1. Introduction
The popularization of electric drive equipment led to the research boom regarding energy storage equipment. Among these, the lithium-ion battery has garnered significant attention due to its high energy density, long cycle life, and other benefits [
1]. State of charge (SOC), as an important parameter to ensure the safe and stable operation of the battery, is the main focus of battery research [
2]. The present research methods for SOC estimation can be classified into three categories: experiment-based methods, model-based methods, and data-driven methods [
3].
The experiment-based method employs the impedance spectrum method, residual capacity method, open-circuit voltage (OCV) method, ampere-hour counting (AH) method, and other methods to establish the mapping relationship between external parameter characteristics and SOC [
4,
5,
6]. While this method yields reliable and accurate results, its limited scope of use restricts its widespread application [
7]. It is mainly used to obtain reference data for comparison with other methods or in situations where high-accuracy SOC estimation is required and sufficient time is available. The AH method can achieve online SOC estimation but suffers from cumulative errors [
8].
The model-based method uses the model plus filter method to achieve SOC estimation, using, for example, the Kalman filter (KF), particle filter, or H-infinity filter [
9,
10,
11,
12]. Commonly used models include the electrochemical mechanism model, equivalent circuit model (ECM), and black-box model [
13]. Because the electrochemical mechanism model is too complex, it has a relatively low level of application [
14]. The ECM, particularly the first-order RC model and second-order RC model, is widely used due to its simplicity, low computational requirements, and ability to reflect the internal mechanism to some extent [
15,
16]. However, the model-based method emphasizes the accuracy of the model, and the variable model parameters under different environments and states make it challenging to maintain SOC estimation accuracy using a fixed-parameter model [
17,
18,
19].
The data-driven method employs algorithms such as machine learning, deep learning, and others to establish the mapping relationship between SOC and battery measurement data [
19,
20,
21,
22]. This method yields accurate estimation results and exhibits strong nonlinearity-handling abilities [
23]. However, this method has obvious disadvantages: it lacks clear physical meaning and interpretability, and data quality affects the performance of the algorithm [
21,
24]. In practical use, ensuring the quality of the collected data is challenging due to the sensor and external environment influences.
Therefore, joint estimation using different methods has become a focal point of research [
25,
26,
27]. Moulik et al. [
28] proposed a hybrid-adaptive method of SOC estimation, considering an OCV method and comparing it with a hybrid method combining two KF-based methods, then used an adaptive method of SOC estimation, which achieved an accurate estimation by combining the experiment-based method with the KF method. More literature is available on the combination of the data-driven method and the KF method. Takyi-Aninakwa et al. [
29] proposed a wide temperature-adaptation method using optimized long short-term memory (LSTM)-weighted fading extended Kalman filtering (EKF) model. To achieve a higher-accuracy SOC estimation at different temperatures, Bai et al. [
30] used the radial basis function neural network combined with the adaptive double-EKF algorithm to estimate the SOC. Liu et al. [
31] combined the EKF with the support vector regression model to estimate the SOC, filtered the features through the Bayesian information criterion, and effectively solved the problem of data redundancy in the combination method, which is more accurate than the combination algorithm of full features. Afterward, Xie et al. [
32] proposed an improved algorithm based on a multi-hidden-layer LSTM (MHLSTM) neural network and suboptimal fading EKF (SFEKF) for synthetic SOC estimation; the battery SOC is roughly evaluated using an MHLSTM network and then SFEKF is used smooth the prediction results. By combining the EKF method with a back-propagation neural network, Liu et al. [
25] considered SOC estimation. Xu et al. [
33] and Cui et al. [
34] used the gated recurrent unit neural network with the unscented Kalman filter (UKF) method, estimated the SOC using the neural network, and filtered the output noise through the UKF, which reduced the requirements of model learning precision and hyperparameter setting. To accurately estimate SOC under uncertain interference levels, Cui et al. [
35] proposed a new robust kernel fuzzy method to minimize the mean and variance of model error and designed a multi-innovation UKF algorithm to achieve an estimation of accuracy.
However, it is noteworthy that the aforementioned joint estimation methods are predominantly characterized by serial connections, with few parallel combinations of multiple methods. This paper aims to fill this gap while addressing the limitations of data-driven methods facing interference caused by complex test conditions and data noise, and model-based methods with an excessive reliance on model accuracy. To this end, this paper proposes a novel method that combines the strengths of both model-based and data-driven methods for a joint estimation of the SOC. Specifically, the UKF and LSTM were employed to simultaneously estimate SOC, followed by further estimation using LSTM to achieve the highest possible accuracy under various conditions. The discharge experiment under dynamic stress test (DST) is used for training and verification, utilizing the federal urban driving schedule (FUDS) and Beijing dynamic stress test (BJDST) conditions at 0 °C, 25 °C, and 45 °C for testing purposes. The experimental findings demonstrate that the proposed method is capable of accurately estimating SOC under diverse conditions and temperatures while maintaining a root mean square error (RMSE) below 2.3%. The key contributions of this paper are summarized as follows:
This paper proposes a novel framework for a parallel estimation of the SOC that combines UKF and LSTM methods and achieves an accurate estimation through a secondary estimation, which effectively combines the robustness of the model-based method with the accuracy of the data-driven method.
In this method, the ECM adopted fixed parameters, which avoids frequent changes in model parameters, and effectively reduces the amount of calculation.
Experiments are carried out at 0 °C, 25 °C and 45 °C under DST, BJDST, and FUDS conditions, and verified on different kinds of batteries and charging data, which proves the accuracy, robustness, and universality of the proposed method.
The remainder of this paper is divided into the following parts.
Section 2 introduces the equivalent model and theoretical knowledge of LSTM used in the proposed method and the framework of the proposed method.
Section 3 describes the experiment process and analyzes the estimation results achieved under DST conditions.
Section 4 verifies and discusses the proposed method.
Section 5 provides a conclusion.
5. Conclusions
This paper proposed a novel method that combines model-based and data-driven methods in parallel to estimate the SOC. The framework of this method can be divided into two parts: the first part was composed of UKF and LSTM, in which the first-order RC model with fixed parameters was used as the basis for UKF estimation and parameter identification was realized by RLS, and the second part was composed of an LSTM. The second part was used to achieve accurate SOC estimation. From the results of the estimation, it can be seen that the SOC cannot be accurately estimated using only using the UKF or LSTM under different working conditions and temperatures. However, combining the first parallel estimation and second estimation could achieve an accurate estimation under three different conditions and three different temperatures, and the RMSE was controlled within 2.3% at 0 °C, 25 °C, and 45 °C, and within 1.4% at 25 °C and 45 °C. This method effectively mitigated the limitations associated with each method, thereby enhancing overall estimation performance, especially at extreme temperatures (0 °C). Through the validation of the A123 battery and charging data, the accuracy, robustness, and universality of the proposed method were demonstrated. At the same time, this method simplified the calculation and did not require model accuracy. Through simulation on MATLAB R2022b, it can be seen that it takes less than one millisecond is needed to update SOC with a single UKF, single LSTM, and the method proposed in this paper. Compared with a single estimation method, the proposed method improves the estimation accuracy, but the operating cost is close to that of a single LSTM, which fully satisfies the requirements of an update to the online battery management system. In the future, we will work to improve the accuracy of this method.