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.     

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 In LSSVM, Vapnik's ε‐insensitive loss function has been replaced by a cost function that corresponds to a form of ridge regression.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.     

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.     

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.     

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.     

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.     

Geostatistical modelling of spatial and depth variability of SPT data for Bangalore

The purpose of this study is to develop a geostatistical model to evaluate the spatial and depth variability of Standard Penetration Test (SPT) data from Bangalore, India. The database consists of 766 boreholes spread over a 220 km² area, with several SPT values (N) in each of them. The geostatistical analysis is done for N corrected (N _corrected) values. The N _corrected value has been corrected for different parameters such as overburden stress, size of the bore hole, type of sampler, hammer energy and length of the connecting rod. The knowledge of the semivariogram of the SPT data is used with kriging theory to estimate the values at points in the subsurface of Bangalore where field measurements are not available. The model is used to compute the variance of estimated data. The model predicts reasonably well the SPT data. The geostatistical model provides valuable results that can be used for seismic hazard analysis, site response and liquefaction studies for the development of microzonation maps. The predicted N values from the developed model can also be used to estimate the subsurface information, allowable bearing pressure of soils and elastic modulus of soils.     

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.     

地球化学异常识别的两种机器学习算法之比较

在Sklearn的Python语言代码基础上,开发了基于孤独森林和一类支持向量机的多元地球化学异常识别方法程序。选择吉林省和龙地区为实验区,从1∶5万水系沉积物资料中提取地球化学异常。把实验区已知矿点的空间分布位置作为"地真"数据,绘制两种机器学习算法的ROC曲线并计算AUC值,用来对比两种方法的多元地球化学异常识别效果。研究结果表明:两种机器学习算法都能够有效识别多元地球化学异常,所提取的多元地球化学异常与已知矿点具有显著的空间关联性;孤独森林算法在数据处理耗时和多元地球化学异常识别效果方面略优于一类支持向量机。     

岩爆分类的支持向量机方法

针对岩爆分类问题,提出了基于支持向量机的分类方法。通过对影响岩爆因素的分析,运用支持向量机理论建立岩爆类别的支持向量机模型。结果表明,基于支持向量机的岩爆分类方法具有较高的准确率,该方法是科学可行的,具有广泛的应用前景。     

福宁高速公路八尺门滑坡变形演化规律预测研究

将进化支持向量机方法用于边坡变形规律的研究,用遗传算法搜索支持向量机最优参数,避免了人为选择支持向量机参数的盲目性,提高了支持向量机的推广预测能力。利用这种方法预测边坡变形规律,并与监测到的历史数据进行对比,以便工程技术人员及时调整设计方案和施工,维护边坡的稳定性。工程实例表明,该方法具有预测精度高和实时性等特点,具有广阔的应用前景。     

加权支持向量回归机及其在水质预测中的应用

支持向量机是一种基于结构风险最小化原理的学习技术，也是一种新的具有很好泛化性能的回归方法。本文对用于回归估计的标准支持向量机加以改进，提出了一种新的用于回归估计的支持向量机学习算法，针对各样本重要性的差异，给各个样本的惩罚系数和误差要求赋予不同权重，并利用加权支持向量回归机的理论及其算法构建水质预测模型。实验结果表明，该方法对水质具有较好的预测效果。     

Intelligent modelling of clay compressibility using hybrid meta-heuristic and machine learning algorithms

Compression index Ccis an essential parameter in geotechnical design for which the effectiveness of correlation is still a challenge.This paper suggests a novel modelling approach using machine learning(ML)technique.The performance of five commonly used machine learning(ML)algorithms,i.e.back-propagation neural network(BPNN),extreme learning machine(ELM),support vector machine(SVM),random forest(RF)and evolutionary polynomial regression(EPR)in predicting Cc is comprehensively investigated.A database with a total number of 311 datasets including three input variables,i.e.initial void ratio e0,liquid limit water content wL,plasticity index Ip,and one output variable Cc is first established.Genetic algorithm(GA)is used to optimize the hyper-parameters in five ML algorithms,and the average prediction error for the 10-fold cross-validation(CV)sets is set as thefitness function in the GA for enhancing the robustness of ML models.The results indicate that ML models outperform empirical prediction formulations with lower prediction error.RF yields the lowest error followed by BPNN,ELM,EPR and SVM.If the ranges of input variables in the database are large enough,BPNN and RF models are recommended to predict Cc.Furthermore,if the distribution of input variables is continuous,RF model is the best one.Otherwise,EPR model is recommended if the ranges of input variables are small.The predicted correlations between input and output variables using five ML models show great agreement with the physical explanation.     

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.

     

基于灰色最小二乘支持向量机的边坡位移预测

利用边坡实测位移序列预测边坡未来时间的位移,可以有效地判断边坡的稳定性。在分析了灰色预测方法和最小二乘支持向量机各自的优缺点的基础上,提出了将二者相结合的一种新的预测模型--灰色最小二乘支持向量机预测模型。新模型既发挥了灰色预测方法中“累加生成”的优点,弱化了原始序列中随机扰动因素的影响,增强了数据的规律性,又充分利用了最小二乘支持向量机求解速度快、易于描述非线性关系的优良特性,避免了灰色预测方法及模型存在的理论缺陷。同时,采用遗传算法进行了模型的参数优化,通过2个工程实例说明灰色最小二乘支持向量机模型预测边坡位移的有效性,具有较高的精度。     

Support vector regression to predict asphalt mix performance

Material properties are essential in the design and evaluation of pavements. In this paper, the potential of support vector regression (SVR) algorithm is explored to predict the resilient modulus (M_R), which is an essential property in designing and evaluating pavement materials, particularly hot mix asphalt typically used in Oklahoma. SVR is a statistical learning algorithm that is applied to regression problems; in our study, SVR was shown to be superior to the least squares (LS). Compared with the widely used LS method, the results of this study show that SVR significantly reduces the mean‐squared error and improves the correlation coefficient. Copyright © 2008 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.     

支持向量机方法在膨胀土分类中的应用

将支持向量机方法应用于膨胀土分类问题中,建立了膨胀土分类的支持向量机模型。以膨胀土实测数据为学习样本,经过训练,得到膨胀土的分类区间。应用该模型对剩余的膨胀土数据进行预测,预测结果表明支持向量机分类模型性能良好、预测精度高、简便易行,是膨胀土判别的一种有效方法,具有广阔的应用前景。     

Relevance vector machine‐based response surface for slope reliability analysis

A new computing method is proposed for reliable analysis. The limit state function is implicit and nonlinear in reliability analysis of slopes and is difficult to apply by traditional reliability methods, especially in large‐scale project applications. Relevance vector machines (RVMs) are capable of approximating the limit state function without the need for additional assumptions regarding the function form, as opposed to traditional polynomial response surfaces. RVMs were adapted to obtain the limit state function. We propose an RVM‐based response surface method combined with the first‐order reliability method for slope reliability analysis and describe its step‐by‐step implementation. The reliability index obtained from the proposed method shows excellent agreement with traditional response surface method results. Copyright © 2017 John Wiley & Sons, Ltd.     

滑坡位移的多模态支持向量机模型预测

将支持向量机（support vector machine,SVM）方法与信号分析中的经验模态分解（empirical mode decomposition, EMD）方法相匹配,提出了一种通过多模态支持向量机函数回归分析建模预测滑坡位移的理论方法。以边坡位移历史观测数据为基础,应用EMD方法获得滑坡形成过程中位移演化的几个特征时间模态,构成了多模态信息统计学习样本,确定了边坡位移演化的自适应多尺度变化信息。对应于每个经验模态的位移变化信息,引入了多模态SVM建模方法,然后合成不同经验模态下边坡位移的计算结果,得到滑坡位移的预测值。以卧龙寺新滑坡和新滩滑坡的监测数据为基础的理论预测结果表明,与采用遗传算法的神经网络方法的预测结果相比,支持向量机经验模态方法具有更强的预测能力,理论预测结果与实际监测值具有很好的一致性