Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 105 (2017) 2354 – 2359
The 8th International Conference on Applied Energy – ICAE2016
Real-time fault diagnosis method of battery system based on Shannon entropy Zhenyu Suna,b, Peng Liua,b,*, Zhenpo Wanga,b a
Collaborative Innovation Center of Electric Vehicles in Beijing , NO.5 South Street, Zhongguancun, Beijing, 100081, China b Beijing Institute of Technology, NO.5 South Street, Zhongguancun, Beijing, 100081, China
Abstract
Ensuring the safety of the power battery is of great significance to make the diagnosis more effective and predict the occurrence of fault because power battery is one of the key technologies of electric vehicles. In this paper, decomposition with 3 layers developed by Daubechies is used to deal with the collected noisy voltage signal of lithium-ion battery from the experiment, which can get relatively smooth voltage signal and eliminate noise interference. A diagnostic method of using Shannon entropy is proposed to process measured data after wavelet transform, and we get a relatively reasonable parameters l = 50 with analysis of interval parameters l. After the 10th cycle, fault of NO.1 cell can be accurately found through calculating Shannon entropy of charge and discharge cycles. The method proposed in this paper can achieve real-time diagnosis but it is easily affected by interval parameter l. © 2017 TheThe Authors. Published by Elsevier Ltd.by ThisElsevier is an open access © 2016 Authors. Published Ltd. article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review undercommittee responsibility of ICAEConference on Applied Energy. Peer-review under responsibility of the scientific of the 8th International Keywords: Shannon entropy; wavelet transform; lithium-ion battery;fault prediction;
1.
Introduction
With the advent of the energy crisis and shortage of resources, a lot of money and resources have been invested to develop renewable energy by many countries, which makes EVs become one of the most promising technology. The most obvious advantage of electric car batteries is that they don't produce the pollution associated with internal combustion engines. However, the drawbacks of short driving ranges and high costs remain obstacles to the rise of EV industry. The disadvantages of EVs are inherited from the expensive power batteries and their energy densities [1]. The battery is a key component of electric cars, but also the major source of failure of electric vehicles. Research on power battery system fault, it can effectively diagnose battery fault, forecasting the occurrence of battery system failure and improving battery life. The project was supported by the Joint Funds of the National Natural Science Foundation of China (No. U1564206). * Corresponding author. Tel.:+010-59419650.fax:+010-68940589 E-mail address:
[email protected],
[email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.676
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Gu W et al[2] indicate the existence of the side effect caused the battery capacity attenuation in the process of the use of lithium ion batteries. In the circulation of charge and discharge process for lithium ion battery, the main side effects and the irreversible capacity attenuation mechanism are caused by many factors. Kim. G [3] introduces a fail-safe design methodology for large-capacity lithium-ion battery systems. Analysis using an internal short circuit response model for multi-cell packs is presented that demonstrates the viability of the proposed concept for various design parameters and operating conditions. Saha B et al[4] explore how the remaining useful life(RUL) can be assessed for complex systems whose internal state variables are either inaccessible to sensors or hard to measure under operational conditions, and think that the most significant challenges for making prognostic predictions are the inherent uncertainties in the system model, external and internal noise, and sensor errors. Meanwhile, they implement a refinement of the PF prognostic framework to further reduce the prediction uncertainty. Yao L et al [5] conduct an experiment to get voltage and use ensemble Shannon entropy to predict battery fault of battery connection failure in real time. Zheng Y et al[6]present a battery pack system in a demonstrated EV with 96 cells in series, and discover the battery power fade fault during the demonstration, introduce an equivalent circuit model (ECM) and identify Fig. 1. The current curve. the cell resistances using the total least squares algorithm. They use the identified cell resistances from 3 months demonstration data to propose a diagnostic method. In this paper, the vibration experiment of the lithium ion battery is done, its platform consisting of a vibrating test bench, the information collecting device, a battery system. Placed above the vibration test bench, battery system is composed of four cells and its connection system that contains the connecting pieces and measuring wires bolted onto the cells' electrodes. At the beginning of the experiment, the connecting nut on cell 1 is loose. The Fig.1 shows the current curve of the charge and discharge cycle experiments, then the voltage data is obtained. 2.
Wavelet transform denoising method
2.1 wavelet theory Wavelet transform is a method about time-scale (Time - Frequency) analysis that has the characteristics of multi-resolution analysis and the ability to characterize the local signal in the time and frequency domain. [7]. Compared to the Fourier transform, wavelet transform has the ability of processing transient signal. Any signal or function f (t ) is defined in the function space or the signal space L2 ( R) . WTf (D ,W ) of f (t ) expansion based on continuous wavelet basis M (D ,W ) (t ) is called continuous wavelet transform.
WT f (D ,W )
Where M D ,W
1
D
§ t W · ¸, C © D ¹ M
M¨
³
M (v ) v
1
D
³ f (t )M
( D ,W )
(t )dt
(1)
R
dv f , and D is a scaling factor (scale), b is translation
factor. Continuous wavelet transform coefficients are coupled and repetitive, requiring further processing during the actual application process. Parameter D and W being a discretization could get the discrete wavelet transform. Discrete wavelet transform is to take discrete values for scale and displacement under the condition of without loss of information to reduce the number of wavelets.
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After discretization of scaling factor and translation factor, discrete wavelet base MD0m , kW 0 and discrete m wavelet transform WTf (D 0 , kW 0 ) can be obtained using formula (1):
MD
m 0 , kW 0
m2
D 0 M (D 0 mt kW 0 ) m2
WT f (D 0m , kW 0 ) D 0
³ f (t )M (D
m 0
(2)
t kW 0 )dt
(3)
R
Wavelet transform sampling step is regulatory for different frequency in the time domain. At low frequencies, the wavelet transform has lower temporal resolution and higher frequency resolution; on the contrary, it has higher temporal resolution and lower frequency resolution at high frequencies, which is consistent with that the low-frequency signal changes slowly and high frequency signal convert rapidly. This is why it is superior to the classical local Fourier transform [8]. 2.2 Wavelet decomposition and reconstruction Noisy signal can be expressed as S (i) f (i) e(i) i 0,1, 2,3 N (4) S ( i ) f ( i ) e ( i ) is noisy raw signal, is noise free signal, is noisy signal. Where Wavelet decomposition use different layers to obtain different low frequency signal and high frequency signals, specific principle as shown in Fig. 2 [9]. Specific processing steps are as follows: a) Noisy raw signal S is divided into high frequency A1 and low frequency signals D1 after first layer of decomposition; b) Signal A1 is divided into low frequency signal A2 and high frequency signal D2 under secondary wavelet decomposition; c) According to this principle, low frequency signal is processed by wavelet transform until it reaches the goal of wavelet decomposition layer. Define function about noisy raw signal S after n layer decomposition S An D1 D2 Dn (5) high frequency signal D1
high frequency signal D2
high frequency signal Dn
low frequency signal A1
low frequency signal A2
low frequency signal An
noisy raw signal S
Fig. 2. Signal decomposition principle diagram
After the completion of the wavelet decomposition, wavelet analysis use threshold to eliminate the high frequency signal. If it is above the threshold, the high frequency signal have been removed; finally, the signal after the wavelet decomposition and threshold processing is reconstructed. Common wavelet basis functions cover Haar wavelet, Mexican Hat wavelet, Symlets wavelet, Daubechies wavelets and so on. In this paper, Daubechies wavelet is adopted according the reference [9]. 2.3 result According to the article of Yao [5], noise is mainly concentrated on the high frequency region, so it is necessary to remove part of the high frequency signal. If wavelet decomposition level is higher, the greater the proportion of the high-frequency signal is removed, but the decomposition level being too large will lead to the loss of its peak characteristic for the voltage curve in Fig.3. In this paper, the wavelet decomposition level i = 3 is selected. The sweep-frequency vibration test is taken for the battery pack, and when the battery pack is charge and discharged, the terminal voltage is measured. Using the method of db3 for Daubechies wavelet can process
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the four cells’ data. Finally the voltage curves of the5th, 10th, 15th, 20th cycle for charging and discharging are shown in Fig. 4.
(a) i=1
(b) i=3 (c) i=5 Fig. 3. Voltage curve of different wavelet decomposition level
(a) the 5th cycle
(b) the 10th cycle
(c) the 15th cycle (d) the 20th cycle Fig.4. Charging and discharging voltage curve. (a) the 5th cycle, (b) the 10th cycle ,(c) the 15th cycle,(d) the 20th cycle.
3.
Fault diagnosis method
3.1 Shannon Entropy Generally, entropy refers to disorder or uncertainty. Shannon entropy was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication". It provides an absolute limit on the best possible average length of lossless encoding or compression of an information source. The formula of the Shannon entropy is n
H (X )
¦ p( xi ) logb p( xi ) i 1
(6)
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Where H(X) is the Shannon entropy, p(xi) is the probability density of data in the 3th interval and n is the number of the interval. b is the base of the logarithm used. Common values of b is 2. When b = 2, the units of entropy are also commonly referred to as bits. Using entropy method is to detect fault voltage. Larger entropy indicated data is scattered. On the contrary, the smaller the Shannon entropy value means that less data changes. A larger Shannon entropy value for the cell voltage is thus more likely to be the contact resistance fault than the internal resistance fault. [6] The calculation processes based on Shannon entropy are as follows: (1) Form matrix Ak un of cell voltage and obtain two extremum of matrix A: , xmin
min ^x(i, j ) i
1, 2,3
k; j
1, 2,3
n` xmax
Where l is the number of the interval, O (3) calculate H ( x) :
0,1, 2
H ( x) bij
l H ¦ i 1 bij , j
Obtain a set of data for cell
1, 2,3
k; j
x x x x O max min , xmin (O 1) max min ) ,form B l l
(2) bi , j is the number of x ( xmin
Where pij
max ^x(i, j ) i
1, 2,3
ªb11 « « «¬ bl1
n`
b1n º » » bln »¼
l
ª¬ H1 , H 2
H j º¼
(7)
l
¦ pij log pij i 1
Interval partition
Calculate the probability of each interval data
Shannon entropy
Fig.5. Shannon entropy calculation process
3.2 Result and analysis Entropy value of each cell is calculated in each cycle whose time is 3 minutes, which can make the relation of cycles and entropy. And then entropy curve in Fig.6 is obtained according to different interval l. With the increase of interval l, entropy valve enlarges, which indicates larger chaos degree of the information. As shown in Fig.6, entropy of NO. 1 cell is obviously different from others after the 10th cycle with the interval parameter l being larger besides the l = 5. NO. 1 cell presents exceptions because its Shannon entropy value is clearly bigger than others after the (a)l=5 (b) l=10 12th cycle. In the case of a certain interval l, Shannon entropy value is stable from the 1th to 10th cycle. However, the smaller entropy value appears after the 10th cycle, which shows that consistent voltage data of NO.2,3,4 cell go up . (c) l=50 (d) l=100 Fig.6 entropy curve for different interval l.
Zhenyu Sun et al. / Energy Procedia 105 (2017) 2354 – 2359
Using interval l=5, the data points from the first to the 700th of voltage are processed when n=5,10,15,30, and Fig. 7 can be obtained through computing the probability of each cell in the third interval . Combined to charging and discharging current curve, a mass of data is in the third interval. It can be seen that the probability of the voltage data for NO. 1 cell gradually reduce after the 10th cycle, but trend of probability for the other three cells is stable, which describes abnormal voltage fluctuation of NO. 1 cell. Therefore, NO.1 cell will be recognized to be fault state. And also NO.1 cell is have virtual fault through examining experimental device. With the test going on, it is obviously observed that the nut on NO.1 cell has been rotated and some sparkle has been detected in the battery connector because of vibration. NO.1 cell has indeed a problem according to the conclusion of Fig. 6 Fig.7. the relation of popularity and cycle-index and Fig.7, which is consistent with experimental phenomena. So the method of Shannon entropy is effective. 4.
Conclusion
Due to the presence of noise, there will be noise pollution for the voltage, so it is very important to deal with the noise voltage curve. Using wavelet analysis to filter, this paper has accurately described the change about characteristic quantity in the process of charging and discharging. At the same time different from the reference [5] which adopted iteration of Shannon entropy, the method proposed in this paper makes relatively calculation simplified and data processing hardware system lower. To calculate entropy whose change can effectively detect the battery fault. When l is 50, abnormal cell can be clearly observed after the 10th cycle in this experiment. In the future, the condition of entropy value influenced by the probability will be researched because the Shannon entropy is determined by the probability not position. References [1] Wagner F T, Lakshmanan B, Mathias M F. Electrochemistry and the future of the automobile[J]. J. Phys. Chem. Lett, 2010, 1(14): 2204-2219. [2]Gu W, Sun Z, Wei X, et al. A Capacity Fading Model of Lithium-Ion Battery Cycle Life Based on the Kinetics of Side Reactions for Electric Vehicle Applications[J]. Electrochimica Acta, 2014, 133(7):107–116. [3] G. Kim, K. Smith, J. Ireland, A. Pesaran, Fail-safe design for large capacity lithium-ion battery systems, J. Power Sources 210 (2012) 234e253. [4] Saha B, Goebel K, Poll S, et al. Prognostics methods for battery health monitoring using a Bayesian framework[J]. IEEE Transactions on Instrumentation and Measurement, 2009, 58(2): 291-296. [5] Yao L, Wang Z, Ma J. Fault detection of the connection of lithium-ion power batteries based on entropy for electric vehicles[J]. Journal of Power Sources, 2015, 293: 548-561. [6] Zheng Y, Han X, Lu L, et al. Lithium ion battery pack power fade fault identification based on Shannon entropy in electric vehicles[J]. Journal of Power Sources, 2013, 223: 136-146. [7] Defeng Zhang. Matlab wavelet analysis and engineering application [M], Beijing : National Defense Industry Press , 2008 . [8] Fei Tan. Fault Diagnosis and Implementation of Electric Vehicle Lithium-ion Battery System.2015. [9] Peikun Sun. Research of State of Health Estimation Method for Electric Vehicle Lithium-ion Power Battery. 2016.
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