Time-dependent reliability modeling and strength degradation path correlation effect analysis of cracked mechanisms based on reliability velocity mapping under small sample conditions

Time-dependent reliability analysis of mechanisms is crucial for ensuring the safe operation of critical equipment in aerospace and other fields. However, traditional models always introduce biases in reliability assessment due to neglecting strength degradation path correlations and challenges posed by small sample data. In this paper, a small-sample time-dependent reliability modeling method based on reliability velocity mapping is proposed for a four-bar mechanism containing crack defects. Based on the neural network model, the dynamic stress of the mechanism is analyzed. Furthermore, a reliability velocity curve mapping strategy is introduced to establish a time-dependent reliability model for the mechanism system, enabling precise characterization of strength degradation path correlation effects under small sample conditions. The validity of the proposed model is verified by Monte Carlo simulation, and the effects of crack depth, initial strength dispersion, and load randomness on the time-dependent are investigated. Results indicate that the strength degradation path correlation effect intensifies significantly with increased crack depth. Greater initial strength and load dispersions exacerbate the strength degradation path correlation effect, while deeper cracks amplify the impact of these factors on strength degradation path correlation. This research provides a high-precision, low-cost solution for time-dependent reliability evaluation of defective mechanisms, which can provide theoretical foundations for safety design and maintenance decisions in engineering applications.