0.0435 0.0010 0.0001 0.0151 0.0063 0.0453 0.0305 0.0190 0.0214 0.0118 PI 1.8580 1.9969 1.9984 1.9704 1.9895 1.8065 1.8936 1.9539 1.9440 1.9758 R2 0.9570 0.9999 1.0000 0.9958 0.9989 0.9361 0.9674 0.9892 0.9883 0.9959 RMSE 0.0525 0.0029 0.0016 0.0192 0.0083 0.0579 0.0398 0.0235 0.0279 0.0152 VAF 95.40 99.99 100.00 99.38 99.89 93.11 96.74 98.86 98.40 99.53 WI 0.9875 1.0000 1.0000 0.9984 0.9997 0.9805 0.9916 0.9970 0.9957 0.9988 WMAPE 0.0312 0.0007 0.0001 0.0109 0.0045 0.0329 0.0221 0.0138 0.0155 0.0086 Table 6 Performance parameters for Case-3. Indices Training Testing ABR DTR ETR GBR BG-ENSM ABR DTR ETR GBR BG-ENSM Adj.R 2 0.9696 0.9998 0.9999 0.9959 0.9993 0.9656 0.9868 0.9947 0.9925 0.9984 MAE 0.0671 0.0026 0.0001 0.0265 0.0078 0.0659 0.0348 0.0231 0.0322 0.0125 PI 1.8496 1.9943 1.9963 1.9555 1.9875 1.8430 1.9288 1.9607 1.9414 1.9808 R2 0.9698 0.9998 0.9999 0.9959 0.9993 0.9665 0.9871 0.9948 0.9926 0.9985 RMSE 0.0829 0.0054 0.0035 0.0340 0.0111 0.0819 0.0451 0.0287 0.0406 0.0160 VAF 96.29 99.98 99.99 99.36 99.93 95.93 98.71 99.48 98.95 99.84 WI 0.9927 1.0000 1.0000 0.9988 0.9999 0.9897 0.9972 0.9989 0.9976 0.9996 WMAPE 0.0396 0.0015 0.0001 0.0157 0.0046 0.0394 0.0208 0.0138 0.0192 0.0075 Table 7 Details of simulated datasets. Sets Parameters with a specific mean Fig. ref. c (kN/m 2 ) ϕ (°) γ (kN/m 3 ) k e ru Set-A 1010–1360 by 25 43 24 0, 0.50. 0.10, 0.15, and 0.20 0 Fig. 10a Set-B 1010–1360 by 25 43 24 0, 0.50. 0.10, 0.15, and 0.20 0.3 Fig. 10b Set-C 1010 43–43.70 by 0.05 24 0, 0.50. 0.10, 0.15, and 0.20 0 Fig. 10c Set-D 1010 43–43.70 by 0.05 24 0, 0.50. 0.10, 0.15, and 0.20 0.3 Fig. 10d Set-E 1010 43 22–23.10 by 0.1 0, 0.50. 0.10, 0.15, and 0.20 0 Fig. 10e Set-F 1010 43 22–23.10 by 0.1 0, 0.50. 0.10, 0.15, and 0.20 0.3 Fig. 10f 5.3. Parametric analysis This study also examines the practicality of influencing parameters by PA. The most optimal BG-ENSM model was utilized for this objective. It is important to note that the goal of PA is to assess the effectiveness of the BG-ENSM model in addressing the issue of overfitting. In order to achieve this objective, the impact of input variables on the FOS was examined based on a virtual dataset. The specific information regarding this dataset is given in Table 7 . There were six different combinations of influencing parameters that were investigated, labelled as Set-A to Set-F. In Sets-A and B, the parameter, c was simulated between 1010 kN/m 2 and 1360 kN/m 2 in increments of 25 kN/m 2 , resulting in a total of 15 datasets. The values of ϕ and γ were assigned as 43° and 24 kN/m 3 , respectively, and were consistent for all five k e values. The values of r u were assigned as 0 and 0.3 for Sets-A and B, respectively. Similarly, datasets for Sets-C and D were generated by systematically changing the value of ϕ from 43° to 43.70° in increments of 0.05°, while leaving all other parameters fixed. The details of other datasets can be seen in Table 7 . Figure 10 depict trends using smooth curves and demonstrate that the FOS increases when c (refer to Fig. 10a and b) and ϕ (refer to Fig. 10c and d) increase. In contrast, γ exhibits a behavior that is completely opposite, as evidenced from Fig. 10e and f. Nevertheless, Fig. 10a-f exhibit a comparable pattern of variation characterized by smooth concave curves which indicates the proposed BG-ENSM framework is capable of accurately estimating the FOS and hence can be considered as a viable framework for stability assessments of the said mountain. 5.4. Discussion of results The performance of the employed paradigms is discussed above. Specifically, four ensemble-based soft computing algorithms namely ABR, DTR, ETR, and GBR, and a bagging-based ensemble framework, BG-ENSM, were employed/developed for stability estimation of Mount St. Helens. Initially, a DEM of the said mountain was created followed by stability analysis using Scoops3D. For this purpose, 100 samples were generated at random and Scoops3D was used to determine the FOS. Five different combinations of k e were considered to determine the FOS with r u = 0 and r u = 0.3 cases. In total, 1000 records were extracted through Scoops3D and used in computational modelling for the estimation of FOS based on different influencing variables including c , ϕ, γ, r u , and k e values. Significantly, the stability assessments were categorized into three scenarios based on the pore-pressure ratio examined in this study. During computational modelling, the values of r u were set to 0 and 0.3 in Cases-1 and 2, respectively. In Case-3, both r u values were taken into account. Thus, a total of 500 datasets were taken into account for Cases-1 and 2, whereas Case-3 combination involved 1000 datasets. The model creation utilized a training set consisting of 80% of the samples, whereas the model validation was performed using a testing set including 20% of the samples. The results of testing set are presented in Table 4 – Table 6 , the BG-ENSM framework that was developed achieved highly accurate estimates of FOS. It had R 2 values of 0.9968, 0.9959, and 0.9985 for Cases-1, 2, and 3, respectively. Among the ensemble frameworks, the ETR model performed second best with R 2 values of 0.9905, 0.9892, and 0.9948 for Cases-1, 2, and 3, respectively. On the other hand, the ABR model was found to be the least effective, with R 2 values of 0.9395, 0.9361, and 0.9665 for Cases-1, 2, and 3, respectively. This level of performance is highly satisfactory when compared to other models that have been built. However, the BG-ENSM model that was constructed achieved the highest level of accuracy throughout the testing phase of FOS estimation. 6. Summary and Conclusion The present study proposes a bagging-based ensemble paradigm for stability estimation of Mount St. Helens. The proposed technique presents a BG-ENSM framework that was utilized to evaluate the failure risk of the mountain. The effect of r u was also studied considering three different cases viz., r u = 0, r u = 0.3, and r u = 0 and 0.3. The outcomes of the developed BG-ENSM framework were compared with four additional ensemble-based frameworks including ABR, DTR, ETR, and GBR. Based on the analysis presented above, it is seen that the proposed BG-ENSM framework achieved the most desired estimation of FOS with R 2 of 0.9968, 0.9959, and 0.9985 against Cases-1, 2, and 3, respectively. However, among the employed ensemble framework, ETR is the second-best framework with R 2 of 0.9905, 0.9892, and 0.9948 against Cases-1, 2, and 3, respectively; while the ABR was seen as the least-effective model with R 2 of 0.9395, 0.9361, and 0.9665 against Cases-1, 2, and 3, respectively. Overall, the proposed BG-ENSM framework gives the most accurate estimation of the FOS in all cases and can be used as a promising approach for stability estimation of Mount St. Helens. The BG-ENSM framework offers several notable advantages from the standpoint of computational modelling: (a) higher predictive precision; (b) higher generalization ability; (c) lesser computational cost, and (d) a combined model. Nevertheless, choosing the most effective BG-ENSM paradigm requires multiple iterations and careful adjustment of hyper-parameters, which is a limitation of the suggested approach. Another limitation is that the solution is not guaranteed to converge to the global minimum due to amalgamation of multiple algorithms; as a result, the performance of a BG-ENSM paradigm could be affected in many situations. Conversely, crucial input parameters such as precipitation, permeability, and rock type, among others, were not accounted for in the computational modelling process. These parameters ought to have been incorporated into the developed model to render it a more universally applicable technique for determining the FOS of additional mountains. However, to the best of the authors' knowledge, this research represents the initial implementation of an ensemble-based framework for estimating the stability of Mount St. Helens under both seismic and non-seismic conditions. Declarations Author contributions : All authors contributed equally in this manuscript. Funding : Nil. Data availability : All data used during the study are available from the corresponding author. Competing interest : None declared. Conflict of interest: None. Acknowledgements : Nil Ethical statements : No conflict of interest. Supplementary Information : Not applicable References Armaghani DJ, Mohamad ET, Narayanasamy MS, et al (2017) Development of hybrid intelligent models for predicting TBM penetration rate in hard rock condition. Tunn Undergr Sp Technol 63:29–43 Balasubramanian A (2017) Digital elevation model (DEM) in GIS. Univ Mysore Bishop AW (1955a) The analysis of stability of slopes. 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Saf Sci 118:505–518 Additional Declarations No competing interests reported. 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. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-4417103\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":306005163,\"identity\":\"b3d36de7-0916-4864-b1f3-b30f0376baec\",\"order_by\":0,\"name\":\"Sumit Kumar\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"National Institute of Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Sumit\",\"middleName\":\"\",\"lastName\":\"Kumar\",\"suffix\":\"\"},{\"id\":306005166,\"identity\":\"47729476-ad99-4af5-9a9b-48117143d82f\",\"order_by\":1,\"name\":\"Sudeep 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2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":48527,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eIllustration of j, k column.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/1c5d3395c87588d5ee832e52.png\"},{\"id\":57442709,\"identity\":\"052bf7e4-baaf-48d6-81ba-1bebca36131b\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:48:07\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":587924,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eMount St Helens prior to its 1980 eruption.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/c193d1e0f6b46642d8fc4ba9.png\"},{\"id\":57442715,\"identity\":\"4e29775f-1c55-4735-95f7-3a79c70c4b17\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:48:07\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":79202,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eIllustration of ensemble-based modelling.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/96d7a7506c7e30d2bb458f58.png\"},{\"id\":57444433,\"identity\":\"0f8c8708-2bcb-45d3-8225-2c9fa37073a6\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:56:07\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":112990,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eFlowchart showing the workflow for model validation.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/650aa229984df7b20a9a7052.png\"},{\"id\":57442710,\"identity\":\"91c32466-3af2-4c12-99f9-b3b504f6f4fe\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:48:07\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":25697,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eIllustration FOS at different k\\u003csub\\u003ee\\u003c/sub\\u003e values (for r\\u003csub\\u003eu\\u003c/sub\\u003e = 0)\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"6.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/af636a8d2fe0eea7a5223373.png\"},{\"id\":57442712,\"identity\":\"1e2b81c6-131d-419e-add0-22a59b517263\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:48:07\",\"extension\":\"png\",\"order_by\":7,\"title\":\"Figure 7\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":24380,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eIllustration FOS at different k\\u003csub\\u003ee\\u003c/sub\\u003e values (for r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.30)\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"7.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/c4b054c63f0a9e4cc1f2c250.png\"},{\"id\":57442716,\"identity\":\"6893eb8c-090c-4d1b-a7db-b9edfe4b8f65\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:48:07\",\"extension\":\"png\",\"order_by\":8,\"title\":\"Figure 8\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":50515,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eRepresentation of maximum and minimum FOS at different k\\u003csub\\u003ee\\u003c/sub\\u003e and r\\u003csub\\u003eu\\u003c/sub\\u003e values.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/31c81e6490b1c41a0cde210e.png\"},{\"id\":57442713,\"identity\":\"f1b6dcc8-b55b-4ef8-9efd-08ff28c43069\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:48:07\",\"extension\":\"png\",\"order_by\":9,\"title\":\"Figure 9\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":120261,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eScatter plots of all input combinations for (a-c) training and (d-f) testing phases.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"9.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/e3b1d891a0507a2cc8c8c359.png\"},{\"id\":57444437,\"identity\":\"027a49df-92e7-410f-85b7-4cbd24150d00\",\"added_by\":\"auto\",\"created_at\":\"2024-05-30 18:56:07\",\"extension\":\"png\",\"order_by\":10,\"title\":\"Figure 10\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":85804,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eIllustration of PA for (a) c vs. FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0, (b) c vs. FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3, (c) ɸ vs. FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0, (d) ɸ vs. FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3, (e) ɣ vs. FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0, and (f) ɣ vs. FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3, at different k\\u003csub\\u003ee\\u003c/sub\\u003e values.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"10.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/894d848e00657c9427b7f0e1.png\"},{\"id\":57905796,\"identity\":\"ade9f1aa-2282-4d43-8ca4-6233a6687563\",\"added_by\":\"auto\",\"created_at\":\"2024-06-07 09:49:08\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":2489645,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-4417103/v1/2b80c548-4237-492b-bc5a-9880bdc971bf.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Stability estimation of Mount St. Helens using Scoops3D and ensemble learning paradigms\",\"fulltext\":[{\"header\":\"1. Introduction\",\"content\":\"\\u003cp\\u003eThe assessment of slope stability inside volcanic structures is one of the important studies in the domain of geological-geological investigation, essential for understanding the complex processes of these distinct natural formations. Volcanic structures, which include cone-shaped or composite edifices, are formed as a consequence of volcanic processes and are distributed over the Earth's surface, frequently occurring in areas associated with tectonic plate boundaries. These structures exhibit a diverse array of inclines, and their stability is critical because it impacts the security of adjacent communities, infrastructure, and the natural surroundings. Thus, the stability of these slopes should be evaluated to comprehend the risks of volcanic eruptions, including landslides, pyroclastic flows, and lava flows, which can cause damage to nearby and distant regions.\\u003c/p\\u003e \\u003cp\\u003eIn the domain of volcanic study, a wide range of slope failures observed in volcanic structures, which span from small-scale rock falls to more substantial collapses. Monumental flank slides, with a volume above 0.1 km\\u003csup\\u003e3\\u003c/sup\\u003e, have caused significant modifications in stratovolcanoes worldwide (Siebert \\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e1984\\u003c/span\\u003e; Siebert et al. \\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e1987\\u003c/span\\u003e). These occurrences are considered to be among the most abrupt, devastating, and hazardous processes. Due to catastrophic flank collapse, significant alterations have been observed in many composite volcanic or stratovolcano structures worldwide (Ui \\u003cspan citationid=\\\"CR43\\\" class=\\\"CitationRef\\\"\\u003e1983\\u003c/span\\u003e; McGuire \\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e1996\\u003c/span\\u003e). Furthermore, the most notable volcanic collapses in history, exemplified by occurrences like the eruptions of Mount St. Helens in the U.S., Bandai in Japan, and Bezymianny in Russia, were all triggered by the displacement along profound and curved failure surfaces (Voight and Elsworth \\u003cspan citationid=\\\"CR44\\\" class=\\\"CitationRef\\\"\\u003e1997\\u003c/span\\u003e). An illustrative example of a catastrophic collapse is the event that took place at Mount St. Helens in the U.S. in 1980, which might be seen as a compelling case study (Voight et al. \\u003cspan citationid=\\\"CR45\\\" class=\\\"CitationRef\\\"\\u003e1983\\u003c/span\\u003e). These significant collapses, often involving a volume of material exceeding 0.1 km\\u003csup\\u003e3\\u003c/sup\\u003e, possess the capacity to initiate debris avalanches that can subsequently develop into calamitous events related to debris, posing substantial risks not only to the structure itself but also to regions located at lower elevations or downstream. Furthermore, stratovolcanoes provide risks to populations living in developing nations, emphasizing the urgent need for quick and affordable hazard assessments. Tragically, almost 20,000 people have perished due to flank collapses in the past (Siebert et al. \\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e1987\\u003c/span\\u003e; Sparks et al. \\u003cspan citationid=\\\"CR39\\\" class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e). The instability of structures can be attributed to a variety of volcano-specific factors like magma intrusion, hydrothermal alteration and slope instability due to increased pore fluid pressures (Reid \\u003cspan citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e1994\\u003c/span\\u003e; Day \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e1996\\u003c/span\\u003e; Voight and Elsworth \\u003cspan citationid=\\\"CR44\\\" class=\\\"CitationRef\\\"\\u003e1997\\u003c/span\\u003e). The stratovolcano structure of Mount St. Helens whose flanks have collapsed many times, is an ideal location to try and validate methodology.\\u003c/p\\u003e \\u003cp\\u003eTraditionally, slope stability is carried out in two dimensions assuming plane strain conditions are valid even though all slopes are in general, 3D structures. Slope stability studies have attracted a lot of attention since 1930s (Bishop \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e1955b\\u003c/span\\u003e; Zhang and Wang \\u003cspan citationid=\\\"CR51\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). In many cases, it would be more appropriate to adopt a 3D assessment when there is a considerable variation in the geometry of the slope, resulting in violation of the applicability of 2D plane strain assumptions (Kalatehjari et al. \\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). The findings of 2D slope stability analyses often show lower factor of safety (FOS) than 3D methods for simple hillslope shapes, but the deviation between the 2D and 3D is generally between 10% and 20% (Hovland \\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e1977\\u003c/span\\u003e; Xing \\u003cspan citationid=\\\"CR48\\\" class=\\\"CitationRef\\\"\\u003e1988\\u003c/span\\u003e; Duncan \\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e1996\\u003c/span\\u003e). Researchers have explored slope stability in three dimensions very recent past (Huang et al. \\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e2002\\u003c/span\\u003e; Hajiazizi and Tavana \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e; Sun et al. \\u003cspan citationid=\\\"CR41\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e; Kumar et al. \\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e2023a\\u003c/span\\u003e). Using 2D Bishop\\u0026rsquo;s method (1955a), Hungr (\\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e1987\\u003c/span\\u003e) proposed an approach for determining 3D FOS. Lam and Fredlund (\\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e1993\\u003c/span\\u003e) proposed a 3D method derived from general limit equilibrium methodology (Fredlund and Krahn \\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e1977\\u003c/span\\u003e). Recently, Kumar et al. (\\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e2023a\\u003c/span\\u003e) conducted a review of recent advances in 3D slope analysis. However, there are several methods that have been developed to analyses slope stability. Amongst them, strength reduction method (SRM) (Sun et al. \\u003cspan citationid=\\\"CR41\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e), limit analysis method (LAM) (Gao et al. \\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e), and the limit equilibrium method (LEM) (Cavounidis \\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e1988\\u003c/span\\u003e) are frequently used techniques. The LEM and SRM approaches are deterministic among them, and they rely on set values for various soil parameters to determine a soil slope\\u0026rsquo;s stability using the FOS.\\u003c/p\\u003e \\u003cp\\u003eDespite giving a conservative result, FOS-based techniques have been proved to be unproductive on multiple occasions (Zhao \\u003cspan citationid=\\\"CR53\\\" class=\\\"CitationRef\\\"\\u003e2008\\u003c/span\\u003e). One of the limitations of FOS-based techniques is that the uncertainties in soil parameters are not expressed explicitly. Also, the calculated values of FOS are often used for a particular purpose, such as long-term slope stability. But it would not appropriate to use the same FOS for all situations with different levels of uncertainty. The soil materials\\u0026rsquo; non-linear stress-strain associations, elasto-plastic behavior, and stress-strain time-conditioning response make them quite complex (Safa et al. \\u003cspan citationid=\\\"CR35\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). So, a full analysis of geotechnical properties is needed to take into consideration the uncertainty that comes with slope stability computations.\\u003c/p\\u003e \\u003cp\\u003eEarthquakes can trigger numerous earth and rock slides, some of which can result in significant damage to critical structures, including dams, hills, vital hill highways, railways, and other infrastructure. In general, slope geometry and soil properties have a substantial influence on its stability. Damage to buildings, roads, railroads, infrastructures, and foundations can result from slope failures due to the resulting ground deformation. Due to their geodynamic and morphological nature, unprecedented rainfall, urbanization, and other influences, hilly terrains are typically at danger for instability. These hilly regions urgently require high-quality roads and highways to improve connectivity, increase tourism, and allow for development activities that are safe.\\u003c/p\\u003e \\u003cp\\u003eIt is needless to say that slope stability assessment considering the spatial variation of related geotechnical parameters of a major volcanic edifice like Mount St. Helen is of paramount importance. AI/ML approaches have previously been employed by numerous researchers for 2D slope stability analysis. The authors Wang et al. (\\u003cspan citationid=\\\"CR46\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e) and Zhou et al. (\\u003cspan citationid=\\\"CR55\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e) proposed the extreme gradient boosting approach. Another relevant machine learning technique is the relevance vector machine. The study conducted by Zhao et al. (\\u003cspan citationid=\\\"CR54\\\" class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e) focused on Gaussian process regression. The study conducted by Huang et al. (\\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e) focused on the application of artificial neural networks. Ray et al. (\\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e) have effectively utilized machine learning techniques to demonstrate regression-based results for 2D slope stability solutions in several scenarios. Xu et al. (\\u003cspan citationid=\\\"CR49\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) performed a review work of conventional and machine learning (ML) methods for analyzing the stability of 2D slopes. Ray et al. (\\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) used MARS, GPR, and FN to conduct a reliability analysis (RA) of a soil slope. Rao et al. (\\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e) also performed RA of a railway embankment considering 3D slope stability.\\u003c/p\\u003e \\u003cp\\u003eIn recent times, several studies have been conducted using ensemble learning frameworks in order to forecast desirable outcomes across several domains of engineering (Lin et al. \\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e; Zhang et al. \\u003cspan citationid=\\\"CR52\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). Ensemble models are particularly noteworthy for their ability to enhance the performance of unstable models by operating at a higher level (Caruana et al. \\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e2004\\u003c/span\\u003e). Significantly, the performance of an ensemble model surpasses that of an individual model when it comprises two or more base models (Laradji et al. \\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). Due to the aforementioned considerations and as a part of ongoing research and to extend the work of Kumar et al. (\\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e2023b\\u003c/span\\u003e), ensemble-based methods were utilized in this investigation to estimate the stability of Mount St. Helens. In particular, a bagging-based ensemble (BG-ENSM) framework and four base models viz., AdaBoost regressor (ABR), decision tree regressor (DTR), extra tree regressor (ETR), and gradient boosting regressor (GBR), were employed. The FOS was initially estimated using Scoops3D and slope geometries of Mount St. Helens, as per the details obtained from Reid et al. (\\u003cspan citationid=\\\"CR34\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). Subsequently, computational modelling was conducted utilizing a range of influencing parameters, including cohesion (\\u003cem\\u003ec\\u003c/em\\u003e), angle of internal friction (ϕ), and bulk density (γ), and pore-pressure ratio (\\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e). At the end, the stability assessment was conducted in seismic and non-seismic conditions.\\u003c/p\\u003e \\u003cp\\u003eThe remaining portion of the work is organized in the following manner. Section 2 addresses the study area, whereas Section 3 presents methodological details. Section 4 offers an in-depth analysis of data processing and the intricacies of computer modelling. Section 5 provides an exposition of the findings and subsequent deliberations. Section 6 contains the summary and findings.\\u003c/p\\u003e\"},{\"header\":\"2. Study area\",\"content\":\"\\u003cp\\u003eThe aim of this study is to analyze Mount St. Helens, which is located in the Washington District of Columbia in the USA and experienced a failure due to an eruption on May 18, 1980 (Voight et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e1983\\u003c/span\\u003e). Although failure surfaces may be readily apparent in simpler geometric features of slopes (e.g., those that are polygonal or polyhedral in shape), this may not hold true for intricate geographical features like Mount St Helens. A topographical illustration of Mount St. Helen and study site are shown in Fig.\\u0026nbsp;1). Prior to the disaster of Mount St. Helens, the 3D distributions of rock strength and density were unknown. Post collapse, Voight et al. (\\u003cspan class=\\\"CitationRef\\\"\\u003e1983\\u003c/span\\u003e) and Glicken (\\u003cspan class=\\\"CitationRef\\\"\\u003e1996\\u003c/span\\u003e) reconstructed the interior geologic structure using geologic sections given by Hopson and Melson (\\u003cspan class=\\\"CitationRef\\\"\\u003e1982\\u003c/span\\u003e). The mountain\\u0026rsquo;s core is composed of older dacite dome lavas and flank breccias, both of which have undergone hydrothermal alteration. Andesitic, basaltic, and tephra lava flows covered this unit. The domes at top and Goat Rocks have been built using relatively recent dacite. In 1980, the dacitic crypto-dome forcefully penetrated each of these elements.\\u003c/p\\u003e\"},{\"header\":\"3. Methodology\",\"content\":\"\\u003cp\\u003eIn this section, an overview of the theoretical particulars of the deterministic analysis that is utilized in the method of computing the three-dimensional FOS is presented. This is accomplished by the implementation of Bishop's simplified technique.\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e3.1. FOS estimation and DEM modelling\\u003c/h2\\u003e\\n\\u003cp\\u003eIn the following section, the theoretical details of deterministic analysis are presented in order to compute the FOS by utilizing Bishop's simplified approach. This study utilizes the Scoops3D computer program to determine the factor of safety of a 3D slope. The program employs the Ordinary and Bishop simplified methods (BSM) to calculate the FOS against slope failure. The present study uses Bishop\\u0026rsquo;s simplified method where the spherical failure surfaces are used for 3D slope analysis. The free-body schematic of the j, k column, in which no external force is acting and the column is subjected to every conceivable combination of forces, is illustrated in Fig.\\u0026nbsp;2.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eIn Fig.\\u0026nbsp;2, W is weight of column; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({E}_{{x}_{j,k}}, {E}_{{y}_{j,k}}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e signify the inter-column normal force in the x and y dimensions;\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({H}_{{x}_{j,k}}, {H}_{{y}_{j,k}}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e show the y-z plane shear force horizontally; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({X}_{{x}_{j,k}}, {X}_{{y}_{j,k}}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e indicate the shear force between columns in the x-z plane; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({N}_{j,k}, {U}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e signify the effective normal force and base pore water force, respectively; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({S}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e denote the mobilized shear force that acts on the base of the column; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\alpha }_{j, k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e refer to slide angle relative to the x\\u0026ndash;y plane; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\alpha }_{x},{\\\\alpha }_{y}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e refer to the base inclination at the midpoint of each column in the x-z and y-z planes, respectively.\\u003c/p\\u003e\\n\\u003cp\\u003eAfter simplifying, the final FOS expression of BSM can be computed for ground water condition as shown in Eq.\\u0026nbsp;(\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ1\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ1\\\" class=\\\"mathdisplay\\\"\\u003e$$FOS=\\\\frac{\\\\sum {R}_{j,k}\\\\left({c}_{j,k}{A}_{j,k}+{W}_{j,k}\\\\left(1-{r}_{uj,k}\\\\right){\\\\text{tan}\\\\varphi }_{j,k}\\\\right)/{m}_{{\\\\alpha }_{j,k}}}{\\\\sum {W}_{j,k}\\\\left[{R}_{j,k}{m}_{z}+{k}_{eq}{e}_{j,k}\\\\right]}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e1\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({m}_{{\\\\alpha }_{j,k}}=\\\\text{cos}{\\\\epsilon }_{j,k}+\\\\text{tan}{\\\\varphi }^{{\\\\prime }}d{m}_{z}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({m}_{z}=\\\\text{sin}{\\\\alpha }_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({c}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e known as effective cohesion; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\varphi }_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e known as effective internal friction angle; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({R}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e distance between the trial slip area of the j,k column to its axis of rotation, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({A}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e denote the trial surface area of column, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({W}_{j,k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e known as column\\u0026rsquo;s weight; \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\text{e}}_{j, k}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e refer to the horizontal driving force moment arm. The sum of normal and shear forces along the columns' sides is considered to be zero along the x and y axes in 3D.\\u003c/p\\u003e\\n\\u003cp\\u003eA digital depiction of the elevation of the land surface, called a digital elevation model (DEM) Balasubramanian (\\u003cspan class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e), is based on any reference data. The most typical DEMs type is regular grids, which are available in a number of variations (Xu et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). The study of geomorphology makes extensive use of DEM. DEMs may represent many different elements of landscapes and have advantages in terms of data format and processing performance. The most crucial fundamental data sources for geographic information at the national level are DEMs. To generate a DEM, data can now be produced or taken from public data sources. Shuttle Radar Topography Mission (SRTM), GTOPO30, Terra Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER GDEM), ALOS Global Digital Surface Model (AW3D30), Digital Terrain Elevation Data (DTED-2), and EU-DEM are just a few examples of the many currents, openly accessible global DEMs. On the other hand, there are an increasing number of free GIS software programs (such as GRASS GIS, SAGA GIS, and QGIS). The type of topography, such as landforms, elevations, texture, ruggedness, and vegetation present, as well as the methods used to collect elevation data, the process used to create the DEM, the kind of grid used for the DEM, and the DEM resolution, all affect the accuracy of the DEM. (Fisher \\u003cspan class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e; Schneider \\u003cspan class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e; Wise \\u003cspan class=\\\"CitationRef\\\"\\u003e2000\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cp\\u003eFor 3D stability studies, the U.S. Geological Survey (USGS) created the downloadable Scoops3D code. (Reid et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). It needs a digital elevation model as its main input (Reid et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2000\\u003c/span\\u003e, \\u003cspan class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). Firstly, it is necessary to make accurate estimations regarding the topography of the ground surface. This DEM can be used to build a 3D model for slope problems because it can easily use spatial and image data from geographic information systems (GIS) (Sulebak \\u003cspan class=\\\"CitationRef\\\"\\u003e2000\\u003c/span\\u003e; Cavazzi et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2013\\u003c/span\\u003e). In addition, DEM representations are readily available due to the increasing use of satellite imagery (e.g., Google Earth) and aerial photography (e.g., drones). Based on the results of a comparative analysis conducted by Reid et al. (\\u003cspan class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e) on these DEMs using cubic convolution in the GRID program of ARC/INFO [Environmental Systems Research Institute (ESRI), 1998], the author selected 100-m resampled DEMs for the subsequent studies since this resolution is adequate for accurately computing the stability of possible failures with a volume\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.1 km3. The digital elevation model (DEM) data used in this analysis was retrieved from Reid et al. (\\u003cspan class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e) and was created from aerial pictures obtained on May 12, 1980 (refer to Fig.\\u0026nbsp;3). The DEM description of Mount St. Helens is also shown in Fig.\\u0026nbsp;3.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e3.2. Details of soft computing paradigms\\u003c/h2\\u003e\\n\\u003cp\\u003eBrief details of the employed paradigms are offered in this sub-section. As sated above, four standalone models namely ABR, DTR, ETR, and GBR were used. In addition, bagging-based ensemble paradigm, called BG-ENSM was used for the estimation of FOS of Mount St. Helens.\\u003c/p\\u003e\\n\\u003cp\\u003eABR is an ensemble-based algorithm and it is a modified version of the Adaboost algorithm used for regression tasks. A basic linear regression or a shallow decision tree is often used as a weak regression model in ABR. It is trained on the dataset first. The errors in the first model are then looked at, and the data points that the model had the most trouble predicting are given more attention. After that, weak regression models are trained with new sample weights, and the goal is to get better predictions for the difficult data points. The final prediction is made by adding up the predictions from each of these weak models, with the weight of each model's input based on how well it did in the iterative training process.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eDTR is a tree-based algorithm consisting multiple branches and nodes and used for regression tasks. In the training phase, a particular function is used to compare the input variable values. A program that takes a list of cases and turns them into a decision tree (DT) is called a DT stimulant. By reducing the fitness function, the algorithm in use tries to identify the best DTs. The dataset is partitioned into numerous split points for each input variable. At each of these division points, DTR is executed to calculate the prediction error using the fitness function discussed before. Subsequently, errors in the split points are analyzed and minimized using iteratively (Tso and Yau \\u003cspan class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cp\\u003eETR is an ensemble technique that is derived from the DT regression algorithm. Ensemble algorithms aim to combine a given number of estimators in order to lower the variance of a model relative to the variance of a single tree. The proposed methodology constructs an ensemble of DTs, whereby each tree incorporates a distinctive modification to conventional DT algorithms. In contrast to conventional DTs and RF, ETR incorporates more unpredictability at two crucial stages. It starts by randomly selecting the training data subsets. Since each tree sees distinct data, overfitting is reduced. Second, instead of using the best feature in standard DTs, it randomly selects a subset of characteristics to split at each node. After building a forest of randomized DT, regression tasks are predicted by averaging their outputs.\\u003c/p\\u003e\\n\\u003cp\\u003eGBR is an ensemble-trained supervised ML model, boosting is the technique of creating a single composite model from several simple models. Boosting is nothing but an additive framework since it involves the sequential addition of basic models while keeping the model's trees unchanged. A better prediction can be obtained by merging more fundamental models. Gradient boosting refers to a technique that aims to minimize losses by employing gradient descent, which is an iterative optimization procedure based on first-order derivatives. Gradient boosting utilizes DTs as weak learners and trains a feeble model to establish a mapping between the inputs and the projected deviations of the weak model. Subsequently, these additions are included into the input of the existing model, so facilitating its achievement of the desired outcome.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e3.3. Bagging ensemble-based modelling\\u003c/h2\\u003e\\n\\u003cp\\u003eThe bagging ensemble is an ensemble framework that consists of multiple learners trained on subsamples collected from the same set. It is employed to address the trade-offs between bias and variance and diminishes the variability of a predictive model. Bagging is a technique that prevents overfitting of data and can be applied to both regression and classification tasks. Bagging ensemble is frequently employed to enhance the accuracy of a model, mainly when introducing variations to the training set can lead to a substantial alteration in the produced prediction. Generally, bagging approach involves three steps: (a) generating numerous datasets by sampling from the original data, (b) using every dataset to train multiple learners, and (c) aggregating the predictions of all learners to get a single estimation. The final result is then derived by taking the average of the outcomes obtained from the used models in a regression study, or by utilizing a majority voting strategy for classification problems (Hern\\u0026aacute;ndez-Lobato et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e). An illustration of bagging ensemble technique is presented in Fig.\\u0026nbsp;4.\\u003c/p\\u003e\\n\\u003c/div\\u003e\"},{\"header\":\"4. Data collection and computational modelling\",\"content\":\"\\u003cp\\u003eBefore its demise caused by volcanic eruptions, the geological features of Mount St. Helens seemed more uniform compared to the other stratovolcanoes. Voight et al. (\\u003cspan class=\\\"CitationRef\\\"\\u003e1983\\u003c/span\\u003e) describe the physical features of debris resulting from the collapse of the said mountain, in which the authors found that the mean values of \\u0026empty; and \\u003cem\\u003ec\\u003c/em\\u003e are 40\\u0026deg; and 1000 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e, respectively, The average specific weight for intact edifice rock, i.e., \\u0026gamma;\\u0026thinsp;=\\u0026thinsp;24 kN\\u0026frasl;m\\u003csup\\u003e3\\u003c/sup\\u003e. As per the study of Voight et al. (\\u003cspan class=\\\"CitationRef\\\"\\u003e1983\\u003c/span\\u003e), slope stability analysis was conducted using \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e = 0.3. In addition, the said analysis was also conducted at no pore-pressure ratio, i.e., \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e = 0. A sum of 100 datasets were formed using \\u003cem\\u003ec\\u003c/em\\u003e\\u0026thinsp;=\\u0026thinsp;1000 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e, \\u0026empty; = 40\\u0026deg;, and \\u0026gamma;\\u0026thinsp;=\\u0026thinsp;24 kN\\u0026frasl;m\\u003csup\\u003e3\\u003c/sup\\u003e. Notably, normal distribution sampling technique was followed during data generation. The given combinations indicate one data sample that was fed as input into the Scoops3D and the slope`s FOS was determined as per 3D Bishop\\u0026rsquo;s simplified method. During FOS estimation, different combinations of \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e and ke were considered. Specifically, the FOS for all the 100 samples was determined for five different values of k\\u003csub\\u003ee\\u003c/sub\\u003e including 0, 0.05, 0.10, 0.15, and 0.20 (designated as Sets 1\\u0026ndash;5), with r\\u003csub\\u003eu\\u003c/sub\\u003e assigning 0 and 0.3 for each set. Therefore, total 1000 datasets (i.e., 100 \\u0026times; 5 \\u0026times; 2, five sets of k\\u003csub\\u003ee\\u003c/sub\\u003e and two sets of \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e) were generated, the particulars of which are tabulated in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e. As per the table, the values of \\u003cem\\u003ec\\u003c/em\\u003e and \\u0026empty; fall in the range of 809.77 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e \\u0026ndash; 1195.17 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e and 35.18\\u0026deg; \\u0026ndash; 49.40\\u0026deg;, respectively. The other variables, \\u0026gamma;\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(,\\\\)\\u003c/span\\u003e\\u003c/span\\u003e \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e,\\u003c/sub\\u003e and k\\u003csub\\u003ee\\u003c/sub\\u003e are ranging from 22.02 kN/m\\u003csup\\u003e3\\u003c/sup\\u003e \\u0026ndash; 25.99 kN/m\\u003csup\\u003e3\\u003c/sup\\u003e, 0\\u0026ndash;0.3, and 0\\u0026ndash;0.20, respectively. Notably, this study simplifies the analysis by assuming consistent material qualities, the existence of groundwater, and the inclusion of seismic stress.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003eDescriptive details of Mount St. Helens.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eParameters\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eMin.\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eAvg.\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eMax.\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eStnd. Dev.\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eKurtosis\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ec\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e809.77\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e1195.17\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e117.31\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-1.26\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eϕ\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e35.18\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e40\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e49.40\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e4.21\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-1.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e\\u0026gamma;\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e22.02\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e24\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e25.99\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.17\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-1.25\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ek\\u003csub\\u003ee\\u003c/sub\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e0.00\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.08\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-1.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e\\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e0.00\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\".\\\"\\u003e\\n\\u003cp\\u003e0.30\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e-\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"char\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003eDetails of different cases.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eCase\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eInputs\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eData dimension\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eOutput\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eCase-1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ec, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\varnothing\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\gamma\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, and k\\u003csub\\u003ee\\u003c/sub\\u003e (with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0)\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\"\\u0026times;\\\"\\u003e\\n\\u003cp\\u003e500 \\u0026times; 4\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFOS\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eCase-2\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ec, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\varnothing\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\gamma\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, and k\\u003csub\\u003ee\\u003c/sub\\u003e (with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3)\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\"\\u0026times;\\\"\\u003e\\n\\u003cp\\u003e500 \\u0026times; 4\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFOS\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eCase-3\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ec, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\varnothing\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\gamma\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, k\\u003csub\\u003ee\\u003c/sub\\u003e, and r\\u003csub\\u003eu\\u003c/sub\\u003e (with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 and 0.3)\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"char\\\" char=\\\"\\u0026times;\\\"\\u003e\\n\\u003cp\\u003e1000 \\u0026times; 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFOS\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eImportantly, this study considers three distinct cases, i.e., Cases-1, 2, and 3 according to the \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e values, as detailed in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e. Specifically, r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 was considered in Case-1 and r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.30 was considered in Case-2. In Case-3, both \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e values were considered. Therefore, the computational modelling was conducted for three-different combinations with \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e = 0, \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e = 0.30, and \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e = 0 and 0.30. In each case, the dataset was partitioned into training and testing sets with 80:20 bifurcation. Notably, data normalization is an essential phase in the process of computational analysis. In the pre-processing step, it is common practice to normalize data in order to mitigate the impact of variable dimensionality. Thus, all the variables were normalized within the range of [0, 1] before model construction. This is achieved by applying the min-max technique. Following normalization, the training and testing sets were created randomly. The training set contained 80% samples (i.e., 400 datasets), whereas the testing set had the remaining 20% (i.e., 100 datasets). However, for Case-3, 1000 sets of data were taken, and the analysis was done like in Case-1. Finally, the best-obtained model was chosen as per multiple parameters viz., adjusted coefficient of determination (Adj.R\\u003csup\\u003e2\\u003c/sup\\u003e), mean absolute error (MAE), performance index (PI), coefficient of determination (R\\u003csup\\u003e2\\u003c/sup\\u003e), root mean squared error (RMSE), variance account factor (VAF), Willmott's Index of agreement (WI), and weighted mean absolute percentage error (WMAPE). The expressions of these indices can be expressed as:\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equ2\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ2\\\" class=\\\"mathdisplay\\\"\\u003e$$Adj.{R}^{2}=1-\\\\frac{(n-1)}{(n-p-1)}(1-{R}^{2})$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e2\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ3\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ3\\\" class=\\\"mathdisplay\\\"\\u003e$$MAE=\\\\frac{1}{n}{\\\\sum }_{i=1}^{n}\\\\left|\\\\left({\\\\widehat{y}}_{i}-{y}_{i}\\\\right)\\\\right|$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e3\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ4\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ4\\\" class=\\\"mathdisplay\\\"\\u003e$$PI=adj.{R}^{2}+0.01VAF-RMSE$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e4\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ5\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ5\\\" class=\\\"mathdisplay\\\"\\u003e$${R}^{2}=\\\\frac{{\\\\sum }_{i=1}^{n}({y}_{i}-{y}_{mean}{)}^{2}-{\\\\sum }_{i=1}^{n}({y}_{i}-{\\\\widehat{y}}_{i}{)}^{2}}{{\\\\sum }_{i=1}^{n}({y}_{i}-{y}_{mean}{)}^{2}}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e5\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ6\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ6\\\" class=\\\"mathdisplay\\\"\\u003e$$RMSE=\\\\sqrt{\\\\frac{1}{n}{\\\\sum }_{i=1}^{n}({y}_{i}-{\\\\widehat{y}}_{i}{)}^{2}}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e6\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ7\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ7\\\" class=\\\"mathdisplay\\\"\\u003e$$VAF \\\\left(\\\\%\\\\right)=(1-\\\\frac{{var}({y}_{i}-{\\\\widehat{y}}_{i})}{{var}({y}_{i})})\\\\times 100$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e7\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ8\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ8\\\" class=\\\"mathdisplay\\\"\\u003e$$WI=1- \\\\left[\\\\frac{{\\\\sum }_{i=1}^{n}({y}_{i}-{\\\\widehat{y}}_{i}{)}^{2}}{\\\\sum _{i=1}^{n}{\\\\left\\\\{\\\\left|{\\\\widehat{y}}_{i}-{y}_{mean}\\\\right|+ \\\\left|{y}_{i}-{y}_{mean}\\\\right| \\\\right\\\\}}^{2}}\\\\right]$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e8\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Equ9\\\" class=\\\"Equation\\\"\\u003e\\n\\u003cdiv id=\\\"FileID_Equ9\\\" class=\\\"mathdisplay\\\"\\u003e$$WMAPE=\\\\frac{{\\\\sum }_{i=1}^{n}\\\\left|\\\\frac{{y}_{i}-{\\\\widehat{y}}_{i}}{{y}_{i}}\\\\right|\\\\times {y}_{i}}{{\\\\sum }_{i=1}^{n}{y}_{i}}$$\\u003c/div\\u003e\\n\\u003cdiv class=\\\"EquationNumber\\\"\\u003e9\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003ewhere n is the sample number, y\\u003csub\\u003emean\\u003c/sub\\u003e specifies the mean value, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({y}_{i}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\widehat{y}}_{i}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e indicate the actual and estimated FOS. The values of the parameters need to match exactly with the respective ideal values (Armaghani et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e; Duan et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e). Below is a brief description of the above indices.\\u003c/p\\u003e\\n\\u003cp\\u003eNotably, when it comes to performance indicators, trends are measured by the PI, R\\u003csup\\u003e2\\u003c/sup\\u003e, VAF, and WI, and errors are measured by the MAE, RMSE, and WMAPE. Error measurement indices quantify the errors, while trend measurement indicators show the trend of the prediction models. The linear correlation between the actual and estimated values is indicated by the R\\u003csup\\u003e2\\u003c/sup\\u003e value. Furthermore, PI shows a comprehensive accuracy of a data-driven model in terms of Adj.R\\u003csup\\u003e2\\u003c/sup\\u003e, VAF, and RMSE, in which VAF measured the percentage variance of error. WI indicates the degree of prediction error in the model. However, the amount of associated error is frequently assessed using MAE, RMSE, and WMAPE. The MAE displays the mean size of the errors, whereas the RMSE displays the mean error in terms of square root. Furthermore, WMAPE calculates the overall weighted mean error. Note that, the predictive capacity is enhanced by higher values of PI, R\\u003csup\\u003e2\\u003c/sup\\u003e, VAF, and WI. A more suitable model is also indicated by lower MAE, RMSE, and WMAPE values. To identify the prediction model with the best performance, the current study thoroughly assessed the performance metrics. An illustration of FOS and estimation and computational modeling is presented in Fig.\\u0026nbsp;5.\\u003c/p\\u003e\"},{\"header\":\"5. Results and discussions\",\"content\":\"\\u003cp\\u003eThis section outlines the outcomes of the stability assessment followed by the implementation of computational approaches for determining the failure of Mount St. Helens. Subsequently, the specifics of parametric analysis (PA) are presented.\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Sec9\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e5.1. Stability analysis\\u003c/h2\\u003e\\n\\u003cp\\u003eTo perform stability analysis of Mount St. Helen, various combinations of \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e and k\\u003csub\\u003ee\\u003c/sub\\u003e were taken into account for this purpose. More precisely, the FOS was calculated for 100 samples for Sets 1 to 5. The FOS determined with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 and r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3 are illustrated in Fig.\\u0026nbsp;6 and Fig.\\u0026nbsp;7, respectively. According to the Fig.\\u0026nbsp;8, the FOS varies in the range of 1.311 to 2.864 and 0.904 to 2.022 for r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 and r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3, respectively. The maximum FOS values for r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 are 2.864, 2.589, 2.355, 2.152, and 1.975, while the minimum values are 1.901, 1.720, 1.565, 1.431, and 1.311. respectively, for Sets 1 to 5. Similarly, the maximum FOS values for r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3 are 2.022, 1.818, 1.644, 1.487, and 1.351, while the minimum values are 1.355, 1.219, 1.098, 0.942, and 0.904. respectively, for Sets 1 to 5. These values indicate that the FOS decreases with the increase in \\u003cem\\u003er\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eu\\u003c/em\\u003e\\u003c/sub\\u003e and k\\u003csub\\u003ee\\u003c/sub\\u003e values and vice versa. For better understanding, Fig.\\u0026nbsp;8 can be referred to.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec10\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e5.2. Model performance\\u003c/h2\\u003e\\n\\u003cp\\u003eThe performance of the employed paradigms along with their configurations are presented. Significantly, the model's performance was assessed by utilizing the training set to evaluate the correctness of the created paradigm. The testing dataset was subsequently employed to verify the model's predictive capability. However, a predictive model that demonstrated exceptional prediction accuracy throughout the validation phase was selected for evaluation. Notably, it is worthwhile to contemplate employing a data reshuffling strategy to choose an optimal framework. In this study, 5-fold cross validation technique was employed and the optimum model was selected as per testing set performance. It should also be emphasized that the selection of an optimum model requires appropriate tuning of hyper-parameters of the employed algorithms. During the training phase, it is crucial to have multiple sets of hyperparameters that have been well tuned. As stated, four standalone and one ensemble models were employed in this study, and hence, different hyper-parameters including n_estimators, n_estimators, min_samples_leaf, max_depth, etc., were tuned within a pre-specified range, as detailed in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e. The optimized values of these hyper-parameters are also tabulated in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003eDetails of hyper-parameters for the employed models.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eModels\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eHyper-parameters\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eValue considered\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eOptimum value\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003en_estimators\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 20 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e50\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003elearning_rate\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.1 to 1.0 by 0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003emin_samples_leaf\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1 to 10 by 1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003emax_depth\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 50 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e10\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003en_estimators\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 20 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e10\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003elearning_rate\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.1 to 1.0 by 0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003emax_depth\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 50 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e3\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003en_estimators\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 20 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e10\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003elearning_rate\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.1 to 1.0 by 0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003emax_depth\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 50 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e3\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003en_estimators\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e5 to 50 by 5\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e45\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003eUsing the details presented in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e, five paradigms were finalized and their performance are outlined in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e, Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e, and Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e. Herein, the performance for both training and testing sets are presented. According to the results, ETR exhibits higher precision in the training phase with R\\u003csup\\u003e2\\u003c/sup\\u003e of 1, 1, and 0.9999 against Cases-1, 2, and 3, respectively. However, in the testing phase, the proposed BG-ENSM realized highest precision with R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.9968, 0.9959, and 0.9985 against Cases-1, 2, and 3, respectively. The employed ETR is the second-best paradigm with R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.9905, 0.9892, and 0.9948 against Cases-1, 2, and 3, respectively. These results indicate that the proposed BG-ENSM paradigm is the most accurate model because a model attained higher precision during the testing phase. The employed ABR model demonstrates the lowest performance in both phases as indicated by its R\\u003csup\\u003e2\\u003c/sup\\u003e metric values of 0.9641 and 0.9395 against Case-1, 0.9570 and 0.9361 against Case-2, and 0.9698 and 0.9665 against Case-3 input combinations, respectively. To better demonstrate the results, scatterplot for the best performing modes is presented in Fig.\\u0026nbsp;9 for both the datasets.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab4\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 4\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003ePerformance parameters for Case-1.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eIndices\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eTraining\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eTesting\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eAdj.R\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9638\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9961\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9989\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9369\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9686\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9901\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9880\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9967\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eMAE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0582\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0008\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0001\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0199\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0079\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0620\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0416\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0238\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0299\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0142\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ePI\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8529\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9969\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9979\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9656\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9862\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.7910\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8852\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9505\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9342\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9745\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eR2\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9641\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9962\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9989\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9395\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9698\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9905\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9884\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9968\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eRMSE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0698\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0030\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0020\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0251\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0115\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0786\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0529\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0298\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0379\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0185\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eVAF\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e95.89\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.99\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e100.00\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.46\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.89\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e93.27\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e96.96\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.02\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e98.42\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.63\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eWI\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9886\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9986\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9997\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9806\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9920\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9975\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9957\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9990\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eWMAPE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0292\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0004\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0001\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0100\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0039\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0315\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0211\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0121\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0152\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0072\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab5\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 5\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003ePerformance parameters for Case-2.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eIndices\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eTraining\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eTesting\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eAdj.R\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9566\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9957\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9989\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9334\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9660\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9888\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9878\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9957\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eMAE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0435\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0010\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0001\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0151\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0063\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0453\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0305\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0190\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0214\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0118\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ePI\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8580\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9969\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9984\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9704\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9895\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8065\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8936\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9539\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9440\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9758\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eR2\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9570\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9958\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9989\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9361\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9674\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9892\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9883\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9959\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eRMSE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0525\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0029\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0016\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0192\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0083\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0579\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0398\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0235\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0279\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0152\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eVAF\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e95.40\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.99\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e100.00\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.38\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.89\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e93.11\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e96.74\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e98.86\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e98.40\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.53\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eWI\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9875\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9984\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9997\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9805\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9916\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9970\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9957\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9988\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eWMAPE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0312\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0007\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0001\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0109\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0045\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0329\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0221\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0138\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0155\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0086\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab6\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 6\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003ePerformance parameters for Case-3.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eIndices\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eTraining\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eTesting\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eABR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eDTR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eETR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eGBR\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eBG-ENSM\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eAdj.R\\u003csup\\u003e2\\u003c/sup\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9696\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9998\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9959\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9993\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9656\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9868\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9947\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9925\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9984\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eMAE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0671\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0026\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0001\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0265\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0078\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0659\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0348\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0231\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0322\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0125\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ePI\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8496\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9943\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9963\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9555\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9875\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.8430\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9288\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9607\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9414\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.9808\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eR2\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9698\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9998\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9959\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9993\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9665\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9871\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9948\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9926\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9985\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eRMSE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0829\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0054\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0035\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0340\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0111\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0819\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0451\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0287\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0406\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0160\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eVAF\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e96.29\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.98\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.99\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.36\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.93\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e95.93\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e98.71\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.48\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e98.95\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e99.84\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eWI\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9927\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1.0000\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9988\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9999\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9897\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9972\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9989\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9976\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.9996\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eWMAPE\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0396\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0015\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0001\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0157\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0046\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0394\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0208\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0138\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0192\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.0075\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003ctable id=\\\"Tab7\\\" border=\\\"1\\\"\\u003e\\u003ccaption\\u003e\\n\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 7\\u003c/div\\u003e\\n\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n\\u003cp\\u003eDetails of simulated datasets.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003c/caption\\u003e\\n\\u003cthead\\u003e\\n\\u003ctr\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSets\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth colspan=\\\"5\\\" align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eParameters with a specific mean\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003cth align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. ref.\\u003c/p\\u003e\\n\\u003c/th\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/thead\\u003e\\n\\u003ctbody\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ec (kN/m\\u003csup\\u003e2\\u003c/sup\\u003e)\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eϕ (\\u0026deg;)\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e\\u0026gamma; (kN/m\\u003csup\\u003e3\\u003c/sup\\u003e)\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003ek\\u003csub\\u003ee\\u003c/sub\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eru\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSet-A\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1010\\u0026ndash;1360 by 25\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e43\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e24\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0, 0.50. 0.10, 0.15, and 0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. 10a\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSet-B\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1010\\u0026ndash;1360 by 25\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e43\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e24\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0, 0.50. 0.10, 0.15, and 0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.3\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. 10b\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSet-C\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1010\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e43\\u0026ndash;43.70 by 0.05\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e24\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0, 0.50. 0.10, 0.15, and 0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. 10c\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSet-D\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1010\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e43\\u0026ndash;43.70 by 0.05\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e24\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0, 0.50. 0.10, 0.15, and 0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.3\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. 10d\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSet-E\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1010\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e43\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e22\\u0026ndash;23.10 by 0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0, 0.50. 0.10, 0.15, and 0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. 10e\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003ctr\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eSet-F\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e1010\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e43\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e22\\u0026ndash;23.10 by 0.1\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0, 0.50. 0.10, 0.15, and 0.20\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003e0.3\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003ctd align=\\\"left\\\"\\u003e\\n\\u003cp\\u003eFig. 10f\\u003c/p\\u003e\\n\\u003c/td\\u003e\\n\\u003c/tr\\u003e\\n\\u003c/tbody\\u003e\\n\\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec11\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e5.3. Parametric analysis\\u003c/h2\\u003e\\n\\u003cp\\u003eThis study also examines the practicality of influencing parameters by PA. The most optimal BG-ENSM model was utilized for this objective. It is important to note that the goal of PA is to assess the effectiveness of the BG-ENSM model in addressing the issue of overfitting. In order to achieve this objective, the impact of input variables on the FOS was examined based on a virtual dataset. The specific information regarding this dataset is given in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e. There were six different combinations of influencing parameters that were investigated, labelled as Set-A to Set-F. In Sets-A and B, the parameter, c was simulated between 1010 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e and 1360 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e in increments of 25 kN/m\\u003csup\\u003e2\\u003c/sup\\u003e, resulting in a total of 15 datasets. The values of ϕ and \\u0026gamma; were assigned as 43\\u0026deg; and 24 kN/m\\u003csup\\u003e3\\u003c/sup\\u003e, respectively, and were consistent for all five k\\u003csub\\u003ee\\u003c/sub\\u003e values. The values of r\\u003csub\\u003eu\\u003c/sub\\u003e were assigned as 0 and 0.3 for Sets-A and B, respectively. Similarly, datasets for Sets-C and D were generated by systematically changing the value of ϕ from 43\\u0026deg; to 43.70\\u0026deg; in increments of 0.05\\u0026deg;, while leaving all other parameters fixed. The details of other datasets can be seen in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e.\\u003c/p\\u003e\\n\\u003cp\\u003eFigure\\u0026nbsp;10 depict trends using smooth curves and demonstrate that the FOS increases when c (refer to Fig.\\u0026nbsp;10a and b) and ϕ (refer to Fig.\\u0026nbsp;10c and d) increase. In contrast, \\u0026gamma; exhibits a behavior that is completely opposite, as evidenced from Fig.\\u0026nbsp;10e and f. Nevertheless, Fig.\\u0026nbsp;10a-f exhibit a comparable pattern of variation characterized by smooth concave curves which indicates the proposed BG-ENSM framework is capable of accurately estimating the FOS and hence can be considered as a viable framework for stability assessments of the said mountain.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003cdiv id=\\\"Sec12\\\" class=\\\"Section2\\\"\\u003e\\n\\u003ch2\\u003e5.4. Discussion of results\\u003c/h2\\u003e\\n\\u003cp\\u003eThe performance of the employed paradigms is discussed above. Specifically, four ensemble-based soft computing algorithms namely ABR, DTR, ETR, and GBR, and a bagging-based ensemble framework, BG-ENSM, were employed/developed for stability estimation of Mount St. Helens. Initially, a DEM of the said mountain was created followed by stability analysis using Scoops3D. For this purpose, 100 samples were generated at random and Scoops3D was used to determine the FOS. Five different combinations of k\\u003csub\\u003ee\\u003c/sub\\u003e were considered to determine the FOS with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 and r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3 cases. In total, 1000 records were extracted through Scoops3D and used in computational modelling for the estimation of FOS based on different influencing variables including \\u003cem\\u003ec\\u003c/em\\u003e, ϕ, \\u0026gamma;, r\\u003csub\\u003eu\\u003c/sub\\u003e, and k\\u003csub\\u003ee\\u003c/sub\\u003e values.\\u003c/p\\u003e\\n\\u003cp\\u003eSignificantly, the stability assessments were categorized into three scenarios based on the pore-pressure ratio examined in this study. During computational modelling, the values of r\\u003csub\\u003eu\\u003c/sub\\u003e were set to 0 and 0.3 in Cases-1 and 2, respectively. In Case-3, both r\\u003csub\\u003eu\\u003c/sub\\u003e values were taken into account. Thus, a total of 500 datasets were taken into account for Cases-1 and 2, whereas Case-3 combination involved 1000 datasets. The model creation utilized a training set consisting of 80% of the samples, whereas the model validation was performed using a testing set including 20% of the samples. The results of testing set are presented in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e \\u0026ndash; Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e, the BG-ENSM framework that was developed achieved highly accurate estimates of FOS. It had R\\u003csup\\u003e2\\u003c/sup\\u003e values of 0.9968, 0.9959, and 0.9985 for Cases-1, 2, and 3, respectively. Among the ensemble frameworks, the ETR model performed second best with R\\u003csup\\u003e2\\u003c/sup\\u003e values of 0.9905, 0.9892, and 0.9948 for Cases-1, 2, and 3, respectively. On the other hand, the ABR model was found to be the least effective, with R\\u003csup\\u003e2\\u003c/sup\\u003e values of 0.9395, 0.9361, and 0.9665 for Cases-1, 2, and 3, respectively. This level of performance is highly satisfactory when compared to other models that have been built. However, the BG-ENSM model that was constructed achieved the highest level of accuracy throughout the testing phase of FOS estimation.\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003cdiv class=\\\"colspec\\\" align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003c/div\\u003e\"},{\"header\":\"6. Summary and Conclusion\",\"content\":\"\\u003cp\\u003eThe present study proposes a bagging-based ensemble paradigm for stability estimation of Mount St. Helens. The proposed technique presents a BG-ENSM framework that was utilized to evaluate the failure risk of the mountain. The effect of r\\u003csub\\u003eu\\u003c/sub\\u003e was also studied considering three different cases viz., r\\u003csub\\u003eu\\u003c/sub\\u003e = 0, r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3, and r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 and 0.3. The outcomes of the developed BG-ENSM framework were compared with four additional ensemble-based frameworks including ABR, DTR, ETR, and GBR. Based on the analysis presented above, it is seen that the proposed BG-ENSM framework achieved the most desired estimation of FOS with R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.9968, 0.9959, and 0.9985 against Cases-1, 2, and 3, respectively. However, among the employed ensemble framework, ETR is the second-best framework with R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.9905, 0.9892, and 0.9948 against Cases-1, 2, and 3, respectively; while the ABR was seen as the least-effective model with R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.9395, 0.9361, and 0.9665 against Cases-1, 2, and 3, respectively. Overall, the proposed BG-ENSM framework gives the most accurate estimation of the FOS in all cases and can be used as a promising approach for stability estimation of Mount St. Helens.\\u003c/p\\u003e \\u003cp\\u003eThe BG-ENSM framework offers several notable advantages from the standpoint of computational modelling: (a) higher predictive precision; (b) higher generalization ability; (c) lesser computational cost, and (d) a combined model. Nevertheless, choosing the most effective BG-ENSM paradigm requires multiple iterations and careful adjustment of hyper-parameters, which is a limitation of the suggested approach. Another limitation is that the solution is not guaranteed to converge to the global minimum due to amalgamation of multiple algorithms; as a result, the performance of a BG-ENSM paradigm could be affected in many situations. Conversely, crucial input parameters such as precipitation, permeability, and rock type, among others, were not accounted for in the computational modelling process. These parameters ought to have been incorporated into the developed model to render it a more universally applicable technique for determining the FOS of additional mountains. However, to the best of the authors' knowledge, this research represents the initial implementation of an ensemble-based framework for estimating the stability of Mount St. Helens under both seismic and non-seismic conditions.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eAuthor contributions\\u003c/strong\\u003e: All authors contributed equally in this manuscript.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eFunding\\u003c/strong\\u003e: Nil.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eData availability\\u003c/strong\\u003e: All data used during the study are available from the corresponding author.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCompeting interest\\u003c/strong\\u003e: None declared.\\u003c/p\\u003e\\n\\u003cp\\u003eConflict of interest: None.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAcknowledgements\\u003c/strong\\u003e: Nil\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eEthical statements\\u003c/strong\\u003e: No conflict of interest.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eSupplementary Information\\u003c/strong\\u003e: Not applicable\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eArmaghani DJ, Mohamad ET, Narayanasamy MS, et al (2017) Development of hybrid intelligent models for predicting TBM penetration rate in hard rock condition. 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Saf Sci 118:505\\u0026ndash;518\\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\":\"info@researchsquare.com\",\"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\":\"3D slope stability, Rock slope stability, Geological engineering, Artificial intelligence, Ensemble learning\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-4417103/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-4417103/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThis research investigates the application of ensemble-based computational paradigms to estimate the stability of Mount St. Helens. Scoops3D was initially utilized for conducting slope stability investigation, followed by computational modelling of the factor of safety (FOS) employing various influencing parameters. Four base models including AdaBoost regressor, decision tree regressor, extra tree regressor, and gradient boosting regressor, and a bagging-based ensemble learning (BG-ENSM) framework, were used for this purpose. In both seismic and non-seismic conditions, the effect of pore-pressure ratio (r\\u003csub\\u003eu\\u003c/sub\\u003e) on the stability of Mount St. Helens was investigated in three different combinations (i.e., Cases-1, 2, and 3) with r\\u003csub\\u003eu\\u003c/sub\\u003e = 0, r\\u003csub\\u003eu\\u003c/sub\\u003e = 0.3, and r\\u003csub\\u003eu\\u003c/sub\\u003e = 0 and 0.3. Post computational modelling, the outcomes of the implemented paradigms were evaluated based on several indicators. Experimental outcomes exhibit that the proposed BG-ENSM framework achieved the most desired estimation of FOS with R\\u003csup\\u003e2\\u003c/sup\\u003e of 0.9968, 0.9959, and 0.9985 against Cases-1, 2, and 3, respectively. Based on the overall results and the outcomes of parametric study, the employed BG-ENSM framework can be considered as a viable tool for stability estimation of Mount St. Helens considering the effect of r\\u003csub\\u003eu\\u003c/sub\\u003e in seismic and non-seismic conditions.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Stability estimation of Mount St. Helens using Scoops3D and ensemble learning paradigms\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-05-30 18:48:02\",\"doi\":\"10.21203/rs.3.rs-4417103/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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\":\"02418016-f374-418b-8ad1-b651175a5e58\",\"owner\":[],\"postedDate\":\"May 30th, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2024-06-07T09:40:59+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2024-05-30 18:48:02\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-4417103\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-4417103\",\"identity\":\"rs-4417103\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}