A Comprehensive Review of Key Technologies for Enhancing the Reliability of Lithium-Ion Power Batteries

Abstract

Fossil fuel usage has a great impact on the environment and global climate. Promoting new energy vehicles (NEVs) is essential for green and low-carbon transportation and supporting sustainable development. Lithium-ion power batteries (LIPBs) are crucial energy-storage components in NEVs, directly influencing their performance and safety. Therefore, exploring LIPB reliability technologies has become a vital research area. This paper aims to comprehensively summarize the progress in LIPB reliability research. First, we analyze existing reliability studies on LIPB components and common estimation methods. Second, we review the state-estimation methods used for accurate battery monitoring. Third, we summarize the commonly used optimization methods in fault diagnosis and lifetime prediction. Fourth, we conduct a bibliometric analysis. Finally, we identify potential challenges for future LIPB research. Through our literature review, we find that: (1) model-based and data-driven approaches are currently more commonly used in state-estimation methods; (2) neural networks and deep learning are the most prevalent methods in fault diagnosis and lifetime prediction; (3) bibliometric analysis indicates a high interest in LIPB reliability technology in China compared to other countries; (4) this research needs further development in overall system reliability, research on real-world usage scenarios, and advanced simulation and modeling techniques.

1. Introduction

With the rapid pace of industrialization, the global community is confronted with mounting environmental pressures and an impending energy crisis. To alleviate the long-standing reliance on conventional fossil fuels such as coal, oil, and natural gas, numerous nations are compelled to explore alternative, environmentally friendly, and sustainable energy sources [1,2,3,4]. In response to this imperative, the automotive industry has embraced a gradual transition towards electrified production [5], giving rise to the development of NEVs powered by lithium batteries [6,7,8]. The advent of electric vehicles (EVs) not only offers a promising solution to mitigate the strain on dwindling oil reserves but also provides a substantial reduction in air pollution and greenhouse gas emissions. As the cornerstone of EV power systems, the technological advancement of power batteries plays a pivotal role in propelling research into enhancing the performance of EVs.

Compared to ordinary batteries, LIPBs exhibit numerous advantageous features [9,10,11]. Firstly, LIPBs boast a notably enhanced energy-storage density, rendering them remarkably lightweight. This attribute proves pivotal in augmenting both the overall energy efficiency and driving performance of EVs. Secondly, the operational efficacy of LIPBs remains unhindered even in the face of extreme temperature regimes, thereby showcasing an exceptional level of thermal stability. Additionally, LIPBs have virtually no memory effect, which means they can be recharged without being fully discharged without negatively affecting the battery’s performance. Moreover, LIPBs typically have a long cycle life and can be subjected to multiple charge/discharge cycles without significantly degrading performance. Considering these comprehensive advantages, it becomes evident that lithium-ion batteries exhibit significant advantages in the context of NEVs [12,13].

However, with the widespread adoption of lithium-ion batteries in EVs, incidents of battery failure leading to EV fires have raised concerns, necessitating focused attention on battery performance [14]. Battery failure primarily occurs due to specific intrinsic factors that result in performance degradation or abnormal operation. Common failures of lithium-ion batteries include capacity degradation, increased internal resistance, internal short circuits, and thermal runaway [15,16,17]. Therefore, to prevent performance degradation, ensure battery safety and promote the sustainable development of lithium-ion batteries in NEVs, it is essential to investigate the reliability technology of lithium-ion batteries [18,19].

In recent years, numerous studies have been conducted on the reliability technology of LIPBs. The reliability of these batteries is primarily achieved through the utilization of a battery management system (BMS). The BMS enables the estimation of battery state, diagnosis of faults, and prediction of battery life [20,21,22,23]. Through real-time monitoring of key parameters such as charge state, temperature, and capacity, the status estimation provides accurate reference data for the normal operation of the battery. Fault diagnosis and lifetime-prediction technologies detect system faults based on monitoring data obtained from state estimation, and also predict the battery’s remaining lifetime, thereby facilitating proactive battery repair and maintenance. These technologies play a crucial role in enhancing the reliability of LIPBs and maximizing the performance and benefits of lithium batteries in NEVs.

However, there is currently a lack of comprehensive reviews summarizing the key technologies related to the reliability of LIPBs. Therefore, to assist designers and researchers in meeting challenges and offering potential recommendations for the safe operation of LIPBs in practical applications, this paper aims to examine previous research on the key technologies pertaining to the reliability of LIPBs from four main perspectives: (1) system structure and reliability assessment; (2) common methods for battery-state estimation; (3) optimization algorithms for fault diagnosis and lifetime prediction; and (4) bibliometric analysis of the relevant literature.

The subsequent sections of the paper are organized as follows: Section 2 provides a summary of research progress on the system structure and reliability assessment of LIPBs. Section 3 analyzes and presents an overview of state-estimation methods. Section 4 examines several commonly used optimization algorithms related to fault diagnosis and remaining lifetime prediction. Section 5 presents a bibliometric analysis of prior research on reliability techniques for lithium-ion batteries. Finally, Section 6 concludes the paper.

2. System Structure and Reliability Assessment

LIPBs serve as efficient electrical energy-storage systems (EESSs), allowing for energy storage and on-demand release. These batteries consist of key components such as the LIPB module, BMS, thermal management system (TMS), battery pack cover, bottom tray, among others [24]. Figure 1 illustrates the simulation diagram of the LIPB. In the later part of this section, this paper summarizes the reliability techniques ensuring the proper functioning of the power battery module, BMS, TMS, and electrical energy-storage system [25,26,27]. Additionally, it consolidates the existing reliability assessment methods applied to each system.

2.1. Power Battery Module

The battery module is commonly understood as a configuration of lithium-ion cells connected in series and parallel. It is further equipped with a single battery monitoring and management system to form the final product. The primary purpose of the battery module is to provide support, stability, and protection to the individual battery cells. The module comprises various components such as module control, battery cells, electrically conductive connectors, plastic frames, cold plates, cooling pipes, and accompanying fasteners [28]. The battery module is designed to facilitate BMS for battery cell management, facilitating maintenance and repair, which improves the reliability and safety of the battery. Currently, researchers are conducting studies on the thermal performance of power battery modules, mainly investigating the thermal characteristics of battery modules under natural convective conditions [29,30,31]. Yi et al. [32] proposed an energy-efficient double-sided thermoelectric device system for the cooling, heating, and wide-range temperature control of a cylindrical battery module. The system has the advantage of integrating and optimizing energy-efficient heating and cooling modes for the thermal management of battery modules.

Reliability Assessment of Battery Modules

Battery packs are generally mobilized from multiple battery modules. Some studies have been performed on the reliability of lithium-ion battery packs, Sun [33] analyzed the reliability of battery packs in both series and parallel connection through reliability theory. It was concluded that the reliability of the battery pack increases with the number of parallel-connected battery modules. Liu et al. [34] used a reliability assessment model to estimate the mean time between failures and made the conclusion that the reliability of parallel-connected series packs is better than that of series-parallel-connected battery packs. Assuming that the cells in a battery pack are independent of each other, Xie et al. [35] proposed a reasonable reliability assessment method. Firstly, the reliability growth test (RGT) is carried out on the individual batteries, and then the battery pack is assessed for reliability. The reliability assessment model is

$$R_B={\displaystyle \sum _{j=P-1}^p{C}_P^j{\left(R_C\right)}^j{\left(1-R_C\right)}^{P-j}}$$

(1)

In this equation, $R_B$ indicates the reliability of the lithium battery pack; $R_C$ is the reliability of the lithium-ion battery cell; $P$ indicates the number of cells in the battery pack; $j$ is the number of lithium battery cells. This method is applicable to the form of lithium battery packs integrated with multiple cells connected in series, which generally allow only one cell to fail.

In order to assess the reliability of lithium-ion batteries more accurately, Wang et al. [36] proposed a reliability model for the whole degradation of lithium-ion battery packs considering the inter-cell dependency. According to the general linear model structure, a linear model is established, which only considers the equation of the internal structural relationship of the battery pack, as follows:

$$F=a{F}_a+c$$

(2)

where $F$ is the joint cumulative probability distribution function; $F_a$ denotes the structure term obtained from the reliability block diagram (RBD); $a$ is the weight factor term; $c$ is the constant term.

A linear model that considers only the internal dependence between cells is established as

$$F=a{F}_0+c$$

(3)

In Equation (3), $F$ denotes the joint cumulative probability distribution function constructed by considering the dependencies between cells; $F_0$ denotes the dependency term obtained for the Copula function; $a$ is the weighting factor term; $c$ is the constant term.

Since the Copula function is advantageous at the quantitative dependency level, a new model that considers both dependency and battery pack structure is constructed in conjunction with the RBD model as

$$F=F_a+a{F}_0+c$$

(4)

$$F=\mathrm{a}\left(F_a+F_0\right)+c$$

(5)

$$F=\mathrm{a}{F}_a+b{F}_0+c$$

(6)

where Equation (4) considers only the weights of the joint cumulative probability distribution function obtained by adjusting the Copula function. Equation (5) considers the structural term $F_a$ and the dependent term $F_0$ with the same weight coefficients. Equation (6) gives different weights to the structural and dependent terms.

However, with the advancement of lithium-ion battery technology, battery packs with topological structures have been increasingly applied. It is necessary to further enhance the research on the reliability assessment of lithium-ion battery packs.

2.2. Battery Management System (BMS)

The BMS is the core of an EV, responsible for monitoring and managing the battery. The BMS is a control system that manages the battery charging and discharging processes by collecting and calculating parameters such as voltage, current, temperature, and state of charge (SOC). It safeguards the battery and enhances overall battery performance. Figure 2 represents the basic functional framework [37].

Existing studies have conducted a lot of work on different functions. For the impact of the inconsistency of series-connected battery packs, Li et al. [38] developed a super capacitor-based Li-ion battery-pack-balancing management system with a group balancing strategy. Xu et al. [39] proposed a novel control strategy, which divides the battery pack’s SOC into three ranges based on different charging states and performance requirements. This approach offers improved performance while maintaining simplicity and ease of implementation. LIPBs possess stringent requirements for charging and discharging processes. In response to these demands, Wang et al. [40] introduced a novel intelligent management system specifically designed for charging and discharging lithium battery packs. This system incorporates the real-time monitoring of the battery pack’s voltage, current, and temperature. It facilitates the controlled and balanced charging and discharging of the battery packs while ensuring protection against overcurrent during charging and discharging. Moreover, the system safeguards the loads against short-circuits and excessive currents.

2.2.1. Reliability Assessment of BMS

BMSs have an extremely important role in ensuring the reliability of LIPBs. Xu et al. [41] proposed a distributed BMS that meets the requirements of reliability design. Chang et al. [42] took the lithium BMS as the research object and analyzed the reliability of the designed system according to the Markov process theory. Cui et al. [43] proposed an alternative method to model the dual-cluster degradation data of the BMS and a reasonable reliability assessment method, as

Degradation Model

The total degradation of the BMS is composed of dispersal among heterogeneous populations and a trend of degradation throughout the population. Equation (7) is the discrete-time quantum walk modeling implemented with the quantum coin-toss operator.

$$C_{\xi ,\theta }=\left(\begin{array}{cc}{e}^{i\xi }\cos (\theta )& \sin (\theta )\\ -\sin (\theta )& e^{-i\xi }\cos (\theta )\end{array}\right)$$

(7)

where $\theta$ restricts the distribution to $\left[-\cos (\theta ),\cos (\theta )\right]$; the intervals of $\xi$ and $\theta$ are $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$ and $\left[0,\frac{\pi }{2}\right]$ respectively.

The dual-cluster asymmetry feature of the degenerate data is modeled using the operator, as

$$M_{\zeta }=\left(\begin{array}{cc}\cos \zeta & \cos \zeta \\ 1-\cos \zeta & 1-\cos \zeta \end{array}\right)$$

(8)

where the range of values of $\zeta$ is $\left[0,\frac{\pi }{2}\right]$.

The degenerate quantity of the characteristic performance parameter $Y(t)$ is constructed as

$$Y(t)\sim \gamma Q(t)$$

(9)

where $\gamma$ denote the scale parameter; $Q(t)$ is the positional distribution of the discrete-time quantum walk represented by the density operator.

$$\rho \left(t+1\right)={\displaystyle \sum _m{ℝ}_{m}S{C}_{\xi ,\theta }\rho (t)C_{\xi ,\theta }^{†}}{S}^{†}{ℝ}_m^{†}+S{M}_{\zeta }\rho (t)M_{\zeta }^{†}{S}^{†}$$

(10)

In Equation (10), ${ℝ}_m$ is the projection of the elemental form of the Kraus operator.

Reliability Assessment

Assuming that $\theta$, $p$ and $\zeta$ varies with stress, the reliability model is in generalized log-linear form as

$$\theta ;p;\zeta ={\alpha }_0+{\displaystyle \sum _{l=1}^3{\alpha }_l{\varphi }_l({\delta }_l)}$$

(11)

where ${\alpha }_l$ is the constant; ${\varphi }_l$ denotes the transformation function of the stress; ${\delta }_l$ denotes the $l\mathrm{th}$ type of stress.

2.3. Thermal Management System (TMS)

In EVs, the high-rate operation of lithium batteries generates a substantial amount of heat, which can significantly impact their performance. This heat generation increases the risk of thermal runaway failures, underscoring the importance of temperature as a critical factor affecting the performance and lifespan of power lithium-ion batteries. Therefore, enhancing the reliability and safety of the TMS becomes particularly crucial [44]. At present, a lot of cooling research has been carried out to address the problem of lithium batteries overheating. There are various forms of thermal management, and the maturity of the air-cooled and liquid-cooled type is higher [45,46,47,48]. Zheng et al. [49] investigated the thermal performance of battery packs in electric vehicles during uphill driving and overtaking through numerical analysis and vehicle experiments. They pointed out that appropriately reducing the intake temperature and airflow can effectively lower the temperature of the battery pack. Xu et al. [50] conducted heat dissipation experiments on battery packs by implementing a liquid-cooled TMS. The results indicated that as the charge and discharge rate increased, the coolant flow rate should be significantly increased to balance the increased heat generated by the battery itself. In response to the shortcomings of air-cooling and liquid-cooling methods, Liu et al. [51] summarized the advantages of phase change materials (PCMs). By absorbing heat, PCMs can effectively lower temperatures and maintain them within the normal operating range for an extended period without the need for any external power source. To enhance heat dissipation, researchers have conducted studies aimed at optimizing heat transfer efficiency, reducing transient response time, and improving control strategies. These endeavors seek to further improve the effectiveness of heat dissipation in TMSs [52,53,54]. For example, Min et al. [55] used a three-dimensional transient analysis method to study the tiny-channel waveform flat tube of liquid-cooling systems and found that increasing the number of channels and contact angles can effectively improve the heat dissipation effect.

2.3.1. Reliability Assessment of TMS

The analysis of the reliability of the TMS of LIPBs can provide valuable references for the reliability design and maintenance strategy of EVs. Liu et al. [56] proposed a reliability analysis algorithm for evaluating the TMS of power batteries in EVs. By constructing a T-S dynamic fault tree, it improves the efficiency of EV fault diagnosis and troubleshooting and ensures the reliability and safety of vehicle use. Zeng et al. [57] proposed a liquid-cooling-based lithium-ion thermal management method, which improves heat dissipation by analyzing the cooling plate with multiple digital channels. Xia et al. [58] proposed a reliability approach considering thermal management based on battery redundancy for the complexity of lithium-ion batteries, as

Reliability of Lithium-Ion Battery Packs

$$\frac{1}{{\lambda }_r}={\displaystyle \sum _i\frac{{\delta }_i}{{\lambda }_i}}$$

(12)

$${\lambda }_z={\displaystyle \sum _i{\delta }_i{\lambda }_i}$$

(13)

where $\frac{1}{{\lambda }_r}$ denotes the thermal conductivity of the battery in the radial direction; ${\lambda }_z$ indicates the thermal conductivity of the battery in the axial direction.

Battery Pack Reliability with Different Redundancy Strategies

The total current of the battery pack with hot standby redundancy satisfies Equation (14) with the same power:

$$I_{pack}=\frac{P}{U}=\frac{P}{n_s{U}_{cell}}$$

(14)

where $I_{pack}$ indicates the current of the battery pack; $n_s$ is the number of the series branch; $P$ is the operating power; $U$ and $U_{cell}$ represent the voltages of the battery pack and cell, respectively.

Since the currents in a series circuit are equal, the current in one unit is equal to the current in each parallel branch by the following equation:

$$I_{cell}=I_{parallel}=\frac{I_{pack}}{n_p}=\frac{P}{n_p{n}_s{U}_{cell}}$$

(15)

where $I_{cell}$ and $I_{parallel}$ denote the currents in the cell and parallel branch, respectively; $n_p$ indicates the number of the parallel branch.

2.4. Electrical Energy-Storage System (EESS)

The LIPB is the main energy-storage device for EVs, which stores electrical energy for use by the EV’s drive system [59,60,61,62,63]. During the charging process of an EV, the LIPB undergoes a conversion of electrical energy into chemical energy, enabling the storage of lithium ions within the positive electrode material. Subsequently, during driving, the LIPB releases the stored electrical energy, converting the chemical energy back into electrical energy to power the EV’s electric motor. Hence, it becomes paramount to accurately estimate the SOC to ensure the safety and reliability of lithium-ion battery energy-storage systems [64,65,66]. Li et al. [67] proposed a new method for estimating the SOC of lithium-ion energy-storage systems based on neural networks. The method is much more accurate compared with the traditional method.

2.4.1. Reliability Assessment of EESS

There are fewer studies on the reliability assessment of LIPB energy-storage systems. Huang et al. [68] proposed an evaluation index to effectively evaluate the health condition of the battery of an energy-storage device and verified the validity of the evaluation index. Cheng et al. [69] provided an algorithm for the reliability assessment of a battery storage system considering the life degradation of lithium-ion batteries, which is a reliability assessment algorithm based on the generalized generating function [70,71,72,73,74,75]. Liu et al. [76] study the reliability problem of battery storage systems composed of battery modules and introduced a reliability assessment method for battery modules based on a generalized generating function, as:

Define the UGF Expression for the Battery Cell

$$U_{SOH}(z)={\displaystyle \sum _{l=1}^{SL}ql{z}^{gl}}$$

(16)

Each element ($ql$) in the set $q$ can be obtained by Equation (17):

$$ql=F\left(gl\_up\right)-F\left(gl\_lower\right)$$

(17)

where $F$ denotes the cumulative distribution function of the normal distribution $N\left(\mu ,{\sigma }^2\right)$; $gl\_up$ and $gl\_lower$ denote the upper and lower limits of $gl$, respectively.

Defining Combinatorial Operators

$$\Omega \left(U_{SOH,i}(z),U_{SOH,j}(z)\right)={\displaystyle \sum _{i=1}^{SL}{\displaystyle \sum _{j=1}^{SL}{q}_i{q}_j{z}^{f(g_i,g_j)}}}$$

(18)

In Equation (18), the vector function $f(g_l,g_m)$ as

$$f(g_l,g_m)=〈\begin{array}{c}\max \left(g_l,g_m\right), cells in parallel\\ \min \left(g_l,g_m\right), cells in series\hfill \end{array}$$

(19)

The UGF of One Cell String

$$U_{string}(z)=\Omega \left(U_{SOH,1}(z),\dots ,U_{SOH,Ns}(z)\right)={\displaystyle \sum _{s=1}^{SL}{q}_s{z}^{g_s}}$$

(20)

where $g_s$ denotes the power battery health state level obtained after series composite operation; $q_s$ is the corresponding probability.

The UGF expression for the battery module is

$$U_{bat}(z)=\Omega \left(U_{string,1}(z),\dots ,U_{string,Np}(z)\right)={\displaystyle \sum _{s=1}^{SL}{p}_s{z}^{h_s}}$$

(21)

where $h_s$ is the health state level of the power battery obtained after series-parallel combination; $p_s$ is the corresponding probability.

The reliability expression for the battery module is

$$R_B=\mathrm{Pr}\left\{h_s\ge \alpha \right\}={\displaystyle \sum _{h_s\ge \alpha }{p}_s}$$

(22)

where $\alpha$ indicates the required level of performance; $\mathrm{Pr}\left\{h_s\ge \alpha \right\}$ is the probability that the battery module performance exceeds the battery health state requirement.

3. Methods for Battery-State Estimation

The BMS not only controls, detects and manages the battery pack but also estimates the state of the LIPB. Since lithium batteries suffer from an aging decline phenomenon in the process of operation, i.e., power reduction, heat generation increase, etc., it is meaningful to estimate the state of LIPBs in order to improve their reliability and prolong the service life of the battery packs [77]. Researchers mainly study the state indicators of LIPBs, including SOC, state of health (SOH), state of function (SOF), state of energy (SOE), state of power (SOP), state of temperature (SOT), and state of safety (SOS) [78]. In this study, we will classify and summarize the estimation methods for seven state indicators. We will also analyze the advantages and disadvantages of commonly used state-estimation methods, providing researchers with a dependable basis for selecting appropriate evaluation methods. Figure 3 describes the functions of the seven state indicators [79].

3.1. SOC Estimation

The SOC of a battery is defined as the ratio of the current remaining capacity of the battery to the total usable capacity at a certain discharge multiplier, which is expressed as follows:

$$SOC=\frac{Q_C}{Q_n}\times 100\%$$

(23)

where $Q_C$ indicates the amount of power remaining in the battery at a given point in time; $Q_n$ indicates the rated capacity of the battery.

In order to improve the estimation accuracy of SOC, previous researchers have conducted a lot of research and proposed many methods. These methods can be categorized into three types according to different principles, and alongside examples of some commonly used methods, they are shown in Figure 4. Below, we provide a detailed introduction to the commonly used methods within the three categories.

3.1.1. Traditional Method

The traditional method is simpler in principle and was used relatively early to perform SOC estimation.

Discharge Test Method

The discharge test method is an extremely reliable method for obtaining SOC estimation results and can be applied to all batteries. This method performs a continuous discharge using a constant current until the battery is exhausted and takes the integral of the current over time as the remaining charge. However, there are two simultaneous shortcomings: (1) it requires high experimental conditions, and the SOC estimation work must be carried out after the battery is interrupted, which is not applicable to the power lithium-ion batteries that are working; (2) the discharging time is long and inefficient, so it takes a lot of time to use this method [80].

Open-Circuit Voltage Method

The open-circuit voltage method is to estimate the SOC using the open-circuit voltage of the cell, which is suitable for SOC estimation when the battery is fully rested to equilibrium. The advantage of this method is that it is easier to realize in practical applications, while the disadvantage is that when the battery changes from the working state to the stationary state, it requires a longer time to measure the open-circuit voltage since the battery needs to rest for a long period of time to reach the voltage temperature state. The expression for SOC obtained by applying the open-circuit voltage method is

$$SO{C}_0=\frac{\left(U_0-n\right)}{\left(m-n\right)}$$

(24)

where $U_0$ indicates open battery voltage; $m$ is the open-circuit voltage when fully charged; $n$ is the open-circuit voltage at full discharge.

Ah Integration Method

The Ah integration method, also known as Coulomb metering, is one of the most commonly used methods of power accumulation. The Ah integration method integrates the current into or out of the battery with the time, which is based on the SOC value at the initial moment of the battery and the remaining power in the battery at a certain moment; the formula is as follows:

$$SOC=SO{C}_0-\frac{1}{C_N}{\displaystyle {\int }_0^t\eta }\times I \mathrm{d}t$$

(25)

where $SO{C}_0$ denotes the SOC value at the initial moment; $C_N$ is the rated capacity of the battery; $\eta$ indicates the charge/discharge efficiency; $I$ indicates that it is battery current.

The Ah integration method is easy to utilise, and the SOC values obtained are more accurate, but there are obvious weaknesses. Due to the interference of uncertainties such as aging and temperature, the method will have an error accumulation effect in the measurement process, which will affect the accuracy of SOC calculation [81]. The initial SOC is also more difficult to determine.

3.1.2. Model-Based Approach

Model-based methods mainly use battery models in combination with other methods, and the most researched and widely applied methods are based on filters and observers.

Linear Model Method

The linear modeling method is a model based on the amount of change in SOC, current, voltage, and the value of SOC at the last point in time. This model is suitable for low currents and slow SOC changes, which are highly robust to measurement errors and erroneous initial conditions [82]. The equation is as follows:

$$\Delta SOC(i)={\beta }_0+{\beta }_{1}U(i)+{\beta }_{2}I(i)+{\beta }_{3}SOC(i-1)$$

(26)

$$SOC(i)=SOC(i-1)+\Delta SOC(i)$$

(27)

where $SOC(i)$ denotes the SOC value at moment $i$; $\Delta SOC(i)$ represents the amount of change in SOC; $U$ and $I$ denote the voltage and current at this moment, respectively; ${\beta }_0$, ${\beta }_1$, ${\beta }_2$ and ${\beta }_3$ are the coefficients obtained by least squares.

Kalman Filter (KF)

The KF is an optimal autoregressive data-processing estimation algorithm based on the least-squares method. It operates recursively and is particularly useful in enhancing the estimation accuracy of SOC. Notably, it offers the advantage of requiring low initial SOC accuracy and does not necessitate extensive data training. However, the KF relies on an accurate battery model and knowledge of noise statistical characteristics, making it a costly approach to implement. Further research into the KF algorithm has resulted in the development of derivative algorithms. Some notable methods include the extended Kalman filter (EKF), sigma point Kalman filter (SPKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). These derivative methods exhibit faster estimation speeds and improved accuracy compared to the original KF. The equation for the KF is:

(1)

The state equation:

$$X_{K+1}=A_K{X}_K+B_K{U}_K+W_K=f\left(X_K,U_K\right)+W_K$$

(28)

(2)

The observation equation:

$$Y_{K+1}=C_K{X}_K+V_K=g\left(X_K,U_K\right)+V_K$$

(29)

where $U_K$ usually contains variables such as battery current, temperature, remaining capacity and internal resistance; $Y_{K+1}$ indicates the operating voltage of the battery; $X_{K+1}$ indicates the state quantity.

The EKF was first proposed by Plett and applied to power battery SOC estimation algorithms for EVs [83,84,85]. Jiang et al. [86] proposed a battery SOC estimation method using EKF. To address the accuracy and convergence speed of SOC estimation, Zhao et al. [87] proposed a filtering algorithm that combines the adaptive EKF and the fading EKF, which solves the problem of systematic noise uncertainty and over-reliance on old data. Since the EKF is not easy to adjust and cannot handle strongly nonlinear system problems, Wang et al. [88] proposed a method called SPKF. This method employs weighted statistical linear regression to address the SOC estimation problem in linear equation systems, thereby minimizing the received linearization errors. The linearization is achieved by passing sigma points in the UKF. Wang et al. [89] proposed an algorithm to estimate the SOC of lithium-ion batteries using a fractional-order UKF. The volumetric KF can solve nonlinear filtering problems from low to high dimensions, Li et al. [90] estimated the SOC using a gas–liquid dynamics modeling approach, which uses a CKF with state constraints to improve the accuracy of the estimation and to achieve energy storage fast convergence of the SOC.

(3)

Particle filter

The particle filter can generate a discrete set of sampling points in the state space based on the experienced distribution of the state vectors of the LIPB. The position and state of the particles are adjusted by the observations, and the optimal particle state is estimated by adjusting the set of particles. The method is suitable for nonlinear systems that can be described by state space models. The advantages are high accuracy, low computational time, and no noise requirements. The standard particle filter algorithm equations are

$${\stackrel{\wedge }{x}}_k={\displaystyle \sum _{i=1}^N{x}_k^{(i)}{W}_k^{(i)}}$$

(30)

where, ${\stackrel{\wedge }{x}}_k$ is the state estimate at moment t; $W_k$ indicates the corresponding weight.

Particle filters are suitable for nonlinear systems with non-Gaussian noise and are commonly used in estimating battery life. Wang et al. [91] proposed a framework for observing the SOC and remaining discharge time of a battery using an odorless particle filter to achieve remaining discharge-time prediction. Ye et al. [92] presented an adaptive particle filter-based SOC estimation algorithm for Li-ion batteries in EVs, with the validation of the SOC estimator conducted using LiFePO4 and NMC Li-ion batteries. In order to obtain accurate and reliable remaining-useful-life prediction data, Duan et al. [93] proposed a novel Extended Kalman Particle Filter. In this filter algorithm, the EKF is utilized as the sampling density function to optimize the particle filter, ensuring the safety and reliability of batteries throughout their lifecycle.

Observer Method

The observer method is a dynamic system that provides approximate estimations of state vectors, addressing the challenge of directly measuring the complete state vector in complex systems. This method demonstrates robust anti-interference capabilities and is particularly suitable for observing internal state quantities of lithium batteries, which reflect complex electrochemical characteristics. Additionally, it offers high precision and stability without requiring consideration of the initial SOC. However, designing an observer can be challenging. Currently, commonly used observers include state observers and proportional-integral observers. State observers are a type of dynamic system that derives estimates of state variables based on measured values of the system’s external variables. Luenberger [94] first introduced the concept of state observer in his work in 1971, which helps in realizing the state feedback or other requirements of a control system. Tang et al. [95] presented a two-circuit state observer for the SOC estimation of LiFePO4 batteries. It is a combination of an open-loop-based current integrator and a proportional-integral-based state observer. Xu et al. [96] constructed a proportional-integral observer to estimate the SOC of lithium-ion batteries in EVs, demonstrating its superiority and compensation properties. To improve the accuracy and reliability, Amir et al. [97] developed an improved adaptive proportional-integral observer, which is useful for power supply applications for lithium-ion batteries.

3.1.3. Data-Driven Approach

The data-driven approach can effectively deal with large amounts of complex data within the EV domain.

Neural Network

One of the most popular neural network models at the moment is the neural network, a multi-layer feed-forward network trained using the error back-propagation technique. It is a complicated network connected by simple neurons through mapping relationships. Choosing the right input variables in a neural network is very important, especially for a complex nonlinear multivariate system. The estimation accuracy of the neural network depends greatly on the input variables of the neural network and the number of input variables. It is applicable to all batteries with no need to build an accurate battery model. The advantage of artificial neural networks is that there can be more than one output. A disadvantage is that it requires a large number of training samples and a powerful processing chip.

The existing research has derived algorithms based on neural networks, such as the feedforward neural network (FNN), convolutional neural network (CNN), recurrent neural network (RNN), and so on. The FNN is a commonly implemented neural network type and is widely applied in the state estimation of LIPBs. Chemali et al. [98] worked on battery SOC estimation using a deep forward-feedback neural network. The method involves driving cyclic loads to lithium-ion batteries at different environmental temperatures, resulting in training data exposing the battery to variable dynamics. CNNs are a class of FNNs that contain convolutional computation and have a deep structure, and they specialize in more complex classification problems and are easier to train. Fan et al. [99] provided a SOC estimation method for lithium-ion batteries based on a CNN with a U-Net structure, which can process variable-length input data and output equal-length SOC estimation results, including the exact SOC at the origin. RNNs include memory and parameter sharing, which gives them an advantage in learning non-linear features of sequences. Since machine learning suffers from the problem of SOC fluctuation estimation when the current fluctuates greatly, Chen et al. [100] proposed a combined SOC estimation method that combines a gated recurrent-unit RNN and an adaptive KF. This method is superior in terms of the initial SOC convergence ability.

Fuzzy Logic Control

Fuzzy logic control is the process of translating knowledge and experience into machine-understandable control rules so that a computer can be used to simulate the implementation that controls a system. This method is not reliant on an accurate model of the battery but requires a large amount of data to build the rule base. Ma et al. [101] developed a dual-input single-output fuzzy logic controller for the energy management of parallel hybrid vehicles. Zheng et al. [102] improved the performance of the synovial observer by introducing a fuzzy logic controller, resulting in a new fuzzy logic sliding-mode observer for SOC estimation. The method has high SOC estimation accuracy and considerable convergence speed. It has better performance than other filters in terms of robustness to current, voltage noise and parameter perturbations.

Support Vector Machine (SVM)

SVM is a learning machine based on statistical learning theory that converges faster and is suitable for small sample cases but requires a large amount of sample data. Chen et al. [103] proposed the SVM-based method for estimating the SOC of EV batteries, which establishes the relationship between SOC and battery current, voltage and temperature. Xuan et al. [104] proposed a new SOC prediction method based on improved support vector regression (SVR) with optimized data classification and training set size. Compared with the traditional SVM method, this method is more time-saving and accurate.

In summary, the advantages and disadvantages of the common SOC estimation methods are summarized as shown in

Table 1. Features of different SOC estimation methods.

Method Types	Typical Methods	Advantages	Disadvantages
Traditional method	Discharge test method	High reliability	Less practical, requires interruption of work when using the method
	Open-circuit voltage method	Easier to achieve Higher accuracy	Requires stationary battery, not suitable for online
	Ah integration method	Easy to operate High accuracy of SOC values	The estimation process is open loop Errors can accumulate
Model-based approach	Linear model method	High robustness to measurement errors and incorrect initial conditions	Suitable for low current Slow SOC change
	Kalman filter	Low initial SOC accuracy requirement No need to train with large amount of data	Requires accuracy in battery modeling and statistical characterization of noise High cost to implement
	Particle filter	High accuracy and low computation time No noise requirements	Calculation complexity
	Observer method	No need to consider the initial SOC value High precision and good stability	Difficult to design
Data-driven approach	Neural network	No need to build accurate battery models Suitable for all batteries	Large number of training samples and powerful processing chip
	Fuzzy logic control	Battery-independent accurate modeling	Large amounts of data are needed to build the rule base
	Support vector machine	Faster convergence	Difficult to implement for large training samples

.

3.2. SOH Estimation

SOH is used to assess the health of a LIPB in its current state. The accurate SOH estimation can provide assurance of reliable battery operation. The SOH estimation can be defined by the capacity, internal resistance and energy of the battery pack:

(1)

Define SOH in terms of capacity:

$$SOH=\frac{Ca{p}_{actual}}{Ca{p}_{nominal}}$$

(31)

where $Ca{p}_{actual}$ represents the maximum capacity that can be discharged when the battery is discharged from the current full state to the cut-off condition; $Ca{p}_{nominal}$ indicates the maximum capacity that can be discharged when the battery is discharged from a full state to the cut-off condition when the battery is shipped from the factory.

(2)

Define SOH in terms of internal resistance:

$$SOH=\frac{R_{pEOL}-R_{pnow}}{R_{pEOL}-R_{pnew}}$$

(32)

where $R_{pEOL}$ denotes the internal resistance of the battery pack when the battery pack reaches the lifetime of the battery pack; $R_{pnow}$ is the internal resistance of the battery pack in its current state; $R_{pnew}$ is the internal resistance of the battery pack as shipped from the factory.

(3)

Define SOH in terms of energy:

$$SOH=\frac{E_{actual}}{E_{nominal}}$$

(33)

where $E_{actual}$ indicates the maximum amount of power that can be stored by the lithium-ion battery pack in the current healthy state; $E_{nominal}$ denotes the maximum amount of electrical energy that the battery pack can store in a completely new state.

Many of the SOC estimation methods are equally applicable to SOH estimation, which is currently categorized into two groups: model-based approach and data-driven approach. In the following, we describe in detail the commonly used methods in both categories.

3.2.1. Model-Based Approach

Existing research has devoted much work to joint estimation methods for SOC and SOH using filters. Lf et al. [105] applied a dual EKF algorithm to jointly estimate SOC and SOH, whereas online estimation could not be achieved while estimating SOH. To solve this problem, Liu et al. [106] proposed an adaptive odorless KF algorithm for the joint estimation of SOC and SOH in lithium-ion batteries, which has higher accuracy and reliability. To enhance the estimation of non-measurable equivalent circuit parameters using online filtering algorithms, Xu et al. [107] introduced a real-time degradation assessment approach for solid-oxide-fuel battery performance based on the UKF. In this study, the UKF was employed to provide an accurate and real-time estimation of degradation indicators for the battery. Chen et al. [108] proposed a joint estimation method of SOC and SOH based on double-slip film observer considering capacity fading factor. The dual-slip film observer can avoid the jitter effect and improve the estimation accuracy with good reliability and robustness. Du et al. [109] proposed an adaptive observer for estimating the SOC and SOH of Li-ion batteries based on an equivalent circuit model of resistive-capacitive networks with a sliding-film approach.

3.2.2. Data-Driven Approach

The main concept of the data-driven approach is to obtain battery aging information and build statistical models based on knowledge and available data. The method combines advanced intelligent algorithms to achieve battery SOH assessment, such as the Gaussian process regression (GPR) model, gray theory and other methods. The GPR model is a nonparametric model that enables state prediction based on a Bayesian framework for low-dimensional and small-sample regression problems. Xiao et al. [110] proposed a new data-driven estimation method for SOH of lithium-ion batteries through a GPR framework. Li et al. [111] suggested a hybrid method of partial incremental capacity and the GPR algorithm. This method combines the data-driven short-term SOH estimation of batteries with long-term battery remaining-useful-lifetime prediction to realize probability-based battery SOH prediction. Yang et al. [112] propose a deep GPR method based on Gaussian processes and deep networks for the SOH assessment of lithium-ion batteries. A comparison is made between this method and different data-driven models to verify the accuracy, reliability and applicability of the proposed model. Gray theoretical methods involve building mathematical models and making predictions based on small, incomplete amounts of information. The method has a wide range of applications, especially in dealing with small sample problems. Zhao et al. [113] developed a health-state evaluation method combining gray clustering and fuzzy comprehensive evaluation. It can consider the characteristics of multiple data sets at the same time, which reduces the influence of data noise on the evaluation results.

In summary, the advantages and disadvantages of commonly used SOH estimation methods are summarized in

Table 2. Features of different SOH estimation methods.

Method Types	Typical Methods	Advantages	Disadvantages
Model-based approach	Kalman filter	High robustness High accuracy and reliability	Computationally intensive
	Synovial observer	Insensitive to model structure errors and external disturbances. Small operation volume and easy model migration	Dependent on model accuracy
Data-driven approach	GPR model	No actual modeling required Suitable for nonlinear systems	Complicated parameter adjustment High calculation volume
	Gray theory method	simple operation Applicable to small samples	Applicable to short- and medium-term forecasts

.

3.3. SOF Estimation

SOF can be interpreted as an estimation of the maximum available power of a battery. It is commonly calculated by dividing the remaining available energy in the battery by the maximum energy capacity it can store. A value of SOF equal to 1 indicates that the battery’s performance meets the desired requirements. Conversely, when SOF equals 0, it signifies that the battery’s performance falls short of the intended specifications. The expression of SOF as

$$SOF=\frac{P-P_{demands}}{P_{\max }-P_{demands}}$$

(34)

In Equation (34), $P$ denotes the power available from the battery; $P_{demands}$ denotes the power on demand; $P_{\max }$ is the maximum power that can be supplied by the battery when operating at a specific temperature.

SOF is typically determined by SOC, SOH, SOT, etc., and Gan et al. [114] proposed a fuzzy logic algorithm to evaluate the continuous and transient load capacity of a battery through the SOC, SOH and C-rate parameters. Shen et al. [115] proposed a joint estimation scheme for the SOC, SOH and SOF of lithium-ion batteries in EVs. Among them, the estimation of SOC is realized by an EKF, and the battery parameters related to battery SOH and SOF are obtained by a recursive least-squares algorithm with a forgetting factor for online identification. This method improves the estimation accuracy and reduces the computational effort.

3.4. SOE Estimation

SOE reflects the remaining available energy of the battery, which is defined as the ratio of the remaining energy of the battery to the total energy. The equation is as follows:

$$SOE(t)=SOE(t_0)+{\eta }_e\frac{{\displaystyle {\int }_{t_0}^{t}P(\tau )\mathrm{d}\tau }}{E_N}$$

(35)

where $SOE(t)$ is the SOE at moment $t$; $SOE(t_0)$ is the SOE at the initial moment t; ${\eta }_e$ indicates the battery energy efficiency; $P(\tau )$ is the power at moment $\tau$; $E_N$ is the energy rating of the battery.

Mamadou et al. [116] first introduced the concept of SOE, and currently, the commonly used approaches are model-based approaches and data-driven approaches. Wang et al. [117] utilized a joint estimator of particle filters to estimate SOC and SOE that was experimentally verified to be robust under dynamic temperature. He et al. [118] proposed a data-driven SOE estimation method based on the center-difference KF algorithm using Gaussian modeling of the battery model, which was evaluated with two types of batteries: LiFePO4 and LiMn204. This method is able to achieve acceptable accuracy; however, it requires extremely high processor performance. Model-based methods cannot achieve reasonable predictions for various operating conditions during battery aging. With the development of algorithms, data-driven methods are widely used in SOE estimation. Liu et al. [119] proposed a new algorithm for SOE with a back-propagation neural network. Simulation experiments on LiFePO4 cells show that the back-propagation neural network (BPNN)-based method can estimate SOE more reliably and accurately. Sharma et al. [120] proposed a combined SOE and SOC estimation framework using a multilayer FNN, which was confirmed to have high accuracy and robustness under dynamic driving and temperature conditions.

3.5. SOP Estimation

SOP is the available power that the battery can provide or absorb from the vehicle powertrain over a period of time, which is defined as the product of the threshold current and the corresponding voltage. The expression is given below:

$$\left\{\begin{array}{c}SO{P}^{charge}(t)=\max \left(P_{\min },V(t+\Delta t)I_{\min }^{charge}\right)\\ SO{P}^{discharge}(t)=\min \left(P_{\max },V(t+\Delta t)I_{\max }^{discharge}\right)\end{array}\right.$$

(36)

where $SO{P}^{charge}(t)$ denotes the SOP for charging at moment $t$; $SO{P}^{discharge}(t)$ represents the SOP of the discharge at moment $t$; $P_{\min }$ and $P_{\max }$ are the minimum and maximum cell power limits, respectively; $\Delta t$ denotes a particular time range; $V(t+\Delta t)$ is the sampled terminal voltage at the first $(t+\Delta t)$ moments; $I_{\min }^{charge}$ and $I_{\max }^{discharge}$ denote the minimum continuous charging current and the maximum continuous discharging current from moment $t$ to moment $(t+\Delta t)$, respectively.

In research, SOP is typically established with other state indicators for joint estimation. Common estimation methods can be categorized into interpolation, multi-constraint estimation, and a data-driven approach. Next, we introduce the three types of common methods in detail.

3.5.1. Interpolation

The interpolation method is a simple-to-operate and more widely applied method for SOP estimation. Hunt et al. [121] first proposed the use of a hybrid power-pulse-characterization test method for SOP evaluation. This method is not applicable to the system at runtime.

3.5.2. Multi-Constraint Estimation

In existing studies, multi-constraint estimation methods are commonly combined with methods such as battery model-based filter squares. Zou et al. [122] applied battery power prediction and management to model predictive control for the first time and conducted a multi-constraint study of battery electro-thermal coupling models. The algorithm is applicable to different lithium-ion battery mathematical models and battery chemistry models. Qin et al. [123] proposed a joint SOC-SOP estimation method for electrothermal modeling and multiparameter constraints. The method first develops an electro-thermal model to characterize the electrical and thermal dynamics of the battery. Secondly, a trace-free KF method is used to accurately estimate the SOC of the battery and predict the SOP of the battery under multi-parameter constraints. Finally, the advantages of high estimation accuracy and computational simplicity are obtained after experimental validation. Guo et al. [124] suggested an enhanced multi-constraint SOP estimation algorithm within a prediction window of 120 s for lithium-ion batteries in EVs. The algorithm specifies a dynamic safe operation region for power regulation in EVs.

3.5.3. Data-Driven Approach

The data-driven approach does not consider the internal reaction mechanism and characteristics of the battery, instead using data analysis and machine learning methods to achieve the estimation of SOP. Sun et al. [125] used the adaptive neuro-fuzzy inference system model of the first-order Sugeno fuzzy inference system for SOP estimation. In this method, the fuzzy sets are generated using a grid-generation method and subtractive clustering method, respectively, and the model is trained by a single BPNN method and hybrid training method, respectively.

3.6. SOT Estimation

SOT is defined as the amount of heat generated and dissipated inside the battery during normal operation; an accurate SOT estimation plays a very important role in the TMS. The expression for the SOT estimation method cited in this paper was proposed by Smith. Currently, Smith et al. [126] provide a model for the total mass of the battery set to represent the overall battery temperature, which has been widely used for battery pack modeling and control.

$$\rho C_p\frac{dT}{dt}=Q+hA\left(T_{\infty }-T\right)$$

(37)

where $\rho$ denotes the total set density; $C_p$ is the specific heat capacity; $h$ is the thermal convection coefficient; $T$ and $T_{\infty }$ represent the battery temperature and ambient temperature over time, respectively; $Q$ is the total heating power; $A$ is the surface area of the battery.

Raijmakers et al. [127] provide some examples of commonly utilized temperature sensors: thermocouples, resistance thermometers, Bragg fiber grating sensors, etc. When estimating the SOT, the temperature data inside the battery can be obtained by direct measurement with the temperature sensor, whereas the method of direct measurement with the sensor is a safety hazard. The model-based method mainly applies the hot battery model and the electro-thermal coupling model for SOT estimation. Kim et al. [128] presented a new method for estimating the internal temperature distribution of cylindrical batteries that takes into account the estimated unknown convective cooling conditions of the model. Dual KF, which is a combination of KF and EKF, is used for the identification of convection coefficients and the estimation of cell temperature. Pang et al. [129] suggested a new estimation procedure for the internal and surface temperatures of lithium-ion battery cells with an improved electro-thermal model, in which the validity and reliability of the method are verified by simulation and experiment.

3.7. SOS Estimation

The SOS can be expressed as the inverse of the probability function of possible abuse, including voltage, temperature, charge/discharge current, internal impedance, battery deformation, and so on. The equations are as follows:

$$f_{SOS}(x)=\frac{1}{f_{abuse}(x)}$$

(38)

where $f_{SOS}(x)$ is the safe function; $f_{abuse}(x)$ indicates misuse of the function; $x$ denotes all state and control variables describing the dynamics of the battery, such as terminal voltage, load current, operating temperature, internal resistance, and external deformation.

Since SOS estimation is a recently emerged concept in the field of battery-state-estimation research, there are not many research results on SOS estimation. Li et al. [130] proposed a safety model for lithium-ion batteries under mechanical abuse conditions using a back-propagation artificial neural network (BP-ANN) optimized by a genetic algorithm (GA), which plays a role in protecting the safety and stability of lithium-ion batteries. Wang et al. [131] introduced a real-time estimation method combining an improved EKF algorithm with a second-order resistor-capacitor circuit network battery model to solve the battery safety protection problem.

4. Optimization Algorithms for Fault Diagnosis and Lifetime Prediction

In the pursuit of the enhanced reliability and availability of battery systems, researchers have dedicated substantial efforts to the study of fault diagnosis and remaining-useful-life (RUL) prediction, in addition to battery-state analysis. Fault diagnosis and RUL prediction play pivotal roles in ensuring the safety, reliability, sustainability, and economic viability of battery systems. By enabling the timely detection and diagnosis of faults, these approaches facilitate the optimization of battery system performance. Moreover, they enable the implementation of appropriate measures to ensure effective operation and prolong the service life of batteries [132,133,134,135]. In this section, a summary and overview of common algorithms for fault diagnosis and RUL prediction are provided in

Table 3. The features and related studies of the most used algorithms.

Method Types	Common Methods	Features	Related Studies
Fault diagnosis	Neural network	Accurately approximate any nonlinear function Fast convergence. Slower training, easily trapped in localized solutions	Wang et al. [136]; Zhang et al. [137]; Ojo et al. [138]; Gao et al. [139]; Duan et al. [140]; Yao et al. [141]
	SVM	Strong robustness Solving the classification of nonlinearities Classification is more effective Difficulties in addressing multiclassification	Yao et al. [142]; Li et al. [143]; Deng et al. [144]; Huo et al. [145]; Gao et al. [146]
	Other methods (random forest classifiers, GPR, logistic regression, etc.)		Yang et al. [147]; Samanta et al. [148]; Wang et al. [149]; Zou et al. [150]; Qiu et al. [151]; Wu et al. [152]; Feng et al. [153]
Lifetime prediction	Deep learning	Improved RUL accuracy Reduced feature testing time requirements The need for big data support Requires high-performance hardware support	Wang et al. [154]; Khumprom et al. [155]; Hong et al. [156]; Ren et al. [157]; Zhang et al. [158]
	Combinatorial optimization method	Optimize the best parameters to improve the accuracy of RUL Better long-term prediction and generalization capabilities Solving the problem of modeling difficulties in the modeling approach A large number of calculations and parameters exist	Chen et al. [159]; Wang et al. [160]; Li et al. [161]; Ji et al. [162]; Ma et al. [163]
	Other methods (XGBoost, SVM Regression, AdaBoost, etc.)		Jafari et al. [164]; Shi et al. [165]; Wei et al. [166]; Wang et al. [167]; Li et al. [168]; Sun et al. [169]; Li et al. [170]

.

4.1. Fault-Diagnosis Methods

Battery fault diagnosis is one of the necessary reliability technologies used to ensure battery safety. Several studies have shown that fault diagnosis of LIPB systems can be solved by various methods. Among the machine-learning-based fault-diagnosis methods, neural network techniques are widely used [136,137,138,139,140,141]. For example, Wang et al. [136] proposed an improved radial basis function (RBF) neural network for EV power battery fault diagnosis, which can accurately approximate any nonlinear function with fast convergence. Since traditional neural networks are slow to train and prone to local solutions, the use of these methods is often combined with parameter optimization algorithms. Zhang et al. [137] proposed a method that combines a BPNN learning algorithm with the simulated annealing GA. In this method, the simulated annealing mechanism is introduced into the GA, meanwhile, the neural network structure and network weights are optimized. In addition, many researchers have used SVMs for the fault diagnosis of battery systems [142,143,144,145,146]. Yao et al. [142] proposed an intelligent fault-diagnosis method for lithium-ion batteries based on SVMs, which is capable of identifying the fault state and degree in a timely and effective manner. Li et al. [143] proposed a diagnostic method that combines least-squares SVM with the ant algorithm and online learning for optimization. In addition, there are some other methods for fault diagnosis, such as random forest classifier, the GPR, logistic regression, and other methods [147,148,149,150,151,152,153]. Next, we introduce two widely used methods in fault diagnosis: neural networks and SVM.

4.1.1. Neural Network-Based Application in Fault Diagnosis

The GA, which is a non-deterministic quasi-natural algorithm, provides an effective method for the optimization of complex systems. Gao et al. [139] integrated a GA to build a single-layer hidden-layer BPNN for fault diagnosis. The method uses GAs to initialize and optimize the connection weights and thresholds of the neural network during the training process of the neural network, respectively. The model of BPNN is constructed as follows:

Fault-Diagnosis Model of BPNN

Assuming the initial value of the weights is 0, and defining the weight between the $j\mathrm{th}$ neuron of layer $\left(k-1\right)\mathrm{th}$ and the $i\mathrm{th}$ neuron of layer $k\mathrm{th}$ as $w_{ij,k}$, the weight adaptation equation is as follows:

$$W_{ij,k}(t_n)=W_{ij,k}(t_{n-1})-\frac{\alpha E(t_n)}{W_{ij,k}(t_{n-1})}\Delta W_{ij,k}(t_{n-1})$$

(39)

where $0<\alpha <1$ and $E=\frac{1}{2}{\displaystyle \sum {\left(y_i-b_i\right)}^2}$. $I=1,\dots ,n$; $y_i$ is $i\mathrm{th}$ actual output; $b_i$ is $i\mathrm{th}$ simulation output.

Fault-Diagnosis Model of GA-BPNN

Determining the initialization GA parameters, the number of elements for each individual can be expressed as

$$N_{sum}=N_{input}\times N_{hidden}+N_{hidden}+N_{hidden}\times N_{output}+N_{output}$$

(40)

In Equation (40), $N_{sum}$ denotes the number of elements per individual; $N_{input}$, $N_{hidden}$ and $N_{output}$ denote the number of elements in the input, hidden and output layers of the BPNN, respectively. The population size here is set to 10.

The fitness function is the sum of the absolute errors between the simulated and actual outputs of the training dataset. The fitness function was used to assess the degree of excellence of an individual in the group as

$$F=k\left({\displaystyle \sum _{i=1}^{n}abs(y_i-o_i)}\right)$$

(41)

where $n$ is the number of neurons in the output layer; $y_i$ and $o_i$ denote the actual and simulated outputs of neuron $i$, respectively; $k$ is the coefficient.

The role of the selection function is to select parents for the next generation depending on the scaling value in the fitness scaling function, and the probability $p_i$ for each individual $i$ can be described as follows:

$$f_i=\frac{k}{F_i}$$

(42)

$$p_i=\frac{f_i}{{\displaystyle \sum _{j=1}^N{f}_j}}$$

(43)

where $F_i$ denotes the fitness value of individual $i$; $N$ is the number of individuals in the aggregate; $k$ denotes the coefficient.

The implementation of crossover and mutation operations, where individual $k$ and individual $l$ perform a crossover operation at element $j$, can be realized through a script with the following equations:

$$a_{kj}=a_{kj}\left(1-b\right)+a_{lj}b$$

(44)

$$a_{lj}=a_{lj}\left(1-b\right)+a_{kj}b$$

(45)

Crossing over facilitates the algorithm’s ability to extract the most optimal traits from various individuals and amalgamate them to potentially yield offspring with superior characteristics. Mutation, on the other hand, enhances the diversity within the population, thereby augmenting the probability of generating individuals exhibiting improved fitness values.

The flowchart of the fault-diagnosis model of GA-BPNN in this study is shown in Figure 5.

4.1.2. SVM-Based Application in Fault Diagnosis

Deng et al. [144] proposed a multiclassification SVM approach for fault diagnosis, which obtains a SVM model with excellent multiclassification capability by training multiple classifiers and combining multiple classifiers according to a good classification logic. The method improves the accuracy and speed of diagnosis. The model of the SVM is constructed as follows:

SVM Modeling

Suppose the sample set is $\left(x_i,y_i\right)$, where $i=1,2,\dots ,n,x\in R^d$. $y\in \left\{+1,-1\right\}$ denotes the sample class. The judgment function is $g(x)=\omega \cdot x+b$. This function is the categorical plane when $g(x)=0$. In order for the classification to be correct, Equation (46) should be satisfied as

$$y_i\left[\left(\omega \cdot x_i\right)+b\right]-1\ge 0$$

(46)

where $i=1,\dots n$; $\omega$ is the weight vector; $b$ is the deviation; The best hyperplane is defined to satisfy Equation (46) while minimizing $‖\omega ‖$. Therefore, under the constraints of Equation (46), redefine the minimization equation as $\phi (\omega )=\frac{1}{2}{‖\omega ‖}^2$. The Lagrange function is defined as follows:

$$L(\omega ,b,\alpha )=\frac{1}{2}\left(\omega \cdot \omega \right)-{\displaystyle \sum _{i=1}^n{\alpha }_i\left\{y_i\left[\left(\omega \cdot x_i\right)+b\right]-1\right\}}$$

(47)

In order to obtain the values minimizing the Lagrange function to $\omega$ and $b$, Equation (48) should be allowed to maximize subject to the constraints on ${\displaystyle \sum _{i=1}^n{y}_i{\alpha }_i=0}$.

$$Q(\alpha )={\displaystyle \sum _{i=1}^n{\alpha }_i}-\frac{1}{2}{\displaystyle \sum _{i,j=1}^n{a}_i{a}_j{y}_i{y}_j\left(x_i\cdot x_j\right)}$$

(48)

In Equation (47), ${\alpha }_i\ge 0, i=1,\dots ,n$.

Then the optimal hyperplane function as

$$f(x)=\mathrm{sgn}\left\{{\displaystyle \sum _{i=1}^n{\alpha }_i^{\ast }{y}_i(x_i\cdot x)+b^{\ast }}\right\}$$

(49)

where $\mathrm{sgn}\left\{\right\}$ denotes the signum function; $b^{\ast }$ denotes the classification threshold.

Optimization of Kernel Function Parameters

Choosing the right kernel function is the key to SVMs. In this case, the RBF is chosen, and the equation is as follows:

$$K\left(x_i,x_j\right)=\exp \left(-g{‖x_i-x_j‖}^2\right)$$

(50)

where $g$ controls the flexibility of the kernel function.

Since the parameter $g$ and the penalty parameter $C$ affect the accuracy and generalization ability of the SVM model in the fault-diagnosis process, cross-validation and grid search are adopted to optimize and evaluate it, and the specific steps are shown in Figure 6.

4.2. Lifetime-Prediction Methods

Lithium-ion battery RUL is an important indicator of battery health management. RUL prediction is the process of predicting the time it will take for a battery to initially decline to the failure threshold due to relatively short periods of battery experimental data. Reliable lifetime-prediction methods can save test time and cost [171,172,173,174,175]. Currently, one of the more commonly used RUL-prediction methods in machine learning is deep learning [154,155,156,157,158]. Deep learning algorithms improve RUL accuracy while reducing feature testing time requirements, offering the potential to improve the power profitability of predictive energy management. Wang et al. [154] analyzed and summarized different adaptive mathematical models of deep learning algorithms for remaining-useful-lifetime prediction. Khumprom et al. [155] proposed a data-driven model based on deep neural network for predicting the RUL of lithium-ion batteries. With the development of technology, the requirements for model training accuracy and training speed increase. In order to improve the prediction performance of the system, researchers typically combine the methods of RUL prediction with parameter optimization algorithms [159,160,161,162,163]. Chen et al. [159] proposed a hybrid algorithm combining a generalized learning system with an relevance vector machine. Wang et al. [160] proposed a non-Markovian fractional-order Brownian motion-prediction method for the RUL of lithium-ion batteries, where the parameters were optimized with a Drosophila optimization algorithm in the prediction process. In recent years, more modern methods have emerged, such as XGBoost, Support Vector Machine Regression (SVMR), AdaBoost, and so on [164,165,166,167,168,169,170]. Subsequently, this paper provides specific examples to elaborate on the commonly used deep learning methods and combinatorial optimization approaches in remaining-useful-life prediction.

4.2.1. Deep Learning-Based Application in RUL

Deep learning is a type of machine learning that clarifies the importance of feature learning. Hong et al. [156] presented the first complete deep learning framework for the fast prediction of the RUL of lithium-ion batteries, which addresses the challenge of predicting the RUL of batteries using short-term measurements. The model is constructed as follows:

End-to-End RUL Prediction for Lithium-Ion Batteries

The RUL of a lithium-ion battery is defined as

$$RUL=C_{EOL}-C_M$$

(51)

where $C_{EOL}$ denotes the number of charge/discharge cycles before the battery reaches EOL; $C_M$ is the number of cycles at the end of the measurement. The input to the neural network is represented as

$$x_{i,j}={\left[\begin{array}{llll}{V}_{i,c_j}\hfill & V_{i,c_j+1}\hfill & \dots \hfill & V_{i,c_j+L-1}\hfill \\ I_{i,c_j}\hfill & I_{i,c_j+1}\hfill & \dots \hfill & I_{i,c_j+L-1}\hfill \\ T_{i,c_j}\hfill & T_{i,c_j+1}\hfill & \dots \hfill & T_{i,c_j+L-1}\hfill \end{array}\right]}_{3\times L}$$

(52)

where $V_{i,c_j}$, $I_{i,c_j}$ and $T_{i,c_j}$ denote the terminal voltage, current and battery temperature of the $i\mathrm{th}$ cell at $c_j\in \left[0,EOL-L+1\right]$, respectively.

Neural Network Architecture

The unfolded convolution of the multiple inputs can be expressed as

$${\widehat{x}}_{n,i}={\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=-⌊(K-1)/2⌋}^{⌊(K-1)/2⌋}{k}_{n,t}{x}_{m,i+dt}}}$$

(53)

In Equation (53), ${\widehat{x}}_{n,i}$ is the output of channel $n$ at time step; $M$ is the number of input channels; $K$ is the length of the kernel; $k_{n,t}$ denotes the $t\mathrm{th}$ kernel coefficient; $x_{m,i}$ is the input that should be channel $m$ at time step $i$.

Uncertainty Estimation of RUL Predictions

In order to reduce the computational cost of the Bayesian neural network, it was decided to use the approximate predictive distribution obtained from sampling, formulated as follows:

$$p(\left.y^{\ast }\right|x^{\ast },\mathrm{D})\approx \frac{1}{H}{\displaystyle \sum _{i=1}^{H}p\left(\left.y^{\ast }\right|x^{\ast },{\theta }^i\right)},{\theta }^i\sim q(\theta )$$

(54)

where $x^{\ast }$ is the test input data; $y^{\ast }$ is the corresponding neural network prediction; $H$ is the number of samples taken; ${\theta }^i$ denotes the weight parameter obtained by sampling from the estimated weight distribution. Uncertainty estimation via negative log likelihood loss instead of MSE loss as

$$NLL=\frac{\log V_{\theta }(x)}{2}+\frac{{\left(y-M_{\theta }(x)\right)}^2}{2V_{\theta }(x)}$$

(55)

In Equation (55), $M_{\theta }$ is the mean of the predictive distribution; $V_{\theta }$ is the variance of the predictive distribution.

Thus, the uncertainty equation for the RUL prediction is obtained as

$$U(x^{\ast })=\frac{1}{M^2}{\displaystyle \sum _{i=1}^M\left({\sigma }_i^2+{\mu }_i^2-{\mu }^2\right)}$$

(56)

where $\mu$ is the mean of the expected predictive distribution; ${\sigma }_i$ is the variance; ${\mu }_i$ is the mean of the predicted RUL distribution for the $i\mathrm{th}$ seed.

The flow of the training and computation algorithm for uncertainty is shown in Figure 7.

4.2.2. Echoing State Network (ESN)-Based Application in RUL

ESNs can greatly reduce the amount of computation for training, which avoids the local optimal problem of gradient-descent optimization algorithms to some extent [176]. Ji et al. [162] proposed an adaptive differential-evolution optimization approach for monotonic ESN prediction. This method addresses issues such as low long-term prediction accuracy, unstable model outputs, and difficulties in selecting key parameters. This model is constructed as follows:

ESN Model

The input signal and output signal expressions for the network are Equation (57) and Equation (58), respectively:

$$x(n+1)=f\left(W^{in}u(n+1)+Wx(n)+W^{back}y(n)\right)$$

(57)

$$y(n+1)=f^{out}\left(W^{out}\left(u(n+1),x(n+1),y(n)\right)\right)$$

(58)

where $f=\left[f_1,f_2,\dots ,f_n\right]$ denotes the output function of the neuron in the repository; $f=\left[f_1^{out},f_2^{out},\dots ,f_n^{out}\right]$ represents the output function of the neurons in the output layer of the network.

According to Equation (57), the equation of the relationship between the input and output of ESN is obtained as

$$y_i(x)={\displaystyle \sum _{}^L{W}_{ij}^{out}{u}_j+}{\displaystyle \sum _{}^N{W}_{i(L+t)}^{out}\tanh \left({\displaystyle \sum _{}^L{W}_{tk}^{in}{u}_k+{\displaystyle \sum _{}^N{W}_{tk}{x}_k}}\right)},i=1,2,\dots ,M$$

(59)

where $L$ is the number of nodes in the input layer; $N$ is a repository neuron; $M$ is the number of nodes in the output layer.

To satisfy the monotonically decreasing relationship between output $y_i$ and input $u_i$, the constraints of Equation (59) are added to the ESN training process with the following expression:

$$\frac{\partial y_i}{\partial u_i}=W_{ij}^{out}+{\displaystyle \sum _{t=1}^N{W}_{i(L+t)}^{out}{W}_{tj}^{in}<0,\forall i,j}$$

(60)

Adaptive Differential Evolution

Determine the equation for population initialization as follows:

$$x_i(0)=L_i^{\min }+rand\left(0,1\right)\times \left(L_i^{\max }-L_i^{\min }\right),i=1,2,\dots ,NP$$

(61)

where $x_i(0)$ denotes an individual from generation zero; $rand\left(0,1\right)$ indicates the random number of $\left[0,1\right]$; $L_i^{\min }$ and $L_i^{\max }$ denote the minimum and maximum values of the parameter values, respectively.

Determine the expression of the variational operator as

$$v_i(G+1)=x_{\min }\left(G\right)+F\left(x_{middle}\left(G\right)-x_{\max }\left(G\right)\right)$$

(62)

$$F=\left\{\begin{array}{c}{F}_{\min },f\left(x_{\min }(G)\right)\le f\left(x_b(G)\right)\hfill \\ F_{\min }+F_{\max }\frac{f\left(x_{middle}(G)\right)-f\left(x_{\min }(G)\right)}{f\left(x_{\max }(G)\right)-f\left(x_{\min }(G)\right)},others\hfill \\ F_{\max },f\left(x_{\min }(G)\right)\ge f\left(x_w(G)\right)\hfill \end{array}\right.$$

(63)

In Equations (62) and (63), $F_{\min }$ and $F_{\max }$ denote the minimum and maximum values of the mutation factor $F$, respectively; $x_b(G)$ and $x_w(G)$ denote the individuals with the best and worst fitness values in the initial population, respectively.

Determine the expression of the crossover operator as

$$u_{ij}(\mathrm{G}+1)=\left\{\begin{array}{c}{v}_{ij}\left(G+1\right),rand\left(0,1\right)\le CR\\ x_{ij}\left(G\right),others\hfill \end{array}\right.$$

(64)

$$CR=\left\{\begin{array}{l}C{R}_{\max },f\left(v_i(G)\right)\le f\left(x_b(G)\right)\\ C{R}_{\max }-\left(C{R}_{\max }-C{R}_{\min }\right)\frac{f\left(v_i(G)\right)-f\left(x_b(G)\right)}{f\left(x_w(G)\right)-f\left(x_b(G)\right)},others\\ C{R}_{\min },f\left(v_i(G)\right)\ge f\left(x_w(G)\right)\end{array}\right.$$

(65)

In Equations (64) and (65), $C{R}_{\max }$ and $C{R}_{\min }$ denote the maximum and minimum values of the crossover factor $CR$, respectively.

Comparison with the fitness value ensures that the algorithm evolves to the global optimum, and the equation for the selection operator is determined as

$$x_i(G+1)=\left\{\begin{array}{l}{u}_i\left(G+1\right),f\left(u_i(G+1)\right)\le f\left(x_i(G)\right)\\ x_i(G),others\end{array}\right.$$

(66)

SADE-MESN Algorithm Implementation Process

The optimal ESN prediction model is obtained by optimizing the output weights of ESN using monotonic relations, and the flowchart is shown in Figure 8.

5. Bibliometric Analysis of the Literature

The exploration of reliability technology in LIPBs has emerged as a prominent research area. This paper summarizes the LIPB reliability-related literature published in SCI-indexed journals from 1 January 2017 to 25 June 2023 using CiteSpace-6.2.4. The search terms employed to retrieve relevant papers were “lithium power battery” and “reliability technology”. To establish representative institutions and countries, we considered the affiliations of the first authors. The statistics of publications are as follows:

5.1. Methods and Data

5.1.1. Methods

To perform the analysis, CiteSpace, a Java program developed in 2006, which is a powerful tool for document analysis and bibliometric visualization, was used [177]. CiteSpace is a freely available software for analyzing scientific literature databases, with a particular focus on bibliometrics and scientometrics. Developed by Dr. Chaomei Chen at Drexel University, this tool offers several essential functions that provide researchers with valuable insights into bibliographic datasets. Its key features include co-citation analysis to identify relationships between papers, burst detection to pinpoint emerging trends and influential works, visualization tools like cluster maps and timeline views to explore research themes and dynamics, keyword co-occurrence analysis, and centrality measures for keywords and authors. CiteSpace also integrates with Web of Science and PubMed, facilitates data sharing and collaboration, and enables time slicing for temporal analysis. With its user-friendly interface and interactive visualizations, CiteSpace empowers researchers, both novice and experienced, to gain a comprehensive understanding of research fields and their evolution over time.

5.1.2. Data

The Web of Science (WOS) was used to collect bibliographic data on the dependability of LIPBs over a period of 7 years (2017–2023). There are a total of 1047 records in WOS (excluding comments).

5.2. Operational Results

In this paper, CiteSpace is used to analyze information from different countries, institutions, journals, and scholars and compare their contributions. The number of articles and the cumulative number of articles related to the reliability technology of LIPBs by year were summarized using CiteSpace, as shown in Figure 9.

Since 2017, there have been 1047 papers published related to LIPB reliability technology. From 2017 to 2023, the number of articles published each year increased from 99 articles published each year to 192 articles published each year. The cumulative number of articles published each year shows a significantly increased tendency, and scholars are paying increasing attention to NEV reliability studies.

5.2.1. Country and Publisher

As shown in Figure 10, the countries with the highest number of publications related to the reliability technology of LIPBs are as follows: China with 568 publications, the United States with 144 publications, England with 55 publications, India with 55 publications, South Korea with 48 publications, Germany with 42 publications, Scotland with 39 publications, Canada with 35 publications, Italy with 34 publications and Australia with 31 publications. Among them, China has the highest number of papers, which is 3.94 times more than the second-ranked United States. This indicates that China pays the highest attention to the field of LIPB reliability technology for NEVs.

As shown in Figure 11, the institutions that published the most papers related to the reliability technology of lithium batteries are Southwest University of Science and Technology—China (50 papers), Beijing Institute of Technology (48 papers), Chinese Academy of Sciences (47 papers), Robert Gordon University (35 papers), Tsinghua University (33 papers), Chongqing University (25 papers), Beihang University (23 papers), Aalborg University (22 papers), Sichuan University (19 articles) and University of Science and Technology of China (17 articles). Among these institutions, there are eight in China, one in the UK and one in Denmark. This shows that China is interested in the research of LIPB reliability technology, which further indicates that China has conducted a lot of work on the development of NEVs compared to other countries.

5.2.2. Author

In this paper, we use CiteSpace to statistically analyze the authors of published research on reliability technology for LIPBs and summarize several authors with high impact in this field, as shown in Figure 12.

As shown in Figure 12, the number of co-occurring nodes is 215, the number of connections is 317, and the network density is 0.0138. Wang, S. has been cited 37 times, followed by Fernandez, C., with 33 citations; in addition, Yu, C. has been cited 16 times, and Meng, J. has been cited 12 times. Among them, Wang, S. is the most influential in the field of reliability technology research of LIPBs, focusing on fault diagnosis and the lifetime prediction of BMS in applications; Fernandez, C. and Yu, C. focus on the methodology of battery-state estimation and Meng, J. focuses more on the functional research of BMS for LIPBs. The research of these authors represents the mainstream trend in the research of reliability technology of LIPBs.

The high impact of these authors in the field of LIPB reliability research can be attributed to the following reasons:

• Their research addresses key challenges in the field of LIPBs, which is crucial for enhancing the reliability and safety of these batteries. As LIPBs are increasingly being used in various applications, such research is highly relevant and timely.
• Their work may introduce novel methods, methodologies, or technologies that advance the theoretical and practical application of reliability techniques in LIPBs.
• The relatively high network density suggests that these authors may have collaborated with other influential researchers, thereby increasing their impact in the field.
• The research conducted by these authors covers different aspects of LIPB reliability technology, thereby enhancing the overall impact of their work.

5.2.3. Thematic Trends

This paper uses CiteSpace to statistically measure topic trends over a 7-year period. Topic trends were evaluated by keyword burstiness (measured by changes in keyword frequency), as shown in

Table 4. Thematic trend analysis over seven years.

Keywords	Strength	Begin	End	2017–2023
lifepo4 battery	5.52	2017	2020	▃▃▃▃▂▂▂
lead acid battery	3.99	2017	2018	▃▃▂▂▂▂▂
polymer battery	2.49	2017	2018	▃▃▂▂▂▂▂
power capability	2.49	2017	2018	▃▃▂▂▂▂▂
available power	2.49	2017	2018	▃▃▂▂▂▂▂
filter	2.32	2017	2018	▃▃▂▂▂▂▂
battery pack	2.2	2017	2020	▃▃▃▃▂▂▂
frequency regulation	2.74	2019	2020	▂▂▃▃▂▂▂
power management	2.09	2020	2022	▂▂▂▃▃▃▂
support vector machine	2.08	2020	2022	▂▂▂▃▃▃▂
dc-dc converter	2.08	2020	2022	▂▂▂▃▃▃▂

. The “strength” based on the statistical formula is used to measure the burstiness of the keywords.

As shown in Table 4, the lines show the topic trends for each of the seven years. From 2017 to 2018, lifepo4 battery, lead acid battery, polymer battery, power capability, available power, filter, and battery pack became popular keywords. This reflects the early trend of new energy battery research. The research in this period is mainly related to battery type and performance. From 2019 to 2020, frequency regulation was the most popular keyword. Considering wind power, photovoltaics, and energy-storage conditions, it is gradually becoming an important research object that the battery has a longer service life, stronger performance, and lower production cost. From 2020 to 2022, power management, SVM, and dc-dc converter became popular keywords. With the wide application of renewable energy, reliability and safety became the key factors for battery system applications. The results reflect the increasing importance of research on optimizing the reliability and safety of new energy vehicle batteries.

6. Conclusions

This paper provides a comprehensive review and summary of the progress in key technologies to enhance the reliability of LIPBs. Through an extensive literature review, the paper begins by providing an overview of the system structure, including the battery module, BMS, TMS, EESS, and so on. Additionally, it analyzes the commonly used reliability assessment methods for each system. Subsequently, the paper delves into the measurement methods for each state indicator of LIPBs. The advantages and disadvantages of common estimation methods for each indicator are analyzed, with model-based and data-driven approaches being more common. Furthermore, the study focuses on fault diagnosis and lifetime prediction, reviewing technologies aimed at improving system reliability. The most commonly used optimization methods in these areas are summarized, with neural networks and deep learning being widely applied in fault diagnosis and lifetime prediction, respectively. Moreover, a bibliometric analysis of the literature pertaining to the study of reliability technologies for LIPBs is conducted, revealing China’s significant attention to LIPB reliability research for NEVs, with a growing emphasis on battery reliability and safety optimization for NEVs.

However, this review highlights several areas that necessitate further development in LIPB reliability optimization research. Firstly, enhancing research on the overall reliability of the battery system is crucial for optimizing the effectiveness and dependability of the entire battery system. Secondly, conducting more studies under real-world usage scenarios is essential to comprehensively understand battery performance in complex environmental conditions, thereby facilitating targeted improvements in battery design and manufacturing processes. Lastly, in-depth battery reliability studies should be conducted utilizing advanced simulation and modeling technologies, enabling more accurate predictions of battery life, performance degradation, and failure probabilities. By doing so, battery design and management will be able to leverage a more scientifically grounded foundation. It is evident that further advancements are needed in LIPB reliability research.