Multivariate Adaptive Regression Splines Model Research Articles

Exploring soil pollution patterns in Ghana's northeastern mining zone using machine learning models

This study assessed the pollution status and effectiveness of machine learning models in predicting pollution indices in soils from a mining area in Northeastern Ghana. 552 soil samples were analysed with an Energy Dispersive X-ray Fluorescence (ED-XRF) spectrometer for their elemental concentrations. Four pollution indices; Nemerow Integrated Pollution Index (NIPI), degree of contamination (Cdeg), modified degree of contamination (mCdeg) and Pollution Load Index (PLI). Additionally, the Multivariate Adaptive Regression Splines (MARS) machine learning approach were used. The high CV%, skewness, and kurtosis values show a high degree of variability and uneven distribution patterns which denotes dispersed hotspots that can be interpreted as an influence of gold anomalies and illegal mining activities in the area. V (120.86 mg/L), Cr (242.42 mg/L), Co (30.92 mg/L) Ba (337.62 mg/L), and Zn (35.42 mg/L) recorded values higher than the global and regional contaminant thresholds. The NIPI shows that 46.74% and 26.81% of samples are slightly and moderately polluted respectively. The Cdeg analysis supports these findings, with 36.96% and 41.49% of samples classified as having “moderate” to “considerable” contamination, respectively. The PLI indicates progressive soil quality deterioration (43.84%) of samples reflecting substantial environmental disturbance. The pollution indices show the effect of illegal mining on Shaega, Buin and other areas in the eastern boundary of the study. The MARS models developed for the study demonstrated high predictive capabilities with an R2 value of 0.9665 for model 1 (NIPI), and RMSE and MAE values of 0.8227 and 0.4287 respectively. For model 2 (Cdeg), R2 value of 0.9863, RMSE and MAE of 1.0416 and 0.6181, respectively. Model 3 (mCdeg) produced an R2 value of 0.9844, RMSE and MAE of 0.1225 and 0.0670. These findings suggest MARS models can be an integral tool for soil quality analysis in cooperation with pollution indices. The study suggests that remedial and legislative measures be implemented to address the issue of illegal mining in the area.

Bond strength prediction of externally bonded reinforcement on groove method (EBROG) using MARS-POA

The Externally Bonded Reinforcement on Grooves (EBROG) method represents an advancement in externally bonded reinforcement (EBR) techniques, specifically addressing the challenge of premature debonding often encountered in conventional Fiber Reinforced Polymer (FRP) applications directly bonded to concrete. This article introduces a novel and straightforward mathematical equation for predicting bond strength in the EBROG method using soft computing techniques for the first time. The study delves into the combined potential of the Multivariate Adaptive Regression Spline (MARS) model and the Pelican Optimization Algorithm (POA) for bond strength prediction in this method. The input parameters include FRP width, FRP thickness, elasticity modulus of FRP, concrete strength, groove length, groove width, and groove depth, while the output is EBROG bond strength. The study demonstrates exceptional accuracy with R2 values of 0.9629 for training and 0.9623 for testing, highlighting the model’s precision. The proposed bond strength prediction equation for the EBROG method undergoes validation against existing models, encompassing thirteen equations for EBR and a recent one specific to EBROG. Statistical metrics confirm the accuracy and reliability of the proposed equation. Notably, FRP stiffness emerges as the parameter with the highest relative importance, while groove width exhibits the lowest impact on bond strength.

Evaluating machine learning models in predicting GRI drought indicators (case study: Ajabshir area)

Examining the condition of groundwater resources and the impact of droughts is valuable for effective water resources management. Today, machine learning (ML) models are recognized as one of the useful tools in time series predictions. In this study, the groundwater condition of one of the most important aquifers in northwest Iran was investigated using MODFLOW, followed by estimating the groundwater resource index (GRI) utilizing the multivariate adaptive regression spline (MARS) and least squares support vector regression (LSSVR) for a period between 2001 and 2019. Meteorological and hydrological drought indicators along with precipitation and flow rate were used as input variables for prediction. The simulation results revealed a groundwater level decrease since the aquifer withdrawal amount is more than the recharge amount. Besides, results showed that there is a limited interaction between surface water and groundwater resources, mainly caused by the decrease in the river flow and aquifer groundwater level drop. Both ML models performed well in GRI estimation, using groundwater flow, streamflow drought index, standardized precipitation index, and runoff as input variables. The performance of the MARS model with RMSE, MAE, and NSE error evaluation criteria of 0.37, − 0.19, and 0.83, respectively, exerted slightly better results than LSSVR with RMSE, MAE, and NSE of 0.48, − 0.06, and 0.80, respectively. The findings reveal the appropriate performance of both models in forecasting drought indicators, highlighting the necessity of using ML models in hydrology and drought prediction problems.

Reliability‐based state parameter liquefaction probability prediction using soft computing techniques

The state parameter (ѱ) accounts for both relative density and effective stress, which influence the cyclic stress or liquefaction characteristic of the soil significantly. This study presents a ѱ‐based probabilistic liquefaction evaluation method using six soft computing (SC) techniques. The liquefaction probability of failure (PL) is calculated using the first‐order second moment (FOSM) method based on the cone penetration test (CPT) database. Then, six SC techniques, such as Gaussian process regression (GPR), relevance vector machine (RVM), functional network (FN), genetic programming (GP), minimax probability machine regression (MPMR) and multivariate adaptive regression splines (MARS), are used to predict PL. The performance of these models is examined using nine statistical indices. Additionally, plots such as regression plots, Taylor diagrams, error matrix and rank analysis are shown to assess the SC model's performance. Finally, sensitivity analysis is performed using the cosine amplitude method (CAM) to assess the influence of input parameters on output. The current study demonstrates that SC models based on state parameter predict PL effectively. RVM and MPMR models closely follow the GPR model in terms of performance, which is superior to the other models. Notably, two equations are generated using GP and MARS models to predict PL. The results of the sensitivity analysis reveal the magnitude of earthquake (Mw) as the most sensitive parameter. The outcomes of this research will offer risk evaluations for geotechnical engineering designs and expand the use of state parameter‐based SC models in liquefaction analysis.

Black-White Differences in Chronic Stress Exposures to Predict Preterm Birth: Interpretable, Race/Ethnicity-Specific Machine Learning Models.

We developed Multivariate Adaptive Regression Splines (MARS) machine learning models of chronic stressors using the Pregnancy Risk Assessment Monitoring System data (2012-2017) to predict preterm birth (PTB) more accurately and identify chronic stressors driving PTB among non-Hispanic (N-H) Black and N-H White pregnant women in the U.S. We trained the MARS models using 5-fold cross-validation, whose performance was evaluated with AUC. We computed variable importance for PTB prediction. Our models showed high accuracy (AUC: 0.754-0.765). The number of prenatal care visits, premature rupture of membrane, and medical conditions were the most important variables in predicting PTB across the populations. Chronic stressors (e.g., low maternal education and violence) and their correlates were pivotal for PTB prediction only for N-H Black women. Interpretable, race/ethnicity-specific MARS models can predict PTB accurately and explain the most impactful life stressors and their magnitude of effect on PTB risk among N-H Black and N-H White women.

Use of data mining algorithms to predict body weight of Dorper sheep Breed in two selected villages of Lepelle-Nkumpi local municipality in Limpopo province, South Africa

Sheep farmers in village areas find it difficult to estimate body weight without the weighing tools. The best fitted model for estimation of sheep body weight is not conclusive. Classification and regression tree (CART), Chi-square automatic interaction detection (CHAID), Exhaustive chi-square automatic interaction detection (Ex-CHAID) and Multivariate adaptive regression spline (MARS) were used to predict body weight (BW) of 306 Dorper sheep (female = 244 and male = 62) aged 1 to 2 years from linear body measurement traits such as rump height (RH), rump length (RL), heart girth (HG), withers height (WH), and body length (BL). Goodness of fit criteria's such as Pearson's correlation coefficients (r), coefficient of determination (R2), Akaike's information criterion AIC and adjusted R2 (Adj.R2) were computed for data mining algorithms performance assessment. The results indicated that MARS was the best data mining algorithm with r of 0.979, R2 of 0.958, Adj.R2 of 0.957, RMSE of 2.503 and AIC of 422.25. The MARS model provided the most appropriate predictive capability in the prediction of body weight for Dorper sheep with HG, WH, RH, BL, and sex (male) as the important traits. As a result, MARS data mining algorithm might be used to identify factors that might be vital to improve body weight of Dorper sheep for breeding programs.

Estimation curve of multivariate adaptive biresponse fuzzy clustering means regression splines approach to stunting and wasting cases in Southeast Sulawesi

This article offers a new method of clustering data. This method is constructed by combining the multivariate adaptive regression spline biresponse continuous model (MARSBC) with the fuzzy clustering means (FCM) approach, called the multivariate adaptive biresponse fuzzy clustering means regression splines (MABFCMRS) model. This method uses patterns obtained from the MARSBC model to separate data into specific groups. Observing unobserved heterogeneity that has not been obtained from previous models. Unlike the classic fuzzy clustering methods that use euclid distances to determine the weight of the object, this method uses the total square of the massed residual distance generated by the MARSBC model. Theoretical studies were conducted to obtain predictions for the MABFCMRS model parameters. Furthermore, this method was applied to stunting and wasting cases in southeastern Sulawesi province. The results of the research show that in the case of stunting modeling and wasting in southeast Sulawesi province, the best clusters were obtained based on the criteria of partition coefficient (PC) and modification of PC (MPC). This research is able to show that the clustering process using the MABFCMRS model has been able to improve generalized cross-validation (GCV) values and determination coefficients.•This paper presents a new, effective method for clustering data based on unobserved heterogeneity.•This is applicable to sizable samples with 3 to 20 predictors.

A framework for estimating the matric suction in unsaturated soils using multiple artificial intelligence techniques

AbstractImplementation of the state‐of‐the‐art understanding of the mechanics of unsaturated soils into geotechnical engineering practice is partly limited due to the lack of quick, reliable, and economical techniques for matric suction measurement. Matric suction is one of the key stress state variables that significantly influences the hydro‐mechanical behavior of unsaturated soils. In this paper, to address this objective, two artificial intelligence (AI) models were developed for estimating matric suction in unsaturated soils based on the particle swarm optimization support vector regression (PSO‐SVR) and multivariate adaptive regression spline (MARS) algorithms. The results suggest that both these models can reasonably estimate matric suction. Compared to the MARS model, the PSO‐SVR model can achieve higher accuracy. Nonetheless, the MARS model facilitates the sensitivity analysis and the selection of essential inputs. A novel integrated framework is proposed and validated, leveraging the strengths, and alleviating the limitations of the PSO‐SVR and MARS algorithms for reliable and rapid estimation of matric suction in the range of 0–1500 kPa for low plastic soils (0 < Ip ≤ 7). Six inputs are required to use this model successfully; some can be measured using conventional laboratory tests, and others can be calculated from mass‐volume relationships.

Strength assessment of structural masonry walls: analysis based on machine learning approaches

ABSTRACT In conventional masonry buildings, masonry walls are key structural load-bearing elements. Likewise, masonry infill walls strengthen framed constructions against lateral stress. The material characteristics of brick units and mortar determine the compressive strength of structural masonry walls. In this study, advanced machine learning (ML) techniques were utilized to estimate the compressive strength of structural masonry walls based on the material properties of brick units and mortar. The Young’s modulus of brick units (Eu), compressive strength of brick units (Fcu), Young’s modulus of mortar (Em), and compressive strength of mortar (Fcm) were used as input parameters to model the compressive strength (Fc) of the structural masonry wall. Gradient Tree Boosting (GTB), Elman Neural Network (ENN), and Multivariate Adaptive Regression Splines (MARS) were developed using four diverse input and output (I/O) combinations to explore the effect of each input parameter on output estimation. The data used for modeling were obtained from prior studies published in the literature. The model’s performance was evaluated based on different statistical (error and efficiency) indices. For the third and fourth (I/O) combinations, the MARS model significantly outperformed other models. However, for the first I/O combination, the GTB model performed well. The study also revealed that the compressive strength of a structural masonry wall is more likely to depend on the strength and quality of the brick units than on the strength of the mortar.

Optimal Implant Sizing Using Machine Learning Is Associated With Increased Range of Motion After Cervical Disk Arthroplasty.

Cervical disk arthroplasty (CDA) offers the advantage of motion preservation in the treatment of focal cervical pathology. At present, implant sizing is performed using subjective tactile feedback and imaging of trial cages. This study aims to construct interpretable machine learning (IML) models to accurately predict postoperative range of motion (ROM) and identify the optimal implant sizes that maximize ROM in patients undergoing CDA. Adult patients who underwent CDA for single-level disease from 2012 to 2020 were identified. Patient demographics, comorbidities, and outcomes were collected, including symptoms, examination findings, subsidence, and reoperation. Affected disk height, healthy rostral disk height, and implant height were collected at sequential time points. Linear regression and IML models, including bagged regression tree, bagged multivariate adaptive regression spline, and k-nearest neighbors, were used to predict ROM change. Model performance was assessed by calculating the root mean square error (RMSE) between predicted and actual changes in ROM in the validation cohort. Variable importance was assessed using RMSE loss. Area under the curve analyses were performed to identify the ideal implant size cutoffs in predicting improved ROM. Forty-seven patients were included. The average RMSE between predicted and actual ROM was 7.6° (range: 5.8-10.1) in the k-nearest neighbors model, 7.8° (range: 6.5-10.0) in the bagged regression tree model, 7.8° (range: 6.2-10.0) in the bagged multivariate adaptive regression spline model, and 15.8° (range: 14.3-17.5°) in a linear regression model. In the highest-performing IML model, graft size was the most important predictor with RMSE loss of 6.2, followed by age (RMSE loss = 5.9) and preoperative caudal disk height (RMSE loss = 5.8). Implant size at 110% of the normal adjacent disk height was the optimal cutoff associated with improved ROM. IML models can reliably predict change in ROM after CDA within an average of 7.6 degrees of error. Implants sized comparably with the healthy adjacent disk may maximize ROM.

Modeling of kappa factor using multivariate adaptive regression splines: application to the western Türkiye ground motion dataset

The recent seismic activity on Türkiye’s west coast, especially in the Aegean Sea region, shows that this region requires further attention. The region has significant seismic hazards because of its location in an active tectonic regime of North–South extension with multiple basin structures on soft soil deposits. Recently, despite being 70 km from the earthquake source, the Samos event (with a moment magnitude of 7.0 on October 30, 2020) caused significant localized damage and collapse in the Izmir city center due to a combination of basin effects and structural susceptibility. Despite this activity, research on site characterization and site response modeling, such as local velocity models and kappa estimates, remains sparse in this region. Kappa values display regional characteristics, necessitating the use of local kappa estimations from previous earthquake data in region–specific applications. Kappa estimates are multivariate and incorporate several characteristics such as magnitude and distance. In this study, we assess and predict the trend in mean kappa values using three–component strong–ground motion data from accelerometer sites with known VS30 values throughout western Türkiye. Multiple linear regression (MLR) and multivariate adaptive regression splines (MARS) were used to build the prediction models. The effects of epicentral distance Repi, magnitude Mw, and site class (VS30) were investigated, and the contributions of each parameter were examined using a large dataset containing recent seismic activity. The models were evaluated using well–known statistical accuracy criteria for kappa assessment. In all performance measures, the MARS model outperforms the MLR model across the selected sites.

Exploring the strategic role of Marketer-Generated-Content analytics towards Airbnb hosts sales optimization

ABSTRACT Although user-generated content is reported to improve Airbnb host’s sales, the impact of Marketer-Generated Content (MGC) on the minimum sales generated from the reviewers who have reviewed the MGC is yet to be explored. This study examines MGC of title descriptions analysis from the City of Los Angeles listing data to understand their importance in predicting hosts’ net sales. The analysis employs two complementary econometric approaches: parametric multiple regression and the non-parametric multivariate adaptive regression spline model across three neighbourhood groups and two price groups. The findings indicate hosts can employ MGC to optimize sales and should highlight feature words in the title that best reflect the property characteristics and appeal to a target group that may be location-specific, price-sensitive, or both. The title should be informative and detailed within a limit of 10 words. The novelty of the work is to identify the influence of total sales for respective feature words from the title description of Airbnb property and to analyze their uses in marketing communications. The practical implications indicate that host-generated feature words are crucial in maximizing net sales for the property.

Identifying and Exploring the Impact Factors for Intraocular Pressure Prediction in Myopic Children with Atropine Control Utilizing Multivariate Adaptive Regression Splines.

The treatment of childhood myopia often involves the use of topical atropine, which has been demonstrated to be effective in decelerating the progression of myopia. It is crucial to monitor intraocular pressure (IOP) to ensure the safety of topical atropine. This study aims to identify the optimal machine learning IOP-monitoring module and establish a precise baseline IOP as a clinical safety reference for atropine medication. Data from 1545 eyes of 1171 children receiving atropine for myopia were retrospectively analyzed. Nineteen variables including patient demographics, medical history, refractive error, and IOP measurements were considered. The data were analyzed using a multivariate adaptive regression spline (MARS) model to analyze the impact of different factors on the End IOP. The MARS model identified age, baseline IOP, End Spherical, duration of previous atropine treatment, and duration of current atropine treatment as the five most significant factors influencing the End IOP. The outcomes revealed that the baseline IOP had the most significant effect on final IOP, exhibiting a notable knot at 14 mmHg. When the baseline IOP was equal to or exceeded 14 mmHg, there was a positive correlation between atropine use and End IOP, suggesting that atropine may increase the End IOP in children with a baseline IOP greater than 14 mmHg. MARS model demonstrates a better ability to capture nonlinearity than classic multiple linear regression for predicting End IOP. It is crucial to acknowledge that administrating atropine may elevate intraocular pressure when the baseline IOP exceeds 14 mmHg. These findings offer valuable insights into factors affecting IOP in children undergoing atropine treatment for myopia, enabling clinicians to make informed decisions regarding treatment options.

Local scour depth at piles group exposed to regular waves: On the assessment of expressions based on classification concepts and evolutionary algorithms

An accurate estimation of local scour depth around piles group is inevitably essential to provide stability of marine structures. Over the past decades, many investigations have been made to understand the scouring process at piles group exposed to waves for field and experimental scales. This study aims to predict the wave-induced local scour depth by various robust Data Driven Models (DDMs) and Machine Learning Models (MLMs) developed by classification and evolutionary concepts: Model Tree (MT), Evolutionary Polynomial Regression (EPR), Multivariate Adaptive Regression Spline (MARS), and Gene-Expression Programming (GEP). From relevant literature, 125 data series were employed to provide empirical relationships for scour depth predictions. The raw variables were related to bed sediment, pile configuration, pile geometry, approaching flow, and wave characteristics. Non-dimensional parameters have been obtained through the Buckingham theorem in order to control local scour depth. In this way, the ratio of spacing between piles to pile diameter (G/D), sediment number (Ns), pile arrangement number (ratio of the number of piles parallel to the flow; m; to the number of piles normal to the flow; n), Shields parameter (θ), and Keulegan-Carpenter (KC) were considered. From the training and testing stages of Artificial Intelligence Models (AIMs), it was found that regression equation given by MARS model provided better performance (e.g., Correlation Coefficient [R] = 0.9297, Root Mean Square Error [RMSE] = 0.3489, and Scatter Index [SI] = 0.2765) than other AI models’ efficiency. Additionally, the performance of AI models was assessed for various ranges of dimensionless parameters (i.e., G/D, Ns, and θ) versus KC variation. MARS model had the best performance for G/D = 0–1 and KC < 10 (R = 0.9917 and RMSE = 0.2198) and 0.4≤θ < 0.5 and 15 < KC < 25 whereas EPR model had promising efficiency in the its highest level for Ns = 1–3 and 10 < KC ≤ 15 (R = 0.9941 and RMSE = 0.0771) than other AI models. For the sensitivity analysis, the mutation rate and number of chromosomes are examined for the GEP model, the K-fold number and number of parameters for the MARS model, and the number of algebraic terms and number of chromosomes for the EPR model. Furthermore, ranking analysis of AI models indicated that MARS model had the best performance (Ranking Performance Index [RPI] = 0.7348) and followed by GEP (0.3412), M5MT (0.2999), and EPR (0.2848).

Multivariate adaptive regression splines-assisted approximate Bayesian computation for calibration of complex hydrological models

Abstract Approximate Bayesian computation (ABC) relaxes the need to derive explicit likelihood functions required by formal Bayesian analysis. However, the high computational cost of evaluating models limits the application of Bayesian inference in hydrological modeling. In this paper, multivariate adaptive regression splines (MARS) are used to expedite the ABC calibration process. The MARS model is trained using 6,561 runoff simulations generated by the soil and water assessment tool (SWAT) model and subsequently replaces the SWAT model to calculate the objective functions in ABC and multi-objective evolutionary algorithm (MOEA). In experiments, MARS can successfully reproduce the runoff time series simulations of the SWAT model at a low time cost, with a runoff variance determination coefficient of 0.90 as compared to the Monte Carlo method. MARS-assisted ABC can quickly and accurately estimate the parameter distributions of the SWAT model. The comparison of ABC with non-Bayesian MOEAs helps in the selection of an appropriate calibration approach.

Landslide susceptibility analysis in the Bhilangana Basin (India) using GIS-based machine learning methods

Landslides are frequent natural hazards in mountainous regions, and harshly upset people's lives and livelihoods. In the present study, we have carried out an analysis of seven GIS-based machine-learning techniques; and asses their performance for landslide susceptibility mapping (LSM) in the Bhilangana Basin, Garhwal Himalaya. A landslide inventory consisting of 423 polygons was prepared using repeated field investigations, and multi-dated satellite images for the periods between 2000 and 2022. The landslide dataset was classified into two groups: training (70%) and test dataset (30%), and 12 predictive variables were used for the LSM. The methods used to produce LSM are boosted regression tree (BRT), Fisher discriminant analysis (FDA), generalized linear model (GLM), multivariate adaptive regression splines (MARS), model-architect analysis (MDA), random forest (RF) and support vector machine (SVM). The sensitivity and performance of these models to predict landslide susceptible areas were carried out using the area under the curve (AUC) method. The RF model (AUC = 0.988) has given the highest precision indicating the best performance. Though MARS (0.974), SVM (0.965) and MDA (0.952) models have also performed adequately for the LSM (all have AUC values above 0.95), however, it is recommended that the RF model is highly suitable for LSM in the mountainous region.

Classification of anemia using Harris hawks optimization method and multivariate adaptive regression spline

Data mining methods are important for the diagnosis and prediction of diseases. Early and accurate diagnosis of patients is vital for their treatment. Various methods have been used in the literature to classify anemia. However, due to the different characteristics of patient datasets, changes in dataset sizes, different parameter numbers and features, and different numbers of patient records, algorithm performances vary according to datasets. In this study, the Harris hawks algorithm (HHA) and the multivariate adaptive regression spline (MARS) were used to classify anemia based on blood data of 1732 patients from the Kaggle database of patients with and without anemia. Six different algorithms were proposed to determine the parameters of the linear anemia approximation, namely multilinear form HHA, multilinear quadratic form HHA, multilinear exponential form HHA, first-order MARS model, second-order MARS model, and the best performing MARS model. The performance of the six proposed algorithms has been analyzed and found to be better than the previous studies in the literature.

Modeling the compressive strength of binary and ternary blended high-performance concrete mixtures using ensemble machine learning models

In the present study, the compressive strength of binary and ternary blended high-performance concrete mixtures was modeled using different machine learning tools, such as artificial neural network (ANN), gradient tree boosting (GTB), and multivariate adaptive regression splines (MARS). The compressive strength of binary and ternary blended concrete at 28 days of curing period was modeled using seven quantitative input parameters such as cement, blast furnace slag, fly ash, superplasticizer, water, coarse aggregate, and fine aggregate based on three different training and testing (Tr–Te) scenarios. The performance of the models developed was analyzed based on several statistical evaluation metrics, of error and efficiency. During the testing phase, the compressive strength estimates obtained via modeling using ANN, GTB, and MARS had Kling–Gupta efficiency (KGE) values of 0.8389, 0.8602, and 0.8423, respectively, for the first Tr–Te scenario; similarly, the KGE values were 0.8025/0.8830, 0.8541/0.8901, and 0.8434/0.8582, respectively, for the second/third Tr–Te scenarios. The estimation accuracy of the GTB model was relatively superior to that of the ANN and MARS models, taking into consideration both the error and efficiency indices. All three models perform relatively well for the first I/O combination compared to the other two combinations.

Design of experiments for the stochastic unit commitment with economic dispatch models

We develop a Design and Analysis of the Computer Experiments (DACE) approach to the stochastic unit commitment problem for power systems with significant renewable integration. For this purpose, we use a two-stage stochastic programming formulation of the stochastic unit commitment-economic dispatch problem. Typically, a sample average approximation of the true problem is solved using a cutting plane method (such as the L-shaped method) or scenario decomposition (such as Progressive Hedging) algorithms. However, when the number of scenarios increases, these solution methods become computationally prohibitive. To address this challenge, we develop a novel DACE approach that exploits the structure of the first-stage unit commitment decision space in a design of experiments, uses features based upon solar generation, and trains a multivariate adaptive regression splines model to approximate the second stage of the stochastic unit commitment-economic dispatch problem. We conduct experiments on two modified IEEE-57 and IEEE-118 test systems and assess the quality of the solutions obtained from both the DACE and the L-shaped methods in a replicated procedure. The results obtained from this approach attest to the significant improvement in the computational performance of the DACE approach over the traditional L-shaped method.

Vulnerability of the rip current phenomenon in marine environments using machine learning models

Hidden and perilous rip currents are one of the primary factors leading to drownings of beach swimmers. By identifying the coastal areas with the highest likelihood of generating rip currents, it becomes possible to prevent fatalities and mitigate economic losses associated with these hazardous currents. Rip currents are characterized as streams of water moving towards the open sea, forming within the area where waves break, due to variations in wave-induced radiation stresses and pressure along the coastline. This study utilized nine different Machine Learning (ML) models, including M5 Model Tree (MT), Multivariate Adaptive Regression Spline (MARS), Gene Expression Programming (GEP), Evolutionary Polynomial Regression (EPR), Random Forest (RF), Support Vector Machine (SVM), Extreme Gradient Boosting (XGBoost), Adaptive Boosting (AdaBoost), and Stacked ML models, to estimate the Relative Tide Range (RTR) values for 50 southern beaches in China. Through this approach, we gathered a reliable dataset from prior research conducted on the southern coast of China. In this study, two parameters, namely dimensionless fall velocity parameter (Ω) and tide range (TR) are used to predict the vulnerability of rip current event. The results of the AI models were assessed by various statistical analyses (Correlation of Coefficient [R], Root Mean Square Error [RMSE], violin diagram, heatmap, and taylor diagram) for training and testing stages. Accordingly, the MARS model exhibited superior performance compared to other AI models in accurately predicting the RTR value. The outcomes substantiated the significant effectiveness and capability in estimating the RTR with high accuracy. Southern China coasts have relative high risk level of rip current, necessitating the attention and strategic management of this dangerous current by the beach managers.