Time-Varying Nonparametric Remaining Useful Life of Systems Based on Adaptive Kernel Auxiliary Particle Filter

In dynamic operating environment, equipment degradation exhibits significant complexity and variability, which can adversely impact the accuracy of predicting the remaining useful life (RUL). A time-varying nonparametric kernel density estimation (KDE) strategy, integrated with an adaptive kernel auxiliary particle filter (AKAPF) is presented, which is used for monitoring the degraded status of systems and enhancing RUL prediction. First, an exponential weighted time-varying RUL prediction model is developed by employing nonparametric KDE in combination with a forgetting factor. Subsequently, the relative density between samples is computed using the k-nearest neighbor (KNN) approach, which facilitates the determination of sparsity and density, enabling the adaptive selection of kernel bandwidth. Next, AKAPF is employed to update the degradation state of the dynamic system and determine the forgetting factor $\omega $ , thereby achieving optimal adaptive time-varying weights. Through iterative updates and loops, this real-time prediction system effectively identifies the degradation state and assesses the RUL. Finally, numerical experiments, along with data from the NASA dataset and a high-temperature furnace case study, are conducted to validate the robustness and practicality of the proposed model.