Application of expectation maximization and Kalman smoothing for prognosis of lumen maintenance life for light emitting diodes

Abstract

Light emitting diodes (LED) have found widespread use for lighting and displays in recent times due to their high efficiency, favorable form factor, impact resistance, robustness, reliability and prolonged lifetime. The extended times to failure of LEDs make the problem of lumen maintenance life prediction for LED light sources using traditional reliability-based failure data collection and analysis methods quite challenging. Therefore, one has to resort to using prognostic approaches such as Kalman or particle filters applied to real time degradation data to make inferences on the remaining useful life (RUL) of such devices. The standard prognostic approach for predicting lumen maintenance life relies on an underlying degradation model with predetermined parameters from previous stress tests. However, these model parameters may vary quite a bit from device to device and for different manufacturing batch lots, thereby leading to large prediction errors. To address this issue, it would be better to learn the model parameters from the current measurement data directly. This study aims to achieve this by estimating the parameter values using the Expectation Maximization (EM) algorithm. Kalman smoothing is then applied to the identified parameter values for predicting the lumen maintenance life of the LED. The accuracy of the EM - Kalman smoothing approach was tested and compared with the standard nonlinear least square (NLS) approach prescribed by the TM-21 standard as well as the standard particle filter approach (without EM). Our results show that the EM method can give better, if not, similar RUL prediction accuracy with respect to the NLS and standard particle filter (PF) algorithms. Moreover, the accuracy of RUL prediction using our proposed algorithm is insensitive to the choice of the initial model parameter values, which paves way for this algorithm to be used in practice for automated predictive analytics of degrading electromechanical systems.