Data-driven method based on particle swarm optimization and k-nearest neighbor regression for estimating capacity of lithium-ion battery Chao Hu ⇑ , Gaurav Jain, Puqiang Zhang, Craig Schmidt, Parthasarathy Gomadam, Tom Gorka Medtronic Energy and Component Center, Brooklyn Center, MN 55430, USA highlights  We develop a data-driven method for the battery capacity estimation.  Five charge-related features that are indicative of the capacity are defined.  The kNN regression model captures the dependency of the capacity on the features.  Results with 10 years’ continuous cycling data verify the effectiveness of the method. article info Article history: Received 23 February 2014 Received in revised form 19 April 2014 Accepted 24 April 2014 Keywords: k-Nearest neighbor Kernel regression Feature weighting Particle swarm optimization Capacity estimation Lithium-ion battery abstract Reliability of lithium-ion (Li-ion) rechargeable batteries used in implantable medical devices has been recognized as of high importance from a broad range of stakeholders, including medical device manufac- turers, regulatory agencies, physicians, and patients. To ensure Li-ion batteries in these devices operate reliably, it is important to be able to assess the battery health condition by estimating the battery capac- ity over the life-time. This paper presents a data-driven method for estimating the capacity of Li-ion bat- tery based on the charge voltage and current curves. The contributions of this paper are three-fold: (i) the definition of five characteristic features of the charge curves that are indicative of the capacity, (ii) the development of a non-linear kernel regression model, based on the k-nearest neighbor (kNN) regression, that captures the complex dependency of the capacity on the five features, and (iii) the adaptation of par- ticle swarm optimization (PSO) to finding the optimal combination of feature weights for creating a kNN regression model that minimizes the cross validation (CV) error in the capacity estimation. Verification with 10 years’ continuous cycling data suggests that the proposed method is able to accurately estimate the capacity of Li-ion battery throughout the whole life-time. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Capacity, which quantifies the available energy stored in a fully charged Li-ion battery cell, is an important indicator of the state of health (SOH) of the cell [1,2]; remaining useful life, also called remaining longevity, refers to the available service time that is left before the capacity fade reaches an unacceptable level [3–5]. It is important to accurately estimate these two parameters in order to monitor the present battery SOH and to enable failure preven- tion through timely maintenance actions. Recent literature reports a variety of approaches to estimate the capacity of Li-ion battery. In general, these approaches can be categorized into the adaptive filtering approach [1,2,6–9], the cou- lomb counting approach [10–12], the neural network (NN) approach [13,14] and the kernel regression approach [15–17]. Joint/dual extended Kalman filter (EKF) [1] and unscented Kalman filter [2,6] were employed to estimate the state of charge (SOC), capacity and/or resistance of Li-ion battery. To improve the perfor- mance of joint/dual estimation, adaptive measurement noise mod- els of the Kalman filter were developed to separate the sequence of SOC and capacity estimation [7]. A multiscale scheme with EKF [8] was developed that decouples the SOC and capacity estimation with respect to both the measurement- and time-scales and employs a state projection schedule for accurate and stable capacity estimation. Most recently, a data-driven multi-scale EKF algorithm was developed that leverages the fast-varying character- istic of SOC and the slow-varying characteristic of capacity, with an http://dx.doi.org/10.1016/j.apenergy.2014.04.077 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 763 514 0231; fax: +1 763 514 1284. E-mail address: chao.x.hu@medtronic.com (C. Hu). Applied Energy 129 (2014) 49–55 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy