As the generalization of fuzzy systems, the belief rule base (BRB) expert system is transparent and interpretable. However, the interpretability of BRB has almost been ignored recently and leads to the decrease of model credibility. The main reason is the lack of unified guidelines for establishing an interpretable BRB expert system. In this article, the interpretability characteristics of BRB are summarized systematically, which can be used as the guideline of BRB establishment. Four interpretability criteria are proposed to ensure the interpretability of BRB in the optimization. A modified optimization algorithm with the interpretability constraints transformed from the interpretability criteria is further developed. As such, an interpretable BRB can be established. A case study for health state evaluation of the aerospace relay is conducted to verify the effectiveness of the proposed method.

In current studies of the belief rule base (BRB) model, the attributes are assumed to be fully reliable and the observation data are directly used as input. However, in engineering practice, the observation data may be affected by some disturbance factors including the quality of the sensors and noise in the environment. Then the reliability of observation data may be affected and the modeling accuracy of BRB is influenced. As such, a new BRB model with attribute reliability (BRB-r) is proposed in this paper. In particular, a calculation method of attribute reliability is given based on the statistical method. Moreover, to integrate the attribute reliability into BRB-r, a new calculation method of matching degree is developed. The model's overall reliability denotes its ability to provide the correct result, and when the attributes are unreliable, the overall reliability of BRB-r is degraded. Thus, a calculation method for the overall reliability of BRB-r is developed to support decision making in engineering practice. A case study of the safety assessment of diesel engine is conducted to demonstrate the efficiency of the proposed BRB-r model.

It is vital to online assess the safety of a complex dynamic system by taking into account the current state, degradation trend, and historical records together. This paper proposes a new safety assessment model with an online algorithm based on the evidential reasoning (ER) approach. It does not only take into account the relative importance of each safety indicator, but also consider the reliability of each indicator. To obtain the integrated safety level, multiple safety indicators are fused at first and the “history,” “current,” and “future” safety states are then integrated. First, a forecasting model based on the third-order Volterra filter is proposed to predict the safety indicators' information online. Second, an adaptive weighting model is developed to automatically adjust to various conditions and track the characteristics of the dynamic system, and the reliability of each indicator is considered to diminish the influence of inherent disturbance and/or noise. Finally, a safety assessment aggregation scheme based on the ER approach is presented to fuse the history, current, and future safety indicators to obtain the corresponding safety state, and the safety states are then fused synthetically to obtain a comprehensive safety assessment result of the complex dynamic system. A numerical study is examined to demonstrate the implementation and effectiveness. Moreover, a practical example of the inertial navigation system is studied to show the potential applications of the proposed ER-based safety assessment method.

Nonlinear complex system modeling has drawn attention from diverse fields and many approaches have been developed. Among those approaches, the advantages of the belief rule base (BRB) expert system have been shown for managing multiple types of information under uncertainty and modeling the nonlinearity present in many theoretical and practical complex systems. However, two challenges still need to be addressed. First, BRB needs to be downsized to conserve modeling and computational effort. For this challenge, a new disjunctive assumption is applied, which can significantly downsize BRB while maintaining its completeness. Second, the structure and parameters of BRB need to be jointly optimized. For this challenge, a new Akaike information criterion (AIC)-based optimization objective is derived to represent both modeling accuracy and modeling complexity. Moreover, a joint bi-level optimization model with an AIC-based objective is constructed for the BRB structure and parameters, and a bi-level optimization algorithm is proposed. Three evolutionary algorithms, namely, the genetic algorithm, particle swarm optimization algorithm, and differential evolutionary algorithm, are tested in a comparative fashion to determine the best fit for the optimization engine. The results of two practical case studies show that the joint optimization approach can identify an optimal configuration for both its structure and parameters, which is referred to as the best decision structure in this paper.