Analyzing and modeling inter-sensor relationships for strain monitoring data and missing data imputation: a copula and functional data-analytic approach

Abstract

Data analysis and modeling are very important in structural health monitoring. A good model is very conducive to better understanding, interpretation, estimation or prediction of structural performance, and dependence of variables. Strain responses are one of the most common measurements in structural health monitoring. Conventional modeling approaches in structural health monitoring for strain monitoring data have limitations in flexibly capturing the complex dependence structures of stochastic components between sensors. Also, addressing the nonlinear phase components is challenging when they are employed to model the inter-sensor relationships for temperature-induced strains. This article presents a refined inter-sensor modeling approach for strain monitoring data, which enables us to better understand the dependence of strain at different locations. Specifically, nonparametric copulas are employed to flexibly describe the dependence structures and the link marginal distributions to form the joint distribution to capture the inter-sensor relationship of stochastic strain responses. As opposed to traditional approaches in structural health monitoring, temperature-induced strains are treated as functional data; the phase and amplitude components are separately modeled by warping functions and a piecewise linear mapping model based on phase–amplitude separation technique; then, phase model and amplitude model are combined to form the final sensor-to-sensor mapping model. A similar functional modeling approach is also discussed for local strain responses resulting from wheel forces. Cooperated by a kernel regression model, applications of the established models in missing data imputation (i.e. replacing missing records by substitute values) are discussed for stochastic strain responses and temperature-induced strains using field monitoring data.