Battery Aging Prediction Using Input-Time-Delayed Based on an Adaptive Neuro-Fuzzy Inference System and a Group Method of Data Handling Techniques

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1 Artcle Battery Agng Predcton Usng Input-Tme-Delayed Based on an Adaptve Neuro-Fuzzy Inference System and a Group Method of Data Handlng Technques Omd Rahbar 1,2, *, Clément Mayet 1,2, Noshn Omar 1,2 and Joer Van Merlo 1,2 1 ETEC Department & MOBI Research Group, Vrje Unverstet Brussel (VUB), Plenlaan 2, 1050 Brussel, Belgum; Clement.Mayet@vub.ac.be (C.M.); noshomar@vub.ac.be (N.O.); joer.van.merlo@vub.ac.be (J.V.M.) 2 Flanders Make, 3001 Heverlee, Belgum * Correspondence: omd.rahbar@vub.ac.be Receved: 3 July 2018; Accepted: 2 August 2018; Publshed: 4 August 2018 Abstract: In ths artcle, two technques that are congruous wth the prncple of control theory are utlzed to estmate the state of health (SOH) of real-lfe plug-n hybrd electrc vehcles (PHEVs) accurately, whch s of vtal mportance to battery management systems. The relaton between the battery termnal voltage curve propertes and the battery state of health s modelled va an adaptve neuron-fuzzy nference system and a group method of data handlng. The comparson of the results demonstrates the capablty of the proposed technques for accurate SOH estmaton. Moreover, the estmated results are compared wth the drect actual measured SOH ndcators usng standard tests. The results ndcate that the adaptve neuron-fuzzy nference system wth ffteen rules based on a SOH estmator has better performances over the other technque, wth a 1.5% maxmum error n comparson to the expermental data. Keywords: state of health estmaton; adaptve neuron-fuzzy nference system (ANFIS); group method of data handlng (GMDH); artfcal neural network (ANN); electrc vehcles (EVs); capacty degradaton; lthum-on battery; tme-delay nput 1. Introducton: Notwthstandng the Pars Agreement, a technologcal transent from a hydrocarbon-based economy to the post-petroleum era, there s less tangble projectve evdence of declnng fossl-fueled based economes all over the world. For nstance, recent nvestgaton nto the projecton perod, conducted n 2017 by the U.S. Energy Informaton Admnstraton [1], ndcates that the demand for lqud fuels wll ncrease from 95 to 113 mllon barrels per day. The proporton of the transportaton demand to the petroleum demand and other lqud fuels has been predcted to ncrease from 54% to 56%, leadng ths sector to be the man topc of electrfcaton [2]. Nevertheless, the electrfcaton of the transportaton sector wth exstng electrcal nfrastructure leads the power system to collapse. However, t can be prevented f electrc vehcles are coordnated and scheduled for a proper chargng tme-perod and rate. In addton, recent progress n harnessng renewable energy sources (RESs), and mprovng battery characterstcs shows that t s possble to completely mtgate the mpact of connectng a large fleet of electrc vehcles (EVs) on the power system. The majorty of scentsts have reached a consensus on vable alternatves for fossl fuels, manly wnd and solar energy, whch have relatvely low generaton costs as well as hgh generaton potental, respectvely. However, ther fluctuatons n output are a serous problem [3]. To allevate the oscllatons of renewable generaton sources, the followng four possble approaches have been proposed: Appl. Sc. 2018, 8,1301; do: /app

2 Appl. Sc. 2018, 8, of 16 (1) Couplng renewable energy systems wth dfferent generaton characterstcs n wder dstrbuton va the transmsson grds; (2) Respondng to the demand by adaptng consumpton patterns; (3) Employng fossl-fueled utltes as a tradtonal back-up (ether for meetng peak demand or provdng spnnng reserve); and (4) Equppng the grd wth storage devces such as compressed ar storage, battery storage, and hydro pump storage. Nevertheless, these approaches suffer from dfferent drawbacks and lmtatons. For nstance, dealng wth the uncertantes of the renewable energy sources wth dfferent characterstcs that are subjected to ther nherent dependency on the weather condtons s a challengng task. Concernng the second approach, adaptng consumers patterns would requre a new nfrastructure to control the consumers equpment. Regardng the man drawback of the thrd soluton, fossl-fueled utltes would ncrease the envronmental concern, whch s contradctory to the objectve of the Pars Agreement. Moreover, electrcal vehcles and electrcal energy storage systems equpped wth lthum-on batteres assume mportant roles as both back-up supply systems and prmary energy sources. Indeed, energy storage systems (ESS) and electrcal vehcles can be used to manage the demand n response to severe tmes (e.g., when RESs have fluctuatons and load exceeds generaton). Therefore, ESSs and EVs (n vehcle-to-grd [V2G] servces) have been consdered as great canddates to provde regulaton servces for frequency fluctuaton, voltage devaton, and ancllary servces. However, EVs and ESSs whose V2G capablty decreases because the battery performance degrades over tme, decreasng both the energy and power capabltes as a result of the dynamc nonlnear nature of the electrochemcal reactons, whch are mpacted by external states such as charge and dscharge methods, usage, temperature, and the chemcal makeup of the cell. In the meanwhle, battery technology s developng rapdly and battery cells wth hgher energy and power denstes are becomng avalable. Hence, mprovng the performance of the battery management system (BMS) s an equally mportant task to make the battery relable, safe, and cost-effectve [4]. Indeed, the accurate estmator algorthms are essental for the smart battery management to estmate and measure the functonal states of the battery, and t should contan state-of-the-art mechansms to protect the battery from hazardous and neffcent operatng condtons. In ths regard, extensve research has been carred out for lthum-on battery systems, nvestgatng ther hgh power densty, energy effcency, fast chargng capablty, lght weght, steady-state float current, wde operatng temperature range, low self-dschargng rate, and the possble memory effect [5]. Furthermore, both the prognostcatons and engneerng mantenance are key fgures n varous ndustry sectors such as aerospace, chemcal, automotve, and so forth. Hence, the obvous formdable obstacles to wholesale EVs s a lack of confdence n the battery lfe-tme and performance [6], leadng the authors to look nto two ntellgent algorthms, whch are capable to be mplemented n the exstng BMS hardware. The state of health can be estmated and classfed nto offlne and onlne procedures, whch have dfferent advantages and drawbacks n terms of accuracy, tme duraton, and mplementaton. Based on the advantages and dsadvantages, vehcle manufacturers select a sutable technque accordng to the applcaton. Battery capacty estmaton, referrng to energy capablty, poses tremendous challenges to researchers, whose attempts have turned to the relatonshp between capacty fade and an ncrease n battery resstance. Nevertheless, t has been observed that the changes n battery mpedance cannot be exactly related to the capacty fade. Moreover, ths approach needs extensve laboratory nvestgatons to establsh the correlaton functon [7]. Consderable research has been recently conducted on state of health (SOH) estmaton models, whch can be splt nto the followng groups: electrochemcal models (EMs), equvalent crcut models (ECMs), and data-drven or black-box models [8,9]. Electrochemcal models are establshed to replcate the growth of a sold electrode nterface (SEI) n lthum-on and descrbe ts nfluence on capacty degradaton. Indeed, they are bult based on concentrated soluton and porous electrode theores. Ths means that the electrochemcal models descrbe and elaborate the basc understandng of the electrochemcal reacton nsde the battery [10]. The EM ncludes mutually coupled non-lnear

3 Appl. Sc. 2018, 8, of 16 partal dfferental equatons (PDEs), ncreasng the numercal complexty and computatonal efforts, whch poses dffcultes n the real-tme mplementaton phase, or large-scale smulaton as a lfe-tme predcton [11]. In ths regard, desperate attempts to reduce the numercal complexty have been recently made through model-order reducton. In the lterature [9], a dual SOH and state of charge (SOC) estmaton technque has been proposed, by applyng the sldng mode technque to the reduced verson of PDE, namely a sngle partal model. The results showed that the proposed technque can track the SOH and SOC accurately. The advantage of the EM approaches s ther ndependence from envronmental condtons. On the other hand, as mentoned prevously, the EM approaches requre ntensve computatonal efforts for system dentfcaton, because of a great quantty of parameters [12]. Moreover, the EM approaches are usually created for a partcular type of battery consstng of specfc anode and cathode materals [13]. The EC models are featured wth ease of mplementaton and parameterzaton, as well as acceptable modelng accuracy [14]. The EC model completely depends on the envronmental and operatng condtons (e.g., SOH and SOC). Ths dependency on model parameters, derved from the operatng condtons, can be addressed and captured va a look-up table, needng extensve expermental efforts to collect a suffcent dataset to descrbe a broad range of operatng condtonng for batteres. The ECM s parameters can be estmated and updated va open-loop or close-loop methods. For the later method, an accurate EC model s requred [15], and the battery parameters should be updated accordng to the agng state of the battery, whch s a challengng task. Many technques have been developed and some combned algorthms have been used to estmate SOC (drectly or ndrectly through the estmaton of the open crcut voltage [OCV]), consequently estmatng the SOH, such as the extended Kalman flter (EKF) and unscented Kalman flter (UKF). The EKF and UKF are effectve technques for SOH estmaton. For nstance, n the lterature [16], a novel jont SOC and capacty estmator based on EKF has been ntroduced. The results showed that the proposed technque can capture the varaton of the parameters n varyng operatng condtons and battery agng. Smlarly, the authors of [17] proposed a new technque for SOH and SOC estmaton, employed Coulomb countng method (CCM) to estmate SOC, takng the benefts of EKF to reduce accumulatve errors of CCM, due to the current sensor noses. Moreover, the SOH was estmated based on the relatonshp between the ds/charge current and estmated SOC. The results demonstrated a reasonable estmaton of SOH and SOC. These technques are called jont estmaton, and can estmate the SOH of the battery as accurately as the battery s modeled. Ths means that the accuracy s hghly dependent on how the battery s modeled. Moreover, large matrx operaton and nversons are requred, leadng to a hgh complexty. Furthermore, the jont estmaton method may have poor numercal condtonng and suffer from nstablty [7]. Nonetheless, for ths method, a dual estmaton technque has been mplemented, meanng that nstead of one estmaton algorthm, two adaptve flters are used. One of the flters estmates SOC and the other one s employed for the estmaton of the model parameters. Sometmes, nstead of the second flter used for model parameters dentfcaton, evolutonary algorthms are used [18]; a battery model was establshed and then a genetc algorthm was used to dentfy the model parameters and then estmate the SOH. In the lterature [19], a mult-scale framework EKF was ntroduced to effectvely estmate the state and parameters of the ECM, appled to a L-on battery for the capacty and SOC estmaton. The results ndcated that the proposed technque has a less than 3% error for the SOC estmaton. In contrast to the jont estmaton, the dual-technque conssts of two adaptve flters. Ths technque demands a lower computatonal effort and the dmensons of the respectve model matrces are lower than the jont estmaton technque. In the lterature [20], an effectve jont SOH and SOC estmaton technque was ntroduced. In ths work, KF and UKF were combned to predct the state of the battery. The result regardng the SOC estmaton s promsng; nevertheless, the error of the SOH ndcator s around 20%. In the lterature [15], an adaptve sldng mode observer was employed to estmate the SOH and SOC of the L-on battery. The ECM conssted of two resstor and capactor networks; furthermore, the results showed a hgh performance and robustness on the SOH and SOC estmatons. However, smlar to the jont technque, an accurate battery model s essental for the SOC and SOH estmatons. Indeed, observer technques, known as a close-loop method, whose

4 Appl. Sc. 2018, 8, of 16 adaptablty and effectveness are utterly dependent on the credblty of the EC models and the robustness of the technque [10]. As stated prevously, the technques employed n ECM, suffer from naccuracy owng to the lack of thorough understandng of the electrochemcal dynamcs and physcs of the battery [21]. Ths drawback could be lessened va data-drven models, utlzng the nformaton of the measurement ensemble. Consequently, pror knowledge of electro-chemstry s not requred as a result of ther capablty to work wth mprecse data and ther self-learnng ablty [22]. Machne learnng s categorzed under data-drven method, whch are wdely employed for battery SOH estmaton. In the lterature [23], a recurrent neural network was used to montor the SOH of a hgh-power lthumon battery. Lu et al. [24] proposed a group method of data handlng, recognzed as a polynomal neural network, n order to estmate the SOH of L-on batteres, and the results show a 5% error vs. the expermental data. The authors have concluded that the technque s unversally vald for other types of battery chemstres. More recently, Chaou et al. [5] employed an artfcal neural network technque to estmate SOC and SOH drectly and smultaneously. The technque used n the artcle s a useful tool for analyzng the system dynamcs that are subjected to uncertantes [25]. In the lterature [26], a nave Bayes model was ntroduced to predct the remanng useful lfe of a battery under dfferent operatng condtons. The comparatve results showed the superorty of the proposed technque over the support vector machne. To reduce and avod the need for computng power and a complex battery model, as well as consderng the random drvng cycle, researchers have been compelled to nvestgate the capacty degradaton phenomena correspondng to SOH durng chargng or dschargng processes, whch could be more predctable than those methods mentoned prevously [27]. Eddahech et al. [28] proposed a constant-voltage (CV) step as an ndcator of capacty degradaton. Then, four battery technologes were compared to show that the mplemented method s very accurate by comparson wth the classc dscharged capacty measurements. Motvaton, Objectve, and Innovaton Contrbuton Consderng the lmtatons of the measurement devces n the present BMS, many external features of the battery are hard or even mpossble to obtan n actual operaton. Moreover, the applcatons of the above-mentoned methods are also lmted by the computatonal capablty of a real BMS. To address the above drawbacks of the methods descrbed n the lterature, ths artcle proposes two states of health estmaton technques for L-on batteres, and then, another technque has been developed and compared to show the robustness of the proposed technque n ths feld. In ths artcle, the proposed method requres only two external states (voltage and current), makng the method sutable for EV applcatons. The key contrbutons of ths artcle are summarzed as follows: Employng an nput tme-delayed strategy to handle dynamc nformaton of system. The Adaptve Neruo-fuzzy Inference System (ANFIS) and group method of data handlng (GMDH) technques are employed to analyze the relatonal grade between the SOH and selected features. Developng two data-drven frameworks to estmate the SOH. Ths artcle utlzes the fuzzy C- means clusterng algorthm to tune and adjust the ANFIS parameter n advance, to create the ntal rules. Accurate and effectve valdaton of the framework n comparson to recently publshed artcles and other methods. The paper s organzed as follows: n Secton 2, a bref ntroducton s done regardng the group method of data handlng and adaptve neuro-fuzzy nference system; n Secton 3, both the dscusson and comparsons between the proposed technques are provded. The outcome of the artcle s summarzed and concluded n Secton Proposed Technques

5 Appl. Sc. 2018, 8, of 16 Based on the lterature, modelng the relaton between external and nternal states s requred for battery state estmaton. Consequently, a battery model s needed for accurate estmaton. Moreover, batteres are complcated electrochemcal devces wth non-lnear behavor, affected by varous nternal and external states. Ths behavor can be descrbed by a model whose formulaton comprsed of both uncertan and unknown parameters, but structurally known. In addton, descrbng the relatonshp between the battery termnal voltage property and battery SOH s an arduous task. As known from the lterature, the chargng process of an EV battery system ncludes two sub-processes, constant-voltage (CV) charge and constant-current (CC) charge. Chargng or dschargng of a certan amount of capacty (Ah) leads to a lower voltage change n fresh battery cells, whle the same amount of Ah creates a hgher voltage change n an aged cell for the same type of battery. Ths prncple, the determnaton of the dfferental voltage responses to the ampere-hours dscharged or charged from the battery before and after dschargng or chargng, s almost employed as the capacty estmaton method. So, n ths method, after a certan amount of energy throughput, the varaton of voltage response s calculated and compared to the expermental data. Ths method s a practcal soluton for battery capacty montorng [29 31]. The advantage of ths method could resde n low nputs. As can be seen n Fgure 1, the termnal voltage curves are plotted at three dfferent SOH levels whle the batteres were charged usng constant-current chargng profle. The termnal voltage curves consderably vary from cycle to cycle. For nstance, the termnal voltage curve of the battery at the begnnng of lfe (BOL) has a lower slope than the voltage curves at 71% SOH. In addton, the ntal, mean, and fnal voltages are not equal n the voltage property curves at dfferent SOH levels. Hence, t can be concluded that the SOH can be reflected by the termnal voltage curve n a specfc chargng/dschargng process. In other words, the battery s termnal voltage generally decreases and ncreases when beng dscharged and charged, respectvely. The chargng and dschargng processes of a fxed number of ampere-hours lead to a lower voltage change for a battery wth a hgher SOH (fresh battery). On the other hand, a hgher voltage change takes place when the battery s SOH s lower (aged battery). Fgure 1 shows the battery chargng profle based Lthum-on battery (LIB) at dfferent SOH from 97% to 71%, aged at 25 C. For nstance, the blue lne represents 97% SOH, has a lower slope than the red lne, and corresponded to 95% of the nomnal capacty. In addton, the lne wth 71% SOH has a bgger slope than the lne wth 95% SOH. Fgure 1. Termnal battery voltage at constant-current chargng protocol (25 C). SOH state of health Group Method of Data Handlng

6 Appl. Sc. 2018, 8, of 16 The group method of data handlng (GMDH) neural networks s a self-organzed algorthm, meanng that the connectons of the network (connectons between neurons) are selected throughout the tranng phase to optmze the network [32]. In ths approach, the neurons are completely not connected wth the functon nodes. Moreover, the number of layers, neurons n hdden layers, and actve neurons are automatcally confgured, because of ther self-organzed capablty. Furthermore, the network structure s modfed untl the best structure s accomplshed, and thereafter, the optmzed network defenses the dependency of the output values on the most notable nput varables. It should be mentoned that GMDH can be employed n a wde range of felds, such as complex system modelng, forecastng, data mnng, and knowledge dscovery. The relaton between nputs and outputs can be descrbed as follows: y a a x a x x a x x x... 0 M M M M M M (1) j j jk j k 1 1 j 1 1 j 1 k 1 ( x, x,..., x ),( a, a,..., a ) and M are the nput varables, the coeffcent, and the where 1 2 M 1 2 M number of nput varables, respectvely. By applyng nput data as a matrx, N pont of observatons of M varables are ncluded. In the learnng step, the network s tuned and estmates the coeffcents of the polynomal, as descrbed by Equaton (2), and the remanng data samples are utlzed to choose the optmal structure of the model, whch can be realzed by mnmzng the error between the expected output (real value) and the estmated value. In ths regard, Equaton (3), known as a mean square error, s defned as a cost functon of the algorthm. y a a x a x a x x a x a x (2) j 3 j 4 5 j 1 N 2 ( y ˆ n yn ) (3) N n 1 where y ˆn and y n are the estmated and expected values, respectvely, and N s the length of the tranng dataset. The nput varables are consdered as pars of ( x, x ), as can be seen by Equaton (2). The regresson polynomal s created and then teratons contnue from two to three steps, untl the mean square error of the test data converge to a constant value. The confguraton of the group method of data handlng s depcted n Fgure 2. j Fgure 2. Group method of data handlng (GMDH) structure.

7 Appl. Sc. 2018, 8, of 16 Fgure 2 llustrates the optmzed structure, confgured automatcally by mnmzng the cost functon, as defned prevously. Furthermore, some node functons were not connected to the network, as can be dstngushed n Fgure Adaptve Neuro-Fuzzy Inference system Fuzzy logc (FL) s a robust system that transforms varables to mathematcal language, whch s consstent wth the ablty of human knowledge modelng. Whle, fuzzy logc tres to model ether lnear or non-lnear systems, t s not possble to be traned by tself n a stochastc condton. Therefore, fuzzy logc systems are dependent on ther operaton rules, whch should be defned by the experts who conclude, usng ther ntuton, the parameters assocated wth membershp functons. To overcome ths problem, FL can be combned wth artfcal neural networks (ANNs), whch have a remarkable ablty to learn from mprecse data. Hence, combnaton of ANNs and FL procedures lead a better parameterzaton, whch presents the fuzzy logc nference, known as the adaptve neuro-fuzzy nference system (ANFIS). Indeed, fuzzy logc and ANNs have both substantal benefts and drawbacks, whch should be taken nto consderaton n terms of system modelng. In fuzzy logc language, called fuzzly, f else statements are used to model the system by human knowledge. Although FLs are not capable of capturng measurement values, and use them to ether adjust or modfy the parameters lke the Gaussan membershp functon varables, ANNs have the capablty to be tuned and learnt by expermental data, leadng a mathematcal model not to be ncluded n the system modelng, whch can be possble by nput output mappng. Moreover, t has been demonstrated that the ANFIS s one of the technques that can be utlzed to any type of battery wth varous operatng condtons (e.g., partal dschargng, constant charge, and dscharge processes) [33]. Two common fuzzy style nferences are Mamdan-style and Sugeno-style, whch have been presented by Lotf Zadeh and Takag-Sugeno-kang, respectvely [3]. To provde a better understandng, an ANFIS structure wth two-nput one-output s llustrated n Fgure 3. The rule base consders two fuzzy f then rules of Takag and Sugeno s type, whch are as follows: rule 1: If x A and y B, then Z p x q y r rule 2: If x A and y B, then Z p x q y r Layer 1 Layer 4 Layer 2 Layer 3 Layer 5 X A 1 W 1 N W1n X Y F1(x,y) W1 nf1 A 2 z Y B 1 B2 W2 N W 2n F2(x,y) X Y W2 nf2 Fgure 3. A general adaptve neural-fuzzy nference system [2]. The basc structure of ANFIS, consderng as a fuzzy nference system, s a fve-layered feedforward type, ANN, ncludng dfferent purpose-bult types of nodes (e.g., non-weghted, adaptve, and non-adaptve connecton lnks). The dfferent layers can be classfed nto fve-layers, whch are as follows:

8 Appl. Sc. 2018, 8, of 16 Layer 1: Ths layer s known as fuzzy-fcaton layer, whch fuzzfes the nput varables; every node conssts of a node functon, whch s O1, A( x), symbolzed by A, x, O 1, where A s the lngustc label accordng to the node functon, x s the nput to the node, and O 1, s the membershp functon of that, specfyng the level for the assumed x. Hence, the membershp functon ascertans the membershp level from the gven nput values. For a bell-shaped functon, three parameters for each node should be defned, for whch the maxmum and mnmum possble value are 1 and 0, respectvely; where ts generalzed functon can be mathematcally descrbed as follows: where 1 ( x) (4) A 2 b 1 [(( x c ) / ( a )) ] a, b, c are the set parameters, called as premse parameters, s commonly chosen as bell-shaped or gauss-shaped, x s the frst nput varable, and the membershp functon varables are adjusted by changng the aforementoned parameters whenever the frst nput varable s fed to the ANFIS. Layer 2: Is called fuzzy and, because n ths layer, only AND operators are allowed. Ths layer s utlzed to compute the frng robustness of every rule. It means product operaton (see Equaton [5]) referred to the weghtng factor of the correspondng rule, s used. O w ( x ) ( x ) for 1,2 (5) 2, A 1 B 2 Layer 3: Is known as normalzaton term. The frng strength of each rule s normalzed va computng the raton of each rule s frng strength to the total of each rules. In Equaton (6), w s defned as the frng strength of each rule, as llustrated below: O 3, w f w w w w w 1 2, for 1,2 (6) Layer 4: Is recognzed as defuzzfcaton. Ths layer tres to compute the output of the prevous layer, based on ts node functon; each node functon s adaptve n accordance wth the node functon, as gven by Equaton (7). where O4, w f w ( p x q x r ), for 1,2 (7) w s the output of the thrd layer and the parameters ( p, q, r ) are set parameters, whch are beng assumed by the condtons of the determned parameter. The parameters n the fuzzy nference layer are consdered as consequent parameters. Layer 5: Is called aggregaton. Ths layer s utlzed to compute the total of the outputs of all of the rules to produce the overall ANFIS output, whose equaton s represented as follows: w f O w f f 5, out w The aforementoned archtecture s employed to adjust ANFIS model for SOH estmaton, as dscussed n the next secton. 3. Result and Dscusson Many methods have been proposed n the lterature to estmate SOH, whereby accurate battery parameters are needed to buld the emprcal model, whch could be neffcent and expensve. (8)

9 Appl. Sc. 2018, 8, of 16 Nevertheless, the above developed technques are capable of dealng wth the complexty of the system modelng, nsuffcent data, and can stll descrbe the system behavor Expermental Data In ths work, the expermental data from Prognostcs Center of Excellence at Natonal Aeronautcs and Space Admnstraton (NASA) Ames s employed to tran and valdate the proposed approaches [34]. Ths approach leads the comparson of the proposed technques wth that of recently publshed papers usng the same dataset to be easer. The dataset conssts of four batteres, aged through three dfferent operatonal profles conductng alternately n the dataset, namely mpedance, charge, and dscharge profles. The mpedance measurement process was performed by employng the electrochemcal mpedance spectroscopy (EIS) technque. Moreover, n the regular charge and dscharge cycle, the batteres were charged and dscharged at CC of 1.5 A and 2 A, respectvely. In the charge step, 1.5 A s mposed to the batteres to reach the maxmum voltage of 4.2 V, followed by the CV process, untl the current decreased from 1.5 A to 20 ma. Nevertheless, n the dscharge profle, the CC dscharge step was conducted by reachng the voltage of 2.7 V, 2.5 V, 2.2 V, and 2.5 V for batteres, No. 05, 06, 07, and 18, respectvely. As a consequence of reoccurrng the above procedure, the capacty of the batteres reached 70% of the nomnal capacty Short-Term State of Health Estmaton In ths subsecton, the performance of the short-term SOH estmaton s presented by employng the proposed technques. Both the GMDH and ANFIS are traned by the collected dataset. The nputs and the outputs of the system n the tranng phase are the battery termnal voltage and the SOH, respectvely. The begnnng-of-lfe (BoL), correspondng to a fresh battery, s defned as a 100% SOH, and the 167th cycle, when the capacty has reached the 1.4 Ah, s consdered as the end-of-lfe. Moreover, the algorthm uses the unt-tme-delays to consder the battery voltage at past tme frames. The voltage s normalzed, whch s a standard procedure when such ntellgent technques are used. Thereafter, the normalzed dataset after the computng and estmatng procedures wll be denormalzed. Owng to the capablty of mprovement n the read performance of the database, ths technque s used. Indeed, each sample s dvded by the maxmum possble measurement. For nstance, a measurement of 4.2 V consttutes as number 1, whle 0 V s represented as number 0, and every other value s between 1 and 0. Furthermore, t should be noted that EVs are not always charged at a certan state of charge, whch means that the technque should be able to estmate the SOH at dfferent SOC levels, correspondng to dfferent ntal voltages. The proposed technques, GMDH and ANFIS, were traned by the expermental results of battery No. 05. As mentoned prevously, durng the tranng phase, the structure and weghts of GMDH and weghts of ANFIS could be optmzed and adjusted n terms of mnmzng the error between the estmated SOH from the network, and the tranng targets from the expermental data. Then, the technques are valdated by employng the expermental data from battery No. 06. For the GMDH whose parameters are the maxmum number of neurons n a layer, the maxmum number of layers and selecton pressure are set to 10, 5, and 0.6, respectvely. It should be ponted out that the dataset for the tranng phase ncludes all of the voltage samples correspondng to 0% SOC to 100% SOC. The GMDH parameters, maxmum number of neurons n a layer, maxmum number of layers, and selecton pressure are set to 250, 10, and 0.6, respectvely. For valdaton, battery No. 06 was used, whose expermental results were used to test the estmaton accuracy of the GMDH technque. The actual and estmated SOH are depcted n Fgure 4. The blue lne shows the actual SOH and the red lne ndcates the estmated SOH at frst and second cycles wth mean square error, and 0.23 root mean square error. It s observed that the relatonshp between the battery voltage and estmated SOH closely matches the actual test dataset. Moreover, the RMSE and MSE show that the GMDH has successfully dscovered the effects of agng of the battery voltage behavor.

10 Appl. Sc. 2018, 8, of 16 Fgure 4. Expermental and estmated results of state of health (SOH) vs. battery voltage by employng GMDH (No. 06) for two cycles. Wth regard to the second technque, as mentoned earler, the combnaton of fuzzy logc and NNs leads to the ANFIS structure, whch s classfed under adaptve networks. Consequently, ANFIS has the ablty to reach a concluson from unclear and complex data, because of the fuzzy logc, wth the capablty to work from mprecse data [35]. In ths regard, ths technque s utlzed to estmate the SOH from a set of curves whose shapes depend on the state of the system. Furthermore, the ANFIS cannot work wthout a tranng phase. Therefore, the battery termnal voltage durng constant current charge profle at dfferent SOH s prepared. Then, the membershp functons should be adapted to the battery charge curves, whch are dverse at dfferent SOH levels. It should be ponted out that the constant-voltage sub-process s not ncluded n the nput dataset. The number of ntal ANFIS rules for the frst nput was set to 15, these rules were generated usng the fuzzy C- means (FCM) clusterng method, and then the ANFIS was traned and tuned by the expermental results of battery No. 05. Moreover, the method used for optmzaton of the parameter of ANFIS, s a combnaton of back-propagaton and least-square estmaton. Note that the traned dataset conssts of all of the voltage ntervals, startng from 0% to 100% SOC. The dataset, related to the battery No. 06, s utlzed to test the developed algorthm. The errors between the expermental data (actual SOH) aganst the estmated SOH at dfferent voltage levels are llustrated n Fgure 5. The mean squared error (MSE) and root mean squared error (RMSE) are and 0.094, respectvely. As can be nferred from the results, the ANFIS has better performance compared wth the GMDH. The results, shown n Fgure 4, have a maxmum error below 0.3. Moreover, the overestmaton and underestmaton s lower than that of the prevous technque, whch demonstrated the adaptve capablty of the ANFIS technque.

11 Appl. Sc. 2018, 8, of 16 Fgure 5. Expermental and estmated results of SOH vs. battery voltage by employng ANFIS (No.06) for two cycles Long-Term State of Health Estmaton In ths subsecton, the proposed technques for the long-term battery state of health estmaton are also evaluated. Note that n ths procedure, all of the short-term SOH and voltage cycles are ntegrated to buld one macro tme scale concept. The charge data for 87 cycles of battery, No. 06, are employed to evaluate the proposed technques for long-term estmaton capablty. Fgure 6 shows the long-term SOH estmaton of battery No. 06. The obtaned MSE and RMSE for the SOH estmaton are 0.714, and 0.845, respectvely. It can be seen that the GMDH, traned and tuned by battery No. 05, can be used to estmate the SOH for other batteres. Nevertheless, t s observed that, despte the better performance of GMDH for short-term estmaton, n long-term SOH estmaton, the fluctuaton of GMDH s the most notceable. Accordng to Fgure 6, the GMDH could not estmate the 1st, 21st, 54th, and 74th accurately. It can be concluded that the GMDH technque for long-term SOH estmaton s nstable. Fgure 6. Long-term SOH estmaton va GMDH for the 87 dscharge cycles of battery No. 06.

12 Appl. Sc. 2018, 8, of 16 The results of SOH estmaton for battery No. 06 based on ANFIS, are plotted n Fgure 7. As t s noted n the fgure, the MSE and RMSE are and 0.203, respectvely, whch shows a better stablty from the GMDH for the long-term SOH estmaton. It can be observed that the ANFIS has successfully learned the effect of capacty degradaton on the battery termnal voltage. Therefore, overchargng and deep-dschargng can be avoded, and also, the proposed technques can be used for smart battery chargng management, as ANFIS and GMDH have the capablty to respond to an optmzaton algorthm as soon as they receve the nputs of the system. Fgure 7. Long-term SOH estmaton va ANFIS for the 87 dscharge cycles of battery No. 06. Table 1 presents the performance of the evaluaton, comparng the proposed technques wth the recent publshed artcles. As shown n the table, the ANFIS model obtans a much better performance over the GMDH model. For nstance, the RMSE and MSE on battery No. 06 based on GMDH s and 0.714, whle the RMSE and MSE based on ANFIS s and 0.041, respectvely. Moreover, n terms of comparson, the present results and the resent publshed artcles used same dataset from NASA, the performance of the models ntroduced n the lterature [16,24,36] are compared n Table 1. As can be observed, the RMSE and MSE based on the ANFIS model are much better than the ntroduced models. Nevertheless, the followng lmtatons need to be addressed n future studes: 1. Whle machne learnng demonstrated an acceptable self-adaptaton and hgh non-lnearty modelng capablty, a large amount of expermental data s requred to obtan a hgh accuracy. 2. Although the ntroduced SOH method s more predctable and accurate under chargng and dschargng processes, t s not a usable method for plug-n hybrd electrc vehcles (PHEVs)/PEVs when they are connected to smart chargng nfrastructure. Table 1. Root mean square error (RMSE) results of long-term capacty estmatons of adaptve neruofuzzy nference system (ANFIS), group method of data handlng (GMDH), and a recent publshed artcle. MSE mean square error; QGPER quadratc polynomal mean functon; DGA geometry based approach. Error RMSE (battery No. 06) Ref. [36] QGPFR Ref. [16] GPR-SE Ref. [24] GMDH-DGA Present Study ANFIS Present Study GMDH

13 Appl. Sc. 2018, 8, of 16 MSE (battery No. 06) Conclusons In ths artcle, two data-drven technques are developed for the state of health estmaton. The developed technques utlze an adaptve neuro-fuzzy nference system and group method of data handlng to tran the relaton of the battery termnal voltage and state of health, enjoyng the advantage over exstng methods, as mentoned prevously (e.g., lower nputs, descrbed system behavor), wth no need for computng power and a complex battery model. The comparatve mert of the method and technques mplemented n ths paper, compared to the exstng ones n the lterature, can be concluded n two man ponts. Frstly, the technques are not dependent on any specfc battery model, due to the fact that they are data-drven technques, as can be nferred. The employed technques can be appled to a great varety of battery technologes. Secondly, the battery operatng dataset s appled to these technques to analyze the nternal structure, whch s naccessble. The comparson between the expermental and estmated results showed a robustness of the developed technques, fast convergence performance, and outstandng accuracy for the battery health estmaton. Author Contrbutons: O.R. desgned the study and manly wrote the paper; N.O., C.M, and J.V.M revsed and proofread the artcle. Fundng: Ths research receved no external fundng Acknowledgments: We acknowledge the support of our research team from Flanders Make. Conflcts of Interest: The authors declare no conflcts of nterest. Abbrevatons ANN ANFIS BMS CC CV DG DGA ESS EV EKF G2V GHG GMDH GP HRES ITDNN KF LS NN NEDC MSE PS PF QGPFR RMSE RBC SG SOC SOH artfcal neural network adaptve neruo-fuzzy nference system battery management system constant current constant voltage dstrbuted generaton geometry based approach energy storage system electrc vehcle extended Kalman flter grd-to-vehcle greenhouse gas group method of data handlng Gaussan process hybrd renewable energy system nput tme-delayed neural network Kalman flter least squares neural network new European drvng cycle mean squared error power system partcle flter quadratc polynomal mean functon (GP) root mean square error remanng battery capacty smart grd state of charge state of health

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