A systematic resilience assessment framework for multi-state systems based on physics-informed neural network

Resilience is crucial for systems to maintain functionality under disturbances, especially in critical applications. However, current methods for assessing resilience in multi-state systems (MSS), particularly those modeled with Markov Repairable Processes (MRP), often face high computational costs and inefficiencies in handling complex dynamics. To address these issues, this paper proposes a systematic framework for resilience assessment of MSS whose recovery process is described as a MRP, integrated with enhanced Physics-Informed Neural Networks (PINN). In the first step of the framework, the computation of resilience indices is performed, based on the MRP of the MSS and considering the system evolution through vulnerable and recovery phases. In the second step of the framework, the enhanced PINN is integrated into the MRP solution. A typical standby MSS structure is analyzed based on the proposed framework. By gradient calibration and momentum-driving training, the computational cost is shown to be reduced by 92.4 %, compared to the eigenvector method of solution. The approach is adaptable to other safety-critical systems, offering a robust tool for more effective resilience evaluation and system optimization.