مقاله انگلیسی رایگان در مورد رگرسیون خطی قدرتمند برای استحکام برشی – اسپرینگر 2018

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]. 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 offset, peripheral points may have a disproportionate effect on fit. Whether the results are desirable or not, it depends on the issue of question [6]. The statistical observations of outliers are significantly different from the other sample values. Least-squares regression is obviously the best option if errors are normally distributed. Then, other means is eagerly required if these errors are not normally distributed. One particular distribution is the long tail error distribution of great concern. One solution is still to use the LLR method after removing the largest remaining value as outliers. However, this solution may be infeasible if several larger residual values exist by reason that the poor nature of the outlier tests. In addition, outlier testing is an acceptance/rejection process. The testing processes are neither smooth or statistically efficient. Robust regression (RR) is another option for least-squares regression in the case of the data contaminated with outliers. It can also be used to detect influential observations when the data is exposed to outliers [7]. It is difficult to define absolute outliers from geotechnical testing data, but it is possible to indicate the least predictable or relatively outlying data points using statistical tools. The objective of this paper is to demonstrate the advantages of RR analysis used in geotechnical data comparing with least square regression analysis. The procedure of RR is discussed shortly, based on LLR method. And then, Regression analysis is operated on undrained shear strength (su) data derived from CPTU test with both RR and LLR. Comparing regression result, the outlier of su data can be detected based on RR method.