Elsevier

Applied Energy

Volume 235, 1 February 2019, Pages 661-672
Applied Energy

State-of-life prognosis and diagnosis of lithium-ion batteries by data-driven particle filters

https://doi.org/10.1016/j.apenergy.2018.10.095Get rights and content

Highlights

  • Li-Ion battery capacity degradation diagnosis/prognosis by an adaptive algorithm.

  • On-line identification of the multi layer perceptron parameters by particle filter.

  • Adaptability to different dynamics/battery types without physics-based models.

  • Anomaly detection based on the particle filter estimation of log-likelihood ratios.

  • Application to actual data taken from NASA Ames Research Center and CALCE databases.

Abstract

The aim of this study is that of presenting a new diagnostic and prognostic method aimed at automatically detecting deviations from the expected degradation dynamics of the batteries due to changes in the operating conditions, or, possibly, anomalous behaviors, and predicting their remaining useful life (RUL) in terms of their state-of-life (SOL), without needing to derive any complex physics-based models and/or gather huge amounts of experimental data to cover all possible operative/fault conditions. The proposed method in fact exploits the real time framework offered by particle filtering and resorts to neural networks in order to build a suitable parametric measurement equation, which provides the algorithm with the capability of automatically adjusting to different battery’s dynamic behaviors. The results of this study demonstrate the satisfactory performances of the algorithm in terms of adaptability and diagnostic sensibility, with reference to suitably identified case studies based on actual Lithium-Ion battery capacity data taken from the prognostics data repository of the NASA Ames Research Center database and of the CALCE Battery Group.

Introduction

In recent years, Lithium-ion (Li-ion) batteries have gained large popularity as portable energy sources due to their significant advantages with respect to other battery types, such as: (i) the lower weight, due to the lightweight lithium and carbon-made electrodes, and, at the same time, the larger energy density, due to the high chemical reactivity of lithium; (ii) the possibility of being recharged also if they are not completely discharged without any detrimental effects (no memory effect); (iii) the lower self-discharge rate, so that they better maintain their charge when not used; (iv) the longer life cycle, since they can operate successfully even after hundreds of charge-discharge cycles. These features have played a major role in their successful use in many different application fields, including consumer electronics (cell phones, laptops, etc.) [1], hybrid and electric vehicles in the automotive industry [2], the more recent development of hybrid/electric aircraft (airplanes and helicopters) [3], balanced management of electric power grids with significant contributions from fluctuating renewable power sources (solar and wind) [4], [5], where studies are carried on aiming even at exploiting, at a domestic scale, Li-ion batteries previously used in electrical vehicles and no more satisfying the requirements of the automotive industry [6] and space exploration manned and unmanned missions [7].

However, due to their rechargeable nature, Li-Ion batteries are subject to irreversible processes occurring during their charging and discharging cycles, such as, for example, the formation of a solid-electrolyte interphase (SEI), which severely affect the batteries’ electrochemistry, as demonstrated by Pinson et al. [8] and modelled by Safari et al. [9]. These processes involve, in general, a continuous capacity fade, which eventually leads to the battery failure, with consequences ranging from a quite safe need to replace the battery of a mobile phone, to the catastrophic failure of an interplanetary probe.

In order to overcome these issues, many efforts have been devoted in literature to devising proper methods for improving the reliability and the availability of Li-Ion batteries. More specifically, a major role is played by the so-called prognostic and health management (PHM) methods, which, on the basis of different kinds of available, but indirect, information, allow to automatically, and in real-time, track some hidden indicators of the degradation state of the batteries, such as, for example the state-of-health (SOH), the state-of-charge (SOC), the state-of-life (SOL), and at predicting their remaining useful lifetime (RUL), either in terms of the end-of-discharge (EOD) or the end-of-life (EOL) times, possibly to support condition- or even prediction-based maintenance policies. In this regard, thorough reviews of many advanced PHM methods can be found in the work by Berecibar et al. and Wu et al. [10], [11]. Traditionally, these methods are classified in three major families, i.e., model (or physics)-based, data-driven or hybrid methods, depending on the type and quality of the information used to perform diagnostics and/or prognostics, as clearly summarized in the work by Guo et al. [12].

Model-based methods focus on identifying proper relationships between the observable quantities and the indicators of interest by building physics-based models of the degradation processes affecting the battery life. For example, Santhanagopalan and White employed a rigorous, porous-electrode based model including high rate limitations together with an unscented filter [13]; Zou et al. combined a first-order RC (resistor–capacitor) model with an extended Kalman filter for combined SOC and SOH estimation; Hu et al. resorted to a simplified equivalent circuit model and applied the Gauss–Hermite particle filter (GHPF) technique to track the capacity fade trend and extrapolate the future capacity values [14]; more recently, Ye et al. addressed a similar problem by using the equivalent circuit Thevenin model and an improved adaptive particle swarm filter; Li et al. proposed a universal capacity model based on charging curve, which inherits the advantages of IC analysis method and avoids the data preprocessing procedure, to estimate SOH of lithium ion batteries [15].

Data-driven methods, on the other hand, aim at mapping the above relationships by some approximating models adaptively built on the basis of available data, such as, for example, statistical models, neural networks (NN), Gaussian process functional regressions, support vector regressions, fuzzy inference engines, etc. Thomas et al., for example, developed a statistical models based on data from accelerated aging experiments [16]; Jungst et al. proposed inductive models for interpolating among the different experimental conditions; Liu et al. used Gaussian process-based regression to capture the actual trend of SOH, including global capacity degradation and local regeneration [17], whereas Wand et al. resorted to relevance vectors to update a double exponential degradation behavior; recently, Wu et al. proposed to employ neural networks to simulate the relation between battery charge curves at constant current and battery RUL [18]; Patil et al. adopted the Support Vector Regression (SVR) technique in order to predict the accurate RUL if the battery is close to the end of life (EOL) [19]; Zhao et al. developed a novel fault diagnosis method for battery systems in electric vehicles based on big data statistical methods [20]. Goebel et al. [21] proposed a suite of data-driven and model based methods for battery prognostic, ranging from probabilistic regression models to particle filtering.

Hybrid methods aim at combining model-based and data-driven methods, when possible, in an attempt to overcome the limitations of the individual methods and, thus, improve diagnostic and prognostic accuracies by better exploiting all the available information. He et al. [22] used the Dempster-Shafer theory for initializing the parameters of a degradation model on the basis of available experimental data, which were then identified by a particle filter algorithm; more recently, Chang et al. combined unscented Kalman filter, complete ensemble empirical mode decomposition (CEEMD) and relevance vector machine to predict the RUL of Li-ion batteries [23]. A promising hybrid strategy seems that of resorting to particle filtering-based algorithms, where the required analytical models representing either the dynamic behavior of the system or the measurement equation are actually suitable data-driven surrogate models. For example, Charkhgard and Farrokhi [24] proposed a combination of extended Kalman filtering (EKF) and neural networks trained off-line, whereas Daroogheh et al. used a particle filter instead of the EKF [25]; also Bai et al. devised a new ANN based battery model and integrated it with the Kalman filtering technique for battery health management [26]. These kind of methods are based on the consideration that, both physics-based model and surrogate models require the identification of suitable model parameters on the basis of some available observations; however, surrogate models do not require any physics/analytic-based derivations, which might turn out to be very time consuming, and are generally much computationally faster, especially with respect to numerical models, which might be a critical feature for real-time applications (as one can devise by reading the thorough review of the state-of-the-art available physical models in [27]).

One important issue which still severely limits the applicability of these approaches is that the surrogate models are trained off-line on the basis of a set of available examples of the input/output mapping of interest, typically collected under some representative, fixed operative conditions, such as those offered by the controlled environments of laboratory tests. Some examples can be found in the above cited Refs. [24], [25], [26]. Actually, this represents a problem also for many other diagnostic/prognostic methods, not being restricted to those relying on surrogate modeling, although the latter mostly suffer from this limitation, due to the fact that their generalization capability only depends on the available data, and not on physical reasoning. For example, many works of literature derive and demonstrate their proposed methods with reference to sets of Li-ion batteries voltage/capacity laboratory measurements acquired at different, but constant discharge rates/currents and under controlled laboratory conditions (e.g. fixed ambient temperature, charge/discharge scheduled procedures, etc.). As the size of the available dataset increases, possibly including information on different operating conditions, this approach allows to devise algorithms with increasing prediction/generalization capabilities; at the same time, however, it does not account for operating conditions varying in real time, as typically occurring when considering the actual batteries mission profiles and/or boundary conditions (e.g., temperature, mechanical degradation, lithium metal plating and other ageing mechanisms, as summarized by Vetter et al.[28]), thus severely limiting its application to real-life problems.

Some works of literature have already attempted to address this issue, which requires the capability of adapting in real time to the changing underlying dynamics. For example, in [29] Wang et al. propounded an adaptive particle filter-based algorithm for predicting the remaining useful life of a battery when operating at different discharge rates; similarly, in [19], an equivalent circuit model accounting for the discharge current is used to perform adaptive diagnosis of Li-ion batteries under real operative mission profiles. Yet, the parameters of the resulting equivalent circuit models are still identified off-line on the basis of available data (e.g., from AC Impedance Spectroscopy) and many of the factors actually influencing the degradation dynamics in real operative conditions are still not taken into account. In [30] some of the same authors of the present work presented a novel hybrid prognostics framework for the prediction of the end of discharge of Li-ion batteries, where the parameters of the surrogate model, i.e. a radial basis function neural network, were identified on-line by a particle filter on the basis of the real-time observations of the degradation process. That work represented a first attempt to create a prognostic tool capable of automatically coping to varying boundary conditions, with no need for explicitly modeling the dependency of the degradation dynamic on the external influencing factors. This allowed to naturally capture possible changes of the degradation dynamics and to accordingly update the RUL estimates. However, the algorithm was still only tailored to the specific EOD prognosis problem, and was still lacking of general optimization strategies which would guarantee its applicability also to different prognostic problems. Furthermore, the algorithm did not allow to perform any diagnostic tasks, which are fundamental for PHM applications.

In this context, the first purpose of this work is that of adapting the hybrid approach introduced in [30], which was restricted to the EOD prediction within individual discharge cycles, to be able to perform also SOL estimation and predict the EOL of Li-ion batteries. First, it is proposed to resort to multi layer perceptron (MLP) neural networks, which have turned out to be simpler and more intuitive for this kind of application. Similarly to [30], the parameters of the MLP networks are adaptively identified on-line by the particle filter on the basis of real-time observations of the Li-ion battery capacity. Then, since, in this case, the algorithm has to predict an individual degradation history, and not several successive discharge curves as in the previous work, a pre-training of the MLP neural network on some reference trajectory is suggested (although not strictly required), so as to significantly restrict the search space of the surrogate model’s parameters and speed-up the algorithm convergence. Note that the actual degradation can be significantly different from the pre-training one, as it is demonstrated in this work, still guaranteeing the adaptation capabilities of the prognostic tool. Moreover, to further increase the algorithm adaptability, the set of particles used by the particle filter (i.e., neural networks weights, see [30]) is artificially enriched by a particle resulting from a back-propagation-based optimization of a network on the basis of the capacity observations available up to the current time.

The second objective of the present work is that of providing the proposed algorithm with an additional, original diagnostic module, based on the particle filter-based estimation of the observations log-likelihood ratio, for the automatic and on-line detection of any changes in the “expected” dynamic degradation process. This represents a very important task for Li-ion batteries, which, to the authors’ knowledge, appears to be somehow overlooked by Li-ion PHM specialists, but may significantly improve the prognostic capabilities and, more generally, the safe management of the batteries, especially when operating in real environments subject to varying boundary conditions.

The proposed method is demonstrated with reference to real degradation transients taken from the NASA Ames Research Center database [31] and the CALCE Battery Group [32]. The available trajectories are also properly modified in order to be able to test the algorithm in varying operating conditions and to prove the effectiveness of its diagnostic module.

The paper is organized as follow. Section 2 briefly recalls the main features of the method proposed for sequentially train MLP-NN models by means of a particle filter algorithm. The multi layer perceptron-based particle filter (MLP-PF) approach here proposed is then customized in order to perform adaptive prognosis of the EOL of Li-Ion batteries and diagnosis of their SOH. Section 3 discusses the performances of the proposed method, demonstrating the capability of the algorithm with reference to the datasets cited above, which are typically used as benchmark case studies in similar works of literature. Section 4 draws some conclusions on the results and proposes future developments of the methodology.

Section snippets

Multi layer perceptron particle filter (mlp-pf) for diagnosis and prognosis

In this Section first the method originally proposed by Freitas et al. [33], and further developed and applied to PHM of Li-ion batteries in [30], is shortly recalled, where particle filters were used to sequentially, on line, train neural network models. The multi layer perceptron-based particle filter (MLP-PF) approach here proposed is tailored to the problem under investigation in order to be able to predict the EOL and to diagnose the SOH of Li-Ion batteries subject to repeated

Results

In this Section the prognostic and diagnostic capabilities of the proposed algorithm are demonstrated, with reference to the SOL datasets by the Prognostic Center of Excellence at NASA Ames Research Center and of the CALCE Battery Group ([31], [32]), shown in Fig. 4. In particular, the datasets labeled “NASA 1, 2 and 3” are taken from the NASA Ames research center database, whereas the one labeled “CALCE” is taken from the CALCE database. The NASA batteries have Graphite anode and a Lithium

Conclusions

In this work an original adaptation of an algorithm introduced by some of the same authors for performing adaptive and on-line prognosis of the end-of-life of Lithium-Ion batteries and diagnosis of their state of health have been proposed.

The use of a multi layer perceptron neural network for approximating the observation equation significantly contributes to the adaptability of the prognostic/diagnostic tool adopted. As demonstrated by the results of this work, the advantage of this feature is

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