On investigation of the Bayesian anomaly in multiple imprecise dependent information aggregation for system reliability evaluation

Abstract

The increasing complexity of the modern engineering system has made the multisource information fusion a necessary yet challenging task. In the context of reliability engineering, the information fusion process is either ineffective or less efficient as the aggregation error increases with respect to the collection of multiple dependent pieces of evidence. To address this challenge, this paper proposes a comprehensive Bayesian approach for system reliability evaluation that considers multiple, dependent sources of information. We show that the so‐called “Bayesian anomaly,” a type of aggregation error, is caused by misuse of the dependent information and could be eliminated if all available information is properly addressed. A topological technique is employed as a tool for information fusion in the likelihood construction. A likelihood‐based approach is then developed to formulate the overall likelihood as well as the reliability model. These two techniques are embedded into a comprehensive Bayesian framework to allow for an efficient evaluation of the system reliability. Our approach has also been extended to include imprecise information, such as interval and/or censored data, which is more frequently encountered in practical engineering. We demonstrate the proposed method through several numerical cases and one real‐life application example. This study provides a better understanding of the role of dependent information in system reliability evaluation. In addition, it presents an efficient pathway to extract the inherent dependency information embedded in imperfect data sets.

Enriching stochastic model updating metrics: An efficient Bayesian approach using Bray-Curtis distance and an adaptive binning algorithm

“…For stochastic model updating, methodologies such as the perturbation method [10,11], the random matrix method [12] and the interval estimation method [13] have been investigated in the literature. Another important method is Bayesian calibration (or Bayesian updating) [14,15]. Bayesian calibration integrates subjective prior information and experimental data to update parameters from a prior distribution towards a posterior distribution [16][17][18][19].…”