Accurate estimation and prediction of the state-of-health (SOH) and remaining useful life (RUL) are fundamental to optimal maintenance strategies formulation for prognostics and health management (PHM) of degraded equipment. However, the performance assessment of health state prognostics and RUL prediction is strongly dependent on the errors and uncertainties in physical measurements, and heterogeneous degradation of equipment in time-varying operating conditions. The objective of this article is to provide a hybrid prognostic framework that integrates a two-phase clustering scheme and a particle filter (PF)-long short-term memory (LSTM) learning algorithm based on PF and LSTM networks for dynamic classification of SOH and long-term RUL prediction in the absence of future observations. The proposed generic hybrid PF-LSTM prognostic approach is demonstrated and compared with other adaptive learning and machine learning methods such as unscented particle filter (UPF) and radial basis function network (RBFN) on the degradation modeling and RUL prediction for lithium-ion batteries. The comparison results show that robust prediction performance can be obtained by the hybrid PF-LSTM prognostic approach with the accurate characterization of equipment degradation states based on the integrated subtractive-fuzzy clustering analysis. The more accuracy on prognostic estimations in probability density function (PDF) of prior and posterior distributions of battery capacity and RUL that are achieved by particle filtering can gain extensive insights to predictive maintenance action guide.

Reliability and safety assurance are of supreme importance in the implementation of digital safety-critical control systems. A deductive method integrated with simulation-based fault injection and testing is presented for out-of-range permanent software fault localization. For fault modeling, an input–output mapping scheme is proposed to characterize the behavior of software modules and represent failure modes in an analogous manner to hardware state definitions. The Markov/cell-to-cell-mapping scheme is used for diagnostics. The diagnostic process is illustrated by several case studies for a boiling water reactor feedwater control system. The case study results show that the diagnostic algorithm is capable of software fault localization in the presence of both single and multiple faults.