Probability-informed neural network-driven point-evolution kernel density estimation for time-dependent reliability analysis

Engineering structures under erosive agents, time-dependent loads, and material degradation, underscores the necessity of time-dependent reliability analysis (TDRA) for predicting safety within the service life. However, conventional TDRA often faces challenges in efficiency, accuracy, and generality, prompting the need for efficient and accurate TDRA methods. This study introduces a novel probability density function-informed method (PDFM), specifically designed for TDRA of time-dependent systems, known as probability-informed neural network-point-evolution kernel density estimation (PNPE). PNPE, founded on point evolution kernel density estimation (PKDE) and integrating Deep Neural Network (DNN) with the general density evolution equation, uniquely merges machine learning with physical equations. This integration addresses the shortcomings of traditional PDFM, enhancing efficiency in TDRA without requiring an extensive number of representative points for improved accuracy. PNPE is validated through four benchmark cases: a simple numerical case, two scenarios involving corroded steel beams, a hydrodynamic turbine blade, and the seismic response of a multi-story shear frame. The results demonstrate the ability of PNPE to estimate time-dependent failure probability accurately and efficiently with a limited number of representative points and without additional samples.