RESEARCH ARTICLE
A Fletcher-Reeves conjugate gradient optimized multi-reservoir echo state network for state of charge estimation in vehicle battery
Tianyu Gu,
Dongqing Wang,
Meng Jiao,
Tianyu Gu
College of Electrical Engineering, Qingdao University, Qingdao, China
Search for more papers by this authorCorresponding Author
Dongqing Wang
College of Electrical Engineering, Qingdao University, Qingdao, China
Correspondence
Dongqing Wang, College of Electrical Engineering, Qingdao University, 308 Ningxia Road, Qingdao 266071, China.
Email: [email protected]
Search for more papers by this authorMeng Jiao
College of Electrical Engineering, Qingdao University, Qingdao, China
Search for more papers by this authorTianyu Gu,
Dongqing Wang,
Meng Jiao,
Tianyu Gu
College of Electrical Engineering, Qingdao University, Qingdao, China
Search for more papers by this authorCorresponding Author
Dongqing Wang
College of Electrical Engineering, Qingdao University, Qingdao, China
Correspondence
Dongqing Wang, College of Electrical Engineering, Qingdao University, 308 Ningxia Road, Qingdao 266071, China.
Email: [email protected]
Search for more papers by this authorMeng Jiao
College of Electrical Engineering, Qingdao University, Qingdao, China
Search for more papers by this authorFunding information: National Natural Science Foundation of China, Grant/Award Number: 61873138
Summary
This paper investigates a Fletcher-Reeves conjugate gradient optimized multi-reservoir echo state network (FRCG-MESN) to identify battery state of charge (SOC). First, an echo state network with multiple reservoirs is established to estimate battery SOC by using its discharge terminal voltage and current as the inputs, and the FR conjugate gradient algorithm is explored to tune the output weights of the MESN to avoid calculating the inverse matrix. Second, an appropriate amount of Gaussian noise with zero mean is added to the training set to prevent overfitting. Finally, a battery test platform is adopted to sample the discharging data under two working conditions: the Los Angeles 92 and the urban dynamometer driving schedule. The simulation results show that the presented FRCG-MESN method can accurately identify the battery SOC with different initial SOCs. Applying an appropriate amount of noise to the training set can prevent overfitting efficiently.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.
REFERENCES
- 1Jiang C, Wang SL, Wu B, Fernandez C, Xiong X, Coffie-Ken J. A state-of-charge estimation method of the power lithium-ion battery in complex conditions based on adaptive square root extended Kalman filter. Energy. 2021; 219:119603. doi:10.1016/j.energy.2020.119603
- 2Bian C, Yang SK, Miao Q. Cross-domain state-of-charge estimation of Li-ion batteries based on deep transfer neural network with multiscale distribution adaptation. IEEE Trans Transp Electrif. 2021; 7(3): 1260-1270. doi:10.1109/TTE.2020.3041604
- 3Din MSE, Hussein AA, Abdel-Hafez MF. Improved battery SOC estimation accuracy using a modified UKF with an adaptive cell model under real EV operating conditions. IEEE Trans Transp Electrif. 2018; 4(2): 408-417. doi:10.1109/TTE.2018.2802043
- 4Hong JC, Wang ZP, Chen W, Wang LY, Qu GH. Online joint-prediction of multi-forward-step battery SOC using LSTM neural networks and multiple linear regression for real-world electric vehicles. J Energy Storage. 2020; 3:101459. doi:10.1016/j.est.2020.101459
- 5Li Z, Huang J, Liaw BY, Zhang JB. On state-of-charge determination for lithium-ion batteries. J Power Sources. 2017; 348: 281-301. doi:10.1016/j.jpowsour.2017.03.001
- 6Guo YJ, Yang ZL, Liu KL, Zhang YH, Feng W. A compact and optimized neural network approach for battery state-of-charge estimation of energy storage system. Energy. 2021; 219:119529. doi:10.1016/j.energy.2020.119529
- 7Lipu MSH, Hannan MA, Hussain A, et al. A review of state of health and remaining useful life estimation methods for lithium-ion battery in electric vehicles: challenges and recommendations. J Cleaner Prod. 2018; 205: 115-133. doi:10.1016/j.jclepro.2018.09.065
- 8Ng KS, Moo CS, Chen YP, Hsieh YC. Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries. Appl Energy. 2009; 86(9): 1506-1511. doi:10.1016/j.apenergy.2008.11.021
- 9Li ZJ, Ding J, Lin JX. Discrete fractional order PID controller design for nonlinear systems. Int J Syst Sci. 2021; 52(15): 3206-3213. doi:10.1080/00207721.2021.1924307
- 10Ding J, Chen LJ, Cao ZX, Guo HH. Convergence analysis of the modified adaptive extended Kalman filter for the parameter estimation of a brushless DC motor. Int J Robust Nonlinear Control. 2021; 31(16): 7606-7620. doi:10.1002/rnc.5706
- 11Wang D, Yang FF, Tsui KL, Zhou Q, Bae SJ. Remaining useful life prediction of lithium-ion batteries based on spherical cubature particle filter. IEEE Trans Instrum Meas. 2016; 65(6): 1282-1291. doi:10.1109/tim.2016.2534258
- 12Feng L, Ding J, Han YY. Improved sliding mode based EKF for the SOC estimation of lithium-ion batteries. Ionics. 2020; 26: 2875-2882. doi:10.1007/s11581-019-03368-9
- 13Li YW, Wang C, Gong JF. A multi-model probability SOC fusion estimation approach using an improved adaptive unscented Kalman filter technique. Energy. 2017; 141: 1402-1415. doi:10.1016/j.energy.2017.11.079
- 14Sun FC, Hu XS, Zou Y, Li SG. Adaptive unscented Kalman filtering for state of charge estimation of a lithium-ion battery for electric vehicles. Energy. 2011; 36(5): 3531-3540. doi:10.1016/j.energy.2011.03.059
- 15Liu MZ, He MF, Qiao SJ, Liu BL, Cao ZH, Wang RL. A high-order state-of-charge estimation model by cubature particle filter. Measurement. 2019; 146: 35-42. doi:10.1016/j.measurement.2019.05.040
- 16Ye M, Guo H, Cao BG. A model-based adaptive state of charge estimator for a lithium-ion battery using an improved adaptive particle filter. Appl Energy. 2017; 190: 740-748. doi:10.1016/j.apenergy.2016.12.133
- 17Cui XY, Jing Z, Luo MJ, Guo YZ, Qiao HM. A new method for state of charge estimation of lithium-ion batteries using square root cubature Kalman filter. Energies. 2018; 11(1): 209. doi:10.3390/en11010209
- 18Li WQ, Yang Y, Wang DQ, Yin SQ. The multi-innovation extended Kalman filter algorithm for battery SOC estimation. Ionics. 2020; 26(12): 6145-6156. doi:10.1007/s11581-020-03716-0
- 19Yao JX, Ding J, Cheng YY, Feng L. Sliding mode based H-infinity filter for SOC estimation of lithium-ion batteries. Ionics. 2021; 27(12): 5147-5157. doi:10.1007/s11581-021-04234-3
- 20Muhammad S, Rafique MU, Li S, Shao ZL, Wang QX, Guan N. A robust algorithm for state-of-charge estimation with gain optimization. IEEE Trans Ind Inform. 2017; 13(6): 2983-2994. doi:10.1109/TII.2017.2699219
- 21Chemali E, Kollmeyer PJ, Preindl M, Emadi A. State-of-charge estimation of Li-ion batteries using deep neural networks: a machine learning approach. J Power Sources. 2018; 400: 242-255. doi:10.1016/j.jpowsour.2018.06.104
- 22Chaoui H, Ibe-Ekeocha CC. State of charge and state of health estimation for lithium batteries using recurrent neural networks. IEEE Trans Veh Technol. 2017; 66(10): 8773-8783. doi:10.1109/TVT.2017.2715333
- 23Jiao M, Wang DQ, Yang Y, Liu F. More intelligent and robust estimation of battery state-of-charge with an improved regularized extreme learning machine. Eng Appl Artif Intel. 2021; 104(2):104407. doi:10.1016/j.engappai.2021.104407
- 24Jiao M, Yang Y, Wang DQ, Gong P. The conjugate gradient optimized regularized extreme learning machine for estimating state of charge. Ionics. 2021; 27(11): 4839-4848. doi:10.1007/s11581-021-04169-9
- 25Jiao M, Wang DQ. The Savitzky-Golay filter based bidirectional long short-term memory network for SOC estimation. Int J Energy Res. 2021; 45(13): 19467-19480. doi:10.1002/er.7055
- 26Jiao M, Wang DQ, Qiu JL. A GRU-RNN based momentum optimized algorithm for SOC estimation. J Power Sources. 2020; 459:228051. doi:10.1016/j.jpowsour.2020.228051
- 27Ma L, Hu C, Cheng F. State of charge and state of energy estimation for lithium-ion batteries based on a long short-term memory neural network. J Energy Storage. 2021; 37:102440. doi:10.1016/j.est.2021.102440
- 28Ruder S. An overview of gradient descent optimization algorithms. Comput Sci. 2016. 10.48550/arXiv.1609.04747.
- 29Kingma DP, Ba J. Adam: a method for stochastic optimization. Comput Sci. 2014. 10.48550/arXiv.1412.6980.
- 30Jaeger H, Haas H. Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science. 2004; 304(5667): 78-80. doi:10.1126/science.1091277
- 31Zhou HW, Huang JQ, Lu F, Thiyagalingam J, Kirubarajan T. Echo state kernel recursive least squares algorithm for machine condition prediction. Mech Syst Signal Process. 2018; 111: 68-86. doi:10.1016/j.ymssp.2018.03.047
- 32Chitsazan MA, Fadali MS, Trzynadlowski AM. Wind speed and wind direction forecasting using echo state network with nonlinear functions. Renew Energy. 2019; 131: 879-889. doi:10.1016/j.renene.2018.07.060
- 33Zhang SH, Sun ZZ, Wang M, Long JY, Bai Y, Li C. Deep fuzzy echo state networks for machinery fault diagnosis. IEEE Trans Fuzzy Syst. 2020; 28(7): 1205-1218. doi:10.1109/TFUZZ.2019.2914617
- 34Hua ZG, Zheng ZX, Pera MC, Gao F. Remaining useful life prediction of PEMFC systems based on the multi-input echo state network. Appl Energy. 2020; 265:114791. doi:10.1016/j.apenergy.2020.114791
- 35Fletcher R, Reeves CM. Function minimization by conjugate gradients. Comput J. 1964; 7(2): 149-154. doi:10.1093/comjnl/7.2.149
- 36Polyak BT. The conjugate gradient method in extremal problems. USSR Comput Math Math Phys. 1969; 9(4): 94-112. doi:10.1016/0041-5553(69)90035-4
10.1016/0041-5553(69)90035-4 Google Scholar
- 37Zhang L, Zhou WJ, Li DH. A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence. IMA J Numer Anal. 2006; 26(4): 629-640. doi:10.1093/imanum/drl016
- 38Li M, Li DH. A modified conjugate-descent method and its global convergence. Pac J Optim. 2012; 8(2): 47-259. doi:10.1007/s11590-011-0295-1
- 39Dai YH, Yuan Y. A nonlinear conjugate gradient method with a strong global convergence property. SIAM J Optim. 1999; 10(1): 177-182. doi:10.1137/S1052623497318992
- 40Shi ZJ, Shen J. Convergence of Liu-Storey conjugate gradient method. Eur J Oper Res. 2007; 182(2): 552-560. doi:10.1016/j.ejor.2006.09.066
- 41Wang DQ, Li LW, Ji Y, Yan YR. Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method. Appl Math Model. 2018; 54: 537-550. doi:10.1016/j.apm.2017.10.005
- 42Wang DQ, Zhang S, Gan M, Qiu JL. A novel EM identification method for Hammerstein systems with missing output data. IEEE Trans Ind Inform. 2020; 16(4): 2500-2508. doi:10.1109/TII.2019.2931792
