Structural health monitoring has arisen as an important tool for managing and maintaining civil infrastructure. A critical problem for all structural health monitoring systems is data loss or data corruption due to sensor failure or other malfunctions, which bring into question in subsequent structural health monitoring data analysis and decision-making. Probability density functions play a very important role in many applications for structural health monitoring. This article focuses on data loss compensation for probability density function estimation in structural health monitoring using imputation methods. Different from common data, continuous probability density functions belong to functional data; the conventional distribution-to-distribution regression technique has significant potential in missing probability density function imputation; however, extrapolation and directly borrowing shape information from the covariate probability density function are the main challenges. Inspired by the warping transformation of distributions in the field of functional data analysis, a new distribution regression approach for imputing missing correlated probability density functions is proposed in this article. The warping transformation for distributions is a mapping operation used to transform one probability density function to another by deforming the original probability density function with a warping function. The shape mapping between probability density functions can be characterized well by warping functions. Given a covariate probability density function, the warping function is first estimated by a kernel regression model; then, the estimated warping function is used to transform the covariate probability density function and obtain an imputation for the missing probability density function. To address issues with poor performance when the covariate probability density function is contaminated, a hybrid approach is proposed that fuses the imputations obtained by the warping transformation approach with the conventional distribution-to-distribution regression approach. Experiments based on field monitoring data are conducted to evaluate the performance of the proposed approach. The corresponding results indicate that the proposed approach can outperform the conventional method, especially in extrapolation. The proposed approach shows good potential to provide more reliable estimation of distributions of missing structural health monitoring data.
A Method of Estimating Probability Density Function by Maximum Entropy Method
