Solving multicollinearity in dam regression model using TSVD

Abstract

Targeting the multicollinearity problem in dam statistical model and error perturbations resulting from the monitoring process, we built a regularized regression model using Truncated Singular Value Decomposition (TSVD). An earth-rock dam in China is presented and discussed as an example. The analysis consists of three steps: multicollinearity detection, regularization parameter selection, and crack opening modeling and forecasting. Generalized Cross-Validation (GCV) function and L-curve criterion are both adopted in the regularization parameter selection. Partial Least-Squares Regression (PLSR) and stepwise regression are also included for comparison. The result indicates the TSVD can promisingly solve the multicollinearity problem of dam regression models. However, no general rules are available to make a decision when TSVD is superior to stepwise regression and PLSR due to the regularization parameter-choice problem. Both fitting accuracy and coefficients' reasonability should be considered when evaluating the model reliability. © 2011 Wuhan University and Springer-Verlag Berlin Heidelberg.