Application of statistical learning algorithms to ultimate bearing capacity of shallow foundation on cohesionless soil

This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (q_u) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of q_u of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of q_u of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.     

Predicted ultimate capacity of laterally loaded piles in clay using support vector machine

The determination of ultimate capacity of laterally loaded pile in clay is a key parameter for designing the laterally loaded pile. The available methods for determination of ultimate resistance of pile in clay are not reliable. This study investigates the potential of a support vector machine (SVM)-based approach to predict the ultimate capacity of laterally loaded pile in clay. The SVM, which is firmly based on statistical learning theory, uses a regression technique by introducing an ?-insensitive loss function. A sensitivity analysis has been carried out to determine the relative importance of the factors affecting ultimate capacity. The results show that SVM has the potential to be a practical tool for prediction of the ultimate capacity of pile in clay.     

Relevance vector machine applied to settlement of shallow foundation on cohesionless soils

The settlement of shallow foundation on cohesionless soil is a key parameter in the design of shallow foundation. The recently introduced relevance vector machine (RVM) technique is applied to predict the settlement of shallow foundation on cohesionless soils. RVM allows computation of the prediction intervals, taking into account the uncertainties of both the parameters and the data. It provides much sparser regressors without compromising performance, and kernel bases give a small but worthwhile improvement in performance. It also estimates the prediction variance. This study shows that compared to the available methods, RVM is better at determining the settlement of shallow foundation on cohesionless soil.     

Support vector machine applied to settlement of shallow foundations on cohesionless soils

The determination of settlement of shallow foundations on cohesionless soil is an important task in geotechnical engineering. Available methods for the determination of settlement are not reliable. In this study, the support vector machine (SVM), a novel type of learning algorithm based on statistical theory, has been used to predict the settlement of shallow foundations on cohesionless soil. SVM uses a regression technique by introducing an ε – insensitive loss function. A thorough sensitive analysis has been made to ascertain which parameters are having maximum influence on settlement. The study shows that SVM has the potential to be a useful and practical tool for prediction of settlement of shallow foundation on cohesionless soil.     

Applicability of Statistical Learning Algorithms for Spatial Variability of Rock Depth

Two algorithms are outlined, each of which has interesting features for modeling of spatial variability of rock depth. In this paper, reduced level of rock at Bangalore, India, is arrived from the 652 boreholes data in the area covering 220 sq⋅km. Support vector machine (SVM) and relevance vector machine (RVM) have been utilized to predict the reduced level of rock in the subsurface of Bangalore and to study the spatial variability of the rock depth. The support vector machine (SVM) that is firmly based on the theory of statistical learning theory uses regression technique by introducing ε-insensitive loss function has been adopted. RVM is a probabilistic model similar to the widespread SVM, but where the training takes place in a Bayesian framework. Prediction results show the ability of learning machine to build accurate models for spatial variability of rock depth with strong predictive capabilities. The paper also highlights the capability of RVM over the SVM model.     

Determination of ultimate capacity of driven piles in cohesionless soil: A Multivariate Adaptive Regression Spline approach

The determination of ultimate capacity (Q) of driven piles in cohesionless soil is an important task in geotechnical engineering. This article adopts Multivariate Adaptive Regression Spline (MARS) for prediction Q of driven piles in cohesionless soil. MARS uses length (L), angle of shear resistance of the soil around the shaft (?_shaft), angle of shear resistance of the soil at the tip of the pile (?_tip), area (A), and effective vertical stress at the tip of the pile as input variables. Q is the output of MARS. The results of MARS are compared with that of the Generalized Regression Neural Network model. An equation has been also presented based on the developed MARS. The results show the strong potential of MARS to be applied to geotechnical engineering as a regression tool. Copyright © 2011 John Wiley & Sons, Ltd.     

Prediction of ultimate axial load-carrying capacity of piles using a support vector machine based on CPT data

The support vector machine (SVM) is a relatively new artificial intelligence technique which is increasingly being applied to geotechnical problems and is yielding encouraging results. In this paper SVM models are developed for predicting the ultimate axial load-carrying capacity of piles based on cone penetration test (CPT) data. A data set of 108 samples is used to develop the SVM models. These data were obtained from the literature containing pile load tests and each sample contains information regarding pile geometry, full-scale static pile load tests and CPT results. Moreover, a sensitivity analysis is carried out to examine the relative significance of each input variable with respect to ultimate strength prediction. Finally, a statistical analysis is conducted to make comparisons between predictions obtained from the SVM models and three traditional CPT-based methods for determining pile capacity. The comparison confirms that the SVM models developed in this paper outperform the traditional methods.     

Least square support vector machine and relevance vector machine for evaluating seismic liquefaction potential using SPT

The determination of liquefaction potential of soil is an imperative task in earthquake geotechnical engineering. The current research aims at proposing least square support vector machine (LSSVM) and relevance vector machine (RVM) as novel classification techniques for the determination of liquefaction potential of soil from actual standard penetration test (SPT) data. The LSSVM is a statistical learning method that has a self-contained basis of statistical learning theory and excellent learning performance. RVM is based on a Bayesian formulation. It can generalize well and provide inferences at low computational cost. Both models give probabilistic output. A comparative study has been also done between developed two models and artificial neural network model. The study shows that RVM is the best model for the prediction of liquefaction potential of soil is based on SPT data.     

基于ICA-SVM的超长大直径钢管桩承载力预测

基于支持向量机（SVM）和独立分量分析（ICA）建立了超长大直径钢管桩极限承载力的预测模型。先采用独立分量分析FastICA算法从实际工程的超长大直径钢管桩试桩的实测数据样本中抽取相互独立的分量,这些分量不仅去除了相关性,还保持统计独立,并服从非高斯分布,能更好地表现数据间的本质结构;然后,确定支持向量机作为分类器,以抽取的独立分量作为支持向量机模型的输入参数,建立超长大直径钢管桩的承载力预测模型ICASVM_Q;最后,采用某大桥的工程数据对预测模型进行测试。结果表明,ICASVM_Q的预测效果明显优于以原始数据作为支持向量机模型输入的SVM_Q模型的预测效果。可见,采用将独立分量分析与支持向量机相结合的方法建模预测超长大直径钢管桩的承载力是可行的,ICASVM_Q模型的预测结果可用于超长大直径钢管桩承载力的设计参考,具有一定的工程应用价值。这种方法还可以用于其他领域的智能预测研究中。     

Relevance vector machine applied to slope stability analysis

This paper examines the potential of relevance vector machine (RVM) in slope stability analysis. The nonlinear relationship between slope stability and its influence factors is presented by the relevance vector learning mechanism based on a kernel‐based Bayesian framework. The six input variables used for the RVM for the prediction of stability slope are density (γ), friction angle (C), friction coefficient (?), slope angle (?_r), slope height (H), and pore water pressure (r_u). Comparison of RVM with some other methods is also presented. RVM has been used to compute the error bar. The results presented in this paper clearly highlight that the RVM is a robust tool for the prediction of slope stability. The experimental results show the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling of Oblique Load Test on Batter Pile Group Based on Support Vector Machines and Gaussian Regression

This paper evaluates the potential of two machine learning approaches i.e. Support vector machine (SVR) and Gaussian processes (GP) regression to model the oblique load capacity of batter pile groups. Linear regression was used to compare the performance of both SVR and GP based regression approaches to model the oblique load. Data set used consists of 147 samples obtained from the laboratory experiments. Out of the total sample size, 105 randomly selected samples were used for training whereas remaining 42 were used for testing the models. Input data set consist of angle of oblique load, pile length, sand relative density, number of vertical piles, number of batter piles where as oblique load was considered as output. Two kernel functions i.e. Polynomial and radial based kernel function were used with both SVR and GP regression. A comparison of results suggest that radial basis function based SVR approach works well in comparison to GP and linear regression based approaches and it could successfully be employed in modelling the oblique load capacity of batter pile groups. Parametric analysis and sensitivity analysis suggest that loading angle, pile length and number of batter pile were important in prediction of oblique load.     

Least‐square support vector machine applied to settlement of shallow foundations on cohesionless soils

This paper examines the potential of least‐square support vector machine (LSVVM) in the prediction of settlement of shallow foundation on cohesionless soil. In LSSVM, Vapnik's ε‐insensitive loss function has been replaced by a cost function that corresponds to a form of ridge regression. The LSSVM involves equality instead of inequality constraints and works with a least‐squares cost function. The five input variables used for the LSSVM for the prediction of settlement are footing width (B), footing length (L), footing net applied pressure (P), average standard penetration test value (N) and footing embedment depth (d). Comparison between LSSVM and some of the traditional interpretation methods are also presented. LSSVM has been used to compute error bar. The results presented in this paper clearly highlight that the LSSVM is a robust tool for prediction of settlement of shallow foundation on cohesionless soil. Copyright © 2008 John Wiley & Sons, Ltd.     

支持向量机在砂土液化预测中的应用研究

介绍了人工智能领域最新的基于结构风险最小化原理的数据挖掘算法——支持向量机算法。根据支持向量机线性分类和可以具有不同核函数的非线性分类两种算法，建立了砂土液化预测模型，并且运用Matlab语言编写了程序。通过试算和分析比较得到了最佳模型，最佳模型的预测结果与实际液化情况基本上一致。认为支持向量机算法无论在学习或者预测精度方面都有很大的优越性，而基于支持向量机理论建立的砂土液化预测模型是可行的，且可以较为准确地实现砂土液化的预测。     

公路软基沉降预测的支持向量机模型

提出了基于支持向量机（SVM）模型对公路软基沉降进行预测的一种新方法,工程实例预测结果表明,在同样的训练均方误差下,SVM模型预测能力要优于BP神经网络模型,同时该模型能够综合利用分级加载过程中的沉降观测数据作为训练样本集,比仅依靠预压期内部分实测沉降数据的双曲线法更能反映地基土的变形趋势。因此,将建立的SVM模型应用于公路软基沉降预测能够更准确地反映实际沉降过程     

基于混合核函数PSO-LSSVM的边坡变形预测

支持向量机（SVM）的核函数类型和超参数对边坡位移时序预测的精度有重要影响。鉴于局部核函数学习能力强、泛化性能弱,而全局核函数泛化性能强、学习能力弱的矛盾,通过综合两类核函数各自优点构造了基于全局多项式核和高斯核的混合核函数,并引入粒子群算法（PSO）对最小二乘支持向量机（LSSVM）超参数进行全局寻优,提出了边坡位移时序预测的混合核函数PSO-LSSVM模型。将模型应用于锦屏一级水电站左岸岩石高边坡变形预测分析,并与传统核函数支持向量机预测结果进行对比分析。结果表明,该模型较传统方法在预测精度上有了明显提高,预测结果科学可靠,在边坡位移时序预测中具有良好的实际应用价值。     

Prediction of Resilient Modulus from Post-compaction Moisture Content and Physical Properties Using Support Vector Regression

The present study assesses the use of support vector machine regression to predict the variation of resilient modulus with post-compaction moisture content of soils commonly encountered in Oklahoma, Pennsylvania and Wisconsin. Results show the prediction model using the support vector regression (SVR) approach is a function of degree of saturation, moisture content and plasticity index. The developed model is compared to current models in the literature. Results indicate the proposed SVR model gives more accurate values than current regression models. This model will better predict changes in the bearing capacity of pavements due to seasonal variations of moisture content.     

基于灰色支持向量机残差修正模型的地面沉降量预测

沉降现象在各地区普遍发生,地面沉降量预测越来越受到重视。本文通过结合灰色(GM(1,1))预测模型和支持向量机(SVM)模型各自的优点,建立灰色支持向量机(GM(1,1)-SVM)残差修正模型,在突出时间序列发展趋势影响的同时降低序列中异常值的消极作用。以某高层建筑的18次地面沉降量数据为实例,检验GM(1,1)-SVM模型的预测效果。结果表明:相对单一的GM(1,1)沉降量预测模型,GM(1,1)-SVM模型相对误差小,预测精度高,对地面沉降量预测有一定指导意义。     

Comparison on landslide nonlinear displacement analysis and prediction with computational intelligence approaches

Landslide displacement is widely obtained to discover landslide behaviors for purpose of event forecasting. This article aims to present a comparative study on landslide nonlinear displacement analysis and prediction using computational intelligence techniques. Three state-of-art techniques, the support vector machine (SVM), the relevance vector machine (RVM), and the Gaussian process (GP), are comparatively presented briefly for modeling landslide displacement series. The three techniques are discussed comparatively for both fitting and predicting the landslide displacement series. Two landslides, the Baishuihe colluvial landslide in China Three Georges and the Super-Sauze mudslide in the French Alps, are illustrated. The results prove that the computational intelligence approaches are feasible and capable of fitting and predicting landslide nonlinear displacement. The Gaussian process, on the whole, performs better than the support vector machine, relevance vector machine, and simple artificial neural network (ANN) with optimized parameter values in predictive analysis of the landslide displacement.     

Analysis of soil erosion characteristics in small watersheds with particle swarm optimization, support vector machine, and artificial neuronal networks

Sand production by soil erosion in small watershed is a complex physical process. There are few physical models suitable to describe the characteristics of the intense erosion in domestic loess plateau. Introducing support vector machine (SVM) oriented to small sample data and possessing good extension property can be an effective approach to predict soil erosion because SVM has been applied in hydrological prediction to some extent. But there are no effective methods to select the rational parameters for SVM, which seriously limited the practical application of SVM. This paper explored the application of intelligence-based particle swarm optimization (PSO) algorithm in automatic selection of parameters for SVM, and proposed a prediction model by linking PSO and SVM for small sample data analysis. This method utilized the high efficiency optimization property and swarm paralleling property of PSO algorithm and the relatively strong learning and extending capacity of SVM. For an example of Huangfuchuan small watershed, its intensive fragmentation and intense erosion earn itself the name of “worst erosion in the world”. Using four characteristics selection algorithms of correlation feature selection, the primary affecting factors for soil erosion in this small watershed were determined to be the channel density, ravine area, sand rock proportion, and the total vegetation coverage. Based on the proposed PSO–SVM algorithm, the soil erosion modulus in the small watershed was predicted. The accuracy of the simulation and prediction was good, and the average error was 3.85%. The SVM predicting model was based on the monitoring data of sand production. The construction of the SVM erosion modulus prediction model for the small watershed comprehensively reflected the complex mechanism of soil erosion and sand production. It had certain advantage and relatively high practical value in small sample prediction in the discipline of soil erosion.     

Modelling pile capacity using Gaussian process regression

This paper investigates the potential of a Gaussian process (GP) regression approach to predict the load-bearing capacity of piles. Support vector machines (SVM) and empirical relations were used to compare the performance of the GP regression approach. The first dataset used in this study was derived from actual pile-driving records in cohesion-less soil. Out of a total of 94 pieces of data, 59 were used to train and the remaining 35 data were used to test the created models. A radial basis function and Pearson VII function kernels were used with both GP and SVM. The results from this dataset indicate improved performance by GP regression in comparison to SVM and empirical relations. To validate the performance of the GP regression approach, another dataset consisting of 38 pieces of data was considered. The results from this dataset also suggest improved performance by the Pearson VII function kernel-based GP regression modelling approach in comparison to SVM.