## 1 Introduction
However, the system structure is usually complex and lacks the ability to handle quantitative data. In summary, there are some results of the current research on the problem of complex system fault diagnosis [13]. However, the BIW-welding robot is a complex production process with multiple processes and conditions, and its failure characteristics are numerous. It becomes very difficult to establish an accurate mathematical analysis model, and accurate results cannot be obtained by relying on qualitative knowledge. Only using data-driven methods lacks interpretability and cannot utilize the experience and knowledge of experts, and the above three methods lack the ability to deal with various types of uncertain information. [PERSON] et al. [14; 15; 16; 17] proposed a belief rule base (BRB) expert system based on an evidential reasoning approach that could handle uncertain information that arises in the human decision-making process. For uncertain information, BRB can express it at the same time and can combine the advantages of quantitative analysis and qualitative analysis to obtain credible fault diagnosis results while ensuring model accuracy. By using numerical data to optimize the initial parameters in the BRB model, the relationship between input and output could be more intuitively described. The initial parameters of the BRB model can be fine-tuned through expert knowledge, and the BRB model reasoning method is used in fault diagnosis, life evaluation, and other fields. Expert systems have the characteristics of multi-type information processing. In contrast to the above disadvantages, the BRB expert system has the ability to handle both the lack of data and conflicting evidence. When dealing with qualitative and quantitative information, the BRB expert-system learning model is an optimization problem with linear and nonlinear constrained optimization. Meanwhile, the BRB model is prone to the combinatorial explosion problem that affects the final results [18]. For the above-mentioned problems, the multi-layer BRB model can be used to solve them. The main idea of the multi-layer BRB is to adopt a bottom-up model. First, the underlying indicators and second, the use of the combination result are combined as the input of the next layer and finally reach the target state [19]. The advantage of multi-layer BRB over single-layer BRB is that the system is built according to the system structure. The multi-layer BRB hierarchy effectively reduces the number of rules and effectively avoids the combination explosion generated by the BRB model. As a result, this paper uses a multi-layer BRB, a semi-quantitative tool, to construct a fault diagnosis model that incorporates expert knowledge and quantitative data. This model addresses the limitations of using only single knowledge for diagnosis by utilizing surveillance data and expert knowledge to produce a better diagnosis. Realizing the comprehensive utilization of the working mechanism, failure mechanism, and the data of the BIW welding and assembly robot can improve the accuracy of diagnosis. The local adjustment of model parameters by the (P-CMA-ES) algorithm [20] can reduce the limitations of expert knowledge. The validity of the method was verified by experiments.