With the growing demand for highly safety in industrial system, fault diagnosis has attracted more and more attention. Currently, belief rule base (BRB) has shown excellent performance in modeling complex system where the expert knowledge is used effectively. Existing BRB models are assumed that the inputs of the attributes are independent and the attribute correlation is not taken into account. However, in some engineering system, there is an obvious correlation among these attributes. The correlated attributes may produce redundant information which limits the abilities of attributes to express the accurate information of system. In this paper a new BRB model with considering attribute correlation (BRB-c) is proposed. Moreover, a decoupling matrix is introduced to eliminate the redundant information from the attributes. The initial parameters of the decoupling matrix are given according to the expert knowledge. And then, when the inputs of the attributes are available, the parameters in the decoupling matrix are trained by an optimization model. The projection covariance matrix adaption evolution strategy (P-CMA-ES) is chosen as an optimization algorithm. A practical case study about fault diagnosis of oil pipeline is conducted and the results show that the BRB-c model can diagnose the leak size and leak time of oil pipeline accurately, which can demonstrate that the proposed model can be widely applied in engineering for fault diagnosis.

The health of a complex electromechanical system is dynamic and is accompanied by a full life cycle. Due to the complexity and coupling of complex electromechanical systems, the establishment of a dynamic and accurate model for the health state is difficult. A belief rule base (BRB) shows outstanding performance in modeling complex systems because it can combine both quantitative information and expert knowledge. In this paper, a double-layer BRB model is proposed to predict the health state of a complex electromechanical system. The two layers achieve different functions: BRB_layer1 is used to establish the dynamic change of the time series of features, BRB_layer2 is employed to combine the features for predicting the health state of the complex electromechanical system. During this process, the infinite irrelevance method is utilized for feature selection in reducing the scale of the BRB model. Considering the initial parameters are given by experts, which may have boundedness and may not be appropriate for engineering practice, the projection covariance matrix adaption evolution strategy (P-CMA-ES) is chosen as the optimization algorithm to train the initial parameters. To verify the rationality and effectiveness of the proposed model, the low-frequency vibration fault of a certain aero-engine is taken as an example. The results show that the proposed method can predict the health state of a complex electromechanical system precisely according to current and historical data.

In the process of rehabilitation treatment for stroke patients, rehabilitation evaluation is a significant part in rehabilitation medicine. Researchers intellectualized the evaluation of rehabilitation evaluation methods and proposed quantitative evaluation methods based on evaluation scales, without the clinical background of physiatrist. However, in clinical practice, the experience of physiatrist plays an important role in the rehabilitation evaluation of patients. Therefore, this paper designs a 5 degrees of freedom (DoFs) upper limb (UL) rehabilitation robot and proposes a rehabilitation evaluation model based on Belief Rule Base (BRB) which can add the expert knowledge of physiatrist to the rehabilitation evaluation. The motion data of stroke patients during active training are collected by the rehabilitation robot and signal collection system, and then the upper limb motor function of the patients is evaluated by the rehabilitation evaluation model. To verify the accuracy of the proposed method, Back Propagation Neural Network (BPNN) and Support Vector Machines (SVM) are used to evaluate. Comparative analysis shows that the BRB model has high accuracy and effectiveness among the three evaluation models. The results show that the rehabilitation evaluation model of stroke patients based on BRB could help physiatrists to evaluate the UL motor function of patients and master the rehabilitation status of stroke patients.

In industry, it is difficult to obtain data for monitoring equipment operation, as mechanical and electrical components tend to be complicated in nature. Considering the contactless and convenient acquisition of sound signals, a method based on variational mode decomposition and support vector machine via sound signals is proposed to accurately perform fault diagnoses. Firstly, variational mode decomposition is conducted to obtain intrinsic mode functions. The fisher criterion and canonical discriminant function are applied to overcome the fault diagnosis accuracy decline caused by intrinsic mode functions with multiple features. Then, the fault features obtained from these intrinsic mode functions are chosen as the final fault features. Experiments on a car folding rearview mirror based on sound signals were used to verify the superiority and feasibility of the proposed method. To further verify the superiority of the proposed model, these final fault features were taken as the input to the following classifiers to identify fault categories: support vector machine, k-nearest neighbors, and decision tree. The model support vector machine achieved an accuracy of 95.8%, i.e., better than the 95% and 94.2% of the other two models.

Fault diagnosis for body-in-white (BIW) welding robots is important for ensuring the efficient production of the welding assembly line. As a result of the complex mechanism of the body-in-white welding robot, its strong correlation of components, and the many types of faults, it is difficult to establish a complete fault diagnosis model. Therefore, a fault diagnosis model for a BIW-welding robot based on a multi-layer belief rule base (BRB) was proposed. This model can effectively integrate monitoring data and expert knowledge to achieve an accurate fault diagnosis and facilitate traceability. First, according to the established fault tree, a fault mechanism was determined. Second, based on the multi-layer relationship of a fault tree, we established a multi-layer BRB model. Meanwhile, in order to improve the accuracy of the model parameters, the projection covariance matrix adaptive evolutionary strategy (P-CMA-ES) algorithm was used to optimize and update the parameters of the fault diagnosis model. Finally, the validity of the proposed model was verified by a simulation experiment for the BIW-welding robot.