Prognostics for state of health estimation of lithium-ion batteries based on combination Gaussian process functional regression Datong Liu a,⇑ , Jingyue Pang a , Jianbao Zhou a , Yu Peng a , Michael Pecht b a Department of Automatic Test and Control, Harbin Institute of Technology, Harbin 150080, China b CALCE, University of Maryland, College Park, MD 20742, USA article info Article history: Received 15 June 2012 Received in revised form 12 March 2013 Accepted 23 March 2013 Available online 17 April 2013 abstract State of health (SOH) estimation plays a significant role in battery prognostics. It is used as a qualitative measure of the capability of a lithium-ion battery to store and deliver energy in a system. At present, many algorithms have been applied to perform prognostics for SOH estimation, especially data-driven prognostics algorithms supporting uncertainty representation and management. To describe the uncer- tainty in evaluation and prediction, we used the Gaussian Process Regression (GPR), a data-driven approach, to perform SOH prediction with mean and variance values as the uncertainty representation of SOH. Then, in order to realize multiple-step-ahead prognostics, we utilized an improved GPR method—combination Gaussian Process Functional Regression (GPFR)—to capture the actual trend of SOH, including global capacity degradation and local regeneration. Experimental results confirm that the proposed method can be effectively applied to lithium-ion battery monitoring and prognostics by quantitative comparison with the other GPR and GPFR models. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Lithium-ion batteries are core components in a wide variety of systems. Therefore, the reliability of lithium-ion batteries is a sub- ject of great interest to the electronics industry [1]. Conventionally, battery reliability monitoring during usage has two different as- pects: state of charge (SOC) and state of health (SOH) [2]. Com- pared to the study of SOC estimation methods which attracts more attentions of current research work, research on SOH estima- tion and prediction is still in its initial stage. With the increasing demand for lithium-ion batteries, and SOH estimation plays an important part in battery prognostics as qualitative measure for the battery to store and deliver energy in the system. The prognos- tics of the SOH can indicate the performance degradation and pre- vent possible accidents, so more research needs to be conducted to develop prognostics algorithms for SOH estimation. An extended Kalman filter (EKF) has been applied for real-time prediction of SOC and SOH of automotive batteries [3]. Neuro-fuz- zy and decision theoretic methods have been utilized to fuse fea- ture vectors derived from battery health sensor data to estimate SOC, SOH, and state of life (SOL) [4–9]. Other approaches, such as combinations of regressions [10], neural networks [11], fuzzy logic [12], and distributed active learning, have been used to predict remaining useful life (RUL) of batteries [13]. However, a common disadvantage of these prediction methods is the lack of uncertainty expression and management for prognostics. In industrial applica- tions, uncertainty in models and data can lead to poor reliability prediction. To address this problem, prognostic algorithms with uncertainty representation have been developed [14]. Relevance vector machines (RVMs) have been applied to implement regres- sion models for SOH prognosis [5]. Particle filters (PFs) have also been applied to predict the RUL of lithium-ion batteries based on impedance spectroscopy data. For example, researchers have used a Rao–Blackwellized PF (RBPF) to reduce the uncertainty in predic- tion frameworks [15]. However, the implementation of impedance measurement not only requires expensive equipment but also is more time-consuming. In addition, PF is a model-based method that requires physical or electrochemical knowledge to model deg- radation trends in batteries. As a result, a prediction approach without complicated system models should be used for lithium- ion battery RUL prediction to achieve low computing complexity as well as uncertainty representation. In this study, we used a Gaussian process regression (GPR) mod- el for battery prognostics. A GPR model is particularly useful be- cause of its flexibility and ability to provide uncertainty representation and facilitate accurate prediction even in the ab- sence of physical models [16]. Recently, GPR algorithms have been applied in the domain of battery prognostics. Researchers have performed regression for internal parameters of batteries over time based on GPR models and have transferred the predicted values to the capacity domain to indicate capacity decay with time [17]. The results are acceptable, but the extrapolation performance deterio- rates rapidly when test data are ‘‘distant’’ from the training data 0026-2714/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2013.03.010 ⇑ Corresponding author. Tel.: +86 45186413533; fax: +86 45186402953. E-mail address: liudatong@hit.edu.cn (D. Liu). Microelectronics Reliability 53 (2013) 832–839 Contents lists available at SciVerse ScienceDirect Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel