1. Introduction
As the main energy component, lithium-ion batteries (LIBs) play an important role in the development of hybrid and electric vehicles (EVs) and other electronic industry, owing to the advantages of high energy density, low-emission, lightweight, etc. [
1]. However, the maximum available capacity gradually fades with the repeated charge and discharge, leading to the end of the battery life. It will cause waste if the battery is replaced too early, while safety accidents may occur when it is replaced too late [
2,
3]. The health monitoring and prognostics for LIBs can make great contributions to improve the safety and reliability of EVs and provide early warning for battery replacement [
4]. One of the most important issues in the condition monitoring and prognostics of LIBs is the prediction of remaining useful life (RUL) via degradation modeling and online inference.
Typically, the methods for an RUL prediction mainly include model-based methods and data-driven methods. The model-based methods, particularly the Kalman filter (KF), the particle filter (PF) and some stochastic models, have been recognized to contribute the state of charge (SOC) and state of health (SOH) estimation of batteries in recent years [
5,
6,
7,
8]. However, for LIBs, the sensitivity of a stochastic model when facing the complicated degradation mechanisms causes a decrease in the model robustness. By contrast, the data-driven methods can learn the battery degradation trends from battery monitoring data directly, whereby it circumvents the analysis of electrochemical reaction and failure mechanism. Hence, these kinds of technologies have attracted great interest recently among researchers [
9].
The accuracy of data-driven RUL prediction methods relies heavily on a health indicator (HI), which usually refers to the indicator that can significantly reflect the degradation behaviors of LIBs. The traditional His [
10,
11,
12], e.g., capacity or impedance, are difficult to measure in real applications due to the expensive instruments and complex operations. To address these issues, in [
13,
14,
15], discharge voltage data are employed to derive indirect His to characterize the battery degradation. However, when applying the above His in practice, the high sensitivity of discharge profiles to dynamic operation conditions may cause big prediction errors [
7]. Comparatively, the charge process is more stable and can provide a more reliable HI, such as the sampling points of terminal voltage used in [
16]. Nevertheless, the reliability of the abovementioned indirect HI is still not assessed, and the local fluctuations in the measuring data are not considered.
Furthermore, prediction modeling has always been the focus of attention on battery RUL predictions. As matters stand, there are many data-driven approaches, with emphasis on artificial intelligence being increasingly applied to RUL estimations, such as a relevance vector machine (RVM) [
13], a support vector machine (SVM) [
17], an artificial neural network (ANN) [
18,
19]. These methods have brought great progress to the field of state prediction, but there are still some issues, including the complex model structure and the low prediction accuracy [
20]. Recently, deep learning with a better learning character and stronger model adaptability has aroused the interest of researchers for improving the prediction accuracy of the model [
21]. One of the most influential methods is the recurrent neural network (RNN) for dealing with the prediction of time series [
22]. However, it lacks the efficient mechanism for selecting key information and may suffer from a vanishing gradient or an exploding gradient. Then, some of the improved RNNs, i.e., the long short-term memory neural network (LSTM NN) [
23], are widely proven to effectively contribute the above problems thanks to the long-term dependencies learning capacity. However, the computation cost of the training and prediction process of the LSTM NN is still large, which limits its practical application. Currently, it is noted that a gated recurrent unit neural network (GRU NN) [
24] is proposed, which not only deal with the long-term dependencies data, but also has the advantages of a lighter structure, fewer parameters and a shorter training time. Thus, a GRU NN is more suitable for the online RUL prediction of LIBs. However, when the aforementioned method is applied to the RUL prediction of LIBs, the prediction result may be unreliable due to the existence of the local regeneration phenomenon [
7]. Local regeneration is a frequent phenomenon in the shelving phase of battery operations, and it has been recognized in [
25,
26]. The regeneration phenomena can result in the local fluctuations of battery monitoring data in reality. However, it is still a challenging mission to design a precise battery RUL prognostics arithmetic using online monitoring data in the presence of local regenerations and fluctuations.
Inspired by the above works, in this paper, we propose an RUL prediction method combining deep learning and soft sensing. To avoid the measurement difficulties of direct HIs in the online application, we firstly extract the constant current duration (CCD) from the voltage and current data of the charge process as the HI to reflex the battery degradation performance. Then, an adaptive sliding window-based GRU prediction model is constructed to synchronously learn the long-term dependencies and capture the local regenerations. Due to the advantages in learning long-term dependencies and capturing the local regenerations and fluctuations, a more accurate prediction result can be expected. The major contributions of this paper are listed as follows:
- (1)
Combining soft sensing with deep learning, a reliable RUL prediction model is proposed, which can accomplish a satisfactory HI estimation and provide an accurate RUL for LIBs in the routine environment.
- (2)
A unique indirect HI, i.e., the CCD extracted from the charge monitoring data, is considered as the indirect HI without complicated measurements and time-consuming calculations, providing a soft measurement of battery performance degradation.
- (3)
A GRU prediction network with an adaptive sliding window is utilized to estimate the HI tendencies and determine the battery residual life. The designed GRU NN can not only learn the long-term dependencies but also fit the local regenerations and fluctuations of the battery degeneration with low computation cost.
3. Algorithm Description
Using the extracted CCD as the HI, an adaptive sliding window-based GRU prediction network is constructed in this section to estimate the HI degradation and predict the RUL of the LIB. The structure of the prediction model is illustrated in
Figure 3. As presented, an adaptive sliding window is designed to dynamically select the input data for training and forecasting. Then, a GRU NN is constructed with the purpose of estimating the decline of CCD online using the trained model parameters and forecasting inputs. At last, the RUL of the LIB can be determined from the predicted CCD values.
3.1. GRU Prediction with Adaptive Sliding Window
As an improved recurrent neural network, a GRU is designed to solve the gradients’ exploding and vanishing problem by virtue of the peculiar memory unit and gate mechanism. Additionally, meanwhile, compared with the traditional LSTM, less training data and time are required to promote the convergence of the model with the streamlined gates. By combining with the GRU cells, an adapted window updating mechanism is designed to contribute the GRU NN construction to conduct the CCD estimation and RUL prediction.
The graphical description of the proposed adaptive sliding window-based GRU prediction structure is revealed in
Figure 4. The amount of CCD data fed into the GRU model in each iteration is updated as the window length changes. Significantly, the number of GRU cells, i.e., the hidden size of the GRU NN, is dynamically consistent with the length of the sliding window. The generation process of learning data for the GRU model using the adaptive sliding window is given as follows:
- (1)
The sliding mode of the window is set as one-step ahead, i.e., the number of the new data in the window adds only one for each step. Let the current point be P, and the next point be P + 1; the value of the CCD at P + 1 needs to be predicted.
We use the priori data captured in the current sliding window to predict the CCD value at
P + 1, and the length of this sliding window is
, which can be updated by using the following formula [
29]:
where
indicates the Euclidean vector of the norm of the difference between
and
, with
and
.
is the mean value of
.
indicates the absolute value of the difference between the
and
, which are the variances of
and
respectively, and
denotes the mean value of
.
and
are hyper-parameters for the proposed sliding window, which are determined by trial and error.
- (2)
In the online training stage, through selecting the initial window length and performing the one-step-ahead prediction, the CCD data for training are expanded into two-dimensional space to explore the structure and parameters of the GRU NN. For each sequence, its length varies with the adaptive mechanism (Equation (2)). With the trained model, the designed GRU NN can predict the CCD of the next cycle one by one. As seen in
Figure 4, the GRU NN is composed of the basic GRU cell with a reset gate (
) and an update gate (
). The information propagating in GRU cells can be controlled by the gate mechanism.
Given that the input at the current time is
and
is the CCD value at the next time, it is
P + 1 that needs to be predicted.
indicates the hidden state of GRU cells at
P, which is also the output of the cell. The reset gate (
) aims to control the data information from the new input information and output information yielded by previous cells. The update gate is employed to maintain the helpful historical information. The reset gate and update gate at time
P + 1 are, respectively, calculated using the following formulas:
where
is the logistic sigmoid function,
and
represent the layer weights and
indicates the biases.
The output of the reset gate is employed to generate the candidate state
using a tanh function for updating the cell state. Then, the output of this cell
can be calculated using
and the output of the update gate,
. The transformation process of the cell states is presented in the following form:
where
means the element-wise product,
and
represent the layer weights and
indicates the biases.
The RUL prediction model is constructed by connecting the above GRU cells. When the predicted CCD is lower than the failure threshold, a failure occurs, and the RUL can be calculated.
3.2. RUL Prediction
An LIB is deemed to fail when the HI reaches its pre-specified failure threshold. Additionally, the length of available service cycles from the current cycle to the end-of-life cycle are referred to as the RUL. In this paper, the end-of-life cycle is the cycle number when the CCD decreases below its failure threshold, and the current cycle is the prediction start cycle.
The high correlation between the capacity and the extracted HI is demonstrated in the subsequent
Section 4.1, then the failure threshold of the normalized CCD (
) can be expressed as follows [
13]:
where
indicates the failure threshold on battery capacity, which is usually set to 70–80% of its nominal value [
10], and
and
are the maximum and minimum of capacity. For convenience, the normalized CCD and its failure threshold are employed in the following experiment and analysis.
The RUL can be calculated using the following [
16]:
where
is the number of residual cycles, i.e., the RUL.
indicates the cycle number when the value of CCDs degrades below
, and
represents the prediction starting cycle.