State-space modeling for degrading systems with stochastic neural networks and dynamic Bayesian layers

To monitor the dynamic behavior of degrading systems over time, a flexible hierarchical discrete-time state-space model (SSM) is introduced that can mathematically characterize the stochastic evolution of the latent states (discrete, continuous, or hybrid) of degrading systems, dynamic measurements collected from condition monitoring sources (e.g., sensors with mixed-type outputs), and the failure process. This flexible SSM is inspired by Bayesian hierarchical modeling and recurrent neural networks without imposing prior knowledge regarding the stochastic structure of the system dynamics and its variables. The temporal behavior of degrading systems and the relationship between variables of the corresponding system dynamics are fully characterized by stochastic neural networks without having to define parametric relationships/distributions between deterministic and stochastic variables. A Bayesian filtering-based learning method is introduced to train the structure of the proposed framework with historical data. Also, the steps to utilize the proposed framework for inference and prediction of the latent states and sensor outputs are discussed. Numerical experiments are provided to demonstrate the application of the proposed framework for degradation system modeling and monitoring.