A novel optimization method for belief rule base expert system with activation rate.

Although the belief rule base (BRB) expert system has many advantages, such as the effective use of semi-quantitative information, objective description of uncertainty, and efficient nonlinear modeling capability, it is always limited by the problem of combinatorial explosion. The main reason is that the optimization of a BRB with many rules will consume many computing resources, which makes it unable to meet the real-time requirements in some complex systems. Another reason is that the optimization process will destroy the interpretability of those parameters that belong to the inadequately activated rules given by experts. To solve these problems, a novel optimization method for BRB is proposed in this paper. Through the activation rate, the rules that have never been activated or inadequately activated are pruned during the optimization process. Furthermore, even if there is a complete data set and all rules are activated, the activation rate can also be used in the parallel optimization process of the BRB expert system, where the training data set is divided into some subprocesses. The proposed method effectively solves the combinatorial explosion problem of BRB and can make full use of quantitative data without destroying the original interpretability provided by experts. Case studies prove the advantages and effectiveness of the proposed method, which greatly expands the application fields of the BRB expert system.

A New Evidential Reasoning Rule Considering Interval Uncertainty and Perturbation.

The evidential reasoning (ER) rule has been widely applied in the multiple attribute decision making (MADM), which makes the decision-making process transparent and credible by using a belief structure. To improve the ability of the ER rule in dealing with the interval uncertainty, a new interval ER (IER) rule is proposed in this article. The interval uncertainty is described as the interval grade in the new frame of discernment (FoD) to model the local ignorance. It is proved that the IER rule is a generalization of the ER rule. To study the influence of perturbation on the IER rule, the perturbation is first introduced to the belief structure, and the perturbation analysis (PA) is conducted for the IER rule. An optimization model is established to estimate the perturbation threshold, which can measure the effectiveness of the inference result under perturbation. Two numerical examples and a case study are carried out, respectively, to show the implementation process of the proposed IER rule and validate its effectiveness in different decision-making scenarios.

A New Evidential Reasoning Rule-Based Safety Assessment Method With Sensor Reliability for Complex Systems.

In current studies of safety assessment for complex systems with the evidential reasoning (ER) rule, the evidence reliability is generally given by experts, which makes the observation data by sensors ignored. However, sensors are inevitably affected by such various uncertainties as perturbations in engineering practice, which can reduce their quality and tracking ability. As such, the observation data may become unreliable, and the modeling accuracy of the ER rule is decreased. In this article, a new ER rule-based safety assessment method with sensor reliability for complex systems is proposed, where sensor reliability and perturbation are considered. The coefficient of the variation-based weighting (CVBW) method is employed to obtain sensor weight. The sensor reliability is calculated by static reliability and dynamic reliability, which are determined by experts and the distance-based method, respectively. The perturbation is quantified as a bounded parameter defined as the perturbation factor, which is used to describe uncertainties and aggregate static reliability and dynamic reliability. The performance analysis of safety assessment is conducted to demonstrate the rationality of perturbation and position poor sensors, followed by a safety assessment algorithm. A case study is carried out to validate the effectiveness of the proposed method.

A New Evidential Reasoning Rule With Continuous Probability Distribution of Reliability.

Evidential reasoning (ER) rule has been widely used in dealing with uncertainty. As an important parameter to measure the inherent property of evidence, the evidence reliability makes the ER rule constitute a generalized reasoning framework. In current research of the ER rule, the evidence reliability tends to be expressed in the form of quantitative value by certain methods or expert knowledge. The single quantitative value lacks the ability to describe the statistical property of reliability, which leads to unreasonable results. In this article, a new ER rule with continuous probability distribution of reliability denoted by ERr-CR is proposed. The combination of two pieces of evidence is discussed in detail, where the reliability is profiled as random variables with specific probability distribution. To characterize the output of ERr-CR, a novel concept of expectation of the expected utility is proposed. In addition, the ERr-CR is expanded to multiple pieces of evidence to show its universality. Further, the basic performances of the ERr-CR are explored to illustrate the rationality. Moreover, a case study of safety assessment of natural gas storage tanks (NGSTs) is conducted to show the potential applications of ERr-CR, which makes the proposed method more practical.