Lithium-ion batteries are the core power sources for electric vehicles (EVs), consumer electronics, and even spacecraft, etc. [1
]. Therefore, the reliability and safety of lithium-ion batteries is a critical problem in the process of actual applications. The performance of batteries gradually deteriorates with the increase of service life, which might not only affect the normal operation of electrical equipment, but also bring about serious consequences [4
]. For example, there was the cell explosion of the Samsung NOTE7, the spontaneous combustion of electric vehicles, and the explosion of battery energy storage boxes in some power plants in recent years [5
In order to avoid such accidents, SOH and RUL prediction of lithium-ion batteries has become a hotspot and challenging subject in the prognostics and health management (PHM) of electronics. In fact, the battery management system (BMS) is designed for various instruments to ensure safe operating conditions. SOH determination and RUL prediction are the key functions of BMS in current practice. They need to be estimated using online measurement data including current, voltage, and temperature, etc.
The existing methods for SOH and RUL prediction of lithium-ion batteries can be roughly divided into two main categories: model-based approaches and data-driven approaches [6
]. The electrochemical model (EChM) and the equivalent circuit model are two common models. The most popular EChM is Doyle–Fuller–Newman (DFN) model [7
]. Safari et al. [10
] developed a multimodal physics-based aging model for the capacity fade of the lithium-ion batteries. The model combined the solvent decomposition kinetics and solvent diffusion through the solid electrolyte interphase (SEI) layer. Considering desolvation as a rate-limiting step, in Ref. [11
], the authors used a one-dimensional model to estimate the aging of the battery by considering both the calendar and cycle phenomena together [13
]. Although the model has high simulation accuracy, it is very complicated to simulate in online applications. Thus, model reduction methods are used to reduce the order of these models. Ramadesigan et al. [14
] employed reformulated models to efficiently extract the effective kinetic and transport parameters from experimental data. An alternative approach, using voltage-discharge curves measured during initial cycles to predict voltage-discharge curves during later cycles, is analyzed. Ashwin et al. [15
] proposed a pseudo-two-dimensional electrochemical lithium-ion battery model to study capacity degradation under cyclic charging and discharging conditions, but this model was largely unable to achieve dynamic tracking, so its accuracy was poor. The major drawback of this method is that the reduction models are obtained under certain conditions, which will limit the achievable accuracy and introduce modeling errors.
Equivalent circuit models are less complicated than EChM, and are easy to implement for real-time applications with medium accuracy. Johnson et al. [16
] developed two classical equivalent circuit models: the battery internal resistance equivalent (Rint) model and the impedance resistance–capacitance (RC) model. Although the implementation of the equivalent circuit model was strong, it was easy to ignore the implicit relationship between the internal state variables of the battery. In Ref. [17
], the simplest Thevenin model with one RC branch is presented, and all the model parameters are constant. When equivalent circuit models are used to estimate battery aging, model parameters include lots of internal battery parameters and resistance aging parameters. Parameter identification requires a large and diverse data set obtained with time-consuming tests. However, due to the incomplete understanding of the capacity degradation mechanism of lithium-ion batteries, it is difficult to determine the main parameters involved in the model-based method. Some parameters of side reactions accompanying the main reaction are also difficult to determine through parameter identification. Moreover, model-based methods exhibit poor real-time performance.
With the rapid development of machine learning and artificial intelligence, data-driven methods have been receiving more and more attention [18
]. In addition, a large number of performance data of lithium-ion batteries can be obtained from actual applications. This provides the foundation for applying data-driven methods to predict the aging life of lithium-ion batteries. Compared with the model-based methods, data-driven methods are nonparametric, and do not consider the electrochemical principles to some extent. Thus, degradation models of lithium-ion batteries are developed with various mapping and regression tools.
Existing approaches include time series analysis, artificial neural network (ANN), support vector machine (SVM), relevance vector machine (RVM), Gaussian process regression (GPR), and so on. Long et al. [21
] applied an improved autoregressive (AR) model by particle swarm optimization (PSO) to make online predictions. The calculation of the AR model was simple, but the prediction results did not have an uncertain expression of the results. Andre et al. [22
] used a structured neural network algorithm to reduce the complexity of network structure and improve the calculation speed, but the prediction results only gave point estimates. The prediction performance was poor when the number of samples was small. Gao et al. [23
] proposed a multikernel SVM (MSVM) based on polynomial kernel and radial basis kernel function to predict RUL of the battery. But SVM easily suffered from the local optimum because of its characteristics.
In recent years, the GPR method has been favored by researchers because it is a probability prediction model under the Bayesian framework [24
]. In order to realize multiple-step-ahead prognostics, Liu et al. [26
] utilized an improved GPR model-combination Gaussian Process Functional Regression (GPFR) to capture the actual trend of SOH, including global capacity degradation and local regeneration. Although it had certain advantages in long-term predictions, the capacity was selected as the degradation data, which had some limitations for practical applications. In Ref. [27
], Peng et al. proposed a fusion method of the wavelet denoising (WD) method and the GPFR model base on that of Liu et al. [26
], where the WD was applied to remove the noise from the original data; the GPFR model was then employed to obtain higher accuracy RUL predictions. The prediction of RUL was improved, but the method only focused on the degradation trend of batteries, and ignored the regeneration phenomenon in battery rest life. Empirical mode decomposition (EMD) was used to extract global tendency and local fluctuations in the battery SOH series, which reduced the affection of the local regenerations in the battery charge procedure [28
]. The multiscale logistic regression (LR) and GPR were further constructed for modeling the global tendency and local fluctuations, respectively. This method took battery capacity recovery into account, but indirect health indicators with more practical significance were not used for prediction. Generally speaking, some of the above methods use capacity degradation series or impendence to predict SOH and RUL. However, since measuring the impedance and the resistance is time-consuming, it is difficult to make online measurements using the capacity fade data to estimate SOH and RUL [28
Therefore, some researchers have applied indirect features to substitute capacity data. These can be measured easily in real-time and online, including current, voltage, and temperature, etc. Compared with Ref. [26
], Yang et al. [29
] extracted four specific parameters from charging curves, and used them as an input of the GPR model instead of cycle numbers. This method was more meaningful in practical application, but by considering only the charging process voltage change curve, some parameters showed low correlation with capacity, which resulted in reduced prediction accuracy. The discharge process of lithium-ion batteries also plays an important role in aging life prediction. Therefore, to overcome the capacity unmeasurable problem in this paper, we will extract measurable degradation indicators from the charge and discharge process of lithium-ion batteries, which are highly relevant to the capacity fade. The main contribution of this paper is that the proposed method can predict the short-term SOH and long-term RUL of lithium-ion batteries with indirect health indicators (IHIs) and the GPR model. Firstly, in order to reduce the cost of the prediction method and improve the prediction accuracy, this paper proposes to extract indirect health indicators from the data that can be collected by ordinary sensors, such as voltage, current, temperature curves. Then, IHIs with high correlation with the capacity degradation curve are chosen as high-dimensional input by means of grey relation analysis, and the GPR model is developed to predict the short-term SOH of lithium-ion batteries. Finally, considering that there is a certain mapping relationship between SOH and RUL, three IHIs and the present SOH value are utilized to predict RUL of lithium-ion batteries through the GPR model.
The paper is organized as follows. The selection and extraction of IHIs are briefly introduced in Section 2
. Section 3
discusses the prediction method based on Gaussian process regression. The simulation results of SOH and RUL are reported in Section 4
. Finally, the conclusions are presented in Section 5
This research focused on the fact that in some practical applications, battery capacity cannot be obtained through online measurement, so it is difficult to predict the SOH and RUL of the battery. A novel SOH and RUL prediction framework of lithium-ion batteries based on GPR with IHIs is developed. Firstly, IHIs replacing the battery capacity are extracted from the data of voltage, temperature, and current, collected by means of some common sensors. GRA is used to select the important IHIs with a high correlation with the battery capacity and to determine the best input. Then, a short-term SOH prediction model is established via the high-dimension GPR model with the linear function as the mean function. According to the predicted SOH and the determined IHIs, the RUL prediction model was developed. The experimental results show that the proposed method in this paper is accurate and effective in SOH and RUL prediction, and that it can significantly improve the prediction performance.
To verify the adaptability of the proposed method, experiments were prepared for lithium-ion batteries under different working conditions, such as different charging currents, changes in ambient temperature, different discharge voltages, etc. Meanwhile, we hope to have a better understanding of the physical model of lithium-ion batteries concerning the capacity degradation process, and will consider the combination of model-based and data-driven methods to further improve the prediction accuracy.