Determination of liquefaction susceptibility of soil: a least square support vector machine approach

This article adopts least square support vector machine (LSSVM) for determination of liquefactions susceptibility of soil based on standard penetration test data. Two models (Models I and II) have been developed. For Model I, input variables are cyclic stress ratio and standard penetration test value (N). Model II employs peak ground acceleration and N as input variables. The developed LSSVM models (Models I and II) give equations for determination of liquefaction susceptibility of soil. The performances of Models I and II are the same. The developed LSSVM gives probabilistic output. The results of LSSVM have been compared with the artificial neural network model. This article shows that N and the peak ground acceleration are sufficient input parameters for determination of liquefaction susceptibility of soil. Copyright © 2012 John Wiley & Sons, Ltd.     

Site characterization model using least‐square support vector machine and relevance vector machine based on corrected SPT data (Nc)

Statistical learning algorithms provide a viable framework for geotechnical engineering modeling. This paper describes two statistical learning algorithms applied for site characterization modeling based on standard penetration test (SPT) data. More than 2700 field SPT values (N) have been collected from 766 boreholes spread over an area of 220 sqkm area in Bangalore. To get N corrected value (N_c), N values have been corrected (N_c) for different parameters such as overburden stress, size of borehole, type of sampler, length of connecting rod, etc. In three‐dimensional site characterization model, the function N_c=N_c (X, Y, Z), where X, Y and Z are the coordinates of a point corresponding to N_c value, is to be approximated in which N_c value at any half‐space point in Bangalore can be determined. The first algorithm uses least‐square support vector machine (LSSVM), which is related to a ridge regression type of support vector machine. The second algorithm uses relevance vector machine (RVM), which combines the strengths of kernel‐based methods and Bayesian theory to establish the relationships between a set of input vectors and a desired output. The paper also presents the comparative study between the developed LSSVM and RVM model for site characterization. Copyright © 2009 John Wiley & Sons, Ltd.     

Support vector machines‐based modelling of seismic liquefaction potential

This paper investigates the potential of support vector machines (SVM)‐based classification approach to assess the liquefaction potential from actual standard penetration test (SPT) and cone penetration test (CPT) field data. SVMs are based on statistical learning theory and found to work well in comparison to neural networks in several other applications. Both CPT and SPT field data sets is used with SVMs for predicting the occurrence and non‐occurrence of liquefaction based on different input parameter combination. With SPT and CPT test data sets, highest accuracy of 96 and 97%, respectively, was achieved with SVMs. This suggests that SVMs can effectively be used to model the complex relationship between different soil parameter and the liquefaction potential. Several other combinations of input variable were used to assess the influence of different input parameters on liquefaction potential. Proposed approach suggest that neither normalized cone resistance value with CPT data nor the calculation of standardized SPT value is required with SPT data. Further, SVMs required few user‐defined parameters and provide better performance in comparison to neural network approach. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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。     

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.     

基于聚类-二叉树支持向量机的砂土液化预测模型

建立在统计学习理论基础之上的支持向量机（SVM）,是一种基于结构风险最小的小样本机器学习方法。经典的支持向量机主要针对二分类问题,而工程实践中遇到的往往是多分类问题。根据影响砂土液化的主要因素,采用聚类分析中的类距离思想,建立了基于聚类-二叉树的多类支持向量机的砂土液化判别模型。该模型可以通过有限样本的学习,建立砂土液化与各影响因素之间的非线性关系。研究结果表明,基于聚类-二叉树支持向量机的层次结构合理,分类精度高,泛化性好,可对砂土液化等级进行较准确判别     

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.     

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.     

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.     

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.     

Application of Relevance Vector Machine for Prediction of Ultimate Capacity of Driven Piles in Cohesionless Soils

This paper examines the potential of relevance vector machine (RVM) in prediction of ultimate capacity of driven piles in cohesionless soils. RVM is a Bayesian framework for regression and classification with analogous sparsity properties to the support vector machine (SVM). In this study, RVM has been used as a regression tool. It can be seen as a probabilistic version of SVM. In this study, RVM model outperforms the artificial neural network (ANN) model based on root-mean-square-error (RMSE) and mean-absolute-error (MAE) performance criteria. It also estimates the prediction variance. An equation has been developed for the prediction of ultimate capacity of driven piles in cohesionless soils based on the RVM model. The results show that the RVM model has the potential to be a practical tool for the prediction of ultimate capacity of driven piles in cohesionless soils.     

Least Square Support Vector Machine Applied to Slope Reliability Analysis

This paper investigates the feasibility of Least square support vector machine (LSSVM) model to cope the problem of implicit performance function during first order second moment (FOSM) method based slope reliability analysis. LSSVM is firmly based on the theory of statistical learning. In LSSVM, Vapnik’s ε -insensitive loss function has been replaced by a cost function which corresponds to a form of ridge regression. Here, LSSVM has been used as a regression technique to approximate implicit performance functions. A slope example has been presented for illustrating the applicability of LSSVM based FOSM method. The developed LSSVM based FOSM has been compared with the artificial neural network (ANN) and least square method. The result shows that the approximation of LSSVM can be used in the FOSM method for slope reliability analysis.     

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     

A Comparative Study of Least Square Support Vector Machines and Multiclass Alternating Decision Trees for Spatial Prediction of Rainfall-Induced Landslides in a Tropical Cyclones Area

The objective of this study is to explore and compare the least square support vector machine (LSSVM) and multiclass alternating decision tree (MADT) techniques for the spatial prediction of landslides. The Luc Yen district in Yen Bai province (Vietnam) has been selected as a case study. LSSVM and MADT are effective machine learning techniques of classification applied in other fields but not in the field of landslide hazard assessment. For this, Landslide inventory map was first constructed with 95 landslide locations identified from aerial photos and verified from field investigations. These landslide locations were then divided randomly into two parts for training (70 % locations) and validation (30 % locations) processes. Secondly, landslide affecting factors such as slope, aspect, elevation, curvature, lithology, land use, distance to roads, distance to faults, distance to rivers, and rainfall were selected and applied for landslide susceptibility assessment. Subsequently, the LSSVM and MADT models were built to assess the landslide susceptibility in the study area using training dataset. Finally, receiver operating characteristic curve and statistical index-based evaluations techniques were employed to validate the predictive capability of these models. As a result, both the LSSVM and MADT models have high performance for spatial prediction of landslides in the study area. Out of these, the MADT model (AUC = 0.853) outperforms the LSSVM model (AUC = 0.803). From the landslide study of Luc Yen district in Yen Bai province (Vietnam), it can be conclude that the LSSVM and MADT models can be applied in other areas of world also for and spatial prediction. Landslide susceptibility maps obtained from this study may be helpful in planning, decision making for natural hazard management of the areas susceptible to landslide hazards.     

A Novel Methodology to Classify Soil Liquefaction Using Deep Learning

In this research, deep learning (DL) model is proposed to classify the soil reliability for liquefaction. The applicability of the DL model is tested in comparison with emotional backpropagation neural network (EmBP). The database encompassing cone penetration test of Chi–Chi earthquake. This study uses cone resistance (q_c) and peck ground acceleration as inputs for prediction of liquefaction susceptibility of soil. The performance of developed models has been assessed by using various parameters (receiver operating characteristic, sensitivity, specificity, Phi correlation coefficient, Precision–Recall F measure). The performance of DL is excellent. Consistent results obtained from the proposed deep learning model, compared to the EmBP, indicate the robustness of the methodology used in this study. In addition, both the developed model was also tested on global earthquake data. During validation on global data, both the models shows good results based on fitness parameters. The developed classification models a simple, but also efficient decision-making tool in engineering design to quantitatively assess the liquefaction potential. The finding of this paper can be further used to capture the relationship between soil and earthquake parameters.

     

Modeling of SPT Seismic Liquefaction Data Using Minimax Probability Machine

The determination of seismic liquefaction potential of soil is an important task in geotechnical engineering. This article uses Minimax Probability Machine (MPM) for determination of seismic liquefaction potential of soil based on Standard Penetration Test value (N). MPM is developed based on the use of hyperplanes. It is a discriminant classifier. This study uses MPM as a classification tool. MPM uses the database collected from Chi–Chi earthquake. Two models (MODEL I and MODEL II) have been developed. MODEL I uses Cyclic Stress Ratio and N as input variables. Peck Ground Acceleration and N have been adopted as inputs for MODEL II. The performance of MODEL I and MODEL II are 97.67 and 96.51 % respectively. The performance of MODEL II is 94.11 % for the global data. The developed MPM shows good generalization capability. The results show that the developed MPM has ability for determination of seismic liquefaction potential of soil.     

Evaluation of liquefaction potential based on CPT results using evolutionary polynomial regression

In this paper a new approach is presented, based on evolutionary polynomial regression (EPR), for determination of liquefaction potential of sands. EPR models are developed and validated using a database of 170 liquefaction and non-liquefaction field case histories for sandy soils based on CPT results. Three models are presented to relate liquefaction potential to soil geometric and geotechnical parameters as well as earthquake characteristics. It is shown that the EPR model is able to learn, with a very high accuracy, the complex relationship between liquefaction and its contributing factors in the form of a function. The attained function can then be used to generalize the learning to predict liquefaction potential for new cases not used in the construction of the model. The results of the developed EPR models are compared with a conventional model as well as a number of neural network-based models. It is shown that the proposed EPR model provides more accurate results than the conventional model and the accuracy of the EPR results is better than or at least comparable to that of the neural network-based models proposed in the literature. The advantages of the proposed EPR model over the conventional and neural network-based models are highlighted.     

Interval prediction of landslide displacement with dual-output least squares support vector machine and particle swarm optimization algorithms

For landslide displacement, interval predictions are generally more realistic and reliable compared with traditional point predictions. This paper presents a new interval prediction method for landslide displacement integrating dual-output least squares support vector machine (DO-LSSVM) and particle swarm optimization (PSO) algorithms. In this new method, the PSO algorithm is employed to optimize coefficients of the least squares support vector machine (LSSVM) model for obtaining point prediction results, and the interval prediction of the landslide displacement is made based on the dual-outputs obtained from the DO-LSSVM model. To assess the rationality of the predictions, three performance evaluation indicators, including the prediction interval coverage probability (PICP), normalized mean prediction interval width (NMPIW), and coverage width-based criterion (CWC), are established. Case studies of the Tanjiahe landslide and the Baishuihe landslide in the Three Gorges Reservoir region are then used to demonstrate the effectiveness of the proposed method in predicting the landslide displacement interval. The case study results demonstrate that this new method has the best overall performance compared with other existing methods, and this new method can provide accurate and reliable results for the medium- to long-term interval prediction of landslide displacement.