• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.479-485
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• 2003

The influence of observations on the Wilks' lambda test of a linear hypothesis in multivariate regression is investigated using the local influence method. The perturbation scheme of case-weights is considered. A numerical example is given to show the effectiveness of the local influence method in identifying the influential observations.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.33-40
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• 1994

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

• Geomechanics and Engineering
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• v.3 no.4
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• pp.285-290
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• 2011

This article employs Multivariate Adaptive Regression Spline (MARS) for determination of friction capacity of driven piles in clay. MARS is non-parametric adaptive regression procedure. Pile length, pile diameter, effective vertical stress, and undrained shear strength are considered as input of MARS and the output of MARS is friction capacity. The developed MARS gives an equation for determination of $f_s$ of driven piles in clay. The results of the developed MARS have been compared with the Artificial Neural Network. This study shows that the developed MARS is a robust model for prediction of $f_s$ of driven piles in clay.

• Geomechanics and Engineering
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• v.7 no.4
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• pp.431-458
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• 2014

Construction of a new cavern close to an existing cavern will result in a modification of the state of stresses in a zone around the existing cavern as interaction between the twin caverns takes place. Extensive plane strain finite difference analyses were carried out to examine the deformations induced by excavation of underground twin caverns. From the numerical results, a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) has been used to relate the maximum key point displacement and the percent strain to various parameters including the rock quality, the cavern geometry and the in situ stress. Probabilistic assessments on the serviceability limit state of twin caverns can be performed using the First-order reliability spreadsheet method (FORM) based on the built MARS model. Parametric studies indicate that the probability of failure $P_f$ increases as the coefficient of variation of Q increases, and $P_f$ decreases with the widening of the pillar.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.937-945
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• 2017

The purpose of using a control chart is to detect any change that occurs in the process. When control charts are used to monitor processes, we want to identify this changes as quickly as possible. Many problems in quality control involve a vector of observations of several characteristics rather than a single characteristic. Multivariate CUSUM or EWMA charts have been developed to address the problem of monitoring covariance matrix or the joint monitoring of mean vector and covariance matrix. However, control charts tend to work poorly when we use the highly correlatted variables. In order to overcome it, Hawkins (1991) proposed the use of regression adjustment variables. In this paper, to monitor covariance matrix, we investigate the performance of MEWMA-type control charts with and without the use of regression adjusted variables.

• Computers and Concrete
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• v.16 no.4
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• pp.569-585
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• 2015

Various computational tools are available for modeling highly nonlinear structural engineering problems that lack a precise analytical theory or understanding of the phenomena involved. This paper adopts a fairly simple nonparametric adaptive regression algorithm known as multivariate adaptive regression splines (MARS) to model the nonlinear interactions between variables. The MARS method makes no specific assumptions about the underlying functional relationship between the input variables and the response. Details of MARS methodology and its associated procedures are introduced first, followed by a number of examples including three practical structural engineering problems. These examples indicate that accuracy of the MARS prediction approach. Additionally, MARS is able to assess the relative importance of the designed variables. As MARS explicitly defines the intervals for the input variables, the model enables engineers to have an insight and understanding of where significant changes in the data may occur. An example is also presented to demonstrate how the MARS developed model can be used to carry out structural reliability analysis.

• Geomechanics and Engineering
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• v.10 no.3
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• pp.269-284
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• 2016

Simplified techniques based on in situ testing methods are commonly used to assess seismic liquefaction potential. Many of these simplified methods were developed by analyzing liquefaction case histories from which the liquefaction boundary (limit state) separating two categories (the occurrence or non-occurrence of liquefaction) is determined. As the liquefaction classification problem is highly nonlinear in nature, it is difficult to develop a comprehensive model using conventional modeling techniques that take into consideration all the independent variables, such as the seismic and soil properties. In this study, a modification of the Multivariate Adaptive Regression Splines (MARS) approach based on Logistic Regression (LR) LR_MARS is used to evaluate seismic liquefaction potential based on actual field records. Three different LR_MARS models were used to analyze three different field liquefaction databases and the results are compared with the neural network approaches. The developed spline functions and the limit state functions obtained reveal that the LR_MARS models can capture and describe the intrinsic, complex relationship between seismic parameters, soil parameters, and the liquefaction potential without having to make any assumptions about the underlying relationship between the various variables. Considering its computational efficiency, simplicity of interpretation, predictive accuracy, its data-driven and adaptive nature and its ability to map the interaction between variables, the use of LR_MARS model in assessing seismic liquefaction potential is promising.

• Steel and Composite Structures
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• v.33 no.4
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• pp.583-594
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• 2019

In the areas highly exposed to earthquakes, concrete-filled steel tube columns (CFSTCs) are known to provide superior structural aspects such as (i) high strength for good seismic performance (ii) high ductility (iii) enhanced energy absorption (iv) confining pressure to concrete, (v) high section modulus, etc. Numerous studies were reported on behavior of CFSTCs under axial compression loadings. This paper presents an analytical model to predict ultimate load capacity of CFSTCs with circular sections under axial load by using multivariate adaptive regression splines (MARS). MARS is a nonlinear and non-parametric regression methodology. After careful study of literature, 150 comprehensive experimental data presented in the previous studies were examined to prepare a data set and the dependent variables such as geometrical and mechanical properties of circular CFST system have been identified. Basically, MARS model establishes a relation between predictors and dependent variables. Separate regression lines can be formed through the concept of divide and conquers strategy. About 70% of the consolidated data has been used for development of model and the rest of the data has been used for validation of the model. Proper care has been taken such that the input data consists of all ranges of variables. From the studies, it is noted that the predicted ultimate axial load capacity of CFSTCs is found to match with the corresponding experimental observations of literature.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.533-545
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• 2017

Quantile regression models provide a variety of useful statistical information by estimating the conditional quantile function of the response variable. However, the traditional linear quantile regression model can lead to the distorted and incorrect results when analysing real data having a nonlinear relationship between the explanatory variables and the response variables. Furthermore, as the complexity of the data increases, it is required to analyse multiple response variables simultaneously with more sophisticated interpretations. For such reasons, we propose a multivariate quantile regression tree model. In this paper, a new split variable selection algorithm is suggested for a multivariate regression tree model. This algorithm can select the split variable more accurately than the previous method without significant selection bias. We investigate the performance of our proposed method with both simulation and real data studies.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.493-500
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• 2000

Rock Mass Rating has been widely applied to the underground tunnel excavation and many other practical problems in rock engineering. However, Rock Mass Rating is hard to make out because it is difficult to estimate each valuation items through all kind of field situations and items of RMR have interdependence. So the experts of tunnel assessment have problems with rating rock mass. In this study, using multivariate analysis based on domestic data(1011EA) of water conveyance tunnel, we presented rock mass rating system which is objective and easy to use. The constituents of RMR are decided to RQD, condition of discontinuities, groundwater conditions, orientation of discontinuities, intact rock strength, spacing of discontinuities in important order. In each step, we proposed the best multiple regression model for RMR system. And using data which have been collected at other site, we examined that presented multiple regression model was useful.