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The belief rule-base (BRB) model is a new intelligent expert system with the characteristics of both expert system and data-driven model. In BRB there are many if-then rules which use belief degrees to express various types of uncertain information, including fuzziness, randomness, and ignorance. As a semi-quantitative modeling tool for complex systems, BRB has the superiorities of dealing both numerical quantitative data and linguistic qualitative knowledge that are derived from heterogeneous sources. Moreover, it is also a white box approach which can provide direct access and transparency to decision makers and stakeholders. Currently, BRB has been widely applied in many fields, such as decision making, reliability evaluation, network security situation awareness, fault diagnosis, and so on. To fully demonstrate the progress of BRB, the original BRB, and some evolution forms are introduced in this article. [ABSTRACT FROM AUTHOR]

Evidential reasoning (ER) rule has been widely used in addressing uncertainty, ignorance, and vagueness information. To explore its performance measure (PM), the perturbation analysis (PA) for the ER rule (ER rule-PA) is conducted, with perturbation taken into consideration. This article aims to analyze the robustness and stability of the ER rule, serving as theoretical basis and technical support for applied research and applications. The combination of two pieces of independent evidence is discussed, and perturbation is added to one piece of evidence. To represent the expected utility of evidence combination under perturbation, perturbation utility is introduced. The novel concept of perturbation coefficient is proposed to characterize the PM of the ER rule (ER rule-PM). The properties of perturbation coefficient are explored to demonstrate the impact of perturbation. The maximum permissible error (MPE) of perturbation coefficient is defined to characterize the acceptability of perturbation. A numerical study is examined to illustrate the implementation process of ER rule-PA. Moreover, a case study of reliability evaluation of aerospace relay is conducted to show the potential applications of ER rule-PA, which makes the proposed method more practical. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is important to predict the hidden behavior of a complex system. In the existing models for predicting the hidden behavior, the hidden belief rule base (HBRB) is an effective model which can use qualitative knowledge and quantitative data. However, the frame of discernment (FoD) of HBRB which is composed of some states or propositions and the universal set including all states or propositions is not complete. The global ignorance and local ignorance cannot be considered at the same time, which may lead to the inaccurate forecasting results. To solve the problems, a new HBRB model named as PHBRB in which the hidden behavior is described on the FoD of the power set is proposed in this correspondence paper. Furthermore, by using the evidential reasoning rule as the inference tool of PHBRB, a new projection covariance matrix adaption evolution strategy is developed to optimize the parameters of PHBRB so that more accurate prediction results can be obtained. A case study of network security situation prediction is conducted to demonstrate the effectiveness of the newly proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is vital to assess the lives of newly developed products by using failure data from various testing environments. In the current methods, two steps are generally included. The first step is transforming the failure data under one testing environment into the actual working environment, and the second step is integrating all failure data under the actual working environment into a unified result. However, most available methods cannot use information that includes part failure data and part expert knowledge simultaneously. To resolve the above issue, based on the belief rule base (BRB) and the evidential reasoning (ER) approach, a new BRB-ER-based model is proposed, where the BRB is used to transform the failure data from one testing environment into the actual working environment. The ER approach, which is adopted to aggregate the failure data from different testing environments, is used to assess the life of a product. To conclude, the BRB-ER-based model is applied to represent and integrate asynchronous multisource information. In the proposed model, the initial BRB system is constructed based on experts’ knowledge, which results in uncertainty because of the ambiguous nature of human judgment and calls for training the parameters in the BRB-ER-based model. Therefore, an optimal algorithm that employs the differential evolutionary algorithm is proposed. The proposed model and the optimal algorithm operate in an integrated manner to improve the assessment precision by using both failure data and expert knowledge effectively. A case study in three scenarios and use of the conventional approach is examined to demonstrate the capability and potential applications of the new BRB-ER-based model. [ABSTRACT FROM AUTHOR]