State reliability analysis methods for nonlinear systems integrating adaptive entropy weighted grey relation and Dempster-Shafer’s Theory

Under uncertain environmental conditions, a nonlinear system may encounter problems like information conflicts, ambiguity, loss, and unclear interdependencies, which can result in low accuracy in predicting abnormal system states. System failures lead to negative impacts. To address these issues, this study proposes an analysis model that incorporates factor weight adaptive adjustment and integrates Dempster-Shafer’s theory (D-S theory) algorithms to construct an evaluation model, and to quantify uncertainty factors and correlation factors within the system. This approach reduces the impact of uncertainty in information features on analysis accuracy, enhances the precision of system reliability state probability assessment, and improves decision-making management levels. The results of the wind turbine system case study indicate that the proposed algorithm achieves a system state identification accuracy of 97% and a system reliability probability of 65%, with an overall accuracy improvement of 4.5% compared to traditional algorithms and a reliability probability assessment accuracy improvement of 5.22%, better aligning with the actual system’s state probability distribution.