Multivariate Adaptive Regression Splines Application for Multivariate Geotechnical Problems with Big Data

Despite the rapid increases in processing speed and memory of low-cost computers, the enormous computational costs of running complicated numerical analyses such as finite element simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization since many geotechnical problems are highly nonlinear and multivariate. To reduce the cost, surrogate models, also known as meta-models, are constructed and then used in place of the actual numerical simulation models. To ensure the surrogate model is more reliable, the ranges of the design variables should be as wide as possible. Thus meta-modeling techniques capable of analyzing multivariate problems are desirable. This paper explores the use of a fairly simple nonparametric regression procedure known as multivariate adaptive regression splines (MARS) in approximating the relationship between the inputs and outputs with a big data. First the basis of the MARS methodology and its associated procedures are explained in detail. Then two complicated geotechnical problems are presented to demonstrate the function approximating capabilities of MARS and its efficiency in dealing with multivariate problems involving large amounts of data. This paper demonstrates that the MARS algorithm is capable of producing simple, accurate and easy-to-interpret models and estimating the contributions of the input variables.     

http://www.sciencedirect.com/science/article/pii/S1674987114001364

Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system's predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines(MARS), as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network(BPNN) and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses(MCS), Maximum tensile stresses(MTS), and Blow per foot(BPF). A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.     

Multivariate Adaptive Regression Spline (Mars) for Prediction of Elastic Modulus of Jointed Rock Mass

This article presents multivariate adaptive regression spline (MARS) for determination of elastic modulus (E_j) of jointed rock mass. MARS is a technique to estimate general functions of high-dimensional arguments given sparse data. It is a nonlinear and non-parametric regression methodology. The input variables of model are joint frequency (J_n), joint inclination parameter (n), joint roughness parameter (r), confining pressure (σ₃) and elastic modulus (E_i) of intact rock. The developed MARS gives an equation for determination of E_j of jointed rock mass. The results from the developed MARS model have been compared with those of artificial neural networks (ANNs) using average absolute error. The developed MARS gives a robust model for determination of E_j of jointed rock mass.     

System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines

A data driven multivariate adaptive regression splines (MARS) based algorithm for system reliability analysis of earth slopes having random soil properties under the framework of limit equilibrium method of slices is considered. The theoretical formulation is developed based on Spencer method (valid for general slip surfaces) satisfying all conditions of static equilibrium coupled with a nonlinear programming technique of optimization. Simulated noise is used to take account of inevitable modeling inaccuracies and epistemic uncertainties. The proposed MARS based algorithm is capable of achieving high level of computational efficiency in the system reliability analysis without significantly compromising the accuracy of results.     

Ore Grade Prediction Using a Genetic Algorithm and Clustering Based Ensemble Neural Network Model

Accurate prediction of ore grade is essential for many basic mine operations, including mine planning and design, pit optimization, and ore grade control. Preference is given to the neural network over other interpolation techniques for ore grade estimation because of its ability to learn any linear or non-linear relationship between inputs and outputs. In many cases, ensembles of neural networks have been shown, both theoretically and empirically, to outperform a single network. The performance of an ensemble model largely depends on the accuracy and diversity of member networks. In this study, techniques of a genetic algorithm (GA) and k-means clustering are used for the ensemble neural network modeling of a lead–zinc deposit. Two types of ensemble neural network modeling are investigated, a resampling-based neural ensemble and a parameter-based neural ensemble. The k-means clustering is used for selecting diversified ensemble members. The GA is used for improving accuracy by calculating ensemble weights. Results are compared with average ensemble, weighted ensemble, best individual networks, and ordinary kriging models. It is observed that the developed method works fairly well for predicting zinc grades, but shows no significant improvement in predicting lead grades. It is also observed that, while a resampling-based neural ensemble model performs better than the parameter-based neural ensemble model for predicting lead grades, the parameter-based ensemble model performs better for predicting zinc grades.     

人工神经网络模型在地学研究中的应用进展

近年来,随着人工神经网络（ANNs）自身技术的不断完善,应用ANNs模型成功解决各类地学问题的案例大量出现。通过对其发展历程进行分析发现,20世纪80年代末国际地学分析中已开始融入ANNs技术,国内则滞后 1～2年。在地学分析中使用的各类人工神经网络类型中,BP模型应用最广,占到85％以上。在10余年的应用过程中,虽然地学的各个分支学科都移植了一种或数种ANNs模型作为其分析工具,但水文、地质、大气、遥感等领域应用较为广泛。传统地学定量分析中的单变量或多变量预测成为人工神经网络地学模型的主要应用客体。同时,诸如模式识别和过程模拟等也是ANNs模型求解的对象。目前,随着建模经验和知识的积累,地学ANNs模型的发展呈现出多种技术综合集成的态势,遗传算法、小波转换、模拟退火算法以及模糊逻辑等方法与ANNs模型融合,成为解决地学分析中非线性问题的利器。     

Reliability Analysis of Quick Sand Condition

First order reliability method (FORM) is generally used for reliability analysis in geotechnical engineering. This article adopts generalized regression neural network (GRNN) based FORM, Gaussian process regression (GPR) based FORM and multivariate adaptive regression spline (MARS) based FORM for reliability analysis of quick sand condition. GRNN is related to the radial basis function (RBF) network. GPR is developed based on probabilistic framework. MARS is a nonparametric regression technique. A comparative study has been carried out between the developed models. The performance of GPR based FORM and MARS based FORM match well with the FORM. This article gives the alternative methods for reliability analysis of quick sand condition.     

Ground movements induced by installation of twin large diameter deeply-buried caissons: 3D numerical modeling

The assessment and control of ground movements during the installation of large diameter deeply-buried (LDDB) caissons are critically important to maintain the stability of surrounding infrastructures. However, for twin LDDB caissons which have been installed worldwide, no well-documented guidelines for assessing the induced ground movements are available due to the complexities of caisson–soil interaction. To this end, considering the mechanical boundaries of caissons and mechanized installation process, this paper presents a simple kinematic mechanical model balancing both computational cost and accuracy, which can be easily incorporated in commercial finite-element (FE) programs. Based on a project of twin LDDB caissons alternately installed employing a newly developed installation technology in wet ground with stiff clays in Zhenjiang, China, a three-dimensional (3D) numerical model is developed to capture the ground movements in terms of surface settlements and radial displacements induced by the installation of twin LDDB caissons. Moreover, hardening soil model with small-strain stiffness (HSSmall model) conceptually capable of capturing the nonlinear soil stiffness from very small to large strain levels is used to simulate undrained ground. The validations against field observations, empirical predictions and centrifuge test data are carried out to demonstrate the accuracy and validity of the developed FE model. Subsequently, the comparisons of ground movements numerically obtained in three frequently used installation schemes (i.e., synchronous, asynchronous and alternating installation) are conducted for installation sequence optimization of twin caissons. It is found that synchronous installation is the optimal scheme for limiting ground movements. Parametric studies considering the effects of horizontal spacing between twin caissons, staged penetration depth, inner diameter, controllable soil-plugging height, frictional coefficient between caisson–soil interface, as well as cutting edge gradient are thus performed in synchronous installation scheme. Based on an artificial data set generated through FE calculation, the multivariate adaptive regression splines (MARS) model capable of accurately capturing the nonlinear relationships between a set of input variables and output variables in multi-dimensions is used to analyze the sensitivity of caisson design parameters. Finally, the MARS mathematical equations for predicting the maximum surface settlement and radial displacement used in preliminary caisson design are proposed.

     

利用多目标地球化学数据识别第四纪沉积物类型——基于概率神经网络方法

针对利用多目标地球化学数据研究第四纪沉积物类型问题,提出了基于概率神经网络的分类识别模型,并给出地球化学特征指标选取、指标归一化、神经网络设置和训练的具体方法、步骤。在吉林省中西部松嫩平原应用表明,该方法识别出8类不同成因的第四纪沉积物,较好地解决了该区第四纪沉积物成因归属问题。概率神经网络模型对第四纪沉积物类型的识别能力远高于常规多元统计方法,且结构简单、训练快捷。     

Simultaneous parameter identification of a heterogeneous aquifer system using artificial neural networks

An artificial neural network (ANN) model is proposed for the simultaneous determination of transmissivity and storativity distributions of a heterogeneous aquifer system. ANNs may be useful tools for parameter identification problems due to their ability to solve complex nonlinear problems. As an extension of previous study—Karahan H, Ayvaz MT (2006) Forecasting aquifer parameters using artificial neural networks, J Porous Media 9(5):429–444—the performance of the proposed ANN model is tested on a two-dimensional hypothetical aquifer system for transient flow conditions. In the proposed ANN model, Cartesian coordinates of observation wells, associated piezometric heads and observation time are used as inputs while corresponding transmissivity and storativity values are used as outputs. The training, validation and testing processes of the ANN model are performed under two scenarios. In scenario 1, all the sampled data are used through the simulation time. However, in the scenario 2, there are data gaps due to irregular observations. By using the determined synaptic network weights, transmissivity and storativity distributions are predicted. In addition, the performance of the proposed ANN is tested for different noise data conditions. Results showed that the developed ANN model may be used in simultaneous aquifer parameter estimation problems.     

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 Fast ICA-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 Fast ICA-MARS approach integrates the multivariate adaptive regression splines(MARS)technique with the Fast ICA 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 Fast ICA-MARS approach with the classical MARS approach.The developed Fast ICA-MARS model can provide more accurate predictions than MARS.Moreover,the developed Fast ICA-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.     

Prediction of the tunnel displacement induced by laterally adjacent excavations using multivariate adaptive regression splines

Excavations may cause excessive ground movements, resulting in potential damage to laterally adjacent tunnels. The aim of this investigation is to present a simple assessment technique using a multivariate adaptive regression splines (MARS) model, which can map the nonlinear interactions between the influencing factors and the maximum horizontal deformation of tunnels. A high-quality case history in Tianjin, China, is presented to illustrate the effect of excavation on the tunnel deformation and to validate the FEM. The hypothetical data produced by the FEM provide a basis for developing the proposed MARS model. Based on the proposed model, the independent and coupled effects of the input variables (i.e. the normalized buried depth of tunnels H_t/H_e, the normalized horizontal distance between tunnels and retaining structures L_t/H_e, and the maximum horizontal displacement of retaining structures, δ_Rmax) on the tunnel response are analysed. The prediction precision and accuracy of the MARS model are validated via the artificial data and the collected case histories.

     

Prediction of unconfined compressive strength of carbonate rocks using artificial neural networks

The unconfined compressive strength (UCS) of intact rocks is an important geotechnical parameter for engineering applications. Determining UCS using standard laboratory tests is a difficult, expensive and time consuming task. This is particularly true for thinly bedded, highly fractured, foliated, highly porous and weak rocks. Consequently, prediction models become an attractive alternative for engineering geologists. The objective of study is to select the explanatory variables (predictors) from a subset of mineralogical and index properties of the samples, based on all possible regression technique, and to prepare a prediction model of UCS using artificial neural networks (ANN). As a result of all possible regression, the total porosity and P-wave velocity in the solid part of the sample were determined as the inputs for the Levenberg–Marquardt algorithm based ANN (LM-ANN). The performance of the LM-ANN model was compared with the multiple linear regression (REG) model. When training and testing results of the outputs of the LM-ANN and REG models were examined in terms of the favorite statistical criteria, which are the determination coefficient, adjusted determination coefficient, root mean square error and variance account factor, the results of LM-ANN model were more accurate. In addition to these statistical criteria, the non-parametric Mann–Whitney U test, as an alternative to the Student’s t test, was used for comparing the homogeneities of predicted values. When all the statistics had been investigated, it was seen that the LM-ANN that has been developed, was a successful tool which was capable of UCS prediction.     

岩土边坡稳定性预报的人工神经网络方法

阐述了经典边坡稳定分析方法的局限性,综合考虑了影响边坡稳定性的因素,建立基于人工神经网络的边坡稳定性预报方法。采用遗传算法优化神经网络的结构,以提高其非线性映射能力和泛化能力,从而,提高预报准确度。基于已有的工程实例训练所建立的神经网络,并对新的边坡稳定性问题进行了预报,预报结果表明,所建立的边坡稳定性预报方法具有较高的预报准确度。     

A case study using support vector machines, neural networks and logistic regression in a GIS to identify wells contaminated with nitrate-N

Accurate and inexpensive identification of potentially contaminated wells is critical for water resources protection and management. The objectives of this study are to 1) assess the suitability of approximation tools such as neural networks (NN) and support vector machines (SVM) integrated in a geographic information system (GIS) for identifying contaminated wells and 2) use logistic regression and feature selection methods to identify significant variables for transporting contaminants in and through the soil profile to the groundwater. Fourteen GIS derived soil hydrogeologic and landuse parameters were used as initial inputs in this study. Well water quality data (nitrate-N) from 6,917 wells provided by Florida Department of Environmental Protection (USA) were used as an output target class. The use of the logistic regression and feature selection methods reduced the number of input variables to nine. Receiver operating characteristics (ROC) curves were used for evaluation of these approximation tools. Results showed superior performance with the NN as compared to SVM especially on training data while testing results were comparable. Feature selection did not improve accuracy; however, it helped increase the sensitivity or true positive rate (TPR). Thus, a higher TPR was obtainable with fewer variables.     

基于机器学习模型的青藏高原日降水数据的订正研究

选择了5种机器学习模型,即k最近邻方法（KNN）、多元自回归样条方法（MARS）、支持向量机（SVM）、多项对数线性模型（MLM）和人工神经网络（ANN）,利用海拔、相对湿度、坡向、植被、风速、气温和坡度等因子订正ITPCAS和CMORPH两种常用的青藏高原日降水数据集。五折交叉验证表明,KNN的订正精度最高。在三个验证站点（唐古拉、西大滩和五道梁）的误差分析,以及对青藏高原年降水量的空间分析均表明,KNN对CMORPH的订正效果显著,对ITPCAS在局部区域有一定订正效果,ITPCAS及其订正值的降水空间分布准确度高于CMORPH的订正值。主成分分析法表明降水订正是气象和环境因子综合作用的结果。     

A study of slope stability prediction using neural networks

The determination of the non-linear behaviour of multivariate dynamic systems often presents a challenging and demanding problem. Slope stability estimation is an engineering problem that involves several parameters. The impact of these parameters on the stability of slopes is investigated through the use of computational tools called neural networks. A number of networks of threshold logic unit were tested, with adjustable weights. The computational method for the training process was a back-propagation learning algorithm. In this paper, the input data for slope stability estimation consist of values of geotechnical and geometrical input parameters. As an output, the network estimates the factor of safety (FS) that can be modelled as a function approximation problem, or the stability status (S) that can be modelled either as a function approximation problem or as a classification model. The performance of the network is measured and the results are compared to those obtained by means of standard analytical methods. Furthermore, the relative importance of the parameters is studied using the method of the partitioning of weights and compared to the results obtained through the use of Index Information Theory.     

Mapping landslide susceptibility with logistic regression, multiple adaptive regression splines, classification and regression trees, and maximum entropy methods: a comparative study

Four statistical techniques for modelling landslide susceptibility were compared: multiple logistic regression (MLR), multivariate adaptive regression splines (MARS), classification and regression trees (CART), and maximum entropy (MAXENT). According to the literature, MARS and MAXENT have never been used in landslide susceptibility modelling, and CART has been used only twice. Twenty independent variables were used as predictors, including lithology as a categorical variable. Two sets of random samples were used, for a total of 90 model replicates (with and without lithology, and with different proportions of positive and negative data). The model performance was evaluated using the area under the receiver operating characteristic curve (AUC) statistic. The main results are (a) the inclusion of lithology improves the model performance; (b) the best AUC values for single models are MLR (0.76), MARS (0.76), CART (0.77), and MAXENT (0.78); (c) a smaller amount of negative data provides better results; (d) the models with the highest prediction capability are obtained with MAXENT and CART; and (e) the combination of different models is a way to evaluate the model reliability. We further discuss some key issues in landslide modelling, including the influence of the various methods that we used, the sample size, and the random replicate procedures.     

基于SFLA-GRNN模型的基坑地表最大沉降预测

为可靠预测基坑周边地表沉降的发展趋势,提出了一种基于混合蛙跳算法和广义回归神经网络模型的基坑地表最大沉降预测模型（SFLA-GRNN模型）。首先,在沉降机制分析并初选输入变量集的基础上,利用灰色相关度分析对模型输入、输出变量的相关性进行量化,并剔除与输出变量相关性明显偏小的输入变量;其次,利用混合蛙跳算法（SFLA）对广义回归神经网络模型（GRNN）的平滑因子进行优化确定,减少人为因素对模型精度和泛化能力的不良影响;最后,利用筛选得到的输入变量集建立基坑地表最大沉降预测的广义回归神经网络模型。实例应用及对比计算结果表明,基于灰色相关度的输入变量筛选和基于混合蛙跳算法的平滑因子优化均能够有效提高广义回归神经网络模型的精度和泛化能力,以上结论可为类似变形预测提供参考。     

Determination of stability of slope using Minimax Probability Machine

This article examines the capability of Minimax Probability Machine (MPM) for the determination of stability of slope. MPM is constructed within a probabilistic framework. This study uses MPM as classification and regression tools. Unit weight (γ), cohesion (c), angle of internal friction (φ), slope angle (β), height (H) and pore water pressure coefficient (r_u) have been used as inputs of the MPM model. The outputs of MPM are stability status of slope and factor of safety (F). The results of MPM have been compared with the artificial neural network models. The experimental results demonstrate that the developed MPM is a promising tool for the determination of stability of slope.