Multivariate Adaptive Regression Splines Model Research Articles

Dynamic Transcriptomic and Phosphoproteomic Analysis During Cell Wall Stress in Aspergillus nidulans

The fungal cell-wall integrity signaling (CWIS) pathway regulates cellular response to environmental stress to enable wall repair and resumption of normal growth. This complex, interconnected, pathway has been only partially characterized in filamentous fungi. To better understand the dynamic cellular response to wall perturbation, a β-glucan synthase inhibitor (micafungin) was added to a growing A. nidulans shake-flask culture. From this flask, transcriptomic and phosphoproteomic data were acquired over 10 and 120 min, respectively. To differentiate statistically-significant dynamic behavior from noise, a multivariate adaptive regression splines (MARS) model was applied to both data sets. Over 1800 genes were dynamically expressed and over 700 phosphorylation sites had changing phosphorylation levels upon micafungin exposure. Twelve kinases had altered phosphorylation and phenotypic profiling of all non-essential kinase deletion mutants revealed putative connections between PrkA, Hk-8-4, and Stk19 and the CWIS pathway. Our collective data implicate actin regulation, endocytosis, and septum formation as critical cellular processes responding to activation of the CWIS pathway, and connections between CWIS and calcium, HOG, and SIN signaling pathways.

Compressive strength prediction of high-performance concrete using gradient tree boosting machine

In structural engineering, concrete compressive strength (CCS) is the most important performance parameter for designing the conventional concrete and high-performance concrete (HPC) structures. The precise prediction of this parameter becomes more crucial when considering this parameter for cost-benefits analysis and time point of view. This research investigates the multivariate adaptive regression splines model (MARS) as a feature extraction method to extract the optimum inputs that use to design the HPC. Furthermore, the extracted feature is feed to a gradient tree boosting machine (GBM) learning technique to predict the CCS. In addition, a comparative study has been done using different framework models (Kernel ridge regression and Gaussian process regression) to find its robustness. A total of 1030 data sets of eight input variables, i.e., cement, blast furnace slag, water, superplasticizer, fine aggregate, concrete age, etc. are used as inputs to estimate the CCS of HPC. The results of the analysis show that the relative importance of each parameters’ weights during the processing of GBM. Amongst the six most influential parameters, concrete age was found to be highly sensitive to predict the CCS. Moreover, the integrated MARS-GBM approach shows a simplified approach for the prediction of CCS of HPC based on different fitness indices (e.g., correlation coefficient and mean absolute error are 0.965 and 0.037 MPa, respectively). Therefore, this research concludes that such an ensemble approach can be a viable option to achieve higher performance with statistical accountability.

Modeling monthly streamflow in mountainous basin by MARS, GMDH-NN and DENFIS using hydroclimatic data

Accurate estimation of streamflow has a vital importance in water resources engineering, management and planning. In the present study, the abilities of group method of data handling-neural networks (GMDH-NN), dynamic evolving neural-fuzzy inference system (DENFIS) and multivariate adaptive regression spline (MARS) methods are investigated for monthly streamflow prediction. Precipitation, temperature and streamflows from Kalam and Chakdara stations at Swat River basin (mountainous basin), Pakistan, are used as inputs to the applied models in the form of different input scenarios, and models’ performances are evaluated on the basis of root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE) and combined accuracy (CA) indexes. Test results of the Kalam Station show that the DENFIS model provides more accurate prediction results in comparison of GMDH-NN and MARS models with the lowest RMSE (18.9 m3/s), MAE (13.1 m3/s), CA (10.6 m3/s) and the highest NSE (0.941). For the Chakdara Station, the MARS outperforms the GMDH-NN and DENFIS models with the lowest RMSE (47.5 m3/s), MAE (31.6 m3/s), CA (26.1 m3/s) and the highest NSE (0.905). Periodicity (month number of the year) effect on models’ accuracies in predicting monthly streamflow is also examined. Obtained results demonstrate that the periodicity improves the models’ accuracies in general but not necessarily in every case. In addition, the results also show that the monthly streamflow could be successfully predicted using only precipitation and temperature variables as inputs.

A comparative study on machine learning modeling for mass movement susceptibility mapping (a case study of Iran)

Mass movements are among the most dangerous natural hazards in mountainous regions. The present study employs machine learning (ML) models for mass movement susceptibility mapping (MMSM) in Iran based on a comprehensive dataset of 864 mass movements which include debris flow, landslide, and rockfall during the last 42 years (1977–2019) as well as 12 conditional factors. The results of validation stage show that RF (random forest) is the most viable model for mass movement susceptibility maps. In addition, MARS (multivariate adaptive regression splines), MDA (mixture discriminant additive), and BRT (boosted regression trees) models also provide relatively accurate results. Results of the AUC for validation of produced maps were 0.968, 0.845, 0.828, and 0.765 for RF, MARS, MDA, and BRT, respectively. Based on MMSM generated by RF model, 32% of study area is identified to be under high and very high susceptibility classes. Most of the endangered areas for mass movement are in the west and central parts of the Chaharmahal and Bakhtiari Province. In addition, our findings indicate that elevation, slope angle, distance from roads, and distance from faults are critical factors for mass movement. Our results provide a perspective view for decision makers to mitigate natural hazards.

Mathematical expression for discharge coefficient of Weir-Gate using soft computing techniques

This research aimed to develop artificial intelligence models, including multivariate adaptive regression splines (MARS), group of method data handling (GMDH), and genetic expression programming(GEP) techniques, in order to estimate the discharge coefficient (Cd) of the Weir-Gate structure. The parameters involved in this problem are the ratios of weir height to the gated opening (), the weir width to the gated opening (), contraction coefficient () and the upstream head to the gated opening (). Results of applied methods declared that all of them have acceptable performance for modeling and predicting the Cd. However, the MARS model outperforms the other models. The error indices of MARS model in training stage were (R 2 = 0.95, RMSE = 0.007) and in the testing were (R 2 = 0.89, RMSE = 0.012). Reviewing the prepared models indicated that and are the impressive factors on the Cd of Weir-Gate.

Regional Flood Frequency Analysis Through Some Machine Learning Models in Semi-arid Regions

The machine learning models (MLMs), including support vector regression (SVR), multivariate adaptive regression spline (MARS), boosted regression trees (BRT), and projection pursuit regression (PPR) are compared to traditional method i.e. nonlinear regression (NLR) in regional flood frequency analysis (RFFA). In this study, the Karun and Karkheh watersheds, which is located in the southwestern of Iran, with the same climatic and physiographic conditions are considered. Fifty-four hydrometric stations with a period of 21 years (1993–2013) are selected based on the instructions of U.S. Federal Agencies Bulletin 17 B were applied for RFFA. The generalized normal (GNO) probability distribution function (PDF) is selected by the L-moment method among five PDFs, including the GNO, generalized Pareto (GP), generalized logistic (GL), generalized extreme value (GEV) and Pearson type 3 (P ІІІ) to estimate flood discharge for the expected return periods. Twenty-five predictor variables, such as physiographic, climatologic, geologic, soil and land use variables are extracted. Follow land, maximum 24-h rainfall, mean watershed slope, compactness coefficient, mean and maximum watershed elevation variables are recognized as the appropriate combination of input using gamma test (GT). The overall results indicate that the SVR, PPR, and MARS models in comparison to the NLR and BRT models have a better performance to estimate flood discharge with the expected return periods. Future, the SVR model based on radial basis function (RBF) kernel is chosen as the best model in terms of the mean of the Nash-Sutcliff coefficient (M-Ef) and the mean of relative root mean squared error (M-RMSEr) (i.e. 0.94 and 63.93, respectively) for different return periods.

Relationships among Leisure Physical Activity, Sedentary Lifestyle, Physical Fitness, and Happiness in Adults 65 Years or Older in Taiwan.

The purpose of this study is to understand the relationship among leisure physical activity, sedentary lifestyle, physical fitness, and happiness in healthy elderly adults aged over 65 years old in Taiwan. Data were recruited from the National Physical Fitness Survey in Taiwan, which was proposed in the Project on the Establishment of Physical Fitness Testing Stations by the Sports Administration of the Ministry of Education. Participants were recruited from fitness testing stations set up in 22 counties and cities from October 2015 to May 2016. A total of 20,111 healthy older adults aged 65–102 years were recruited as research participants. The fitness testing procedure was described to all participants, who were provided with a standardized structured questionnaire. Participants’ data included sex, city or county of residence, living status (living together with others or living alone), education level, and income. Physical fitness testing was conducted in accordance with The Fitness Guide for Older Adults published by the Sports Administration of the Ministry of Education. The testing involved cardiorespiratory endurance, muscle strength, muscle endurance, flexibility, balance, and body composition. The t-test was used to evaluate the differences between continuous and grade variables under the two classification variables of sex, city or county of residence, and living status. We used the MARS (multivariate adaptive regression splines) model to analyze the effects of physical fitness variables and leisure physical activity variables on happiness. Among healthy elderly adults, sex, age, living status, body mass index, and leisure physical activity habits proved to be related to happiness. Aerobic endurance (2-min step test), muscular strength and endurance (30-s arm curl and 30-s chair stand tests), flexibility (back stretch and chair sit-and-reach tests), and balance ability (8-foot up-and-go tests and one-leg stance with eyes open tests) were found to be related to happiness. The results of this study indicate that increased physical activity and intensity, as well as physical fitness performance, are associated with improved happiness.

Determining Factors of Length of Stay of Indian Domestic Tourists

There is a trend of shortening lengths of stay (LOSs) in tourism, coupled with more frequent trips. Since tourism revenue derives from the duration of stay of tourists at destinations, tourism marketers are interested in attracting those tourists who stay for longer, and thus more profitable durations. Indian domestic tourism is a huge market but it has been insufficiently researched. As a result, destination marketing organizations (DMOs) are constrained to depend more on hunches in their efforts to attract tourists. This study attempts to identify the determining factors of length of stay of Indian domestic tourists with empirical evidence adopting multiple regression and the MARS (multivariate adaptive regression splines) model. The findings fill an essential gap in the tourism literature, as pertains to lengths of stay at Indian destinations. They also help destination marketing organizations better understand the nuances of tourist behavior, so they can craft appropriate marketing strategies that attract those tourists who tend to stay for longer durations.

Modelling of daily lake surface water temperature from air temperature: Extremely randomized trees (ERT) versus Air2Water, MARS, M5Tree, RF and MLPNN

Prediction of rivers and lakes water temperature plays an important role in hydrology, ecology, and water resources planning and management. Recently, machines learning approaches have been widely used for modelling water temperature, and the obtained results vary depending on the kind of models and the selections of the appropriates predictors. In the present paper, a new family of machines learning are proposed and compared to the famous air2stream model, using a large data set collected at 25 lakes in the northern part of Poland. The proposed models were: (i) the extremely randomized trees (ERT), (ii) the multivariate adaptive regression splines (MARS), (iii) the M5 Model tree (M5Tree), (iv) the random forest (RF), and (v) the multilayer perceptron neural network (MLPNN). The models were developed using the air temperature as input variables and the component of the Gregorian calendar (year, month and day) number. Results obtained were evaluated using several statistical indices: the root mean square error (RMSE), the mean absolute error (MAE), correlation coefficient (R) and Nash-Sutcliffe efficiency coefficient (NSE). Obtained results reveals that the air2stream model outperformed all other machines learning models and worked best with high accuracy at all the 25 lakes, and none of the ERT, MARS, M5Tree, RF and MLPNN models was able to provides an improvement of the water temperature prediction compared to the air2stream.

Estimation of summer maize evapotranspiration using MARS model in the semi-arid region of northwest China

Evapotranspiration (ET) is a crucial parameter of agricultural water management, and its accurate estimation is of great significance to implement precision irrigation and optimal allocation of regional water resources. This study investigated the efficiency of the multivariate adaptive regression splines (MARS) model for estimating daily ET of summer maize under twelve input combinations, including complete and incomplete meteorological factors and crop growth indicators for the period 2011–2013. The performance of the MARS model was compared with the empirical Priestley-Taylor (P-T), Shuttleworth-Wallace (S-W) and Two-Patch (T-P) models as well as the back-propagation neural networks (BPNN) model. The optimal MARS and BPNN models achieved better ET prediction than the optimal empirical models at each growth stage.The MARS model was superior to the BPNN model at all growth stages in terms of mean absolute error: seedling emergence to tasseling (0.8476 mm/d vs. 0.9833 mm/d), tasseling to grouting (0.6777 mm/d vs. 0.7162 mm/d), grouting to harvest (0.3342 mm/d vs. 0.4336 mm/d) and the entire growth period (0.8752 mm/d vs. 0.9577 mm/d). Generally, the MARS model outperformed the BPNN model and empirical models at all growth stages, indicating that the optimal MARS models accurately modeled the complex nonlinear relationships between ET and the meteorological factors and crop growth indicators. The MARS model is thus highly recommended for estimating ET during the entire growth period of summer maize in the semi-arid regions when lack of adequate meteorological factors or crop growth indicators.

Sand Content Prediction in Urban WWTPs Using MARS

The pre-treatment stage of wastewater treatment plants (WWTP), where most of the larger waste, including sand and fat, is removed, is of great importance for the performance and durability of these plants. This work develops a model that predicts the sand content that reaches the plant. For this purpose, data were collected from one operation year of the Villapérez Wastewater Treatment Plant located in the northeast of the city of Oviedo (Asturias, Spain) and the MARS (Multivariate Adaptive Regression Splines) method was used for modelling. The accuracy of the MARS model developed using the determination coefficient is R2 = 0.74 for training data and R2 = 0.70 in validation data. These results indicate that it is possible to predict trend changes in sand production as a function of input variables changes such as flow rate, pH, ammonia, etc. This will prevent the plant from possible operational problems, as actions could be taken, such as starting up more pre-treatment lines or emptying the containers, so that the arrival of the sand can be assumed without any problem. In this way, the possibility of letting sand contents over the established limits pass that could affect the following processes of the treatment plant is avoided.

Estimating the short-term and long-term wind speeds: implementing hybrid models through coupling machine learning and linear time series models

Wind speed data are of particular importance in the design and management of wind power projects. In the current study, three types of linear time series models including autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) were employed to estimate short-term (i.e., daily) and long-term (i.e., monthly) wind speeds. The required data were gathered, respectively, from the Tabriz and Zahedan stations in the northwest and southeast of Iran. The MA models outperformed the AR and ARMA on the both daily and monthly scales. Daily and monthly wind speed values, as a function of lagged wind speed data, were then estimated using two machine learning models of random forests (RF) and multivariate adaptive regression splines (MARS). It was found that the RF and MARS provided similar results; however, RF performed slightly better than the MARS. Finally, the stand-alone time series and machine learning models were coupled to improve the accuracy of the wind speed estimation. Accordingly, the hybrid RF-AR, RF-MA, RF-ARMA, MARS-AR, MARS-MA, and MARS-ARMA models were implemented. It was concluded that, the hybrid models outperformed the stand-alone RF and MARS for both short- and long-term wind speed estimations where, the RF-AR and MARS-AR hybrid models provided the best performances. The hybrid models tested in the present study could be effective alternatives to the stand-alone machine learning-based RF and MARS models for the estimation of wind speed time series.

Efficiency of three advanced data-driven models for predicting axial compression capacity of CFDST columns

Abstract This study aims to investigate the performance of three advanced data-driven models, namely multivariate adaptive regression spline (MARS), artificial neural network (ANN), and adaptive neural fuzzy inference system (ANFIS), for predicting the axial compression capacity of circular concrete-filled double-skin steel tube (CFDST) columns. For this purpose, 125 experimental data sets collected from the literature were used to develop the MARS, ANN, and ANFIS models. In this regard, the column length, the outer diameter, the outer thickness and yield strength of the outer steel tube, the inner diameter, the inner thickness and yield strength of the inner steel tube, and the compressive strength of concrete were considered as input variables, meanwhile, axial compression capacity was considered as the output variable. The performance of the three data-driven models was compared with six equations proposed by design codes and other authors. The comparisons showed that three data-driven models achieved more accuracy than previous equations, of which, the ANN model has an advantage over the ANFIS and MARS models. Finally, a graphical user-friendly interface (GUI) was developed to make the MARS, ANN, and ANFIS models become more attractive for practical use.

Nonparametric Multivariate Adaptive Regression Splines Models for Investigating Lane-Changing Gap Acceptance Behavior Utilizing Strategic Highway Research Program 2 Naturalistic Driving Data

Gap acceptance is one of the crucial components of lane-changing analysis and an important parameter in microsimulation modeling. Drivers’ poor gap judgment, and failure to accept a necessary safety gap, make it one of the major causes of lane-changing crashes on roadways. Several studies have been conducted to investigate lane-changing gap acceptance behavior; however, very few studies examined the behavior in complex real-world situations, such as in naturalistic settings. This study examined lane-changing gap acceptance behavior from the big Strategic Highway Research Program 2 (SHRP2) Naturalistic Driving Study (NDS) datasets using a nonparametric multivariate adaptive regression splines (MARS) approach to better understand the complex effects of different factors in gap acceptance behavior. The study developed a unique methodology to identify lane-changing events of the non-NDS-vehicles using the front-mounted radar data from NDS vehicles and extract necessary parameters for analyzing gap acceptance behavior. In addition, surrogate measures of safety, that is, time-to-collision (TTC), was utilized to understand the impact of lane-changing on the NDS following vehicle safety. Moreover, different distributions of gap acceptance were fitted to identify the trend of gap acceptance behavior. The results from the MARS model revealed that different factors including relative speed between lane-changing vehicle (LCV) and lead vehicle (LV)/following vehicle (FV), traffic conditions, acceleration of LCV and FV, and roadway geometric characteristics have significant effects on gap acceptance behavior. The results of this study have significant implications, which could be used in microsimulation model calibration and safety improvements in connected and autonomous vehicles (CAV).

Spatial Forecasting of Dissolved Oxygen Concentration in the Eastern Black Sea Basin, Turkey

The aim of this study was to model, as well as monitor and assess the surface water quality in the Eastern Black Sea (EBS) Basin stream, Turkey. The water-quality indicators monitored monthly for the seven streams were water temperature (WT), pH, total dissolved solids (TDS), and electrical conductivity (EC), as well as luminescent dissolved oxygen (LDO) concentration and saturation. Based on an 18-month data monitoring, the surface water quality variation was spatially and temporally evaluated with reference to the Turkish Surface Water Quality Regulation. First, the teaching–learning based optimization (TLBO) algorithm and conventional regression analysis (CRA) were applied to three different regression forms, i.e., exponential, power, and linear functions, to predict LDO concentrations. Then, the multivariate adaptive regression splines (MARS) method was employed and three performance measures, namely, mean absolute error (MAE), root means square error (RMSE), and Nash Sutcliffe coefficient of efficiency (NSCE) were used to evaluate the performances of the MARS, TLBO, and CRA methods. The monitoring results revealed that all streams showed the same trend in that lower WT values in the winter months resulted in higher LDO concentrations, while higher WT values in summer led to lower LDO concentrations. Similarly, autumn, which presented the higher TDS concentrations brought about higher EC values, while spring, which presented the lower TDS concentrations gave rise to lower EC values. It was concluded that the water quality of the streams in the EBS basin was high-quality water in terms of the parameters monitored in situ, of which the LDO concentration varied from 9.13 to 10.12 mg/L in summer and from 12.31 to 13.26 mg/L in winter. When the prediction accuracies of the three models were compared, it was seen that the MARS method provided more successful results than the other methods. The results of the TLBO and the CRA methods were very close to each other. The RMSE, MAE, and NSCE values were 0.2599 mg/L, 0.2125 mg/L, and 0.9645, respectively, for the best MARS model, while these values were 0.4167 mg/L, 0.3068 mg/L, and 0.9086, respectively, for the best TLBO and CRA models. In general, the LDO concentration could be successfully predicted using the MARS method with various input combinations of WT, EC, and pH variables.

ARTIFICIAL INTELLIGENCE TECHNIQUES FOR PREDICTING TIDAL EFFECTS BASED ON GEOGRAPHIC LOCATIONS IN GHANA

Tidal forces as a result of attraction of external bodies (Sun, Moon and Stars) through gravity and are a source of noise in many geoscientific field observations. The solid earth tides cause deformation. This deformation results in displacement in geographic positions on the surface of the earth. The displacement due to tidal effects can result in deformation of engineering structures, loss of lives, and economic cost. Tidal forces also help in detecting other environmental and tectonic signals. This study quantifies the effects of solid earth tides on stationary survey controls in five regions of Ghana. The study is in two stages: firstly, the solid earth tides were estimated for each control by a geometric approach (combining Navier’s equation of motion and Love theories). Secondly, estimation using two artificial intelligence methods (Multivariate Adaptive Regression Splines (MARS) and Backpropagation Artificial Neural Network (ANN)). Based on statistical indices of Mean Square Error (MSE) and Correlation Coefficient (R), BPANN, and MARS models can be used as a realistic alternative technique in quantifying solid earth tides for the study area. The MSE and R (MSE; BPANN = 1.3249 × 10–04 and MSE; MARS = 2.2052 × 10–06; R; BPANN = –0.6067 and R; MARS 0.6570) values indicate that MARS outperforms BPANN in quantifying solid earth tides in the study area. BPANN and MARS can be used as an efficient tool for quantifying tidal values based on geographic positions for geodetic deformation studies within the study area.

Role of Regression Models in Bridge Pier Scour Prediction

Scour monitoring is an important concern in the design of any hydraulic structure. This study introduces the application of regression models in the prediction of scour depth around a bridge pier. Feedforward Neural Network (FFNN) and Multivariate Adaptive Regression Spline (MARS) models have been developed using different flow parameters. The flow parameters taken into consideration are the flow depth, flow velocity, pier diameter, and Froude's number. The FFNN models with different combinations of input parameters along with a simultaneous variation in the number of hidden neurons were developed to further increase the prediction accuracy. The best combination of hidden neurons and input parameters was selected and compared with the developed MARS model. Further, these models were compared with the selected empirical models to find out the best possible model for bridge pier scour prediction. All the developed regression models and selected empirical models were compared using standard statistical performance evaluation measures such as Root Mean Square Error (RMSE), Nash-Sutcliffe Efficiency (NSE), Mean Absolute Percentage Error (MAPE) and Percentage BIAS (PBIAS). The FFNN model developed with 4-input parameters performed better compared with other combinations of input parameters. The performance indices of all developed models show that as the input parameter increases, prediction accuracy also increases. A superior prediction accuracy was observed with FFNN model with 4-input parameters compared to MARS model and other selected empirical models.

Daily flow forecasting of perennial rivers in an arid watershed: a hybrid ensemble decomposition approach integrated with computational intelligence techniques

Abstract Accurate estimating of daily streamflow forecasting is one of the prominent topics in water resources activities. In this paper, an integrated method including decomposition technique based on the ensemble empirical mode decomposition (EEMD) combined with multivariate adaptive regression spline (MARS) was carried out to predict daily streamflow values. Daily streamflow value datasets collected from two stations in Iran (Gachsar and Kordkheyl) were selected. After dividing into calibration and validation datasets, each of them was decomposed by EEMD. Crow search algorithm (CSA) was used to optimize the MARS parameters (MARS-CSA). The performance of the integrated model (EEMD-MARS-CSA) was investigated by error indices (correlation coefficient (R), root mean squared error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), as well as RMSE to standard deviation ratio (RSR)). From the results, EEMD was an important tool for increasing model accuracy and EEMD-MARS-CSA outperformed other alternative methods for daily streamflow estimation. According to one-day-ahead flow forecasting, EEMD-MARS-CSA (R = 0.94, RMSE = 5.94 m3/s (Kordkheyl) and R = 0.98, RMSE = 0.71 m3/s (Gachsar)) outperformed EEMD-MT/MARS, MT, and MARS models. Furthermore, RSR criterion of EEMD-MARS-CSA was reduced by 18%, 16%, and 17% for 3-days, 1-week, and 2-weeks-ahead streamflow forecasting compared to MARS-CSA model, respectively, for Gachsar station.

Estimating Soil Available Phosphorus Content through Coupled Wavelet–Data-Driven Models

Soil phosphorus (P) is a vital but limited element which is usually leached from the soil via the drainage process. Soil phosphorus as a soluble substance can be delivered through agricultural fields by runoff or soil loss. It is one of the most essential nutrients that affect the sustainability of crops as well as the energy transfer for living organisms. Therefore, an accurate simulation of soil phosphorus, which is considered as a point source pollutant in elevated contents, must be performed. Considering a crucial issue for a sustainable soil and water management, an effective soil phosphorus assessment in the current research was conducted with the aim of examining the capability of five different wavelet-based data-driven models: gene expression programming (GEP), neural networks (NN), random forest (RF), multivariate adaptive regression spline (MARS), and support vector machine (SVM) in modeling soil phosphorus (P). In order to achieve this goal, several parameters, including soil pH, organic carbon (OC), clay content, and soil P data, were collected from different regions of the Neyshabur plain, Khorasan-e-Razavi Province (Northeast Iran). First, a discrete wavelet transform (DWT) was applied to the pH, OC, and clay as the inputs and their subcomponents were utilized in the applied data-driven techniques. Statistical Gamma test was also used for identifying which effective soil parameter is able to influence soil P. The applied methods were assessed through 10-fold cross-validation scenarios. Our results demonstrated that the wavelet–GEP (WGEP) model outperformed the other models with respect to various validations, such as correlation coefficient (R), scatter index (SI), and Nash–Sutcliffe coefficient (NS) criteria. The GEP model improved the accuracy of the MARS, RF, SVM, and NN models with respect to SI-NS (By comparing the SI values of the GEP model with other models namely MARS, RF, SVM, and NN, the outputs of GEP showed more accuracy by 35%, 30%, 40%, 50%, respectively. Similarly, the results of the GEP outperformed the other models by 3.1%, 2.3%, 4.3%, and 7.6%, comparing their NS values.) by 35%-3.1%, 30%-2.3%, 40%-4.3%, and 50%-7.6%, respectively.

Application of Multivariate Adaptive Regression Splines and Classification and Regression Trees to Estimate Wave-Induced Scour Depth Around Pile Groups

Pile groups are employed in sea and ocean environments in order to support marine and offshore structures. Estimation of scour depth around pile groups is one of the important factors in the design of coastal and marine structures. The scour phenomenon is a serious hazard that threats the structural stability of piles. Data-driven methods are being used more and more for the prediction of scour depth around pile groups due to the complexity of the process involved. The previous studies have indicated that the M5 model tree (M5MT) was able to provide more accurate results for wave-induced scour around pile groups compared to the empirical equations. Recently, multivariate adaptive regression splines (MARS) approach has been used as a relatively novel technique of data-driven methods for modeling and approximating nonlinear civil engineering problems. In this paper, MARS models are developed and used for estimation of the scour depth around pile groups in terms of the most influential dimensionless parameters using experimental data and field observations. Moreover, the classification and regression trees (CART) algorithm as a well-known decision tree algorithm is also used for prediction of the wave-induced scour depth around pile groups. The main feature of MARS is to provide a simple linear regression equation that calculates quickly and easily scour depth. In addition, CART presents decision rules without the need for any mathematical calculations, and it predicts scour depth straightforwardly. Statistical indices demonstrate that MARS with the root mean square error (RMSE) = 0.24 and correlation coefficient (CC) = 0.95 is more accurate than two well-known decision tree algorithms, namely M5MT (RMSE = 0.34 and CC = 0.92) and CART (RMSE = 0.35 and CC = 0.90). In addition, the sensitivity analysis declares that the Keulegan–Carpenter number (KC) is the most important variable that affects the scour depth.