In the fault diagnosis of the flywheel system, the input information of the system is uncertain. This uncertainty is mainly caused by the interference of environmental factors and the limited cognitive ability of experts. The BRB (belief rule base) shows a good ability for dealing with problems of information uncertainty and small sample data. However, the initialization of the BRB relies on expert knowledge, and it is difficult to obtain the accurate knowledge of flywheel faults when constructing BRB models. Therefore, this paper proposes a new BRB model, called the FFBRB (fuzzy fault tree analysis and belief rule base), which can effectively solve the problems existing in the BRB. The FFBRB uses the Bayesian network as a bridge, uses an FFTA (fuzzy fault tree analysis) mechanism to build the BRB’s expert knowledge, uses ER (evidential reasoning) as its reasoning tool, and uses P-CMA-ES (projection covariance matrix adaptation evolutionary strategies) as its optimization model algorithm. The feasibility and superiority of the proposed method are verified by an example of a flywheel friction torque fault tree.

As the propulsion part of a space launch vehicle and nuclear weapon missile, the health status of the liquid rocket determines whether the space launch vehicle and nuclear weapon missile can function normally. Therefore, it is of great significance to evaluate the health status of the liquid rocket. As the structure of the liquid rocket is becoming increasingly sophisticated, subjective judgment alone can no longer meet the needs of the actual system. As an expert system and a gray-box model, the belief rule base (BRB) can process both qualitative and quantitative information. The expert knowledge base is used in the safety assessment of a liquid rocket. However, in practical applications, the traditional BRB model still has two problems, which are that (1) when there are too many premise attributes, it easily leads to the explosion of combination rules, and (2) the reliability of rules is not considered in the process of model reasoning. Therefore, this paper proposes the BRB model with intervals (intervals-BRB) on the basis of traditional BRB. The interval-BRB retains the advantage of the traditional BRB, which can handle semi-quantitative information. In addition, the proposed model changes the reference point of the prerequisite attribute to the reference interval and changes the rule combination. This solves the problem of the traditional BRB explosive combination rule. The ER-rule (evidential reasoning rule) is introduced into the reasoning procedure, and the weight of the rule and the reliability of the rule are considered at the same time, which solves the shortcoming of the traditional BRB, which does not consider the reliability of the rule in reasoning. Finally, the CMAES optimization algorithm is used to optimize the initial model to obtain better performance. Finally, the model is verified by the actual data set of a liquid rocket, and the experimental results show that the model can achieve good experimental results.

Fault diagnosis is crucial for complex system health management. The intelligent fault diagnosis model based on belief rule bases (BRB) effectively handles small sample data and uncertain information. However, due to the limitations of expert knowledge, simply utilizing this knowledge to construct initial rules may not fully capture the highly nonlinear relationships between inputs and outputs in complex systems, resulting in reduced model accuracy. While optimization algorithms can dynamically adjust the parameters and structure of the rule base to improve model accuracy, the iterative process of seeking an optimal solution can inevitably compromise the model's interpretability. To address the aforementioned issues, a fault diagnosis model based on interpretable BRB with fault tree analysis (FTA) has been proposed. In this model, initial rules are constructed through a structured representation of fault relationships using FTA. Additionally, interpretability constraints are introduced during optimization to limit the range of parameters, ensuring that the optimization results align with real-world situations. A case study on a CNC milling machine was conducted to validate the proposed method. The results indicate that the model identifies fault states in complex systems more effectively and accurately than existing models, maintaining a balance between accuracy and interpretability throughout the diagnosis process.