A systematic correlation analysis for regression model selection: Application to bridge response prediction using contact and remote sensor systems

Correlation analysis is a crucial step before undertaking any regression modeling for data prediction because it helps reveal the relationships between predictors and responses, especially in terms of linearity and nonlinearity. This analysis is often essential for selecting the most appropriate regression model. A major challenge is that linear correlation measures are suitable only for linear relationships, and there are limited measures for assessing nonlinearity. Moreover, a significant issue arises from the influence of unknown predictor data, which can lead to unrealistic and inaccurate outputs from both linear and nonlinear correlation measures. To address these challenges, this paper proposes a systematic correlation analysis that first assesses the impact of unknown predictors and then selects the most suitable regressor for modeling and forecasting. The proposed method utilizes a linear measure known as canonical correlation analysis and a nonlinear measure called maximal information criterion. Based on the correlation values obtained from these measures, one can suggest low, moderate, and high correlation levels. The effectiveness of the proposed method is demonstrated using measured data related to long-span bridge structures. This data includes temperature records, serving as a single predictor, and bridge displacement responses obtained from synthetic aperture radar images as products of remote sensing technology. Results confirm that the proposed method is highly effective and applicable for selecting the best regression model for prediction.