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A multi-fault diagnosis method based on modified Sample Entropy for lithium-ion battery strings
Journal of Power Sources 446 (2020) 227275
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A multi-fault diagnosis method based on modified Sample Entropy for lithium-ion battery strings Yunlong Shang a, Gaopeng Lu b, Yongzhe Kang a, Zhongkai Zhou a, Bin Duan a, Chenghui Zhang a, * a b
School of Control Science and Engineering, Shandong University, Jinan, 250061, China School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai, 264005, China
H I G H L I G H T S
� A multi-fault diagnosis method is proposed to detect the early battery faults. � The proposed diagnosis method is based on the modified Sample Entropy. � A coefficient is introduced to detect the fault type and time of fault occurring. � A moving window is used to maintain the detection sensitivity and less computation. � By optimizing the tolerance, the proposed method can prevent false detections. A R T I C L E I N F O
A B S T R A C T
Keywords: Fault diagnosis Short circuit Open circuit Sample entropy Lithium-ion batteries Electric vehicles
The conventional fault-diagnosis methods are difficult to detect the battery faults in the early stages without obvious battery abnormality because lithium-ion batteries are complex nonlinear time-varying systems with absolute cell inconsistency. Therefore, this paper proposes a real-time multi-fault diagnosis method for the early battery failure based on modified Sample Entropy. By detecting the modified Sample Entropy of the cell-voltage sequences in a moving window, the proposed diagnosis method can diagnose and predict different early battery faults, including short-circuit and open-circuit faults, and can also predict the time of the faults occurring. The experimental results and the comparison with the conventional methods verify the validity of the proposed solution with strong robustness, high reliability and low computational cost, and without the need of a precise model. In summary, the proposed multi-fault diagnosis approach is feasible and promising in real electric vehicle applications.
1. Introduction
effective diagnosis methods for the early faults of lithium-ion batteries to prevent battery failure. The common battery faults mainly include overvoltage, under voltage, loose connection, insulation, external short circuit, internal short circuit, open circuit, sensor failure, and so on [8–13]. Compared with the other faults, the overvoltage, undervoltage, and short-circuit faults are more hazardous to batteries, which will cause lithium-ion deposition and accelerate battery aging [6]. It is important to note that different from the mechanical and electrical systems, fault diagnosis for lithium-ion batteries is much more complex because of the immea surable internal states of lithium-ion batteries [7]. In fact, only the cell voltage and current are the available indicators for battery faults. The voltage abnormality, e.g., the abrupt increase or decrease in the cell
Due to the energy crisis, environmental pollution, and climate change, electric vehicles (EVs) (e.g., Tesla) are becoming more and more popular [1,2]. As the power sources of EVs, lithium-ion batteries have significant influences on vehicle power, economy, and safety [3,4]. According to the statistics on 1.95 million EVs, 52% breakdown is caused by the onboard lithium-ion batteries [5]. Two main causes can be found. On the one hand, the electrochemical reaction inside lithium-ion batteries is extremely complicated, which is sensitive to environment temperature and battery aging [6]. On the other hand, a lithium-ion battery string is usually made up of thousands of cells with absolute inconsistency [7]. Therefore, it is important and worth developing * Corresponding author. E-mail address: [email protected] (C. Zhang).
https://doi.org/10.1016/j.jpowsour.2019.227275 Received 31 July 2019; Received in revised form 17 September 2019; Accepted 7 October 2019 Available online 31 October 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
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Journal of Power Sources 446 (2020) 227275
voltages, may imply more early faults including short circuit, open cir cuit, etc. [8,9]. Therefore, the detection for the abnormal changes of cell voltages can locate and analyze the catastrophic faults in advance. However, it is extremely challenging to analyze the abnormalities hid den beneath the surface (cell voltages) due to the strong nonlinearity, time-varying characteristic, hysteresis, and inconsistency of lithium-ion batteries [6–13]. Many battery fault diagnosis methods have been proposed, which can be classified into three categories: threshold-based [14,15], model-based [16–25], and data-driven-based [26–38] solutions. The threshold-based method can detect battery faults when any cell voltage exceeds the cut-off voltage, which has been widely applied to battery management systems (BMSs) of EVs [14,15]. However, this so lution is difficult to detect the early battery faults when the abnormal cell voltages do not exceed the threshold voltages. For example, on Jan. 16 2013, fire occurred in a 787 airplane caused by battery failure, where the onboard BMS did not raise any alarm at the early stage of the fault because the cell voltages did not trigger the threshold [39]. In fact, choosing an appropriate threshold is another challenge for this solution. If the threshold is too high, the sensitivity of the fault diagnosis is too low because the abnormal cell voltages hardly trigger the threshold. On the contrary, if the threshold is too low, false alarms may be raised because the normal cell voltages may trigger the threshold. The model-based method requires the extensive effort in testing and modeling batteries for different faults, leading to the complex imple mentation, low accuracy, and poor robustness [16–25]. Sidhu et al. [16] proposed a fault detection solution based on multiple nonlinear models and adaptive extended Kalman filters (AEKF). The fault information can be detected by estimating the residual signals between the cell voltage and the terminal voltage of each model based on AEKF. According to the same principle, Liu et al. [17] proposed an analogous diagnostic solution to detect the current or voltage sensor fault. Chen et al. [18] proposed an external short-circuit detection method based on battery model for lithium-ion batteries. Bohlen et al. [19] proposed an on-line mod el-based fault detection solution by identifying the battery internal resistance. According to the above analyses, it can be seen that the model-based diagnostic methods are only applicable to a specific fault but cannot detect the other faults without modeled, leading to narrow applicability. In addition, due to the complex implementation and poor robustness, the model-based methods are difficult to be applied to BMSs of EVs. Recently, due to the good nonlinear mapping, the data-driven-based approaches have been widely applied to battery fault detection field [26–32]. Hu et al. [26] invented a battery health indication and prog nosis method based on machine learning. The battery health could be estimated by establishing the relation between Sample Entropy (SampEn) of the cell voltage sequence and the battery capacity based on Sparse Bayesian. Sun et al. [27] proposed a battery fault detection so lution based on the charge/discharge curve, which is smooth under the normal working conditions. Thus, the potential battery faults can be detected based on the changes of the battery charge/discharge curve. Barr�e et al. [28] investigated the main battery ageing factors during EV use based on statistical analysis, which can be used to diagnose battery health. Zhao et al. [29] proposed a machine-learning-based fault detection approach, which could detect the abnormal changes of the cell voltages. Xia et al. [30] proposed a correlation-based detection solution for the battery short-circuit fault, which can identify the abnormal voltage change according to the correlation coefficients of each two cell voltages. It can be noted that the above data-driven-based methods either need a big quantity of data to build the potential relation between the signal and the faults, leading to high computational cost and difficult real-time application, or are sensitive to the training battery data, resulting in poor robustness. Fortunately, as one of the data-driven-based methods, the entropybased approach can identify battery faults by measuring the complexity of the cell voltage or current sequence [33–38]. Yao et al.
[33] proposed a connection fault detection method based on ensemble Shannon entropy of the cell voltages, which achieves relatively small amount of calculation and simple on-line and real-time implementation. Wang et al. [34] proposed a battery fault detection approach based on modified Shannon entropy of the cell voltages. Liu et al. [35] proposed an overvoltage-fault detection method based on entropy theory and an entropy weight was employed to reduce the subjectivity and improve the reliability. Sun et al. [36] proposed a SampEn-based diagnosis method to estimate the state of health (SOH) of the lead-acid battery at the end of each discharging cycle only by measuring the voltage and current of the lead-acid battery. It can be concluded that the entropy of the cell voltage or current representing the salient feature of the battery string can be used to forecast the early battery faults. In addition, the entropy-based method requires less computational cost because of the nonuse of the accurate battery model, which can be easily applied on line. However, because the entropy is nonnegative, the existing entropy-based methods only can detect a kind of battery fault, and cannot distinguish the fault type and predict the accurate time of battery failure. Particularly, the conventional methods have low reliability and practicability for real applications because of the insensitiveness to battery faults. In addition, it is worth mentioning that the SampEn-based method was never used to predict battery faults. In summary, the early detection of battery faults is a critical but challenging issue in BMSs of EVs. The conventional methods are difficult to diagnose the abnormal battery changes at the early stage and predict the time of the failure occurrence in real EV applications because lithium-ion batteries are complex nonlinear time-varying systems with absolute inconsistency. Therefore, in order to bridge these drawbacks, an early multi-fault detection approach for diagnosing the potential abnormality of the cell voltages is proposed based on modified SampEn. Specifically, four original contributions are made in this paper. Firstly, a simple fault detection solution based on cell-voltage SampEn is proposed to forecast the early battery faults without obvious battery abnormality. Secondly, a coefficient α presenting the voltage fluctuation information is introduced to detect the fault type (including battery short circuit, open circuit, and so on) and forecast the time of the faults occurring. Thirdly, a moving window is used to update the battery data, and maintain the diagnosis sensitivity to faults and less computation, leading to an easy real-time implementation. Finally, by optimizing the toler ance, the proposed method can prevent false detections and achieve a high robustness to the measurement noise and battery inconsistency. The rest of this paper is summarized as follows. The SampEn algo rithm is presented in Section II. In Section III, the verification outcomes are discussed, and the robustness of the proposed method is analyzed. A comprehensive comparison with the traditional methods is made in Section IV. Section V finally summarizes the conclusions. 2. Proposed diagnosis method based on modified SampEn 2.1. Algorithm description The SampEn proposed by Joshua S. Richman and J. Randall Moor man in 2000 has been widely used to evaluate the complexity of the time series data [39–41]. SampEn is the negative natural logarithm of an estimate of the conditional probability that the subseries of length m that match pointwise within a tolerance r also match at the next point [39–41]. It exhibits strong robustness, good representation, and low computational cost, which is feasible in strongly interactive systems [39–41]. As stated, the cell voltage is an available indicator for battery faults. When a short-circuit fault occurs in a battery cell, it will cause an abrupt cell-voltage drop [30]. Whereas, the cell voltage abruptly rises, which implies an open-circuit or sensor fault. The abrupt voltage drop or rise will also cause a significant change in the SampEn of the cell-voltage sequence, which is promising to forecast battery faults. The proposed SampEn algorithm for a cell-voltage sequence is shown 2
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as follows [39–41]. For a given cell-voltage length N, a cell voltage vector V(i) can be formulated as VðiÞ ¼ ½VðiÞ; Vði þ 1Þ; …; Vði þ m
1Þ�; i ¼ 1; 2; … ; N
mþ1
shorter moving window can provide better diagnostic precision for battery faults. However, according to (5)–(7), when the window size is less than 5, the SampEn value will be identically equal zero regardless of the abnormal voltage changes. This implies that the proposed approach is unable to detect any fault with a too short moving window. Theo retically, the optimal moving-window size is 5 to achieve a strong robustness to the measurement noise and disturbance, and small calculation effort.
(1)
where m is the window length, and is usually set as 2 to accurately measure the change in the cell voltages [39–42]. The distance d½Vm ðiÞ; Vm ðjÞ� between vectors Vm ðiÞ and Vm ðjÞ is the maximum absolute difference, which can be expressed as d½Vm ðiÞ; Vm ðjÞ� ¼ max½jVm ði þ kÞ
Vm ðj þ kÞj�; 0 � k � m
1
2.3. Algorithm improvement
(2)
It is important to note that the SampEn of the cell-voltage sequence (i.e., the conditional probability) is always nonnegative regardless of the abrupt drop or rise in the cell voltage. As a result, the SampEn-based method cannot forecast the kind of battery faults. In fact, it is neces sary for battery safety to detect different battery faults and forecast the fault time. The SampEn algorithm should be improved to accommodate for the multi-fault diagnosis requirement of battery systems. Therefore, a correction coefficient α presenting the voltage fluctuation information is introduced to detect the fault types and forecast the time of the faults occurring. According to the above analyses, the SampEn of a cell-voltage sequence can be modified as
Define the function Bmi ðrÞ ¼
1 W m ðiÞ; i ¼ 1; 2 ; …; N mþ1
N
mþ1
(3)
where Wm ðiÞ is the number of d½Vm ðiÞ;Vm ðjÞ� � r; i 6¼ j. Similarly, define another function Ami ðrÞ ¼
1 W mþ1 ðiÞ; i ¼ 1; 2 ; …; N mþ1
N
mþ1
(4)
where Wmþ1 ðiÞ is the number of d½Vmþ1 ðiÞ; Vmþ1 ðjÞ� � r; i 6¼ j. The probability of two time series matching for m voltage points can be expressed as Bm ðrÞ ¼
N m X
1 N
m
Bmi ðrÞ
S ¼ α � SampEnðm; r; NÞ
(5)
where α is the correction coefficient, which can be given by 8 < 1 When VðtÞ < Vavg α ¼ 1 When VðtÞ > Vavg : 0 Otherwise
i¼1
Analogously, the probability of two time series matching for mþ1 voltage points can be expressed as Am ðrÞ ¼
N m X
1 N
m
Ami ðrÞ
(6)
SampEn is the conditional probability that mþ1 voltages match when m voltage points match within a tolerance r, which can be expressed as ln½Am ðrÞ = Bm ðrÞ�
(9)
where V(t) is the real-time cell voltage at t. Vavg is the cell average voltage in a moving window. According to (8)–(9), it can be observed that when the battery voltage abruptly drops (i.e., VðtÞ < Vavg ), a negative SampEn is gener ated. When the cell voltage abruptly increases (i.e., VðtÞ > Vavg ), a positive SampEn is generated. Therefore, the proposed modified SampEn-based algorithm can detect the abrupt rise or drop in the cell voltage and further diagnose the fault type based on the positive or negative SampEn of the cell-voltage sequence. A flow chart of the pro posed modified SampEn-based algorithm is illustrated in Fig. 1.
i¼1
SampEnðm; r; NÞ ¼
(8)
(7)
According to (1)–(7), it can be seen that a smaller SampEn represents more self-similarity in the cell-voltage sequence, implying no fault occurrence in the cell. On the contrary, a larger SampEn represents less self-similarity in the cell-voltage sequence, indicating potential faults in the battery cell. Therefore, the SampEn can be used to describe the regularity and complexity of the cell voltages, which is promising to detect battery faults even though the cell voltages are within the safe limits. It is important to note that the tolerance (threshold) r should be carefully selected. According to (3)–(4), a smaller tolerance may cause false detections, while a larger tolerance may lead to a failure of fault detection. Theoretically, the tolerance r will approach zero for an infinite number of data [42]. However, for a finite number of data with measurement noise, the tolerance r should be typically between 10 and 20% of the standard deviation of the data [42].
3. Experiment results and discussion An experiment platform is built to validate the effectiveness and robustness of the proposed multi-fault detection solution. The experi ment platform consists of an AVL battery tester, a BMS, and an AVL control cabinet. The tested batteries, including four LiFePO4 cells, are connected in series, whose parameters are shown in Table 1. The AVL battery tester is used to charge and discharge batteries under urban dynamometer driving schedule (UDDS). The BMS and AVL control cabinet are employed to monitor and record the cell voltages of LiFePO4 cells. In order to accurately capture the fault information, the mea surement frequency is set to about 400 Hz. The measurement accuracy of the cell voltage is 0.1%.
2.2. Moving window For the online implementation, the SampEn of the cell-voltage sequence should be calculated in real time. Thus, a moving window is employed to update the battery data in real time and maintain the sensitivity to faults. Specifically, the SampEn at each time instant is calculated based on the cell voltages in a history moving window prior to now. It is worth mentioning that N in (1) represents the movingwindow size. In fact, the moving-window size N essentially determines the SampEn value and sensibility to faults. According to (5)–(7), for the same cell-voltage sequence, the smaller the window size, the larger the SampEn value, which indicates a higher sensitivity to faults. Therefore, a
3.1. Fault diagnosis results of the proposed method Fig. 2 (a) presents the voltage sequences of three LiFePO4 cells connected in series with the short-circuit and open-circuit faults under the UDDS cycle. Overall, the battery string has bad consistency, where B3 has lower voltage than B1 and B2. Nevertheless, their fluctuation trends are consistent because of the same charge/discharge current. At 41.92 s of the UDDS cycle, an open-circuit fault occurs in B3 (see the fault ① in Fig. 2 (b)), causing the cell voltage abruptly increasing to approximate 3.512 V. At 54.54 s, a jump wire is used to short-circuit B2 3
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Fig. 1. The flowchart of the proposed multi-fault diagnosis method based on modified SampEn.
for about 0.13 s, leading to an abrupt decrease (here is 0.487 V) in the cell voltage (see the fault ② in Fig. 2 (a)). It can be noted that the voltage recovers when the short-circuit fault is removed. At 69.53 s, another open-circuit fault occurs in B1, resulting in an abrupt increase (here is 0.414 V) in the cell voltage (see the fault ③ in Fig. 2 (a)). It is important to note that all the cell voltages in case of faults do not touch the charge and discharge cut-off voltages presented in Table 1. Thus, the thresholdbased detection method cannot raise any alarm. In addition, the voltage difference among the cells is up to 0.3 V due to the bad consistency. Therefore, a false fault may be flagged when the voltage difference threshold is applied. Analogously, when the model-based method is applied to track the cell voltages, it may also result in a false fault
Table 1 Specification of the tested batteries. Item
Parameter
Battery type Nominal voltage Nominal rated capacity Charge cut-off voltage Discharge cut-off voltage Max pulse discharge
Cylindrical 18650 3.2 V 1.35 Ah 3.65 V 2.5 V 4.05 A
4
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Journal of Power Sources 446 (2020) 227275
Fig. 2. (a) The cell voltage sequences of three cells connected in series with the short-circuit and open-circuit faults under the UDDS working condition. (b) The zoom-in figure for the open-circuit fault ①. (c) The fault diagnosis results based on the conventional SampEn for the cell voltage sequences shown in (a). (d) The zoom-in figure of the conventional SampEn for the open-circuit fault ①. (e) The fault diagnosis results based on the modified SampEn for the cell voltage sequences shown in (a). (f) The zoom-in figure of the modified SampEn for the open-circuit fault ①.
5
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detection due to the bad cell consistency. Fig. 2 (c) and (d) present the fault diagnosis results based on the conventional SampEn for the cell voltage sequences shown in Fig. 2 (a). The size of the moving window is set as 60. The tolerance r is set as 0.15. It can be clearly observed that the SampEn of the cell voltage sequences abruptly increases (here greater than 0.04) when the faults occur because of the abrupt voltage fluctuations. Nevertheless, the SampEn is nearly zero for the normal cell voltages, which shows that the proposed SampEn-based method would not mis-trigger the alarm under normal circumstances. It is worth mentioning that compared with the cell voltages, the SampEn is more sensitive to the abnormal voltages, which is promising to detect battery faults even though the cell voltages are within the safe limits. However, as shown in Fig. 2 (c), the SampEn of the cell voltage sequences is always positive no matter what kind of battery faults occurs, e.g., the short-circuit or open-circuit fault because the SampEn is the conditional probability of the similarity of the voltage sequence. Therefore, the conventional SampEn cannot distinguish the fault type. By contrast, Fig. 2 (e) and (f) present the fault diagnosis results based on the modified SampEn under the same conditions. Because a correc tion coefficient α dependent of the cell voltage and the average voltage is introduced, the modified SampEn can effectively predict the abrupt in crease or decrease of the cell voltages and further identify the fault type. As shown in Fig. 2 (b), for the open-circuit fault ① in B3, when the fault happens at t ¼ 41.92 s, due to VB3(t) ¼ 3.519 V > Vavg ¼ 3.429 V, a posi tive SampEn is firstly generated at the same time, as shown in Fig. 2 (f). When the fault disappears at t ¼ 44.01 s, due to VB3(t) ¼ 3.153 V < Vavg ¼ 3.316 V, a negative SampEn is then generated at the same time, as shown in Fig. 2 (f). It is worth mentioning that as shown in Fig. 2 (b) and (f), the times of the abnormal voltages happening and disappearing are consistent with the times of the modified SampEn increasing and decreasing. Therefore, the modified SampEn can accu rately forecast the time of faults occurring. For the short-circuit fault ② in B2, the SampEn firstly decreases when the fault happens at t ¼ 54.54 s, and then increases abruptly when the fault is removed at t ¼ 54.68 s. Analogously, it is not difficult to find that the modified SampEn of the cell voltage of B1 rises abruptly when the fault ③ happens and disap pears, which implies an open-circuit fault. In summary, it can be concluded that the proposed method can effectively forecast both the type and time of the battery faults in spite of the bad consistency among
cells. 3.2. Fault diagnosis results of the traditional correlation-based method In order to show the superiority of the proposed SampEn-based method, Fig. 3 presents the fault diagnosis results based on the tradi tional correlation-based method [30] for the cell voltage sequences shown in Fig. 2 (a). The size of the moving window is set as 6000. Rij (i ¼ 1, 2, j ¼ 2, 3) in Fig. 3 (a) means the correlation coefficient between Bi and Bj. As shown in Fig. 3 (a), when no fault occurs, the correlation coefficients Rij for any two cells are close to 1, indicating the three cells have the same voltage fluctuation. Whereas, the correlation coefficients R13 and R23 drop abruptly (i.e., from 0.997 to 0.878) at 41.92 s when the open-circuit fault occurs (see the fault ① shown in Fig. 2 (b)) because of the abrupt voltage increase in B3. Then, the correlation coefficients R13 and R23 raise slightly (i.e., from 0.878 to 0.901) at 41.92 s, as shown in Fig. 3 (b), when the open-circuit fault ① disappears. However, the correlation coefficients R13 and R23 continue to decrease after the open-circuit fault ① disappearing because of the inconsistency among cell voltages. Analogously, the locations of the faults ② and ④ can be also determined according to the same drops in R12, R13 and R12, R23, respectively. It is important to note that the correlation coefficient for every two cells exhibits more fluctuations than the modified SampEn shown in Fig. 2 (e), showing a lower prediction accuracy. Particularly, the fluc tuation will become larger as the decrease of the size of the moving window, leading to poor robustness, owing to the increased sensitivity to noises. In addition, the correlation-based solution [30] cannot di agnose the battery fault type because the correlation coefficient always decreases regardless of the increase or decrease in the cell voltages. 3.3. Sensitivity to the moving-window size In order to show the robustness of the proposed detection method to the moving-window size (denoted by N), Fig. 4 presents the fault diag nosis results with different moving-window sizes for the cell voltage sequences shown in Fig. 2 (a). The tolerance is set as r ¼ 0.15. As shown in Fig. 4 (a), when the size of the moving window increases to 90, the SampEn values decreases to 0.028–0.034 compared with that (i.e., 0.043) with N ¼ 60 shown in Fig. 2 (e). This shows with a longer moving
Fig. 3. The fault diagnosis results based on the correlation-based method [30] for the cell voltage sequences shown in Fig. 2 (a). (a) The whole figure. (b) The zoom-in figure for the open-circuit fault ①. 6
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Fig. 4. The fault diagnosis results based on the modified SampEn with different moving-window sizes. (a) N ¼ 90. (b) N ¼ 30. (c) N ¼ 5. (d) N ¼ 4.
window, the proposed detection method is less sensitive to the abnormal voltage variation, which may lead to failure of battery fault detection. As shown in Fig. 4 (b) and (c), when the size of the moving window
decreases to 30 and 5, the SampEn values of the abnormal voltage variations increase to 0.094 and 1.099, respectively. This shows the smaller the size of the moving window, the more sensitive to the
Fig. 5. The fault diagnosis results based on the modified SampEn with different tolerances. (a) r ¼ 0.1. (b) r ¼ 0.5. 7
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abnormal voltages the proposed detection method. However, as shown in Fig. 4 (d), when the size of the moving window decreases to 4, the proposed method is unable to work and fails to detect any fault. Therefore, the experimental results prove that 5 is the optimal window size, which agrees with the theoretical analyses.
3.5. Sensitivity to the measurement noise In order to show the robustness of the proposed method to the measurement noise, Fig. 6 presents the fault diagnosis results for the cell voltage sequences with white noise at 40 dB signal noise ratio (SNR). As shown in Fig. 6 (a), the curves of the cell voltages become thicker compared with those shown in Fig. 2 (a) because the white noise at 40 dB SNR is added to the cell voltages, respectively. As shown in Fig. 6 (b), with the moving-window size of N ¼ 60, a false fault is detected for B1 and B3, respectively, at t ¼ 4.35s due to the effect of the white noise. As shown in Fig. 6 (c), when the moving-window size decreases to N ¼ 5, the proposed method can accurately predict the short-circuit and opencircuit faults with a larger SampEn value and without any false detec tion. This proves that by optimizing the moving-window size, the pro posed fault diagnosis approach is strongly robust to the measurement noise. Table 2 further presents a comparison in terms of Sample Entropy value and computation time with different moving-window sizes. It can be seen that the smaller the moving-window size, the larger the Sample Entropy value, the stronger the robustness, and the shorter the compu tation time. Therefore, the optimal moving-window size is 5 for the proposed algorithm.
3.4. Sensitivity to the tolerance r In order to show the robustness of the proposed detection method to the tolerance r, Fig. 5 presents the fault diagnosis results based on the modified SampEn with different tolerances for the cell voltage sequences shown in Fig. 2 (a). The size of the moving window is set as N ¼ 60. As shown in Fig. 5 (a), with a smaller tolerance (i.e., r ¼ 0.1), a false fault ④ is flagged under the normal transition of the charge/discharge status (see the voltage fluctuation ④ in Fig. 2 (a)) because the proposed method is too sensitive to the fluctuation of the cell voltages. However, as shown in Fig. 5 (b), with a larger tolerance (e.g., r ¼ 0.5), the pro posed method will fail to detect any fault because the proposed method is insensitive to the fluctuation of the cell voltages. Therefore, the tolerance r should be carefully selected based on different applications, which is typically between 10 and 20% of the standard deviation of the cell voltages [42].
Fig. 6. The fault diagnosis results based on the modified SampEn with measurement noise. (a) The cell voltage sequences with white noise. (b) The modified SampEn of the cell voltages with N ¼ 60. (c) The modified SampEn of the cell voltages with N ¼ 5. 8
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fault diagnosis approach is strongly robust to the voltage disturbance.
Table 2 A comparison in terms of sample entropy value and computation time with different moving-window sizes. Moving Window Size
Sample Entropy Value
Computation Time (s)
Robustness
5 30 60 90
1.099 0.094 0.043 0.028
165 201 233 263
Stronger Strong Poor Poorer
3.7. Sensitivity to the inconsistency among cells In order to show the adaptability of the proposed detection method, Fig. 8 presents the cell voltage sequences and the diagnosis results for four cells connected in series with a good consistency under the UDDS working condition. The tolerance and the size of the moving window are set as 0.15 and 60, respectively. As shown in Fig. 8 (a) and (b), it is not difficult to find that there are an open-circuit fault and a short-circuit fault in B3 and B4, respectively. As shown in Fig. 8 (c) and (d), all cells with abnormal voltages and the durations of the faults can be accurately detected by the modified SampEn curves, which verifies the good adaptability of the proposed detection method.
3.6. Sensitivity to the voltage disturbance In order to verify the robustness of the proposed method to the disturbance, Fig. 7 presents the fault diagnosis results for the cell voltage sequences with voltage disturbances. As shown in Fig. 7 (a), a voltage disturbance with the amplitude of 0.15 V is added in B1 and B3 at 23.41 s and 31.80 s, respectively. As shown in Fig. 7 (b), with the movingwindow size of N ¼ 60, a false fault with the SampEn value of 0.04 is detected for B1 and B3, respectively, because of the voltage disturbances. As shown in Fig. 7 (c), when the moving-window size decreases to N ¼ 5, the false detections are restrained, and the normal detections for the short-circuit and open-circuit faults are kept with a larger SampEn value. This proves that by optimizing the moving-window size, the proposed
4. Comparison of different detection methods In order to evaluate the performance of the proposed modified SampEn-based solution, a comprehensive comparison is made with five conventional fault detection methods. Table 3 illustrates the detailed comparison results in terms of the model, accuracy, fault type, compu tational cost, robustness, and implementation. The voltage threshold-based solution [15] can detect battery faults
Fig. 7. The fault diagnosis results based on the modified SampEn with voltage disturbances. (a) The cell voltage sequences with disturbances. (b) The modified SampEn of the cell voltages with N ¼ 60. (c) The modified SampEn of the cell voltages with N ¼ 5. 9
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Fig. 8. (a) The cell voltage sequences of four cells connected in series with a good consistency under the UDDS working condition. (b) The zoom-in figure of the cell voltage sequences for the short-circuit fault ②. (c) The fault diagnosis results based on the modified SampEn. (d) The zoom-in figure of the modified SampEn for the short-circuit fault ②. Table 3 A comparison of fault diagnosis solutions. Detection method
Model
Accuracy
Fault Type
Computational Cost
Robustness
Implementation
Voltage threshold based [15] Adaptive nonlinear model based [16] Machine learning based [26] Correlation based [30] Shannon entropy based [34] Proposed modified SampEn based
No Yes No No No No
Low Low High Low High High
Yes Yes Yes No No Yes
Low High High High Low Low
Poor Poor Strong Poor Poor Strong
Easy Difficult Difficult Easy Easy Easy
(e.g., overcharge or undercharge) by judging whether the cell voltages exceed the threshold, which is the most straightforward solution and can be easily implemented online without the need of accurate battery model. However, this method cannot detect the early battery faults when the cell voltages do not exceed the threshold voltages, leading to poor robustness. The adaptive nonlinear model-based method [16] uses multiple nonlinear models to predict different faults, e.g., the battery overcharge and undercharge. Because multiple EKFs are employed to estimate the
voltage of each battery model and further determine the battery faults, this solution has high calculation cost and bad flexibility, resulting in a complex online implementation. Particularly, it heavily depends on the accuracy of the battery models. A false alarm may be raised when the accuracy of the battery models is lower or the consistency among cells is worse, leading to poor robustness. The machine learning-based method [26] uses advanced Sparse Bayesian methodology to build the potential relation between the ca pacity loss and the SampEn of the short voltage sequences. It has the 10
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advantages of great convenience, strong applicability, good nonlinear mapping, and model-free characteristics. Unfortunately, the SampEn of the short voltage sequence has great randomness and is sensitive to the quantity and quality of the short voltage sequence, leading to a low prediction accuracy and poor robustness. Particularly, this solution needs a big quantity of battery data to train the model representing the relation of the capacity loss and the SampEn of the voltage sequence, leading to a difficult online implementation in EVs. The correlation-based method [30] only needs the cell voltages for the battery short-circuit fault detection without the requirement of any additional hardware or effort in battery modeling. Therefore, this so lution can be easily implemented online. However, it is a computa tionally expensive method, which requires a large amount of time to calculate the mean value, variance, covariance, and so on. Moreover, it is very sensitive to the cell-voltage inconsistency and noise, leading to poor robustness. In addition, because the correlation coefficient is al ways positive, this method cannot distinguish the battery fault type. The Shannon entropy-based method [34] can predict the overvoltage or undervoltage fault through monitoring the cell voltages without the need of the precise battery model. It is worth mentioning that this so lution can detect both the time and location of the faults within the battery strings in real time. In addition, a Z-score-based security man agement approach is used to represent the abnormity level. However, this method has poor robustness for real applications because of the insensitiveness to battery voltage abnormality. Moreover, it cannot predict the battery fault type because the Shannon entropy is always positive no matter what kind of battery fault occurs. The proposed solution can diagnose the early battery faults without obvious voltage abnormality only through detecting the modified SampEn of the cell voltages, which saves the effort in battery modeling or training. Moreover, by introducing a coefficient α presenting the voltage fluctuation information, the proposed solution can forecast both the type and time of battery faults. By utilizing a moving window, the proposed method achieves a high detection sensitivity to faults and less computation, leading to an easy real-time implementation. In addition, by optimizing the tolerance and moving-window size, the proposed approach can prevent false detections and achieves strong robustness to the measurement noise and battery inconsistency.
(4) Decreasing the tolerance r can significantly improve the sensi tivity to the abnormal voltages, but causing false fault alarm. Increasing the tolerance r can effectively prevent false fault alarm, but will lead to failure in detecting battery faults because of the insensitivity to the fluctuation of the cell voltages. (5) By selecting an appropriate moving-window size and tolerance, the proposed fault diagnosis method is strongly robust to the measurement noise and battery inconsistency, leading to a high reliability. In summary, the proposed solution has the advantages of small calculation effort, good flexibility, high accuracy, strong robustness, and model-free characteristics, leading to an easy and reliable implementa tion in real safety management systems. In the future, we will further study a new diagnosis strategy based on the cross Sample Entropy of the current and the cell voltage to further detect the sensor fault, connection fault, cross faults among batteries, and so on. However, it is very challenging because the current variation may not be successfully captured since the battery faults, e.g., the short circuit, may bypass the hall sensor. Acknowledgement The authors would like to acknowledge the funding support from National Natural Science Foundation of China (No. 61903223, 61527809, U1764258, 61633015, U1864205). References [1] Z. Du, B. Lin, C. Guan, Development path of electric vehicles in China under environmental and energy security constraints, Resour. Conserv. Recycl. 143 (2019) 17–26. [2] J. Du, D. Ouyang, Progress of Chinese electric vehicles industrialization in 2015: a review, Appl. Energy 188 (2017) 529–546. [3] L.G. Lu, X.B. Han, J.Q. Li, J.F. Hua, M.G. Ouyang, A review on the key issues for lithium-ion battery management in electric vehicles, J. Power Sources 226 (2013) 272–288. [4] C.Y. Wang, G. Zhang, S. Ge, T. Xu, Y. Ji, X.G. Yang, Y. Leng, Lithium-ion battery structure that self-heats at low temperatures, Nature 529 (7587) (2016) 515–518. [5] What causes car batteries to fail?. http://batteryuniversity.com/learn/archive/ what_causes_car_batteries_to_fail. [6] J. Zhang, J. Lee, A review on prognostics and health monitoring of Li-ion battery, J. Power Sources 196 (2011) 6007–6014. [7] M.A. Hannan, M.S.H. Lipu, A. Hussain, A. Mohamed, A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: challenges and recommendations, Renew. Sustain. Energy Rev. 78 (2017) 834–854. [8] X.N. Feng, C.H. Weng, M.G. Ouyang, J. Sun, Online internal short circuit detection for a large format lithium ion battery, Appl. Energy 161 (2016) 168–180. [9] X. Feng, X. He, L. Lu, M.G. Ouyang, Analysis on the fault features for internal short circuit detection using an electrochemical-thermal coupled model, J. Electrochem. Soc. 165 (2) (2018) A155–A167. [10] Z. Chen, R. Xiong, J. Lu, X. Li, Temperature rise prediction of lithium-ion battery suffering external short circuit for all-climate electric vehicles application, Appl. Energy 213 (2018) 375–383. [11] R. Xiong, Q. Yu, W. Shen, C. Lin, F. Sun, A sensor fault diagnosis method for a Lithium-ion battery pack in electric vehicles, IEEE Trans. Power Electron. (2019) 2893622, https://doi.org/10.1109/TPEL. [12] C. Zhang, Y. Jiang, J. Jiang, G. Cheng, W. Diao, W. Zhang, Study on battery pack consistency evolutions and equilibrium diagnosis for serial-connected lithium-ion batteries, Appl. Energy 207 (2017) 510–519. [13] D.P. Finegan, J. Darst, W. Walker, Q.B. Li, C.B. Yang, R. Jervis, T.M.M. Heenan, J. Hack, J.C. Thomas, A. Rack, D.J.L. Brett, P.R. Shearing, M. Keyser, E. Darcy, Modelling and experiments to identify high-risk failure scenarios for testing the safety of lithium-ion cells, J. Power Sources 417 (2019) 29–41. [14] B. Xia, Z. Chen, C. Mi, B. Robert, External Short Circuit Fault Diagnosis for LithiumIon Batteries, IEEE Transportation Electrification Conference and Expo (ITEC), 2014, 15-18 June 2014. [15] R. Zhao, J. Liu, J. Gu, Simulation and experimental study on lithium on battery short circuit, Appl. Energy 173 (2016) 29–39. [16] A. Sidhu, A. Izadian, S. Anwar, Adaptive nonlinear model-based fault diagnosis of Li-ion batteries, IEEE Trans. Ind. Electron. 62 (2) (2015) 1002–1011. [17] Z. Liu, H. He, Model-based sensor fault diagnosis of a lithium-ion battery in electric vehicles, Energies 8 (7) (2015) 6509–6527. [18] W. Chen, W.T. Chen, M. Saif, M.F. Li, H. Wu, Simultaneous fault isolation and estimation of lithium-ion batteries via synthesized design of Luenberger and learning observers, IEEE Trans. Control Syst. Technol. 22 (1) (2014) 290–298.
5. Conclusion This paper proposes a real-time multi-fault detection approach for the early battery faults without obvious voltage abnormality based on modified SampEn. The proposed approach can effectively forecast both the type and time of battery faults without the need of a precise battery model, which is independent of the inconsistency among cells. The al gorithm description, working principle, feasibility analyses, fault detection results under different conditions, and a comparison with the conventional detection methods are presented. Some conclusions can be obtained as: (1) By detecting the modified SampEn of the cell voltages, the pro posed fault detection method can effectively forecast the early battery faults even though the cell voltages are within the safe limits. (2) By introducing a coefficient α presenting the voltage fluctuation information, the proposed method can detect different battery faults, e.g., the short-circuit fault, open-circuit fault, and so on. (3) Decreasing the moving-window size N can dramatically increase the SampEn value of the abnormal voltages, leading to a high sensitivity to battery faults but a low sensitivity to measurement noise and disturbance. Increasing the moving window size N will decrease the SampEn value of the abnormal voltages, leading to a low sensitivity to battery faults but a high sensitivity to mea surement noise and disturbance. Studies show that the optimal moving-window size is 5. 11
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Journal of Power Sources 446 (2020) 227275 [30] B. Xia, Y.L. Shang, T. Nguyen, C. Mi, A correlation based fault detection method for short circuits in battery packs, J. Power Sources 337 (2017) 1–10. [31] Y.Z. Kang, B. Duan, Z.K. Zhou, Y.L. Shang, C.H. Zhang, A multi-fault diagnostic method based on an interleaved voltage measurement topology for series connected battery packs, J. Power Sources 417 (2019) 132–144. [32] Z. Zhang, S. Li, Y. Xiao, Y. Yang, Intelligent simultaneous fault diagnosis for solid oxide fuel cell system based on deep learning, Appl. Energy 233 (2019) 930–942. [33] L. Yao, Z.P. Wang, J. Ma, Fault detection of the connection of lithium-ion power batteries based on entropy for electric vehicles, J. Power Sources 293 (2015) 548–561. [34] Z.P. Wang, J.C. Hong, P. Liu, L. Zhang, Voltage fault diagnosis and prognosis of battery systems based on entropy and Z-score for electric vehicles, Appl. Energy 196 (2017) 289–302. [35] P. Liu, Z.Y. Sun, Z.P. Wang, J. Zhang, Entropy-based voltage fault diagnosis of battery systems for electric vehicles, Energies 136 (2018) 1–15. [36] Y.H. Sun, H.L. Jou, J.C. Wu, Auxiliary diagnosis method for lead-acid battery health based on sample entropy, Energy Convers. Manag. 50 (2009) 2250–2256. [37] M. Widodo, M. Shim, W. Caesarendra, Intelligent prognostics for battery health monitoring based on sample entropy, Expert Syst. Appl. 38 (2011) 11763–11769. [38] W. Nicholas, H. Wei, H. Christopher, P. Michael, Lessons learned from the 787 dreamliner issue on lithium-ion battery reliability, Energies 6 (2013) 4682–4695. [39] J.S. Richman, J.R. Moorman, Physiological time-series analysis using approximate entropy and sample entropy, Am. J. Physiol. Heart Circ. Physiol. 278 (2000) H2039–H2049. [40] D.E. Lake, J.S. Richman, M.P. Griffin, J.R. Moorman, Sample entropy analysis of neonatal heart rate variability, Am. J. Physiol. Regul. Integr. Comp. Physiol. 283 (2002) 789–797. [41] S.M. Pincus, Approximate entropy as a measure of system complexity, in: Proc. Natl. Acad. Sci. USA, vol 88, 1991, pp. 2297–2301. [42] S.C. Li, Q.F. Zhou, S.H. Wu, E.F. Dai, Measurement of climate complexity using sample entropy, Int. J. Climatol. 26 (2006) 2131–2139.
[19] O. Bohlen, S. Buller, R.W.D. Doncker, Impedance based battery diagnosis for automotive applications, in: 2004 35th Annual IEEE Power Electronics Specialists Conference, Aachen, Germany, 2004, pp. 2792–2797. [20] S. Dey, Z.A. Biron, S. Tatipamula, N. Das, S. Mohon, B. Ayalew, P. Pisu, Modelbased real-time thermal fault diagnosis of Lithium-ion batteries, Contr. Eng. Pract. 56 (2016) 37–48. [21] Z. Chen, R. Xiong, J. Tian, X. Shang, J. Lu, Model-based fault diagnosis approach on external short circuit of lithium-ion battery used in electric vehicles, Appl. Energy 184 (2016) 365–374. [22] M. Ouyang, M. Zhang, X. Feng, L. Lu, J. Li, X. He, Y. Zheng, Internal short circuit detection for battery pack using equivalent parameter and consistency method, J. Power Sources 294 (2015) 272–283. [23] P. Ping, Q.S. Wang, Y. Chung, J. Wen, Modelling electro-thermal response of lithium-ion batteries from normal to abuse conditions, Appl. Energy 205 (2017) 1327–1344. [24] Z. Liu, H. He, Sensor fault detection and isolation for a lithium-ion battery pack in electric vehicles using adaptive extended Kalman filter, Appl. Energy 185 (2017) 2033–2044. [25] W.K. Gao, Y.J. Zheng, M.G. Ouyang, J.Q. Li, X. Lai, X.S. Hu, Micro-short circuit diagnosis for series-connected lithium-ion battery packs using mean-difference model, IEEE Trans. Ind. Electron. 66 (3) (2019) 2132–2142. [26] X.S. Hu, J.C. Jiang, D.P. Cao, B. Egardt, Battery health prognosis for electric vehicles using sample entropy and sparse bayesian predictive modeling, IEEE Trans. Ind. Electron. 63 (4) (2015) 1–11. [27] Y.H. Sun, H.L. Jou, J.C. Wu, K.D. Wu, Auxiliary health diagnosis method for leadacid battery, Appl. Energy 87 (2010) 3691–3698. [28] A. Barre, F. Suard, M. Gerard, M. Montaru, D. Riu, Statistical analysis for understanding and predicting battery degradations in real-life electric vehicle use, J. Power Sources 245 (2014) 846–856. [29] Y. Zhao, P. Liu, Z.P. Wang, L. Zhang, J.C. Hong, Fault and defect diagnosis of battery for electric vehicles based on big data analysis methods, Appl. Energy 207 (2017) 354–362.
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Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
A multi-fault diagnosis method based on modified Sample Entropy for lithium-ion battery strings Yunlong Shang a, Gaopeng Lu b, Yongzhe Kang a, Zhongkai Zhou a, Bin Duan a, Chenghui Zhang a, * a b
School of Control Science and Engineering, Shandong University, Jinan, 250061, China School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai, 264005, China
H I G H L I G H T S
� A multi-fault diagnosis method is proposed to detect the early battery faults. � The proposed diagnosis method is based on the modified Sample Entropy. � A coefficient is introduced to detect the fault type and time of fault occurring. � A moving window is used to maintain the detection sensitivity and less computation. � By optimizing the tolerance, the proposed method can prevent false detections. A R T I C L E I N F O
A B S T R A C T
Keywords: Fault diagnosis Short circuit Open circuit Sample entropy Lithium-ion batteries Electric vehicles
The conventional fault-diagnosis methods are difficult to detect the battery faults in the early stages without obvious battery abnormality because lithium-ion batteries are complex nonlinear time-varying systems with absolute cell inconsistency. Therefore, this paper proposes a real-time multi-fault diagnosis method for the early battery failure based on modified Sample Entropy. By detecting the modified Sample Entropy of the cell-voltage sequences in a moving window, the proposed diagnosis method can diagnose and predict different early battery faults, including short-circuit and open-circuit faults, and can also predict the time of the faults occurring. The experimental results and the comparison with the conventional methods verify the validity of the proposed solution with strong robustness, high reliability and low computational cost, and without the need of a precise model. In summary, the proposed multi-fault diagnosis approach is feasible and promising in real electric vehicle applications.
1. Introduction
effective diagnosis methods for the early faults of lithium-ion batteries to prevent battery failure. The common battery faults mainly include overvoltage, under voltage, loose connection, insulation, external short circuit, internal short circuit, open circuit, sensor failure, and so on [8–13]. Compared with the other faults, the overvoltage, undervoltage, and short-circuit faults are more hazardous to batteries, which will cause lithium-ion deposition and accelerate battery aging [6]. It is important to note that different from the mechanical and electrical systems, fault diagnosis for lithium-ion batteries is much more complex because of the immea surable internal states of lithium-ion batteries [7]. In fact, only the cell voltage and current are the available indicators for battery faults. The voltage abnormality, e.g., the abrupt increase or decrease in the cell
Due to the energy crisis, environmental pollution, and climate change, electric vehicles (EVs) (e.g., Tesla) are becoming more and more popular [1,2]. As the power sources of EVs, lithium-ion batteries have significant influences on vehicle power, economy, and safety [3,4]. According to the statistics on 1.95 million EVs, 52% breakdown is caused by the onboard lithium-ion batteries [5]. Two main causes can be found. On the one hand, the electrochemical reaction inside lithium-ion batteries is extremely complicated, which is sensitive to environment temperature and battery aging [6]. On the other hand, a lithium-ion battery string is usually made up of thousands of cells with absolute inconsistency [7]. Therefore, it is important and worth developing * Corresponding author. E-mail address: [email protected] (C. Zhang).
https://doi.org/10.1016/j.jpowsour.2019.227275 Received 31 July 2019; Received in revised form 17 September 2019; Accepted 7 October 2019 Available online 31 October 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
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Journal of Power Sources 446 (2020) 227275
voltages, may imply more early faults including short circuit, open cir cuit, etc. [8,9]. Therefore, the detection for the abnormal changes of cell voltages can locate and analyze the catastrophic faults in advance. However, it is extremely challenging to analyze the abnormalities hid den beneath the surface (cell voltages) due to the strong nonlinearity, time-varying characteristic, hysteresis, and inconsistency of lithium-ion batteries [6–13]. Many battery fault diagnosis methods have been proposed, which can be classified into three categories: threshold-based [14,15], model-based [16–25], and data-driven-based [26–38] solutions. The threshold-based method can detect battery faults when any cell voltage exceeds the cut-off voltage, which has been widely applied to battery management systems (BMSs) of EVs [14,15]. However, this so lution is difficult to detect the early battery faults when the abnormal cell voltages do not exceed the threshold voltages. For example, on Jan. 16 2013, fire occurred in a 787 airplane caused by battery failure, where the onboard BMS did not raise any alarm at the early stage of the fault because the cell voltages did not trigger the threshold [39]. In fact, choosing an appropriate threshold is another challenge for this solution. If the threshold is too high, the sensitivity of the fault diagnosis is too low because the abnormal cell voltages hardly trigger the threshold. On the contrary, if the threshold is too low, false alarms may be raised because the normal cell voltages may trigger the threshold. The model-based method requires the extensive effort in testing and modeling batteries for different faults, leading to the complex imple mentation, low accuracy, and poor robustness [16–25]. Sidhu et al. [16] proposed a fault detection solution based on multiple nonlinear models and adaptive extended Kalman filters (AEKF). The fault information can be detected by estimating the residual signals between the cell voltage and the terminal voltage of each model based on AEKF. According to the same principle, Liu et al. [17] proposed an analogous diagnostic solution to detect the current or voltage sensor fault. Chen et al. [18] proposed an external short-circuit detection method based on battery model for lithium-ion batteries. Bohlen et al. [19] proposed an on-line mod el-based fault detection solution by identifying the battery internal resistance. According to the above analyses, it can be seen that the model-based diagnostic methods are only applicable to a specific fault but cannot detect the other faults without modeled, leading to narrow applicability. In addition, due to the complex implementation and poor robustness, the model-based methods are difficult to be applied to BMSs of EVs. Recently, due to the good nonlinear mapping, the data-driven-based approaches have been widely applied to battery fault detection field [26–32]. Hu et al. [26] invented a battery health indication and prog nosis method based on machine learning. The battery health could be estimated by establishing the relation between Sample Entropy (SampEn) of the cell voltage sequence and the battery capacity based on Sparse Bayesian. Sun et al. [27] proposed a battery fault detection so lution based on the charge/discharge curve, which is smooth under the normal working conditions. Thus, the potential battery faults can be detected based on the changes of the battery charge/discharge curve. Barr�e et al. [28] investigated the main battery ageing factors during EV use based on statistical analysis, which can be used to diagnose battery health. Zhao et al. [29] proposed a machine-learning-based fault detection approach, which could detect the abnormal changes of the cell voltages. Xia et al. [30] proposed a correlation-based detection solution for the battery short-circuit fault, which can identify the abnormal voltage change according to the correlation coefficients of each two cell voltages. It can be noted that the above data-driven-based methods either need a big quantity of data to build the potential relation between the signal and the faults, leading to high computational cost and difficult real-time application, or are sensitive to the training battery data, resulting in poor robustness. Fortunately, as one of the data-driven-based methods, the entropybased approach can identify battery faults by measuring the complexity of the cell voltage or current sequence [33–38]. Yao et al.
[33] proposed a connection fault detection method based on ensemble Shannon entropy of the cell voltages, which achieves relatively small amount of calculation and simple on-line and real-time implementation. Wang et al. [34] proposed a battery fault detection approach based on modified Shannon entropy of the cell voltages. Liu et al. [35] proposed an overvoltage-fault detection method based on entropy theory and an entropy weight was employed to reduce the subjectivity and improve the reliability. Sun et al. [36] proposed a SampEn-based diagnosis method to estimate the state of health (SOH) of the lead-acid battery at the end of each discharging cycle only by measuring the voltage and current of the lead-acid battery. It can be concluded that the entropy of the cell voltage or current representing the salient feature of the battery string can be used to forecast the early battery faults. In addition, the entropy-based method requires less computational cost because of the nonuse of the accurate battery model, which can be easily applied on line. However, because the entropy is nonnegative, the existing entropy-based methods only can detect a kind of battery fault, and cannot distinguish the fault type and predict the accurate time of battery failure. Particularly, the conventional methods have low reliability and practicability for real applications because of the insensitiveness to battery faults. In addition, it is worth mentioning that the SampEn-based method was never used to predict battery faults. In summary, the early detection of battery faults is a critical but challenging issue in BMSs of EVs. The conventional methods are difficult to diagnose the abnormal battery changes at the early stage and predict the time of the failure occurrence in real EV applications because lithium-ion batteries are complex nonlinear time-varying systems with absolute inconsistency. Therefore, in order to bridge these drawbacks, an early multi-fault detection approach for diagnosing the potential abnormality of the cell voltages is proposed based on modified SampEn. Specifically, four original contributions are made in this paper. Firstly, a simple fault detection solution based on cell-voltage SampEn is proposed to forecast the early battery faults without obvious battery abnormality. Secondly, a coefficient α presenting the voltage fluctuation information is introduced to detect the fault type (including battery short circuit, open circuit, and so on) and forecast the time of the faults occurring. Thirdly, a moving window is used to update the battery data, and maintain the diagnosis sensitivity to faults and less computation, leading to an easy real-time implementation. Finally, by optimizing the toler ance, the proposed method can prevent false detections and achieve a high robustness to the measurement noise and battery inconsistency. The rest of this paper is summarized as follows. The SampEn algo rithm is presented in Section II. In Section III, the verification outcomes are discussed, and the robustness of the proposed method is analyzed. A comprehensive comparison with the traditional methods is made in Section IV. Section V finally summarizes the conclusions. 2. Proposed diagnosis method based on modified SampEn 2.1. Algorithm description The SampEn proposed by Joshua S. Richman and J. Randall Moor man in 2000 has been widely used to evaluate the complexity of the time series data [39–41]. SampEn is the negative natural logarithm of an estimate of the conditional probability that the subseries of length m that match pointwise within a tolerance r also match at the next point [39–41]. It exhibits strong robustness, good representation, and low computational cost, which is feasible in strongly interactive systems [39–41]. As stated, the cell voltage is an available indicator for battery faults. When a short-circuit fault occurs in a battery cell, it will cause an abrupt cell-voltage drop [30]. Whereas, the cell voltage abruptly rises, which implies an open-circuit or sensor fault. The abrupt voltage drop or rise will also cause a significant change in the SampEn of the cell-voltage sequence, which is promising to forecast battery faults. The proposed SampEn algorithm for a cell-voltage sequence is shown 2
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as follows [39–41]. For a given cell-voltage length N, a cell voltage vector V(i) can be formulated as VðiÞ ¼ ½VðiÞ; Vði þ 1Þ; …; Vði þ m
1Þ�; i ¼ 1; 2; … ; N
mþ1
shorter moving window can provide better diagnostic precision for battery faults. However, according to (5)–(7), when the window size is less than 5, the SampEn value will be identically equal zero regardless of the abnormal voltage changes. This implies that the proposed approach is unable to detect any fault with a too short moving window. Theo retically, the optimal moving-window size is 5 to achieve a strong robustness to the measurement noise and disturbance, and small calculation effort.
(1)
where m is the window length, and is usually set as 2 to accurately measure the change in the cell voltages [39–42]. The distance d½Vm ðiÞ; Vm ðjÞ� between vectors Vm ðiÞ and Vm ðjÞ is the maximum absolute difference, which can be expressed as d½Vm ðiÞ; Vm ðjÞ� ¼ max½jVm ði þ kÞ
Vm ðj þ kÞj�; 0 � k � m
1
2.3. Algorithm improvement
(2)
It is important to note that the SampEn of the cell-voltage sequence (i.e., the conditional probability) is always nonnegative regardless of the abrupt drop or rise in the cell voltage. As a result, the SampEn-based method cannot forecast the kind of battery faults. In fact, it is neces sary for battery safety to detect different battery faults and forecast the fault time. The SampEn algorithm should be improved to accommodate for the multi-fault diagnosis requirement of battery systems. Therefore, a correction coefficient α presenting the voltage fluctuation information is introduced to detect the fault types and forecast the time of the faults occurring. According to the above analyses, the SampEn of a cell-voltage sequence can be modified as
Define the function Bmi ðrÞ ¼
1 W m ðiÞ; i ¼ 1; 2 ; …; N mþ1
N
mþ1
(3)
where Wm ðiÞ is the number of d½Vm ðiÞ;Vm ðjÞ� � r; i 6¼ j. Similarly, define another function Ami ðrÞ ¼
1 W mþ1 ðiÞ; i ¼ 1; 2 ; …; N mþ1
N
mþ1
(4)
where Wmþ1 ðiÞ is the number of d½Vmþ1 ðiÞ; Vmþ1 ðjÞ� � r; i 6¼ j. The probability of two time series matching for m voltage points can be expressed as Bm ðrÞ ¼
N m X
1 N
m
Bmi ðrÞ
S ¼ α � SampEnðm; r; NÞ
(5)
where α is the correction coefficient, which can be given by 8 < 1 When VðtÞ < Vavg α ¼ 1 When VðtÞ > Vavg : 0 Otherwise
i¼1
Analogously, the probability of two time series matching for mþ1 voltage points can be expressed as Am ðrÞ ¼
N m X
1 N
m
Ami ðrÞ
(6)
SampEn is the conditional probability that mþ1 voltages match when m voltage points match within a tolerance r, which can be expressed as ln½Am ðrÞ = Bm ðrÞ�
(9)
where V(t) is the real-time cell voltage at t. Vavg is the cell average voltage in a moving window. According to (8)–(9), it can be observed that when the battery voltage abruptly drops (i.e., VðtÞ < Vavg ), a negative SampEn is gener ated. When the cell voltage abruptly increases (i.e., VðtÞ > Vavg ), a positive SampEn is generated. Therefore, the proposed modified SampEn-based algorithm can detect the abrupt rise or drop in the cell voltage and further diagnose the fault type based on the positive or negative SampEn of the cell-voltage sequence. A flow chart of the pro posed modified SampEn-based algorithm is illustrated in Fig. 1.
i¼1
SampEnðm; r; NÞ ¼
(8)
(7)
According to (1)–(7), it can be seen that a smaller SampEn represents more self-similarity in the cell-voltage sequence, implying no fault occurrence in the cell. On the contrary, a larger SampEn represents less self-similarity in the cell-voltage sequence, indicating potential faults in the battery cell. Therefore, the SampEn can be used to describe the regularity and complexity of the cell voltages, which is promising to detect battery faults even though the cell voltages are within the safe limits. It is important to note that the tolerance (threshold) r should be carefully selected. According to (3)–(4), a smaller tolerance may cause false detections, while a larger tolerance may lead to a failure of fault detection. Theoretically, the tolerance r will approach zero for an infinite number of data [42]. However, for a finite number of data with measurement noise, the tolerance r should be typically between 10 and 20% of the standard deviation of the data [42].
3. Experiment results and discussion An experiment platform is built to validate the effectiveness and robustness of the proposed multi-fault detection solution. The experi ment platform consists of an AVL battery tester, a BMS, and an AVL control cabinet. The tested batteries, including four LiFePO4 cells, are connected in series, whose parameters are shown in Table 1. The AVL battery tester is used to charge and discharge batteries under urban dynamometer driving schedule (UDDS). The BMS and AVL control cabinet are employed to monitor and record the cell voltages of LiFePO4 cells. In order to accurately capture the fault information, the mea surement frequency is set to about 400 Hz. The measurement accuracy of the cell voltage is 0.1%.
2.2. Moving window For the online implementation, the SampEn of the cell-voltage sequence should be calculated in real time. Thus, a moving window is employed to update the battery data in real time and maintain the sensitivity to faults. Specifically, the SampEn at each time instant is calculated based on the cell voltages in a history moving window prior to now. It is worth mentioning that N in (1) represents the movingwindow size. In fact, the moving-window size N essentially determines the SampEn value and sensibility to faults. According to (5)–(7), for the same cell-voltage sequence, the smaller the window size, the larger the SampEn value, which indicates a higher sensitivity to faults. Therefore, a
3.1. Fault diagnosis results of the proposed method Fig. 2 (a) presents the voltage sequences of three LiFePO4 cells connected in series with the short-circuit and open-circuit faults under the UDDS cycle. Overall, the battery string has bad consistency, where B3 has lower voltage than B1 and B2. Nevertheless, their fluctuation trends are consistent because of the same charge/discharge current. At 41.92 s of the UDDS cycle, an open-circuit fault occurs in B3 (see the fault ① in Fig. 2 (b)), causing the cell voltage abruptly increasing to approximate 3.512 V. At 54.54 s, a jump wire is used to short-circuit B2 3
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Fig. 1. The flowchart of the proposed multi-fault diagnosis method based on modified SampEn.
for about 0.13 s, leading to an abrupt decrease (here is 0.487 V) in the cell voltage (see the fault ② in Fig. 2 (a)). It can be noted that the voltage recovers when the short-circuit fault is removed. At 69.53 s, another open-circuit fault occurs in B1, resulting in an abrupt increase (here is 0.414 V) in the cell voltage (see the fault ③ in Fig. 2 (a)). It is important to note that all the cell voltages in case of faults do not touch the charge and discharge cut-off voltages presented in Table 1. Thus, the thresholdbased detection method cannot raise any alarm. In addition, the voltage difference among the cells is up to 0.3 V due to the bad consistency. Therefore, a false fault may be flagged when the voltage difference threshold is applied. Analogously, when the model-based method is applied to track the cell voltages, it may also result in a false fault
Table 1 Specification of the tested batteries. Item
Parameter
Battery type Nominal voltage Nominal rated capacity Charge cut-off voltage Discharge cut-off voltage Max pulse discharge
Cylindrical 18650 3.2 V 1.35 Ah 3.65 V 2.5 V 4.05 A
4
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Fig. 2. (a) The cell voltage sequences of three cells connected in series with the short-circuit and open-circuit faults under the UDDS working condition. (b) The zoom-in figure for the open-circuit fault ①. (c) The fault diagnosis results based on the conventional SampEn for the cell voltage sequences shown in (a). (d) The zoom-in figure of the conventional SampEn for the open-circuit fault ①. (e) The fault diagnosis results based on the modified SampEn for the cell voltage sequences shown in (a). (f) The zoom-in figure of the modified SampEn for the open-circuit fault ①.
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detection due to the bad cell consistency. Fig. 2 (c) and (d) present the fault diagnosis results based on the conventional SampEn for the cell voltage sequences shown in Fig. 2 (a). The size of the moving window is set as 60. The tolerance r is set as 0.15. It can be clearly observed that the SampEn of the cell voltage sequences abruptly increases (here greater than 0.04) when the faults occur because of the abrupt voltage fluctuations. Nevertheless, the SampEn is nearly zero for the normal cell voltages, which shows that the proposed SampEn-based method would not mis-trigger the alarm under normal circumstances. It is worth mentioning that compared with the cell voltages, the SampEn is more sensitive to the abnormal voltages, which is promising to detect battery faults even though the cell voltages are within the safe limits. However, as shown in Fig. 2 (c), the SampEn of the cell voltage sequences is always positive no matter what kind of battery faults occurs, e.g., the short-circuit or open-circuit fault because the SampEn is the conditional probability of the similarity of the voltage sequence. Therefore, the conventional SampEn cannot distinguish the fault type. By contrast, Fig. 2 (e) and (f) present the fault diagnosis results based on the modified SampEn under the same conditions. Because a correc tion coefficient α dependent of the cell voltage and the average voltage is introduced, the modified SampEn can effectively predict the abrupt in crease or decrease of the cell voltages and further identify the fault type. As shown in Fig. 2 (b), for the open-circuit fault ① in B3, when the fault happens at t ¼ 41.92 s, due to VB3(t) ¼ 3.519 V > Vavg ¼ 3.429 V, a posi tive SampEn is firstly generated at the same time, as shown in Fig. 2 (f). When the fault disappears at t ¼ 44.01 s, due to VB3(t) ¼ 3.153 V < Vavg ¼ 3.316 V, a negative SampEn is then generated at the same time, as shown in Fig. 2 (f). It is worth mentioning that as shown in Fig. 2 (b) and (f), the times of the abnormal voltages happening and disappearing are consistent with the times of the modified SampEn increasing and decreasing. Therefore, the modified SampEn can accu rately forecast the time of faults occurring. For the short-circuit fault ② in B2, the SampEn firstly decreases when the fault happens at t ¼ 54.54 s, and then increases abruptly when the fault is removed at t ¼ 54.68 s. Analogously, it is not difficult to find that the modified SampEn of the cell voltage of B1 rises abruptly when the fault ③ happens and disap pears, which implies an open-circuit fault. In summary, it can be concluded that the proposed method can effectively forecast both the type and time of the battery faults in spite of the bad consistency among
cells. 3.2. Fault diagnosis results of the traditional correlation-based method In order to show the superiority of the proposed SampEn-based method, Fig. 3 presents the fault diagnosis results based on the tradi tional correlation-based method [30] for the cell voltage sequences shown in Fig. 2 (a). The size of the moving window is set as 6000. Rij (i ¼ 1, 2, j ¼ 2, 3) in Fig. 3 (a) means the correlation coefficient between Bi and Bj. As shown in Fig. 3 (a), when no fault occurs, the correlation coefficients Rij for any two cells are close to 1, indicating the three cells have the same voltage fluctuation. Whereas, the correlation coefficients R13 and R23 drop abruptly (i.e., from 0.997 to 0.878) at 41.92 s when the open-circuit fault occurs (see the fault ① shown in Fig. 2 (b)) because of the abrupt voltage increase in B3. Then, the correlation coefficients R13 and R23 raise slightly (i.e., from 0.878 to 0.901) at 41.92 s, as shown in Fig. 3 (b), when the open-circuit fault ① disappears. However, the correlation coefficients R13 and R23 continue to decrease after the open-circuit fault ① disappearing because of the inconsistency among cell voltages. Analogously, the locations of the faults ② and ④ can be also determined according to the same drops in R12, R13 and R12, R23, respectively. It is important to note that the correlation coefficient for every two cells exhibits more fluctuations than the modified SampEn shown in Fig. 2 (e), showing a lower prediction accuracy. Particularly, the fluc tuation will become larger as the decrease of the size of the moving window, leading to poor robustness, owing to the increased sensitivity to noises. In addition, the correlation-based solution [30] cannot di agnose the battery fault type because the correlation coefficient always decreases regardless of the increase or decrease in the cell voltages. 3.3. Sensitivity to the moving-window size In order to show the robustness of the proposed detection method to the moving-window size (denoted by N), Fig. 4 presents the fault diag nosis results with different moving-window sizes for the cell voltage sequences shown in Fig. 2 (a). The tolerance is set as r ¼ 0.15. As shown in Fig. 4 (a), when the size of the moving window increases to 90, the SampEn values decreases to 0.028–0.034 compared with that (i.e., 0.043) with N ¼ 60 shown in Fig. 2 (e). This shows with a longer moving
Fig. 3. The fault diagnosis results based on the correlation-based method [30] for the cell voltage sequences shown in Fig. 2 (a). (a) The whole figure. (b) The zoom-in figure for the open-circuit fault ①. 6
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Fig. 4. The fault diagnosis results based on the modified SampEn with different moving-window sizes. (a) N ¼ 90. (b) N ¼ 30. (c) N ¼ 5. (d) N ¼ 4.
window, the proposed detection method is less sensitive to the abnormal voltage variation, which may lead to failure of battery fault detection. As shown in Fig. 4 (b) and (c), when the size of the moving window
decreases to 30 and 5, the SampEn values of the abnormal voltage variations increase to 0.094 and 1.099, respectively. This shows the smaller the size of the moving window, the more sensitive to the
Fig. 5. The fault diagnosis results based on the modified SampEn with different tolerances. (a) r ¼ 0.1. (b) r ¼ 0.5. 7
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abnormal voltages the proposed detection method. However, as shown in Fig. 4 (d), when the size of the moving window decreases to 4, the proposed method is unable to work and fails to detect any fault. Therefore, the experimental results prove that 5 is the optimal window size, which agrees with the theoretical analyses.
3.5. Sensitivity to the measurement noise In order to show the robustness of the proposed method to the measurement noise, Fig. 6 presents the fault diagnosis results for the cell voltage sequences with white noise at 40 dB signal noise ratio (SNR). As shown in Fig. 6 (a), the curves of the cell voltages become thicker compared with those shown in Fig. 2 (a) because the white noise at 40 dB SNR is added to the cell voltages, respectively. As shown in Fig. 6 (b), with the moving-window size of N ¼ 60, a false fault is detected for B1 and B3, respectively, at t ¼ 4.35s due to the effect of the white noise. As shown in Fig. 6 (c), when the moving-window size decreases to N ¼ 5, the proposed method can accurately predict the short-circuit and opencircuit faults with a larger SampEn value and without any false detec tion. This proves that by optimizing the moving-window size, the pro posed fault diagnosis approach is strongly robust to the measurement noise. Table 2 further presents a comparison in terms of Sample Entropy value and computation time with different moving-window sizes. It can be seen that the smaller the moving-window size, the larger the Sample Entropy value, the stronger the robustness, and the shorter the compu tation time. Therefore, the optimal moving-window size is 5 for the proposed algorithm.
3.4. Sensitivity to the tolerance r In order to show the robustness of the proposed detection method to the tolerance r, Fig. 5 presents the fault diagnosis results based on the modified SampEn with different tolerances for the cell voltage sequences shown in Fig. 2 (a). The size of the moving window is set as N ¼ 60. As shown in Fig. 5 (a), with a smaller tolerance (i.e., r ¼ 0.1), a false fault ④ is flagged under the normal transition of the charge/discharge status (see the voltage fluctuation ④ in Fig. 2 (a)) because the proposed method is too sensitive to the fluctuation of the cell voltages. However, as shown in Fig. 5 (b), with a larger tolerance (e.g., r ¼ 0.5), the pro posed method will fail to detect any fault because the proposed method is insensitive to the fluctuation of the cell voltages. Therefore, the tolerance r should be carefully selected based on different applications, which is typically between 10 and 20% of the standard deviation of the cell voltages [42].
Fig. 6. The fault diagnosis results based on the modified SampEn with measurement noise. (a) The cell voltage sequences with white noise. (b) The modified SampEn of the cell voltages with N ¼ 60. (c) The modified SampEn of the cell voltages with N ¼ 5. 8
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fault diagnosis approach is strongly robust to the voltage disturbance.
Table 2 A comparison in terms of sample entropy value and computation time with different moving-window sizes. Moving Window Size
Sample Entropy Value
Computation Time (s)
Robustness
5 30 60 90
1.099 0.094 0.043 0.028
165 201 233 263
Stronger Strong Poor Poorer
3.7. Sensitivity to the inconsistency among cells In order to show the adaptability of the proposed detection method, Fig. 8 presents the cell voltage sequences and the diagnosis results for four cells connected in series with a good consistency under the UDDS working condition. The tolerance and the size of the moving window are set as 0.15 and 60, respectively. As shown in Fig. 8 (a) and (b), it is not difficult to find that there are an open-circuit fault and a short-circuit fault in B3 and B4, respectively. As shown in Fig. 8 (c) and (d), all cells with abnormal voltages and the durations of the faults can be accurately detected by the modified SampEn curves, which verifies the good adaptability of the proposed detection method.
3.6. Sensitivity to the voltage disturbance In order to verify the robustness of the proposed method to the disturbance, Fig. 7 presents the fault diagnosis results for the cell voltage sequences with voltage disturbances. As shown in Fig. 7 (a), a voltage disturbance with the amplitude of 0.15 V is added in B1 and B3 at 23.41 s and 31.80 s, respectively. As shown in Fig. 7 (b), with the movingwindow size of N ¼ 60, a false fault with the SampEn value of 0.04 is detected for B1 and B3, respectively, because of the voltage disturbances. As shown in Fig. 7 (c), when the moving-window size decreases to N ¼ 5, the false detections are restrained, and the normal detections for the short-circuit and open-circuit faults are kept with a larger SampEn value. This proves that by optimizing the moving-window size, the proposed
4. Comparison of different detection methods In order to evaluate the performance of the proposed modified SampEn-based solution, a comprehensive comparison is made with five conventional fault detection methods. Table 3 illustrates the detailed comparison results in terms of the model, accuracy, fault type, compu tational cost, robustness, and implementation. The voltage threshold-based solution [15] can detect battery faults
Fig. 7. The fault diagnosis results based on the modified SampEn with voltage disturbances. (a) The cell voltage sequences with disturbances. (b) The modified SampEn of the cell voltages with N ¼ 60. (c) The modified SampEn of the cell voltages with N ¼ 5. 9
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Fig. 8. (a) The cell voltage sequences of four cells connected in series with a good consistency under the UDDS working condition. (b) The zoom-in figure of the cell voltage sequences for the short-circuit fault ②. (c) The fault diagnosis results based on the modified SampEn. (d) The zoom-in figure of the modified SampEn for the short-circuit fault ②. Table 3 A comparison of fault diagnosis solutions. Detection method
Model
Accuracy
Fault Type
Computational Cost
Robustness
Implementation
Voltage threshold based [15] Adaptive nonlinear model based [16] Machine learning based [26] Correlation based [30] Shannon entropy based [34] Proposed modified SampEn based
No Yes No No No No
Low Low High Low High High
Yes Yes Yes No No Yes
Low High High High Low Low
Poor Poor Strong Poor Poor Strong
Easy Difficult Difficult Easy Easy Easy
(e.g., overcharge or undercharge) by judging whether the cell voltages exceed the threshold, which is the most straightforward solution and can be easily implemented online without the need of accurate battery model. However, this method cannot detect the early battery faults when the cell voltages do not exceed the threshold voltages, leading to poor robustness. The adaptive nonlinear model-based method [16] uses multiple nonlinear models to predict different faults, e.g., the battery overcharge and undercharge. Because multiple EKFs are employed to estimate the
voltage of each battery model and further determine the battery faults, this solution has high calculation cost and bad flexibility, resulting in a complex online implementation. Particularly, it heavily depends on the accuracy of the battery models. A false alarm may be raised when the accuracy of the battery models is lower or the consistency among cells is worse, leading to poor robustness. The machine learning-based method [26] uses advanced Sparse Bayesian methodology to build the potential relation between the ca pacity loss and the SampEn of the short voltage sequences. It has the 10
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advantages of great convenience, strong applicability, good nonlinear mapping, and model-free characteristics. Unfortunately, the SampEn of the short voltage sequence has great randomness and is sensitive to the quantity and quality of the short voltage sequence, leading to a low prediction accuracy and poor robustness. Particularly, this solution needs a big quantity of battery data to train the model representing the relation of the capacity loss and the SampEn of the voltage sequence, leading to a difficult online implementation in EVs. The correlation-based method [30] only needs the cell voltages for the battery short-circuit fault detection without the requirement of any additional hardware or effort in battery modeling. Therefore, this so lution can be easily implemented online. However, it is a computa tionally expensive method, which requires a large amount of time to calculate the mean value, variance, covariance, and so on. Moreover, it is very sensitive to the cell-voltage inconsistency and noise, leading to poor robustness. In addition, because the correlation coefficient is al ways positive, this method cannot distinguish the battery fault type. The Shannon entropy-based method [34] can predict the overvoltage or undervoltage fault through monitoring the cell voltages without the need of the precise battery model. It is worth mentioning that this so lution can detect both the time and location of the faults within the battery strings in real time. In addition, a Z-score-based security man agement approach is used to represent the abnormity level. However, this method has poor robustness for real applications because of the insensitiveness to battery voltage abnormality. Moreover, it cannot predict the battery fault type because the Shannon entropy is always positive no matter what kind of battery fault occurs. The proposed solution can diagnose the early battery faults without obvious voltage abnormality only through detecting the modified SampEn of the cell voltages, which saves the effort in battery modeling or training. Moreover, by introducing a coefficient α presenting the voltage fluctuation information, the proposed solution can forecast both the type and time of battery faults. By utilizing a moving window, the proposed method achieves a high detection sensitivity to faults and less computation, leading to an easy real-time implementation. In addition, by optimizing the tolerance and moving-window size, the proposed approach can prevent false detections and achieves strong robustness to the measurement noise and battery inconsistency.
(4) Decreasing the tolerance r can significantly improve the sensi tivity to the abnormal voltages, but causing false fault alarm. Increasing the tolerance r can effectively prevent false fault alarm, but will lead to failure in detecting battery faults because of the insensitivity to the fluctuation of the cell voltages. (5) By selecting an appropriate moving-window size and tolerance, the proposed fault diagnosis method is strongly robust to the measurement noise and battery inconsistency, leading to a high reliability. In summary, the proposed solution has the advantages of small calculation effort, good flexibility, high accuracy, strong robustness, and model-free characteristics, leading to an easy and reliable implementa tion in real safety management systems. In the future, we will further study a new diagnosis strategy based on the cross Sample Entropy of the current and the cell voltage to further detect the sensor fault, connection fault, cross faults among batteries, and so on. However, it is very challenging because the current variation may not be successfully captured since the battery faults, e.g., the short circuit, may bypass the hall sensor. Acknowledgement The authors would like to acknowledge the funding support from National Natural Science Foundation of China (No. 61903223, 61527809, U1764258, 61633015, U1864205). References [1] Z. Du, B. Lin, C. Guan, Development path of electric vehicles in China under environmental and energy security constraints, Resour. Conserv. Recycl. 143 (2019) 17–26. [2] J. Du, D. Ouyang, Progress of Chinese electric vehicles industrialization in 2015: a review, Appl. Energy 188 (2017) 529–546. [3] L.G. Lu, X.B. Han, J.Q. Li, J.F. Hua, M.G. Ouyang, A review on the key issues for lithium-ion battery management in electric vehicles, J. Power Sources 226 (2013) 272–288. [4] C.Y. Wang, G. Zhang, S. Ge, T. Xu, Y. Ji, X.G. Yang, Y. Leng, Lithium-ion battery structure that self-heats at low temperatures, Nature 529 (7587) (2016) 515–518. [5] What causes car batteries to fail?. http://batteryuniversity.com/learn/archive/ what_causes_car_batteries_to_fail. [6] J. Zhang, J. Lee, A review on prognostics and health monitoring of Li-ion battery, J. Power Sources 196 (2011) 6007–6014. [7] M.A. Hannan, M.S.H. Lipu, A. Hussain, A. Mohamed, A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: challenges and recommendations, Renew. Sustain. Energy Rev. 78 (2017) 834–854. [8] X.N. Feng, C.H. Weng, M.G. Ouyang, J. Sun, Online internal short circuit detection for a large format lithium ion battery, Appl. Energy 161 (2016) 168–180. [9] X. Feng, X. He, L. Lu, M.G. Ouyang, Analysis on the fault features for internal short circuit detection using an electrochemical-thermal coupled model, J. Electrochem. Soc. 165 (2) (2018) A155–A167. [10] Z. Chen, R. Xiong, J. Lu, X. Li, Temperature rise prediction of lithium-ion battery suffering external short circuit for all-climate electric vehicles application, Appl. Energy 213 (2018) 375–383. [11] R. Xiong, Q. Yu, W. Shen, C. Lin, F. Sun, A sensor fault diagnosis method for a Lithium-ion battery pack in electric vehicles, IEEE Trans. Power Electron. (2019) 2893622, https://doi.org/10.1109/TPEL. [12] C. Zhang, Y. Jiang, J. Jiang, G. Cheng, W. Diao, W. Zhang, Study on battery pack consistency evolutions and equilibrium diagnosis for serial-connected lithium-ion batteries, Appl. Energy 207 (2017) 510–519. [13] D.P. Finegan, J. Darst, W. Walker, Q.B. Li, C.B. Yang, R. Jervis, T.M.M. Heenan, J. Hack, J.C. Thomas, A. Rack, D.J.L. Brett, P.R. Shearing, M. Keyser, E. Darcy, Modelling and experiments to identify high-risk failure scenarios for testing the safety of lithium-ion cells, J. Power Sources 417 (2019) 29–41. [14] B. Xia, Z. Chen, C. Mi, B. Robert, External Short Circuit Fault Diagnosis for LithiumIon Batteries, IEEE Transportation Electrification Conference and Expo (ITEC), 2014, 15-18 June 2014. [15] R. Zhao, J. Liu, J. Gu, Simulation and experimental study on lithium on battery short circuit, Appl. Energy 173 (2016) 29–39. [16] A. Sidhu, A. Izadian, S. Anwar, Adaptive nonlinear model-based fault diagnosis of Li-ion batteries, IEEE Trans. Ind. Electron. 62 (2) (2015) 1002–1011. [17] Z. Liu, H. He, Model-based sensor fault diagnosis of a lithium-ion battery in electric vehicles, Energies 8 (7) (2015) 6509–6527. [18] W. Chen, W.T. Chen, M. Saif, M.F. Li, H. Wu, Simultaneous fault isolation and estimation of lithium-ion batteries via synthesized design of Luenberger and learning observers, IEEE Trans. Control Syst. Technol. 22 (1) (2014) 290–298.
5. Conclusion This paper proposes a real-time multi-fault detection approach for the early battery faults without obvious voltage abnormality based on modified SampEn. The proposed approach can effectively forecast both the type and time of battery faults without the need of a precise battery model, which is independent of the inconsistency among cells. The al gorithm description, working principle, feasibility analyses, fault detection results under different conditions, and a comparison with the conventional detection methods are presented. Some conclusions can be obtained as: (1) By detecting the modified SampEn of the cell voltages, the pro posed fault detection method can effectively forecast the early battery faults even though the cell voltages are within the safe limits. (2) By introducing a coefficient α presenting the voltage fluctuation information, the proposed method can detect different battery faults, e.g., the short-circuit fault, open-circuit fault, and so on. (3) Decreasing the moving-window size N can dramatically increase the SampEn value of the abnormal voltages, leading to a high sensitivity to battery faults but a low sensitivity to measurement noise and disturbance. Increasing the moving window size N will decrease the SampEn value of the abnormal voltages, leading to a low sensitivity to battery faults but a high sensitivity to mea surement noise and disturbance. Studies show that the optimal moving-window size is 5. 11
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