Mixed Skewness Probability Modeling and Extreme Value Predicting for Physical System Input–Output Based on Full Bayesian Generalized Maximum-Likelihood Estimation

Dynamic parameterization of the statistical characteristics of structural systems’ measured input and output data is an important task for the digital twin modeling and intelligent risk assessment of transportation infrastructures. Characteristics of mixed skewness probability are common in structural systems, and its extreme value represents the risk state closest to the critical limit. The generalized extreme value mixture model (GEVMM) can consider multiple factors that interfere with each other, based on which the generalized maximum likelihood estimation (GMLE) of full Bayesian is introduced. The proposed GMLE-GEVMM can conduct the modeling of mixed skewness probability (mainly including strong uni-factor and multifactor statistical characteristics) by fusing the prior physical information for each parameter. A reliable paradigm for predicting the dynamic extreme value of practical engineering is presented. The proposed method can overcome the probabilistic modeling problem for complex mixed skewness characteristics and significantly improve the prediction accuracy of the extreme value of probability. The continuous monitoring data from a real bridge is used for validation. The modeling and predicting results verified the proposed methods’ strong applicability and high accuracy for complex probabilistic system input and output characteristics from in-service structures.