Correlation-oriented complex system structural risk assessment using Copula and belief rule base

Abstract

Structural risk assessment is very important for maintaining the safe operations of many complex systems. However, there are two major requirements that still need to be addressed, namely the correlation among multiple factors and high interpretability to produce a trustworthy result. For the first challenge on correlation, the Copula model is applied to quantitatively measure the correlation among the data gathered from multiple sources. For the second challenge on interpretability, the Belief Rule Base (BRB) model is applied since it is essentially a white-box approach that can provide good interpretability by its transparent inferencing and decision-making process. With this, a novel approach is proposed by combining the Copula model and BRB, namely Copula-BRB. Moreover, two frameworks are separately designed as well. The first is a knowledge-driven inferencing framework when experts’ knowledge is available but with limited data. The second is a data-driven optimization framework when there is a large quantity of data. Correspondingly, a numerical case with only limited data and another practical case with 1000 sets of data are studied to explain and validate the two frameworks of the Copula-BRB approach, respectively. The numerical case is mainly used to explain the knowledge-driven Copula-BRB inferencing framework, and the practical case is conducted in a comparative fashion where three Copula functions are used, namely Clayton, Frank, and Gumbel, and the results are compared with the Support Vector Machine (SVM) and conventional BRB (without consideration of the attribute correlation). The results of the two case studies show that, by using the Copula-BRB which incorporates the attribute correlation into the conventional BRB, superior performance has been achieved in comparison with SVM and BRB. A detailed exploration of how this superior performance concerning outputs in intervals has been conducted as well.