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.

A transparent digital twin (DT) is designed for output control using the belief rule base (BRB), namely, DT-BRB. The goal of the transparent DT-BRB is not only to model the complex relationships between the system inputs and output but also to conduct output control by identifying and optimizing the key parameters in the model inputs. The proposed DT-BRB approach is composed of three major steps. First, BRB is adopted to model the relationships between the inputs and output of the physical system. Second, an analytical procedure is proposed to identify only the key parameters in the system inputs with the highest contribution to the output. Being consistent with the inferencing, integration, and unification procedures of BRB, there are also three parts in the contribution calculation in this step. Finally, the data-driven optimization is performed to control the system output. A practical case study on the Wuhan Metro System is conducted for reducing the building tilt rate (BTR) in tunnel construction. By comparing the results following different standards, the 80% contribution standard is proved to have the highest marginal contribution that identifies only 43.5% parameters as the key parameters but can reduce the BTR by 73.73%. Moreover, it is also observed that the proposed DT-BRB approach is so effective that iterative optimizations are not necessarily needed.