Multivariate Adaptive Regression Splines Approach Research Articles

Prediction of load-displacement performance of grouted anchors in weathered granites using FastICA-MARS as a novel model

With the rising needs of better prediction of the load-displacement performance of grouted anchors in an era of developing large-scale underground infrastructures, the existing methods in literature lack an accurate analytical model for the real-life projects or rigorous understanding of the parameters such as grouting pressures. This paper proposes FastICA-MARS as a novel data-driven approach for the prediction of the load-displacement performance of uplift-resisting grouted anchors. The hybrid and data-driven FastICA-MARS approach integrates the multivariate adaptive regression splines (MARS) technique with the FastICA algorithm which is for Independent Component Analysis (ICA). A database of 4315 observations for 479 different anchors from 7 different projects is established. The database is then used to train, validate and compare the FastICA-MARS approach with the classical MARS approach. The developed FastICA-MARS model can provide more accurate predictions than MARS. Moreover, the developed FastICA-MARS model is easy to interpret since the evaluation of the parameter importance of the independent components can be conducted along with the considerations of the correlations with the original variables. It is noteworthy to point out that the grouting pressures play a central role in the proposed model, which is considered of paramount importance in engineering practices but has not been properly taken into account in any prior analytical or empirical predictive models for the load-displacement relationships.

Estimation of transverse mixing coefficient in streams using M5, MARS, GA, and PSO approaches.

Transverse mixing coefficient is one of the key elements of pollutant in two-dimensional modeling. In this study, four data-driven models, M5 model tree, multivariate adaptive regression splines (MARS), genetic algorithm (GA), and particle swarm optimization (PSO), were used to estimate the transverse mixing coefficient. For this purpose, techniques with a wide range of experimental and field data were performed to train and test the data-driven models. Statistical analysis and Monte Carlo simulation were used to validate the performance of each model. Based on statistical indices, the efficiency of M5 and MARS models was better than GA and PSO algorithms. In straight streams, M5 and MARS provided similar performances, but the MARS model estimated the transverse mixing coefficient more accurately in meander streams. In meander streams, the performance of all models was lower than straight streams due to the lack of experimental and field measurements for large meandering streams. Applying Monte Carlo simulation showed that the MARS model overestimated the transverse mixing coefficient in many cases. In addition, the results of global sensitivity analysis showed that 70% of output variance was determined by main effects in the M5 model and 30% by interaction effects. In this regard, the most influential parameters were flow depth and shear velocity, while the average velocity was the least influential factor.

Using AR, MA, and ARMA Time Series Models to Improve the Performance of MARS and KNN Approaches in Monthly Precipitation Modeling under Limited Climatic Data

Precipitation is one of the most important components of the hydrologic cycle as it is required for multi-objective applications including flood estimation, drought monitoring, watersheds management, hydrology, agriculture, etc. Therefore, its estimation and modeling via a suitable method is a challenging task for hydrologists. The present study seeks to model monthly precipitation at two stations located in Iran. Two artificial intelligence (AI)-based models consisting of multivariate adaptive regression splines (MARS) and k-nearest neighbors (KNN) were used as the modeling techniques. In doing so, nine single-input scenarios under limited climatic data are implemented using minimum, maximum, and mean air temperatures, dew point temperature, station pressure, vapor pressure, relative humidity, wind speed, and antecedent precipitation data. The attained results illustrate that the performance of single MARS and KNN is relatively poor when modeling the monthly precipitation. Additionally, this study develops hybrid models to enhance the precipitation modeling through combining the MARS and KNN models with three diverse types of the time series (TS) models, namely autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA). The most important justification for integrating the models applied is that the AI and TS-based models are respectively capable of modeling the non-linear and linear terms of the hydrological variables such as precipitation. It is therefore necessary to be considered both of the aforementioned terms in the modeling procedure. A performance comparison of the single and hybrid models denotes the higher accuracy of hybrid models than the single ones. However, the hybrid models generated by combining the KNN and the TS models used are the best-performing models.

Prediction of the compressive strength of self-compactingconcrete using surrogate models

In this paper, surrogate models such as multivariate adaptive regression splines (MARS) and M5P model tree (M5P MT) methods have been investigated in order to propose a new formulation for the 28-days compressive strength of selfcompacting concrete (SCC) incorporating metakaolin as a supplementary cementitious materials. A database comprising experimental data has been assembled from several published papers in the literature and the data have been used for training and testing. In particular, the data are arranged in a format of seven input parameters covering contents of cement, coarse aggregate to fine aggregate ratio, water, metakaolin, super plasticizer, largest maximum size and binder as well as one output parameter, which is the 28-days compressive strength. The efficiency of the proposed techniques has been demonstrated by means of certain statistical criteria. The findings have been compared to experimental results and their comparisons shows that the MARS and M5P MT approaches predict the compressive strength of SCC incorporating metakaolin with great precision. The performed sensitivity analysis to assign effective parameters on 28-days compressive strength indicates that cementitious binder content is the most effective variable in the mixture.

Multivariate relationships between campus design parameters and energy performance using reinforcement learning and parametric modeling

For the past two decades, extensive research has been conducted to evaluate the performance of urban form scenarios such as sky view factors, solar radiation, or energy performance. The relationships between urban design parameters and multiple performance should be stipulated to evaluate scenarios for supporting timely and reliable design decisions. However, there are three major challenges: (1) only a few design alternatives are devised, (2) the multiple performance has not been provided synthetically, and (3) the relationships between design parameters and performance are difficult to be determined because they are multivariate relationships. This research proposes a new methodology applying a generative design approach using a reinforcement learning algorithm, a parametric performance modeling, and a multivariate adaptive regression splines approach to identify relationships between design parameters and urban performance. This research aims to support decision-making of urban design to achieve an energy efficient and visually qualified urban environment. A data-driven urban design approach is proposed to generate possible design alternatives using reinforcement learning, and a design-driven analysis is conducted to evaluate multiple performance of urban buildings using parametric modeling. The multivariate analysis presented relationships between urban geometric forms and performance criteria by using 30 samples. The findings show that to maintain optimal solar potential, the building coverage ratio is recommended to be bigger than 0.17. To maintain the optimal energy balance, the threshold for sky view factor is recommended as 54.17%. These relationships contribute to deriving design strategies and guidelines for designing a sustainable campus.

Multivariate Adaptive Regression Splines (MARS) approach to blast-induced ground vibration prediction

ABSTRACTModelling and prediction of blast-induced ground vibration is a significant aspect of mining and civil engineering operations, as ground vibration has dire consequences on both the environment, mine production and successful implementation of engineering projects. This study proposes the Multivariate Adaptive Regression Splines (MARS) as a novel alternative technique to model and predict blast-induced ground vibration. The MARS approach was compared with three artificial neural network methods and four conventional ground vibration predictors. The statistical analyses revealed that the MARS produced the best performance and can successfully be used for the prediction of blast-induced ground vibration.

New robust formulations for bond strength of FRP reinforcements externally glued on masonry units

The bond interface between fiber-reinforced polymer (FRP) and masonry units is one of the weakest links in tensile strengthened masonry structures. Several empirical formulae have been proposed for estimation of bond strength between FRP reinforcements and masonry units. However, the accuracy of existing formulae for predicting bond strength seems to be significantly limited. In the present study, the M5´ and Multivariate adaptive regression splines approaches are employed to predict the bond strength between FRP reinforcement and masonry units. To develop new models, a comprehensive database including 575 test series (230 distinctive specimens) is collected from different sources in the literature. The newly proposed formulations consider several preeminent parameters involved in the debonding process including the reinforcement width, the ratio between widths of FRP reinforcement and masonry unit, the tensile strength of substrate, the axial strength of reinforcement, and bond length. A comparative study is conducted to evaluate the performances of the developed models against the well-known equations. Results indicated that the proposed models remarkably outperform the existing equations in terms of accuracy. Furthermore, a sensitivity analysis is done to determine the most important parameters in predicting the bond strength. Finally, the safety of different methods is evaluated based on the demerit point classification scale.

Reliability estimation of public bus routes: Applicability of multivariate adaptive regression splines approach

The performance of public bus lines is generally evaluated by comparing demand and ridership. However, reliability gain or loss by a proposed bus route should also be considered in the decision-making process to ensure a service that is preferable for users and operable for providers. In this study, it is aimed to provide a tool for predicting the reliability of a proposed bus route by considering route layout and traffic conditions. Travel time based reliability is predicted by using a novel nonparametric method, multivariate adaptive regression splines (MARS). Some critical thresholds of route layout parameters that should be considered for higher reliability are found. It is concluded that route lengths longer than 10 km, and number of intersections over 22 considerably decrease whole day based reliability. For peak hour based reliability, the types and numbers of intersections are found to be more efficient than the ones in whole day based model and a reliability regulator impact of roundabout numbers under nine is observed.

Compressive Strength Prediction of Self-Compacting Concrete Incorporating Silica Fume Using Artificial Intelligence Methods

This paper investigates the capability of utilizing Multivariate Adaptive Regression Splines (MARS) and Gene Expression Programing (GEP) methods to estimate the compressive strength of self-compacting concrete (SCC) incorporating Silica Fume (SF) as a supplementary cementitious materials. In this regards, a large experimental test database was assembled from several published literature, and it was applied to train and test the two models proposed in this paper using the mentioned artificial intelligence techniques. The data used in the proposed models are arranged in a format of seven input parameters including water, cement, fine aggregate, specimen age, coarse aggregate, silica fume, super-plasticizer and one output. To indicate the usefulness of the proposed techniques statistical criteria are checked out. The results testing datasets are compared to experimental results and their comparisons demonstrate that the MARS (R2=0.98 and RMSE= 3.659) and GEP (R2=0.83 and RMSE= 10.362) approaches have a strong potential to predict compressive strength of SCC incorporating silica fume with great precision. Performed sensitivity analysis to assign effective parameters on compressive strength indicates that age of specimen is the most effective variable in the mixture.

Utilizing naturalistic driving data for in-depth analysis of driver lane-keeping behavior in rain: Non-parametric MARS and parametric logistic regression modeling approaches

It is known that adverse weather conditions can affect driver performance due to reduction in visibility and slippery surface conditions. Lane keeping is one of the main factors that might be affected by weather conditions. Most of the previous studies on lane keeping have investigated driver lane-keeping performance from driver inattention perspective. In addition, the majority of previous lane-keeping studies have been conducted in controlled environments such as driving simulators. Therefore, there is a lack of studies that investigate driver lane-keeping ability considering adverse weather conditions in naturalistic settings. In this study, the relationship between weather conditions and driver lane-keeping performance was investigated using the SHRP2 naturalistic driving data for 141 drivers between 19 and 89 years of age. Moreover, a threshold was introduced to differentiate lane keeping and lane changing in naturalistic driving data. Two lane-keeping models were developed using the logistic regression and multivariate adaptive regression splines (MARS) to better understand factors affecting driver lane-keeping ability considering adverse weather conditions. The results revealed that heavy rain can significantly increase the standard deviation of lane position (SDLP), which is a very widely used method for analyzing lane-keeping ability. It was also found that traffic conditions, driver age and experience, and posted speed limits have significant effects on driver lane-keeping ability. An interesting finding of this study is that drivers have a better lane-keeping ability in roadways with higher posted speed limits. The results from this study might provide better insights into understanding the complex effect of adverse weather conditions on driver behavior.

Estimation of daily reference evapotranspiration (ETo) using artificial intelligence methods: Offering a new approach for lagged ETo data-based modeling

Evapotranspiration (ET) is considered as a key factor in hydrological and climatological studies, agricultural water management, irrigation scheduling, etc. It can be directly measured using lysimeters. Moreover, other methods such as empirical equations and artificial intelligence methods can be used to model ET. In the recent years, artificial intelligence methods have been widely utilized to estimate reference evapotranspiration (ETo). In the present study, local and external performances of multivariate adaptive regression splines (MARS) and gene expression programming (GEP) were assessed for estimating daily ETo. For this aim, daily weather data of six stations with different climates in Iran, namely Urmia and Tabriz (semi-arid), Isfahan and Shiraz (arid), Yazd and Zahedan (hyper-arid) were employed during 2000–2014. Two types of input patterns consisting of weather data-based and lagged ETo data-based scenarios were considered to develop the models. Four statistical indicators including root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and mean absolute percentage error (MAPE) were used to check the accuracy of models. The local performance of models revealed that the MARS and GEP approaches have the capability to estimate daily ETo using the meteorological parameters and the lagged ETo data as inputs. Nevertheless, the MARS had the best performance in the weather data-based scenarios. On the other hand, considerable differences were not observed in the models' accuracy for the lagged ETo data-based scenarios. In the innovation of this study, novel hybrid models were proposed in the lagged ETo data-based scenarios through combination of MARS and GEP models with autoregressive conditional heteroscedasticity (ARCH) time series model. It was concluded that the proposed novel models named MARS-ARCH and GEP-ARCH improved the performance of ETo modeling compared to the single MARS and GEP. In addition, the external analysis of the performance of models at stations with similar climatic conditions denoted the applicability of nearby station' data for estimation of the daily ETo at target station.

Retrieval of fractional snow covered area from MODIS data by multivariate adaptive regression splines

In this paper, a novel approach to estimate fractional snow cover (FSC) from MODIS data in a complex and heterogeneous Alpine terrain is represented by using a state-of-the-art nonparametric spline regression method, namely, multivariate adaptive regression splines (MARS). For this purpose, twenty MODIS - Landsat 8 image pairs acquired between April 2013 and December 2016 over European Alps are used. Fifteen of the image pairs are employed during model training and five images are reserved as an independent test dataset. MARS models are trained by using MODIS top-of-atmosphere reflectance values of bands 1–7, normalized difference snow index, normalized difference vegetation index and land cover class as predictor variables. Reference FSC maps are generated from higher spatial resolution Landsat 8 binary snow cover maps. Multilayer feedforward artificial neural network (ANN) models are also trained by using the same input data. During the training and the testing, the effects of the training data size and the sampling type on the predictive performance of ANN and MARS models are investigated. An additional search is also conducted to reveal whether the choice of the transfer function used in the output layer of ANN has a significant contribution to the network's FSC mapping performance. The final ANN and MARS FSC products are at 500m spatial resolution. The results on the independent test scenes indicate that the developed ANN models with linear and hyperbolic tangent transfer functions in the output layer and the MARS models are in good agreement with reference FSC data with the same average values of R=0.93. In contrast, the standard MODIS snow fraction product, namely, MOD10 FSC, exhibits slightly poorer performance with average R=0.88. The proposed MARS approach is statistically proven to have the same performance with ANN, yet it is computationally more efficient in model building.

Multivariate Adaptive Regression Splines Approach to Estimate Lateral Wall Deflection Profiles Caused by Braced Excavations in Clays

Based on a database including a total of 30 case histories for braced excavation in stiff, medium and soft clays, a multivariate adaptive regression splines (MARS) approach for estimating wall deflection profile caused by deep braced excavations is presented in this study. For each soil type, ten case histories with information on subsurface soil conditions, geometry characteristics, excavation support system details, the maximum wall deflections and the wall deflection profile against embedded depth are provided. Seven input variables, including wall length, excavation depth, excavation length, system stiffness, average unit weight and undrained shear strength of the soil, and the depth below the ground surface, are adopted as inputs to the MARS deflection profile model. Comparison with three more excavation case histories indicates that the developed MARS model can give an accurate graphical representation of the wall deflection profile. It is capable of not only predicting the value of maximum wall deflection but also estimating the possible depth at which maximum lateral deformation occurs.

Development of predictive models for shear strength of HSC slender beams without web reinforcement using machine-learning based techniques

Shear failure of slender beams made of high strength concrete (HSC) is one of the most crucial failures in design of reinforced concrete members. The accuracy of the existing design codes for HSC unlike the normal strength concrete (NSC) beams seems to be limited in prediction of shear capacity. This paper proposes a new set of shear strength models for HSC slender beams without web reinforcement using conventional multiple linear regression, advanced machine learning methods of multivariate adaptive regression splines (MARS) and group method of data handling (GMDH) network. In order to achieve high-fidelity and robust regression models, this study employs a comprehensive database including 250 experimental tests. Various influencing parameters including the longitudinal steel ratio, shear span-to-depth ratio, compressive strength of concrete, size of the beam specimens, and size of coarse aggregate are considered. The results indicate that the MARS approach has the best estimation in terms of both accuracy and safety aspects in comparison with regression methods and GMDH approach. Moreover, the accuracy and safety of predictions of MARS model is also remarkably more than the most common design equations. Furthermore, the robustness of proposed models is confirmed through sensitivity and parametric analyses.

Data-driven fuel consumption estimation: A multivariate adaptive regression spline approach

Providing guidance and information to drivers to help them make fuel-efficient route choices remains an important and effective strategy in the near term to reduce fuel consumption from the transportation sector. One key component in implementing this strategy is a fuel-consumption estimation model. In this paper, we developed a mesoscopic fuel consumption estimation model that can be implemented into an eco-routing system. Our proposed model presents a framework that utilizes large-scale, real-world driving data, clusters road links by free-flow speed and fits one statistical model for each of cluster. This model includes predicting variables that were rarely or never considered before, such as free-flow speed and number of lanes. We applied the model to a real-world driving data set based on a global positioning system travel survey in the Philadelphia-Camden-Trenton metropolitan area. Results from the statistical analyses indicate that the independent variables we chose influence the fuel consumption rates of vehicles. But the magnitude and direction of the influences are dependent on the type of road links, specifically free-flow speeds of links. A statistical diagnostic is conducted to ensure the validity of the models and results. Although the real-world driving data we used to develop statistical relationships are specific to one region, the framework we developed can be easily adjusted and used to explore the fuel consumption relationship in other regions.

Wavelet coupled MARS and M5 Model Tree approaches for groundwater level forecasting

In this study, two different machine learning models, Multivariate Adaptive Regression Splines (MARS) and M5 Model Trees (MT) have been applied to simulate the groundwater level (GWL) fluctuations of three shallow open wells within diverse unconfined aquifers. The Wavelet coupled MARS and MT hybrid models were developed in an attempt to further increase the GWL forecast accuracy. The Discrete Wavelet Transform (DWT) which is particularly effective in dealing with non-stationary time-series data was employed to decompose the input time series into various sub-series components. Historical data of 10years (August-1996 to July-2006) comprising monthly groundwater level, rainfall, and temperature were used to calibrate and validate the models. The models were calibrated and tested for one, three and six months ahead forecast horizons. The wavelet coupled MARS and MT models were compared with their simple counterpart using standard statistical performance evaluation measures such as Root Mean Square Error (RMSE), Normalized Nash-Sutcliffe Efficiency (NNSE) and Coefficient of Determination (R2). The wavelet coupled MARS and MT models developed using multi-scale input data performed better compared to their simple counterpart and the forecast accuracy of W-MARS models were superior to that of W-MT models. Specifically, the DWT offered a better discrimination of non-linear and non-stationary trends that were present at various scales in the time series of the input variables thus crafting the W-MARS models to provide more accurate GWL forecasts.

Exploring contributory factors to highway accidents: A nonparametric multivariate adaptive regression spline approach

ABSTRACTPoisson and negative binomial regression models have been commonly applied to identify the significant factors that affect accident frequency on highways or at intersections. This study explores the application of an alternate method, the nonparametric multivariate adaptive regression spline (MARS) technique, to identify the effects of highway geometric characteristics, traffic factors, and environmental conditions on the frequency of highway accidents. The 2007 to 2008 accident data for National Freeway 1 in Taiwan were collected to develop MARS models. Results indicate that horizontal alignment, vertical alignment, average daily traffic volume (ADT), heavy vehicle ADT, and precipitation all have nonlinear effects on highway accidents.

Determination of earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach

A major consideration in urban tunnel design is to estimate the ground movements and surface settlements associated with the tunnelling operations. Excessive ground movements may result in damage to adjacent buildings and utilities. Numerous empirical and analytical solutions have been proposed to relate the shield tunnel characteristics and surface/subsurface deformation. Numerical analyses, either 2D or 3D, have also been applied to such tunnelling problems. However, substantially fewer approaches have been developed for earth pressure balance (EPB) tunnelling. Based on instrumented data on ground deformation and shield operation from three separate EPB tunnelling projects in Singapore, this paper utilizes a multivariate adaptive regression splines (MARS) approach to establish relationships between the maximum surface settlement and the major influencing factors, including the operation parameters, the cover depth and the ground conditions. Since the method has the ability to map input to output patterns, MARS enables one to map all influencing parameters to surface settlements. The main advantages of MARS over other soft computing techniques such as ANN, RVM, SVM and GP are its capacity to produce a simple, easy-to-interpret model, its ability to estimate the contributions of the input variables, and its computational efficiency.

Using evolutionary multivariate adaptive regression splines approach to evaluate the eutrophication in the Pozón de la Dolores lake (Northern Spain)

Eutrophication is a water enrichment in nutrients (mainly phosphorus) that generally leads to symptomatic changes when the productions of algae and other aquatic vegetations are increased, and deterioration of water quality and all its uses in general. In this sense, eutrophication has caused a variety of impacts, such as high levels of Chlorophyll a (Chl-a). Consequently, anticipate its presence is a matter of importance to prevent future risks. The aim of this study was to obtain a predictive model able to perform an early detection of the eutrophication in water bodies such as lakes. This study presents a novel hybrid algorithm, based on multivariate adaptive regression splines (MARS) approach in combination with the artificial bee colony (ABC) technique, for predicting the eutrophication from biological and physical-chemical input parameters determined experimentally through sampling and subsequent analysis in a certificate laboratory. This optimization technique involves hyperparameter setting in the MARS training procedure, which significantly influences the regression accuracy. The results of the present study are two-fold. In the first place, the significance of each biological and physical-chemical variables on the eutrophication is presented through the model. Secondly, a model for forecasting eutrophication is obtained with success. Indeed, regression with optimal hyperparameters was performed and coefficients of determination equal to 0.85 for the Total phosphorus estimation and 0.84 for the Chlorophyll concentration were obtained when this hybrid ABC–MARS–based model was applied to the experimental dataset, respectively. The agreement between experimental data and the model confirmed the good performance of the latter. Finally, conclusions of this innovative research work are exposed.

A New Predictive Model for the State-of-Charge of a High-Power Lithium-Ion Cell Based on a PSO-Optimized Multivariate Adaptive Regression Spline Approach

Batteries play a key role in achieving the target of universal access to reliable affordable energy. Despite their relevant importance, many challenges remain unsolved with regard to the characterization and management of batteries. One of the major issues in any battery application is the estimation of the state-of-charge (SoC). SoC, which is expressed as a percentage, indicates the amount of energy available in a battery. An accurate SoC estimation under realistic conditions improves battery performance, reliability, and lifetime. This paper proposes an SoC estimation method based on a new hybrid model that combines multivariate adaptive regression splines (MARS) and particle swarm optimization (PSO). The proposed hybrid PSO–MARS-based model uses data obtained from a high-power load profile (dynamic stress test) specified by the United States Advanced Battery Consortium (USABC). The results provide comparable accuracy to other more sophisticated techniques but at a lower computational cost.