Slope Stability Analysis Using Multivariate Adaptive Regression Spline
01 Jan 2013-pp 327-342
TL;DR: In this paper, the capability of multivariate adaptive regression spline (MARS) for slope stability analysis was investigated and the results confirmed that the developed MARS has the ability to predict FOS of slope.
Abstract: This chapter investigates the capability of multivariate adaptive regression spline (MARS) for slope stability analysis MARS, a multivariate, nonparametric regression procedure, is a local regression method that uses a series of local so-called basis functions to model complex relationships The six input variables used for the MARS model in this study were unit weight ( d ), cohesion ( c ), angle of internal friction ( ϕ ), slope angle ( β ), height ( H ), and pore water pressure coefficient ( r u ) The factor of safety (FOS) of slope was the output of MARS An equation is presented for the determination of the FOS of slope based on the developed MARS A sensitivity analysis was carried out to determine the effect of each input parameter on the predicted FOS The results confirm that the developed MARS has the ability to predict FOS of slope
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TL;DR: The results showed that the proposed ELM model achieved an adequate level of prediction accuracy, improving MARS, M5 Tree and SVR models, and could be employed as a reliable and accurate data intelligent approach for predicting the compressive strength of foamed concrete.
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TL;DR: In this paper, the authors used multivariate adaptive regression splines (MARS), least square support vector machine (LSSVM), and M5Tree models by forecasting SPI in eastern Australia.
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TL;DR: It is advocated that the RVM model can be employed as a promising machine learning tool for the prediction of evaporative loss.
Abstract: The forecasting of evaporative loss (E) is vital for water resource management and understanding of hydrological process for farming practices, ecosystem management and hydrologic engineering. This study has developed three machine learning algorithms, namely the relevance vector machine (RVM), extreme learning machine (ELM) and multivariate adaptive regression spline (MARS) for the prediction of E using five predictor variables, incident solar radiation (S), maximum temperature (T
max), minimum temperature (T
min), atmospheric vapor pressure (VP) and precipitation (P). The RVM model is based on the Bayesian formulation of a linear model with appropriate prior that results in sparse representations. The ELM model is computationally efficient algorithm based on Single Layer Feedforward Neural Network with hidden neurons that randomly choose input weights and the MARS model is built on flexible regression algorithm that generally divides solution space into intervals of predictor variables and fits splines (basis functions) to each interval. By utilizing random sampling process, the predictor data were partitioned into the training phase (70 % of data) and testing phase (remainder 30 %). The equations for the prediction of monthly E were formulated. The RVM model was devised using the radial basis function, while the ELM model comprised of 5 inputs and 10 hidden neurons and used the radial basis activation function, and the MARS model utilized 15 basis functions. The decomposition of variance among the predictor dataset of the MARS model yielded the largest magnitude of the Generalized Cross Validation statistic (≈0.03) when the T
max was used as an input, followed by the relatively lower value (≈0.028, 0.019) for inputs defined by the S and VP. This confirmed that the prediction of E utilized the largest contributions of the predictive features from the T
max, verified emphatically by sensitivity analysis test. The model performance statistics yielded correlation coefficients of 0.979 (RVM), 0.977 (ELM) and 0.974 (MARS), Root-Mean-Square-Errors of 9.306, 9.714 and 10.457 and Mean-Absolute-Error of 0.034, 0.035 and 0.038. Despite the small differences in the overall prediction skill, the RVM model appeared to be more accurate in prediction of E. It is therefore advocated that the RVM model can be employed as a promising machine learning tool for the prediction of evaporative loss.
121 citations
Cites background or methods from "Slope Stability Analysis Using Mult..."
...As such, they have been applied extensively in prediction of hydro-meteorological parameters (Abraham and Steinberg 2001; Adamowski et al. 2012; Samui 2012; Sephton 2001; Sharda et al. 2008) although to our best knowledge, this research is the first one to apply the MARS model for the prediction of…...
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...As such, they have been applied extensively in prediction of hydro-meteorological parameters (Abraham and Steinberg 2001; Adamowski et al. 2012; Samui 2012; Sephton 2001; Sharda et al. 2008) although to our best knowledge, this research is the first one to apply the MARS model for the prediction of monthly E in Australia....
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...If several basis functions are chosen, overfitting can occur so some basis functions need to be deleted in the fine-tuning phase of the model development (Samui 2012)....
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TL;DR: The newly designed multi-model ensemble-based approach can be considered as a pragmatic step for mapping groundwater contamination risks of multiple aquifer systems with multi- model techniques, yielding the high accuracy of the ANN committee-based model.
106 citations
Cites background or methods from "Slope Stability Analysis Using Mult..."
...…c penalty which is usually set to 2 or 3 (k − 1) / 2 is the number of hinge-function knots, so the formula penalizes the addition of knots In the final model selection phase, the optimal model with the lowest GCV is chosen where the redundant basis functions are deleted (Samui, 2012b; Kisi, 2015)....
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...…to the ELM, the MARS model is also able to determine the basic feature relationships between input(s) and output variables without assumptions (Friedman, 1991; Samui, 2012a), and therefore, was also considered as another machine learning model used to construct the ANN-based committeemodel....
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TL;DR: In this article, a standard mix design method for Class F, low calcium fly ash based geopolymer concrete using Multivariate Adaptive Regression Spline (MARS) model is proposed.
74 citations
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Abstract: In this letter we discuss a least squares version for support vector machine (SVM) classifiers. Due to equality type constraints in the formulation, the solution follows from solving a set of linear equations, instead of quadratic programming for classical SVM‘s. The approach is illustrated on a two-spiral benchmark classification problem.
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TL;DR: In this article, a new method is presented for flexible regression modeling of high dimensional data, which takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data.
Abstract: A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions.
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2,139 citations
TL;DR: In this paper, a method for statically determinating the shape of a slip surface is presented, and the assumptions necessary to make the problem statically determinate are discussed; the solution of the governing equations ensures that all equilibrium and boundary conditions are satisfied.
Abstract: Synopsis Within the framework of limit equilibrium methods of stability analysis, no restriction need be placed at the outset upon the shape of the possible slip surface. In many cases, the critical surface may deviate significantly from a circle or a plane and therefore a method that facilitates the analysis of surfaces of arbitrary shape is of interest. A method for doing this is presented. The assumptions necessary to make the problem statically determinate are discussed. The solution of the governing equations ensures that all equilibrium and boundary conditions are satisfied. The method has been programmed for a digital computer and some examples of its application are given. Comparisons are also made with other methods of analysis. Dans la cadre des methodes d'equilibre limite d'analyse de stabilite, il n'y a pas besoin d'imposer de restrictions au depart sur la forme de la surface de glissement eventuelle. Dans bien des cas, la surface critique peut devier d'une maniere significative d'un cercle ou...
1,579 citations
TL;DR: In this paper, the authors present the results of the effective stress analysis in terms of stability coeffcients from which the factor of safety can be rapidly obtained and illustrate the use of these coefficients with the distributions of pore pressure encountered in typical earth dams and cuts.
Abstract: Synopsis The application of the effective stress analysis to earth slopes has suffered through lack of a general solution such as that presented by Taylor (1937) for the total stress analysis. Recent developments in computing technique have been applied to the slip circle method and have made it possible to present the results of the effective stress analysis in terms of stability coeffcients from which the factor of safety can be rapidly obtained. Illustrations are given of the use of these coefficients with the distributions of pore pressure encountered in typical earth dams and cuts. L'application de principe des tensions efficace sur l'analyse des pentes de terre c'est empecher de l'absence d'une solution generale, telle que celle du Taylor (1937) pour l'analyse des pentes en termes des tensions totales. L'application des progres recents dans la technique de computation, a la methode du cercle de glissement, a rendu possible la presentation des resultats en termes de coef-ficients de stabilitte, baser...
369 citations