A novel nonlinear causal inference approach using vector‐based belief rule base

A complex system health state assessment method with reference value optimization for interpretable BRB

Health condition assessment is the basis for formulating and optimizing maintenance strategies of complex systems, which is crucial for ensuring the safe and stable operation of these systems. In complex system health condition assessment, it is not only necessary for the model to handle various uncertainties to ensure the accuracy of assessment results, but also to have a transparent and reasonable assessment process and interpretable, traceable assessment results. belief rule base (BRB) has been widely used as an interpretable modeling method in health condition assessment. However, BRB-based models currently face two issues: (1) inaccuracies in expert-provided parameters that can affect the model's accuracy, and (2) after model optimization, interpretability may be reduced. Therefore, this paper proposes a new method for complex system health condition assessment called interpretable BRB with reference value optimization (I-BRB). Firstly, to address the issue of inaccurate reference values, a reference value optimization algorithm with interpretability constraints is designed, which optimizes the reference values without compromising expert knowledge. Secondly, the remaining parameters are optimized using the projection covariance matrix adaptation evolution strategy (P-CMA-ES) with interpretability constraints to improve the model's accuracy. Finally, a case study evaluating the bearing components of a flywheel system is conducted to validate the proposed method. Experimental results demonstrate that I-BRB achieves higher accuracy in health condition assessment.

Evolutionary Optimization for the Belief-Rule-Based System: Method and Applications

Evolutionary optimization (EO) has been proven to be highly effective computation means in solving asymmetry problems in engineering practices. In this study, a novel evolutionary optimization approach for the belief rule base (BRB) system is proposed, namely EO-BRB, by constructing an optimization model and employing the Differential Evolutionary (DE) algorithm as its optimization engine due to its ability to locate an optimal solution for problems with nonlinear complexity. In the EO-BRB approach, the most representative referenced values of the attributes which are pre-determined in traditional learning approaches are to be optimized. In the optimization model, the mean squared error (MSE) between the actual and observed data is taken as the objective, while the initial weights of all the rules, the beliefs of the scales in the conclusion part, and the referenced values of the attributes are taken as the restraints. Compared with the traditional learning approaches for the BRB system, the EO-BRB approach (1) does not require transforming the numerical referenced values of the attributes into linguistic terms; (2) does not require identifying any initial solution; (3) does not require any mathematical deduction and/or case-specific information which verifies it as a general approach; and (4) can help downsize the BRB system while producing superior performances. Thus, the proposed EO-BRB approach can make the best use of the nonlinear modeling ability of BRB and the optimization superiority of the EO algorithms. Three asymmetry numerical and practical cases are studied to validate the efficiency of the proposed EO-BRB approach.