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.

The evidential reasoning (ER) rule has been widely used in the data analysis, which provides a transparent and credible inference process and can effectively deal with various uncertainties. However, the traditional ER rule requires the evidence to be strictly independent of each other, which may not be easily satisfied in engineering practice. In addition, the perturbation can affect the sample data and cause unstable inference results. As such, in this article, a new ER rule with likelihood analysis and perturbation analysis (PA) is proposed based on the maximum likelihood ER (MAKER). The likelihood analysis is used to acquire probabilistic evidence from the sample data. The interdependence index of evidence is defined on the marginal probability and joint probability. A parameter optimization model is established based on the maximum likelihood (ML). The PA is conducted on the proposed ER rule to study its robustness, and a generalized PA method is explored to facilitate its potential applications. A case study of the performance evaluation of laser gyros is carried out to show the implementation of the proposed method and validate its effectiveness in reality.

Advanced persistent threat (APT) is a special attack method, which is usually initiated by hacker groups to steal data or destroy systems for large enterprises and even countries. APT has a long-term and multi-stage characteristic, which makes it difficult for traditional detection methods to effectively identify. To detect APT attacks requires solving some problems: how to deal with various uncertain information during APT attack detection, how to fully train the APT detection model with small attack samples, and how to obtain the interpretable detection results for subsequent APT attack forensics. Traditional detection methods cannot effectively utilize multiple uncertain information with small samples. Meanwhile, most detection models are black box and lack a transparent calculation process, which makes it impossible for managers to analyze the reliability and evidence of the results. To solve these problems, a novel detection method based on belief rule base (BRB) is proposed in this paper, where expert knowledge and small samples are both utilized to obtain interpretable detection results. A case study with numerical simulation is established to prove the effectiveness and practicality of the proposed method.

Belief rule base (BRB) model suffers from the rule explosion problem when it is applied in modeling complex systems. The rule explosion problem makes it difficult to establish and optimize the BRB model effectively. Aiming at this problem, a new multilayer BRB (MLBRB) model is proposed, which consists of the extracting block and the processing block. In the extracting block, the inputs are first divided into two groups, and then each group is used to construct a hierarchical BRB model. The outputs of extracting block are treated as the inputs of the processing block. To obtain the optimal MLBRB, the layerwise learning strategy and the layer adaptive growth strategy are proposed to optimize these two blocks, respectively. A case study for the safety assessment of the liquefied natural gas storage tank is conducted to verify the effectiveness of the proposed method.