Particle filter models and phase sensitive detection for prognostication and health monitoring of leadfree electronics under shock and vibration

In this paper, a prognostication health management (PHM) methodology has been presented for electronic components subjected to mechanical shock and vibration. Electronic assemblies have been monitored using state-space vectors from resistance spectroscopy, phase-sensitive detection and particle filtering (PF) to quantify damage initiation, progression and remaining useful life of the electronic assembly. The presented methodology is an advancement of the state-of-art, which presently focuses on reactive failure detection and provides limited or no insight into the system reliability and residual life. Previously damage initiation, damage progression, and residual life in the pre-failure space has been correlated with micro-structural damage based proxies, feature vectors based on time, spectral and joint time-frequency characteristics of electronics [Lall2004^a-d, 2005^a-b, 2006^a-f, 2007^a-e, 2008^a-f]. Precise resistance measurements based on the resistance spectroscopy method have been used to monitor interconnects for damage and prognosticate failure [Lall 2009^{a, b}, 2010^{a, b}, Constable 1992, 2001]. In this paper, the effectiveness of the proposed particle filter and resistance spectroscopy based approach in a prognostic health management (PHM) framework has been demonstrated for electronics. The measured state variable has been related to the underlying damage state using non-linear finite element analysis. The particle filter has been used to estimate the state variable, rate of change of the state variable, acceleration of the state variable and construct a feature vector. The estimated state-space parameters have been used to extrapolate the feature vector into the future and predict the time-to-failure at which the feature vector will cross the failure threshold. Remaining useful life has been calculated based on the evolution of the state space feature vector. Standard prognostic health management metrics were used to quantify the performance of the algorithm against the actual remaining useful life. Application to part replacement decisions for ultra-high reliability system has been demonstrated. Using the technique described in the paper the appropriate time to re-order a replacement part could be monitored, and defended statistically. Robustness of the prognostication algorithm has been quantified using standard performance evaluation metrics.