A reliability modeling method for accelerated degradation process with memory effects based on artificial neural network supported fractional Brownian motion

For degradation prediction of high-reliability equipment, accelerated degradation test data is often used to extrapolate the degradation state under normal stress levels. Previous studies typically model degradation using memoryless Markovian processes. However, due to the inherent degradation mechanisms and external stress influences, the degradation process often exhibits varying levels of memory effects, which significantly impact modeling accuracy when using Markovian methods. fractional Brownian motion quantifies memory effects through the Hurst exponent, but existing research often fixes the time-scale function to basic forms, leading to potential errors. This paper proposes a hybrid model combining artificial neural networks with fractional Brownian motion to simultaneously capture memory effects and the time-scale function that best reflects the actual degradation trend. The hybrid model employs a unified loss function and a gradient-based optimization algorithm to iteratively update the parameters of both the neural network and fractional Brownian motion, ensuring optimal alignment. The effectiveness of the proposed method is validated through numerical simulations and real-world degradation datasets, and the results demonstrate that the approach more accurately captures global memory effects and global degradation trends, outperforming traditional models.