宋顯華 姚全正
基于片段充電數(shù)據(jù)和DEKF-WNN-WLSTM的鋰電池健康狀態(tài)實(shí)時估計(jì)
宋顯華 姚全正
(哈爾濱理工大學(xué)理學(xué)院 哈爾濱 150080)
實(shí)時準(zhǔn)確地評估電動汽車鋰電池健康狀態(tài)(SOH)對電動汽車的穩(wěn)定行駛至關(guān)重要。因此,該文提出一種基于鋰電池日常片段充電數(shù)據(jù)和雙擴(kuò)展卡爾曼濾波-小波神經(jīng)網(wǎng)絡(luò)-小波長短時記憶神經(jīng)網(wǎng)絡(luò)(DEKF-WNN-WLSTM)的電池全充時間估計(jì)模型,進(jìn)而提高了片段充電數(shù)據(jù)評估電池健康狀態(tài)的準(zhǔn)確度。首先,設(shè)計(jì)雙擴(kuò)展卡爾曼濾波預(yù)測-校正算法,分別用來估計(jì)片段充電數(shù)據(jù)對應(yīng)的全充時間和校正擴(kuò)展卡爾曼濾波的狀態(tài)初值,以提高估計(jì)的準(zhǔn)確性。然后,設(shè)計(jì)了小波神經(jīng)網(wǎng)絡(luò)-小波長短時神經(jīng)網(wǎng)絡(luò)來學(xué)習(xí)擴(kuò)展卡爾曼濾波遞推過程的觀測值。最后,通過實(shí)驗(yàn)仿真,驗(yàn)證了所提算法在鋰電池健康狀態(tài)實(shí)時估算中的準(zhǔn)確性和有效性。
電池健康狀態(tài) 片段數(shù)據(jù) 雙擴(kuò)展卡爾曼濾波 小波神經(jīng)網(wǎng)絡(luò) 小波長短時記憶神經(jīng)網(wǎng)絡(luò)
由于鋰電池具有重量輕、壽命長、效率高、成本低等優(yōu)點(diǎn),是電動汽車的主要動力來源[1],因此對于電動汽車的鋰電池進(jìn)行性能評價具有重要意義。通常情況下,鋰電池通過電池管理系統(tǒng)(Battery Management System, BMS)進(jìn)行性能評價[2]。BMS的評價指標(biāo)主要包括荷電狀態(tài)(State of Charge, SOC)、剩余使用壽命(Remaining Useful Life, RUL)和健康狀態(tài)(State of Health, SOH)[3-5]。一般來說,SOH描述電池長期的狀態(tài)變化,因此獲得準(zhǔn)確的SOH估計(jì)值對于電池長期安全穩(wěn)定的使用至關(guān)重要。
主要的SOH評估方法可以分為三類:直接測量法、基于經(jīng)驗(yàn)的方法和數(shù)據(jù)驅(qū)動方法。典型的直接測量法是通過累積電流積分測量電池的SOH[6]。但在實(shí)際應(yīng)用中,該方法對電流采樣精度敏感,應(yīng)用效果不佳。電化學(xué)阻抗譜(Electrochemical Impedance Spectroscopy, EIS)是另一種直接方法[7-8],通過分析電池在不同頻率下的交流阻抗譜,得到電池內(nèi)部的化學(xué)狀態(tài),進(jìn)而評價電池的外部特征。然而電池內(nèi)部參數(shù)的采集需要特殊且昂貴的設(shè)備,且參數(shù)分析過程復(fù)雜?;诮?jīng)驗(yàn)的方法包括周期計(jì)數(shù)法、面向事件的累積法、安時法以及加權(quán)安時法等[9]。然而,在實(shí)際應(yīng)用中,電池的工作條件往往與標(biāo)準(zhǔn)工作條件不一致,這將導(dǎo)致較大的估計(jì)誤差。最后一個主流的方法是數(shù)據(jù)驅(qū)動方法,該方法通過學(xué)習(xí)隱藏于數(shù)據(jù)中的信息來估計(jì)SOH,不需要電池系統(tǒng)的先驗(yàn)知識。因此,數(shù)據(jù)驅(qū)動方法可以避免模型獲取困難的問題,是一種更加實(shí)用的估計(jì)方法。
支持向量機(jī)(Support Vector Machine, SVM)是一種常用的數(shù)據(jù)驅(qū)動算法,它通過核函數(shù)將低緯度空間的非線性問題映射到高緯度空間[10]的線性問題來估計(jì)SOH,但該方法不易選擇合適的核函數(shù)且對交叉訓(xùn)練和正則化方法依賴程度高。相關(guān)向量機(jī)(Relevance Vector Machine, RVM)的原理與支持向量機(jī)大致相同,不同的是其網(wǎng)絡(luò)權(quán)值是用稀疏貝葉斯理論結(jié)構(gòu)獲得的[11]。然而,由于RVM模型的稀疏矩陣,RVM對訓(xùn)練數(shù)據(jù)的需求較高且預(yù)測結(jié)果的穩(wěn)定性較差。高斯過程回歸(Gaussian Process Regression, GPR)是另一種基于貝葉斯框架的估計(jì)方法[12-13],但該算法中超參數(shù)較多,訓(xùn)練中調(diào)整過程繁瑣?;谏窠?jīng)網(wǎng)絡(luò)的方法作為一種高效的數(shù)據(jù)驅(qū)動方法,正在成為電池性能評估的主流方法[14-18]。其中,小波神經(jīng)網(wǎng)絡(luò)(Wavelet Neural Network, WNN)結(jié)合自學(xué)習(xí)和非線性函數(shù)逼近能力,具有精度高和細(xì)節(jié)描述能力強(qiáng)的優(yōu)點(diǎn)[19-20]。J. Zhang等提出了將離散小波多分辨率分解與多層感知器相結(jié)合的四層小波神經(jīng)網(wǎng)絡(luò),與反向傳播神經(jīng)網(wǎng)絡(luò)(Back Propagation Neural Networks, BPNN)相比具有較好的預(yù)測性能。但該方法局限于多分辨率分析,結(jié)構(gòu)不靈活且魯棒性不強(qiáng)[21]。Xia Bizhong等通過引入小波伸縮因子和小波平移因子,調(diào)整小波神經(jīng)網(wǎng)絡(luò)的結(jié)構(gòu),使網(wǎng)絡(luò)具有較強(qiáng)的魯棒性[22]。但由于它只是一個三層網(wǎng)絡(luò),其估計(jì)精度遠(yuǎn)遠(yuǎn)低于深度網(wǎng)絡(luò)。與BPNN相比,循環(huán)神經(jīng)網(wǎng)絡(luò)(Recurrent Neural Network, RNN)可以保存輸入數(shù)據(jù)與SOH值之間的信息,因此常被用于SOH估計(jì)[23]。但由于梯度消失和梯度爆炸的問題,RNN無法用于長期估計(jì)。為了解決這一問題,引入了長短時記憶神經(jīng)網(wǎng)絡(luò)(Long Short Term Memory, LSTM)[24-26]。LSTM具有單元狀態(tài),可以保存輸入和輸出之間的重要信息。然而,由于LSTM的單元特性,當(dāng)測試數(shù)據(jù)與訓(xùn)練數(shù)據(jù)之間的相關(guān)性不高時,其估計(jì)效果不好,意味著該方法的魯棒性不強(qiáng)。
因此,本文設(shè)計(jì)了一種小波神經(jīng)網(wǎng)絡(luò)和小波長短時記憶神經(jīng)網(wǎng)絡(luò)(Wavelet LSTM, WLSTM)。該網(wǎng)絡(luò)包括輸入層、兩個隱藏層和輸出層。雙隱層由WNN層和WLSTM層組成,WLSTM層的激活函數(shù)用Morlet小波函數(shù)代替。因此,該網(wǎng)絡(luò)同時具有WNN和LSTM的優(yōu)點(diǎn)。
此外,為了能夠更安全穩(wěn)定地使用純電力電動汽車,隨時了解電池當(dāng)前時刻的健康狀態(tài)是十分有必要的,即實(shí)時估計(jì)電池的SOH。然而,鋰電池是一個機(jī)制復(fù)雜、內(nèi)部狀態(tài)未測量的綜合系統(tǒng),SOH的在線估計(jì)通常依賴電池模型和關(guān)鍵參數(shù)之間的擬合關(guān)系。電池模型參數(shù)反映電池內(nèi)部的動態(tài)響應(yīng),并會隨著電池的退化而發(fā)生相應(yīng)的變化。程澤等[27]在二階RC網(wǎng)絡(luò)等效電路模型的基礎(chǔ)上,聯(lián)合Sage-Husa自適應(yīng)濾波思想,設(shè)計(jì)了自適應(yīng)平方根無跡卡爾曼濾波(Adaptive Square Root Unscented Kalman Filter, ASRUKF)算法;通過對電池參數(shù)的實(shí)時更新,實(shí)現(xiàn)電池SOH的實(shí)時估計(jì),雖然不涉及電化學(xué)分析過程,但是其電池特性變化的分析過程依舊較復(fù)雜。
王萍等[28]提出了一種基于數(shù)據(jù)驅(qū)動和經(jīng)驗(yàn)?zāi)P徒Y(jié)合的在線實(shí)時估計(jì)方法。其實(shí)時估計(jì)的核心為在固定循環(huán)次數(shù)下,利用觀測器對模型的參數(shù)進(jìn)行更新。該方法雖然實(shí)現(xiàn)了預(yù)測SOH的實(shí)時性,減少了監(jiān)測器的負(fù)荷,但每次的參數(shù)更新需要離線操作,具有一定的不便性。
周頔等[29]用擴(kuò)展卡爾曼濾波和高斯過程回歸(Extended Kalman Filter and Gaussian Process Regression, EKF-GPR),不需要完成整個充放電操作,僅對日常片段充電數(shù)據(jù)進(jìn)行處理,通過估計(jì)片段數(shù)據(jù)的全充時間,進(jìn)而得到電池在當(dāng)前時刻的SOH,實(shí)現(xiàn)了電池的實(shí)時估計(jì),該方法的平均絕對誤差在2%以下,短期內(nèi)的評估值基本滿足現(xiàn)實(shí)要求,解決了短時間內(nèi)的動力電池鋰電池健康狀態(tài)的實(shí)時估計(jì)問題,具有一定的應(yīng)用價值,但長期的預(yù)測精度不理想。
為了解決實(shí)時估計(jì)的精度問題,本文設(shè)計(jì)了雙擴(kuò)展卡爾曼濾波-小波神經(jīng)網(wǎng)絡(luò)-小波長短時記憶神經(jīng)網(wǎng)絡(luò)(DEKF-WNN-WLSTM)模型,用一次全充數(shù)據(jù)和三次片段數(shù)據(jù)分別訓(xùn)練兩個WNN-WLSTM網(wǎng)絡(luò),然后將兩個訓(xùn)練好的網(wǎng)絡(luò)融入DEKF中,為EKF的循環(huán)遞推提供相應(yīng)的輸出值。此外,構(gòu)建雙EKF實(shí)現(xiàn)電池全充時間的實(shí)時估計(jì),其中第一個EKF用于估計(jì)片段數(shù)據(jù)對應(yīng)的全充時間;第二個EKF用來估計(jì)當(dāng)前循環(huán)下電池全充時間的估計(jì)值與真實(shí)值的誤差,并實(shí)時修正當(dāng)前循環(huán)次數(shù)下估計(jì)的全充時間,進(jìn)而為下次循環(huán)中第一個EKF提供較準(zhǔn)確的狀態(tài)初值。實(shí)驗(yàn)結(jié)果表明,本文所提算法的平均絕對誤差遠(yuǎn)遠(yuǎn)低于EKF-GPR,并且隨著循環(huán)次數(shù)的增加,DEKF-WNN-WLSTM的累積誤差也遠(yuǎn)遠(yuǎn)低于后者。
一般情況下,SOH的定義為
式中,M為測量放電容量;N為電池標(biāo)稱放電容量。該公式表示鋰電池在標(biāo)準(zhǔn)條件下從充滿狀態(tài)以一定倍率放電到截止電壓所放出的容量與其所對應(yīng)的標(biāo)稱容量的比值[29]。
用充電數(shù)據(jù)估算SOH具有簡便快捷的顯著優(yōu)勢,并且由文獻(xiàn)[29]可知:充電容量計(jì)算的SOH和放電容量計(jì)算的SOH具有一致性,因此,本文采用片段充電數(shù)據(jù)作為輸入,估計(jì)電池的全充時間,進(jìn)而估算電池的健康狀態(tài)是合理的。
電池容量是指在某種條件下,活性物質(zhì)參加電化學(xué)反應(yīng)所釋放電量的多少,有時也會將電池所能充入的最大電量作為電池容量。相同地,基于恒流充電的動力電池SOC計(jì)算公式為
基于式(4),定義基于充電容量的SOH為
該方法可以簡便地計(jì)算動力電池的SOC和SOH,缺點(diǎn)是電池需要從零容量充電至截止電壓,該過程費(fèi)時且不方便。
通常情況下,在充電效率一定時,電池從零容量開始充電至充滿狀態(tài)所用的時間越長,電池的容量也就越大。隨著電池不斷的循環(huán)充放電,其恒流充電時間在不斷縮短[30],這與SOH整體下降的趨勢一致。而在本文中,由式(5)可知,SOH和電池的充電時間成正比,二者具有較強(qiáng)的相關(guān)性,基于此,只要得到電池的全充時間,即可得到電池的SOH。
由于電動汽車在實(shí)際的使用情況較復(fù)雜,其動力電池的充電情況往往是片段的,而非完全充電,例如,SOC從30%或50%充至80%或100%的充電情況,就無法根據(jù)充電情況判斷出電池的實(shí)時全充時間和可用容量。本文基于該情況,同文獻(xiàn)[29],構(gòu)建利用從任意的起始SOC值處進(jìn)行恒流充電至100%這樣的片段數(shù)據(jù),估計(jì)鋰電池當(dāng)前的全充時間,進(jìn)而計(jì)算電池當(dāng)前時刻的SOH。
本節(jié)主要介紹基于DEKF-WNN-WLSTM算法并使用片段數(shù)據(jù)對電池的實(shí)時全充時間進(jìn)行預(yù)測。
擴(kuò)展卡爾曼濾波算法是由卡爾曼濾波轉(zhuǎn)變而來,其核心在于對非線性系統(tǒng)的局部線性化。該算法的實(shí)質(zhì)是基于遞歸估算的最優(yōu)自適應(yīng)算法。EKF是廣泛使用的非線性系統(tǒng)的最優(yōu)狀態(tài)估計(jì)算法[31]。一般情況下,擴(kuò)展卡爾曼濾波由狀態(tài)方程和測量方程組成,算法方程為
小波神經(jīng)網(wǎng)絡(luò)以全連接網(wǎng)絡(luò)和小波理論為基礎(chǔ),用小波分析理論構(gòu)建并改進(jìn)神經(jīng)網(wǎng)路結(jié)構(gòu),與通常使用的全連接神經(jīng)網(wǎng)絡(luò)相比(如BPNN),其激活函數(shù)被一組小波函數(shù)代替,這些函數(shù)由Morlet小波母函數(shù)產(chǎn)生[22]。
圖1 三層小波神經(jīng)網(wǎng)絡(luò)結(jié)構(gòu)
Fig.1 Schematic structure of the WNN
相比于循環(huán)神經(jīng)網(wǎng)絡(luò)(RNN)存在梯度消失和梯度爆炸等問題,長短時記憶神經(jīng)網(wǎng)絡(luò)在處理具有時間序列特性的數(shù)據(jù)時具有明顯的優(yōu)勢,因?yàn)楹笳哂幸粋€可以保存重要的信息記憶狀態(tài)。圖2描述了長短時記憶神經(jīng)網(wǎng)絡(luò)的細(xì)胞結(jié)構(gòu),它用遺忘門、輸入門、輸出門和記憶單元訓(xùn)練網(wǎng)絡(luò)。
圖2 LSTM的細(xì)胞結(jié)構(gòu)示意圖
該過程可以用公式表示為
最后獲得輸出為
圖3 WNN-WLSTM結(jié)構(gòu)示意圖
隱藏層二是小波長短時記憶層,該層的激活函數(shù)是Morlet小波函數(shù),因此,修改后的LSTM層公式(11)~式(14)和式(16)為
在式(17)~式(21)中為Morlet小波函數(shù)。此外,因?yàn)槭剑?6)中沒有激活函數(shù),所以WLSTM層依舊采用原公式。
調(diào)整后的WLSTM層依舊可以提取數(shù)據(jù)間的時間序列特征,實(shí)驗(yàn)表明WNN-WLSTM能夠?yàn)閿U(kuò)展卡爾曼濾波提供較為準(zhǔn)確的測量值。
損失函數(shù)用于量化模型預(yù)測值與實(shí)測值之間的差異,并根據(jù)差異更新網(wǎng)絡(luò)的各項(xiàng)參數(shù),本文所用的損失函數(shù)為
最小化損失函數(shù)是由優(yōu)化器確定的,本文選擇RMSprop優(yōu)化器。
本文提出的算法將WNN-WLSTM融入擴(kuò)展卡爾曼濾波中,采用兩個WNN-WLSTM網(wǎng)絡(luò)以及雙卡爾曼濾波提高系統(tǒng)模型預(yù)測性能,模型的流程如圖4所示,其中為循環(huán)的次數(shù)上限。
圖4 DEKF-WNN-WLSTM流程
步驟(2)~(4)為訓(xùn)練階段:該階段訓(xùn)練兩個WNN-WLSTM。
狀態(tài)方程為
測量方程為
步驟(5)~(10)為測試階段該階段,融合WNN-WLSTM和DEKF,估計(jì)片段數(shù)據(jù)對應(yīng)的全充時間
(6)擴(kuò)展卡爾曼濾波一:循環(huán)遞推
預(yù)測:
利用差商近似雅可比矩陣更新模型為
計(jì)算增益:
更新狀態(tài):
更新協(xié)方差:
狀態(tài)方程:
測量方程:
(8)擴(kuò)展卡爾曼濾波二:循環(huán)遞推
預(yù)測:
利用差商近似雅可比矩陣進(jìn)行更新模型:
計(jì)算增益
更新狀態(tài)
更新協(xié)方差
(9)預(yù)測全充時間與真實(shí)的全充時間的誤差
為了展示所提算法的有效性,本文選用深圳新威爾電子公司提供的三元鋰電池充放電數(shù)據(jù)庫進(jìn)行實(shí)驗(yàn),該電池首先在2 100 mA的恒流條件下充電,直到電池電壓達(dá)到8.4 V;然后在恒流2 100 mA水平下放電,直到電池電壓達(dá)到5.6 V,如圖5和圖6所示。實(shí)驗(yàn)首先驗(yàn)證了DEKF-WNN-WLSTM算法的有效性,然后和EKF-GPR算法做對比,驗(yàn)證本文算法準(zhǔn)確性,最后用DEKF算法估計(jì)的全充時間評估電池的健康狀態(tài)。
圖5 恒流充電模式
圖6 恒流放電模式
實(shí)驗(yàn)硬件設(shè)施采用Inter(R) Core(TM) i5-7200u CPU @ 2.50 GHz處理器,Windows7旗艦版64位操作系統(tǒng)和8 GB運(yùn)行內(nèi)存。編程軟件為Matlab 2018和Python 3.8,其中Python以深度學(xué)習(xí)框架Keras為支撐,實(shí)現(xiàn)了基于TensorFlow的WNN-WLSTM仿真模型的構(gòu)建,為Matlab構(gòu)建的雙卡爾曼濾波模型提供相應(yīng)的測量值。
圖7是估計(jì)的全充時間和真實(shí)的全充時間對比圖,可以看到,除個別變化較快的周期外,二者變化情況基本完全一致。這說明本文提出的DEKF-WNN-WLSTM算法能夠在較低的誤差范圍內(nèi)利用日常片段充電數(shù)據(jù)估計(jì)電池的全充時間。
圖7 估計(jì)的全充時間和真實(shí)的全充時間
圖8 估計(jì)全充時間的絕對誤差
圖9 估計(jì)全充時間的相對誤差
圖10 估計(jì)全充時間的相對誤差絕對值
為了進(jìn)一步證明所提方法的預(yù)測性能,本節(jié)與周頔等[29]提出的基于EKF-GPR方法進(jìn)行比較。圖11為兩種方法估計(jì)和真實(shí)的全充時間對比圖。從圖中可以看到:本文所提的算法相比于EKF-GPR更接近真實(shí)值,尤其是在循環(huán)次數(shù)為125~135和170~180時。這說明隨著循環(huán)次數(shù)的增加,DEKF-WNN-WLSTM方法能夠緩解一定的誤差增長,在不人為進(jìn)行一次全放全充操作以更新初始全充時間值的條件下,本文所提方法具有更好的估計(jì)效果。
圖11 兩種估計(jì)方法的結(jié)果比較
表1為兩種方法的平均相對誤差,DEKF-WNN-WLSTM的平均相對誤差為0.010 1,低于EKF-GPR的0.017 6,進(jìn)一步說明本文所提方法的準(zhǔn)確性高。
表1 兩種方法的平均相對誤差
Tab.1 The average relative error of the two methods
圖12~圖14分別為兩種估計(jì)方法的絕對誤差、相對誤差和相對誤差絕對值??梢园l(fā)現(xiàn):DEKF-WNN-WLSTM相對于EKF-GPR而言,其誤差曲線普遍低于后者,尤其是循環(huán)次數(shù)在165~180之間時,二者的誤差曲線相差最遠(yuǎn),這說明本文方法具有較好的預(yù)測能力。
圖12 兩種方法的絕對誤差
圖13 兩種方法的相對誤差
圖14 兩種方法的相對誤差絕對值
本文采用式(3)所示的基于充電容量評估電池SOH的模型。由式(2)和式(3)可得電池的SOH為
式中,()為第次循環(huán)的全充時間。
圖15 本文方法估計(jì)的SOH
圖16 兩種方法估計(jì)的SOH
本文提出了基于DEKF-WNN-WLSTM和日常片段充電數(shù)據(jù)的鋰電池健康狀態(tài)估計(jì)算法,其核心為利用小波神經(jīng)網(wǎng)絡(luò)-小波長短時記憶神經(jīng)網(wǎng)絡(luò)優(yōu)秀的學(xué)習(xí)和預(yù)測性能,去學(xué)習(xí)擴(kuò)展卡爾曼濾波的量測方程,在一定的噪聲假設(shè)下,可以實(shí)現(xiàn)電池健康狀態(tài)的實(shí)時預(yù)測,有利于電池的維護(hù)以及電動汽車在現(xiàn)實(shí)生活中的廣泛使用。實(shí)驗(yàn)仿真結(jié)果表明,相比于EKF-GPR電池SOH實(shí)時估計(jì)模型,本文所提方法能夠有效緩解誤差的累積,且短期內(nèi)的預(yù)測值和真實(shí)值的差異基本可以控制在1%左右。最后,利用充電容量估算SOH模型,實(shí)現(xiàn)了電池SOH的實(shí)時評估。
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Real-Time State of Health Estimation for Lithium-Ion Batteries Based on Daily Segment Charging Data and Dual Extended Kalman Filters-Wavelet Neural Network-Wavelet Long Short-Term Memory Neural Network
Song Xianhua Yao Quanzheng
(School of Science Harbin University of Science and Technology Harbin 150080 China)
As a clean technology to solve carbon emissions, electric vehicles have been widely used in modern vehicles. Due to its high energy density, light weight, long life and low self discharge, lithium-ion batteries have become the main energy storage equipment of electric vehicles. Real time and accurate evaluation of the state of health (SOH) of the lithium batteries is critical to the stable driving of electric vehicles. However, most traditional SOH forecast methods are offline, which makes it difficult to obtain the SOH of the batteries in real time. Recently, some methods were presented to forecast the SOH of lithium-ion batteries, but most of them suffered from inconvenient adjustment of battery model parameters and accumulation of errors. To address these issues, this paper proposes a battery full charging time estimation model and dual extended Kalman filters-wavelet neural network-wavelet long short-term memory neural network (DEKF-WNN-WLSTM). By taking the daily segment charging data of lithium batteries as input, to predict the full time charging of the battery, and then get the SOH in real time.
Firstly, based on the strong robustness of wavelet neural network (WNN) and the ability of long short term memory (LSTM) to extract the time series features of the data, the neural network of WNN-WLSTM is designed. Secondly, two WNN-WLSTM networks are trained with one full charging data and three fragment data of lithium batteries, respectively. Thirdly, a real-time estimation algorithm named DEKF is constructed, in which the first EKF is used to estimate the full charging time corresponding to the segment data, and the second EKF is used to predict the error between the estimated and measured battery full charging time under the current cycle. Then the two trained networks are integrated into DEKF to provide corresponding output values for the cyclic recursion of EKF. Finally, a real-time SOH estimation model based on daily segment charging data is designed. The segment data from constant current charging to full charging at any time is used as the input of DEKF-WNN-WLSTM, to estimate the current full charging time of lithium batteries, then calculate the SOH of the battery at the current time. In this real-time model, the WNN-WLSTM alleviates the inconvenient adjustment of battery model parameters problem, addresses the long-term dependence problem. The DEKF uses the daily segment charging data as the input, which extends the practical application of the model.
Simulation results on the actual battery charging and discharging data show that, the mean relative error of the predictions for the entire 80 cycles is 0.010 1, the estimated error for the first 50 cycles is completely less than 2%, and less than 1% at most times. The comparison between DEKF-WNN-WLSTM and extended Kalman filter and Gaussian process regression (EKF-GPR) shows that, the mean relative error of EKF-GPR is 0.017 6, which is higher than DEKF-WNN-WLSTM, especially in the 170~180 cycles, which indicates that the model of DEKF-WNN-WLSTM can alleviate certain error growth with the increase of cycles. The proposed method has a better estimation effect under the condition that no artificial full recharge operation is performed to update the initial full charging time value.
The following conclusions can be drawn from the simulation analysis: (1)The proposed method integrates WNN-WLSTM neural network, which address the problems of long-term dependence and the inconvenient adjustment of battery model parameters. (2) Compared with EKF-GPR, the DEKF-WNN-WLSTM not only improves the prediction accuracy, but also alleviates the error accumulation. (3) The proposed model only needs the daily segment charging data. In this sense, it is practical in the real world.
State of health, segment data, dual extended Kalman filter, wavelet neural network, wavelet long short-term memory
10.19595/j.cnki.1000-6753.tces.222241
TM911
黑龍江省自然科學(xué)基金聯(lián)合引導(dǎo)項(xiàng)目(LH2022F032)和山東省自然科學(xué)基金聯(lián)合基金培育項(xiàng)目(ZR2022LLZ003)資助。
2022-12-28
2023-02-14
宋顯華 女,1981年生,博士,副教授,博士生導(dǎo)師,研究方向?yàn)闄C(jī)器學(xué)習(xí)和智能狀態(tài)監(jiān)測、圖像安全和量子計(jì)算等。E-mail:songxianhua@hrbust.edu.cn(通信作者)
姚全正 男,1997年生,碩士研究生,研究方向?yàn)闄C(jī)器學(xué)習(xí)以及電動汽車動力電池健康狀態(tài)評估。E-mail:2311884748@qq.com
(編輯 郭麗軍)