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.

This paper develops a new trustworthy fault diagnosis (TFD) method based on belief rule base expert system with combining multi-source uncertainty information for vehicle, such as flying machine. To improve the performance of fault diagnosis for vehicle, a new belief rule base expert system with multi-source uncertainty information (BRB-MU) is developed, where the influence of the random environment disturbance is addressed by introducing uncertain factors of input characteristics. In BRB-MU, the uncertain factors of input characteristics are calculated by the signal to noise ratio based method. The new developed BRB-MU model aims to handle three problems: unbalanced observation data of system states, uncertain expert knowledge and random environment disturbance. The first two problems are solved by the combination of expert knowledge and observation data. In parallel, the third problem is handled by the new introduced uncertain factors based on singular value decomposition (SVD) in BRB-MU. To quantitatively analyze the influence of the uncertain information to the TFD output, the traceability analysis of BRB-MU is conduced that can provide support for decision making of vehicle optimization design. It is analyzed based on the modeling traceability and parameters interpretability. To demonstrate the effectiveness of the TFD method, an experiment illustration is conduced.

In the technology of wireless sensor network (WSN), wireless sensor fault diagnosis based on fusion data analysis has attracted attention in the wireless sensor field. It can detect and correct the faults of sensor nodes in time to improve the accuracy of sensor data fusion. In this paper, the data characteristics of WSN are analyzed, and a method is proposed for fault diagnosis of WSN based on a belief rule base (BRB) model. First, the sensor fault diagnosis process is described based on the characteristics of a wireless sensor in WSN. Then, the characteristics of sensors are analyzed from the aspects of time, space, and attributes. Finally, a fault diagnosis model is proposed based on the hierarchical BRB model. To make the results more accurate, a covariance matrix adaptation evolution strategy algorithm is used to optimize the initial parameters of the proposed model. A case study using the Intel lab data set of sensors is designed to verify the effectiveness of the proposed model. The results show that the proposed method is effective in fault diagnosis of WSN.

As sensors readings are used for vehicle flight control, their reliability directly affects the flight performance. This paper develops a new fault diagnosis and tolerance method for sensor failures of vehicles by addressing three problems:unavailable faulty data, difficulty in establishing analytical system, and inconsistence of expert cognitive ability. For the purpose, a new belief rule base model with multi-expert joint (BRB-ME) is proposed. The first two problems are handled by combining the small size of observation data and the uncertain knowledge from multiple experts in BRB-ME. For the third problem, a new multi-expert joint strategy is proposed in the BRB-ME model. The experts first construct their own models, and then the models are fused with different weights according to the experts’ ability, such as research fields, the working time and etc. Then, a new fault diagnosis and tolerance framework is developed based on BRB-ME for detecting vehicles’ sensor failures, where the sensor failures are tolerated by the reconstruction strategy for faulty sensor output. Moreover, in order to address the influence of the uncertain expert knowledge, an optimization model is constructed for obtaining the optimal solutions for the framework. An experimental illustration is conducted for accelerometer failure. The diagnosis accuracy is 97.50%, and the developed framework can ensure the navigation accuracy of the vehicle under accelerometer failure.

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.