Multiple distribution-to-distribution regression and missing data imputation via improved Wasserstein regression and optimized D-vine copula

Continuous missing of recorded monitoring data together with losing of the corresponding data probability distributions significantly affect structural health monitoring system assessments. Therefore, imputing missing data and restoring their probability distributions is crucial. Although many deep learning-based missing data imputation methods have been developed, limitations remain as no guarantees can be made for the imputed data following the probability distribution of original missing data. Moreover, the recent Wasserstein regression approach is only applicable to one-to-one probability distribution regression and thus fails to leverage multiple intact sensor data probability distributions, resulting in underutilization of available information. With the missing probability distribution restored, copula-based methods can be used for missing data imputation but struggle with imputing correlated multi-sensor data. In this paper, two methods are proposed to solve the above existing problems, respectively. The first method improves the recent Wasserstein regression to multiple probability distribution-to-distribution regression by systematically embedding a functional partial least squares-based multiple function-to-function regression into the tangent space. The second method enhances the optimized D -vine copula by incorporating non-parametric estimation, enabling efficient modeling of joint conditional distributions and accurate imputation of continuous missing data. The effectiveness of the two proposed methods is validated using field-measured acceleration data from the Dowling Hall Footbridge and wind-speed data from a wind observation array.