Application of the ridge regression in the back analysis of a virgin stress field

When the least square approach is used to solve regression coefficients during the back analysis of a virgin stress field, the multicollinearity among independent variables may cause negative, too large, or non-significant regression coefficients, which can lead to an unreasonable virgin stress field. To make the virgin stress field obtained by a back analysis more reasonable, it is proposed that the ridge regression can be used to solve regression coefficients if multicollinearity exists. In the ridge regression, a small constant term was added to all diagonal elements of the correlation matrix to eliminate multicollinearity. Then this constant term was determined by ridge traces, the residual sum of squares, variance inflation factors, and statistical significance tests. To show the feasibility of determining a virgin stress field by the ridge regression, it was applied to the Heai tunnel located in Huili County, Sichuan Province, China. Results show that the ridge regression can avoid negative, too large, or non-significant regression coefficients effectively, and the virgin stress field obtained by the ridge regression is more reasonable and reliable than that obtained by the least square approach.