Battery remaining useful life prediction at different discharge rates Dong Wang, Fangfang Yang ⁎, Yang Zhao, Kwok-Leung Tsui Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China abstract article info Article history: Received 6 October 2016 Received in revised form 24 August 2017 Accepted 6 September 2017 Available online xxxx Lithium-ion batteries are widely used in hybrid electric vehicles, consumer electronics, etc. As of today, given a room temperature, many battery prognostic methods working at a constant discharge rate have been proposed to predict battery remaining useful life (RUL). However, different discharge rates (DDRs) affect both usable bat- tery capacity and battery degradation rate. Consequently, it is necessary to take DDRs into consideration when a battery prognostic method is designed. In this paper, we propose a discharge-rate-dependent battery prognostic method that is able to track usable battery capacity affected by DDRs in the process of battery degradation and to predict RUL at DDRs. An experiment was designed to collect accelerated battery life testing data at DDRs, which are used to investigate how DDRs influence usable battery capacity, to design a discharge-rate-dependent state space model and to validate the effectiveness of the proposed battery prognostic method. Results show that the proposed battery prognostic method can work at DDRs and achieve high RUL prediction accuracies at DDRs. © 2017 Elsevier Ltd. All rights reserved. Keywords: Remaining useful life Lithium-ion batteries Particle filter Prognostics and health management Different discharge rates 1. Introduction Lithium-ion batteries are widely used in hybrid electric vehicles, consumer electronics, etc. Considering several significant battery capac- ity degradation factors [1], including storage voltage, environment tem- perature, discharge rate, depth of discharge, etc., one needs to take these factors into consideration in battery prognostics and health manage- ment [2], especially battery remaining useful life (RUL) prediction. Here, battery RUL can be regarded as how many charge/discharge cycles are left before battery capacity fails to provide reliable power for electric systems and products [3]. As of today, many battery prognostic methods have been proposed to predict battery RUL at a constant discharge rate. Among these battery prognostic methods, particle filter (PF) based battery prognostic methods [4–9] have attracted lots of attention because PF provides a way to solve numerical integration required in non-linear state space models. Moreover, PF based methods have been demonstrated to be ef- fective in diagnostics and prognostics of other critical components, such as bearing [10], gear [11], carrier plate [12], gas turbine [13], aluminum electrolytic capacitors [14], fatigue crack [15,16], etc. For PF based bat- tery prognostics, Saha et al. [17] proposed to combine relevance vector machine and PF so as to predict battery RUL at a constant discharge rate. In their further comparison study [18], they experimentally demon- strated that the PF based prognostic method has higher RUL prediction accuracies than autoregressive integrated moving average and extend- ed Kalman filter based prognostic methods. Following the work done by Saha et al., He et al. [19] used a bi-exponential function as an empir- ical battery degradation model so as to fit battery degradation data at a constant discharge rate and they experimentally found that the bi-ex- ponential function has good ability to fit the battery degradation data. Based on the empirical battery degradation model, they built a state space model at a constant discharge rate and used PF to posteriorly es- timate parameters distributions for battery RUL prediction at a constant discharge rate. To better fit local battery degradation behavior, Xing et al. [20] combined an exponential function and a polynomial function with an order of 2 to form an ensemble empirical battery degradation model and they experimentally demonstrated that the new empirical battery degradation model is able to predict battery RUL at a constant discharge rate better than the bi-exponential function based prognostic method. Since then on, many other researchers have tried to improve battery RUL prediction accuracies at a constant discharge rate by en- hancing the performance of PF, including its particle diversity [21,22], model adaptation [23] and its importance function [24–26]. Even though the aforementioned battery prognostic methods had good RUL prediction accuracies at a constant discharge rate, these prog- nostic methods did not consider the influence of discharge rate on bat- tery degradation. Actually, given a room temperature, discharge rate is one of the most significant factors to influence battery capacity degrada- tion [27]. Normally, the higher a discharge rate, the faster a capacity degradation rate. Moreover, discharge rate affects usable capacity. The higher a discharge rate, the smaller a usable capacity. And, when a dis- charge rate is changed from a high rate to a low rate, most ‘lost’ capacity caused by the high rate is revoked [28]. This is the reason why we use Microelectronics Reliability 78 (2017) 212–219 ⁎ Corresponding author. E-mail addresses: dongwang4-c@my.cityu.edu.hk (D. Wang), fangfyang2-c@my.cityu.edu.hk (F. Yang), yangzhao9-c@my.cityu.edu.hk (Y. Zhao), kltsui@cityu.edu.hk (K.-L. Tsui). http://dx.doi.org/10.1016/j.microrel.2017.09.009 0026-2714/© 2017 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel