Robust Linear Regression for Undrained Shear Strength Data
Outlier data has attracted considerable interesting geotechnical data. When doing classical linear least squares regression, if the regression data satisfied certain regression weights, the ordinary least squares regression is considered as the best metho
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Institute of Geotechnical Engineering, Southeast University, Nanjing, Jiangsu, China [email protected] Department of Civil Engineering, The University of Texas at Arlington, Arlington, TX, USA
Abstract. Outlier data has attracted considerable interesting geotechnical data. When doing classical linear least squares regression, if the regression data satisfied certain regression weights, the ordinary least squares regression is considered as the best method. However, the estimating and regression results may be inaccurate in case of these data not meeting given assumptions. Particularly in least squares regression analysis, there is some data (outliers) violating the assumption of normally distributed residuals. Under situation of regression data blending to outliers, robust regression is the best fit method. It can discriminate outliers and offer robust results when the regression data exists outliers. The purpose of this study is to make use of robust regression method to trend regression in geotechnical data analysis. Without defining absolute outliers from geotechnical testing data, outlier data of undrained shear strength is detected based on robust regression result. Keywords: Undrained shear strength
Robust regression Outlier data
1 Introduction Geotechnical engineers face a number of uncertainties [1, 2]. Soil materials formed from geological weathering processes, and by physical means to deliver the soil to the current position [3]. In the forming process, the soil is influenced by various stress, pore fluid, and physical and chemical changes. Therefore, it is not surprising that there are always some outliers in geotechnical data. When dealing with geotechnical problems, empirical correlations between in situ or laboratory test results and geotechnical parameters are often used in geotechnical design. When establishing such empirical correlations, mostly adopted method is regression analysis, including linear or nonlinear regression [4]. Linear least squares regression (LLR) is a modeling approach by far the most widely used. When people say they use “regression”, “linear regression” or “least squares” to adapt their data, they usually mean doing LLR. LLR is not only the most widely used method of modeling, but also have adapted to a variety of circumstances, beyond its immediate scope [5].
© Springer Nature Singapore Pte Ltd. 2018 L. Hu et al. (Eds.): GSIC 2018, Proceedings of GeoShanghai 2018 International Conference: Multi-physics Processes in Soil Mechanics and Advances in Geotechnical Testing, pp. 509–515, 2018. https://doi.org/10.1007/978-981-13-0095-0_57
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A mathematical method that finds the best-fit curve for a given set of points is to minimizing the sum of the squares of the distances of regression data deviating from the curve. The sum of squares of the offset distances is used instead of the absolute values of the offset distances because this allows the residuals to be treated as a continuously differentiable quantity. Whereas, because of the use of the square of the o
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