With excellent interpretability, the fuzzy rule-based method stands as a formidable instrument for knowledge representation and learning. Nowadays, the knowledge representation problem with multidimensional input information is widespread, leading to a large rule base and making it difficult to embed expert knowledge. In addition, human knowledge is not entirely reliable, causing inaccurate reasoning results. In this article, a novel large-scale linguistic Z-number belief rule base (LSLZ-BRB) method is proposed for the above multidimensional and unreliable knowledge representation and learning. Specifically, a multidimensional knowledge mapping representation method under the probabilistic framework is proposed to generate an LSLZ-BRB. It allows experts to embed knowledge via conditional probability and prior probability. To reduce the modeling error caused by uncertainty of knowledge, an online interactive learning mechanism of uncertain knowledge is developed. This mechanism ensures that LSLZ-BRB has high real-time performance and improves the accuracy of knowledge representation. A performance evaluation case for the laser inertial measurement unit (LIMU) and experiments on some public datasets illustrate the implementation process of the proposed method and further verify its effectiveness.

Sensor disturbance has a significant impact on the performance state of complex systems in engineering. In this article, a new performance evaluation model for complex systems considering sensor disturbance is proposed. First, belief rule base (BRB) is used as a white-box model to establish a transparent performance evaluation model. To evaluate the influence of disturbance on the performance state, the sensor disturbance is described as an interval and added in the model input. The fluctuation range of the disturbed performance state is calculated. Then, to assist diminish the damage of disturbance on the performance state, the robustness of the sensor is analyzed for two types of tasks with different robustness requirements. In general tasks, the antidisturbance ability of sensors is analyzed based on the sensitivity analysis method. In specific tasks with strong robustness requirements, the disturbance tolerance interval (DTI) of the sensor to tolerate disturbances is calculated by the Newton-downhill method. A gyroscope performance evaluation case is used to verify the effectiveness of the proposed 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.

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.