**1. Introduction**

The most sustainable strategy to accomplish clean and efficient transport is to stimulate the automotive hybrid electric vehicles (HEVs)/electric vehicles (EVs) industry by developing the most advanced battery technologies. There is massive

competition in the markets for selling batteries with different chemistry, especially between the most common nickel-metal hydride (Ni-MH), nickel-cadmium (Ni-Cad) and lithium-ion (Li-ion) batteries. More recently, it seems that the most promising future and great potential of development for HEVs/EVs automotive industry worldwide have the Li-ion batteries due to their advantages compared with other strong competitors on the market. They surpass these competitors by features such as lightweight, high-energy-density, little memory effect, and relatively low self-discharge, as is mentioned in [1, 2]. Furthermore, after substantial improvements and research investments, the Li-ion batteries have become safer and less toxic. The battery state of charge (SOC) represents the available capacity of the battery cell that changes corresponding to the fluctuations in the input charging and discharging current profile during a cycle. It is worth mentioning that the SOC plays a crucial role in keeping the battery safe for various operating conditions and significantly extending battery life [3, 4]. Moreover, the SOC is an essential internal battery parameter of great significance constantly monitored by the battery management system (BMS) [1–6]. In real life, a specialized software package integrated onboard the vehicle estimates the value of the battery SOC due to the lack of an accurate measurement sensor integrated into BMS [1–7]. Let us see why the battery SOC has become a topic of great interest for researchers working in the field, very dedicated for developing the most suitable estimation techniques and strategies supported today by an impressive number of research papers published in the literature. The most used model-based Kalman filter (KF) can estimate the battery SOC with a high accuracy grade [3–7]. The BMS monitors the battery system through sensors and state estimation algorithms to detect any abnormalities during the battery system operation [8, 9]. The performance of the battery SOC estimators' model is highly dependent on the battery model accuracy. If the battery model is accurate, then the different SOC estimation versions will estimate the battery SOC with the same accuracy. Consequently, the battery model is essential for implementing the most suitable SOC estimators. It is always desirable to get a battery model as accurate as the actual battery to reduce the mismatch between the model and the existing battery. Moreover, the battery SOC is "a critical factor **in** guaranteeing that a battery system operates safely and reliably," as is mentioned in [10]. Also, "many uncertainties and noises, such as current, sensor measurement accuracy and bias, temperature effects, calibration errors or even sensor failure, etc.**,** pose a challenge to the accurate estimation of SOC in real applications" [10].

Additionally, over time, the effects of battery aging will be more noticeable in degrading its performance, and the mismatch between the battery model and the actual battery will also increase. In the "real-life" applications subjected to the plant/ process identification, fixing the possible mismatches between the plant/process and their corresponding models with repeated effective re-identification procedures is almost inapplicable and time-consuming, as is revealed in [10–12]. Therefore, mismatch detection is essential for different plants/processes modeling and identification strategies to isolate defective submodules to avoid complete re-identification, as mentioned in [11].

#### **1.1 State-of-the-art Li-ion battery models and SOC estimators**

A suitable identification plant/process strategy is developed in [10–12] that is a polynomial discrete state-space representation of the plant/process models based on a *Investigations of Using an Intelligent ANFIS Modeling Approach for a Li-Ion Battery… DOI: http://dx.doi.org/10.5772/intechopen.105529*

plant/process input-output measurement data set collected in an open loop. The plant/ process input-output measurement data set is used to develop and implement two attractive statistical models.

The first model is a linear discrete state-space autoregressive exogenous input (ARX) polynomial representation, beneficial to model a 60 Ah LiFePO4 battery module [10]. Based on this model, an extended Kalman filter (EKF) battery SOC estimator is developed for BMSs. The second model is an auto-regressive moving average with exogenous input (ARMAX) model developed in [12]. The adaptability of ARX battery models developed in [10] for designing a robust and accurate EKF SOC estimator is rigorously assessed in the same reference [10]. Some simulation results indicate that the proposed EKF SOC battery module estimator based on the ARX model shows a "great performance" in terms of robustness and SOC accuracy [10]. Additionally, the proposed EKF battery estimator "increases the model output voltage accuracy, thereby having the potential to be used in real applications, such as EVs and HEVs" [10]. Two MIMO ARMAX models are developed in [12] for modeling and identification of heating, ventilation, and air-conditioning (HVAC) multi-input multi-output (MIMO) centrifugal chiller plant. This model is built and implemented in a MATLAB simulation environment to develop two accurate MIMO proportional integral-plus (PIP) control strategies in a closed loop for temperature control and refrigerant liquid control level. For comparison purposes in [11], ARX and ARMAX polynomial discrete-time plant representations are built as decorrelation models for detecting model-plant mismatch for a column distillation integrated into a model predictive control (MPC) strategy. Detailed simulations in [11] show that the ARMAX models provide:


Moreover, in [12], ARMAX models are developed for an MIMO HVAC centrifugal chiller open-loop control system using the identification techniques presented in MATLAB Identification Toolbox [13]. Also, for the same HVAC plant, an MIMO ARMAX open-loop polynomial model helps implement an interesting closed-loop proportional integral-plus (PIP) control strategy of chiller plant temperature and liquid-level refrigerant. Both ARX and ARMAX models are helpful in [12] for implementing an extended MIMO PIP control strategy as a new modeling approach in a non-minimal discrete-time state-space system representation (NMSS). The MATLAB simulation results show a superior accuracy of the MIMO NMSS centrifugal chiller model compared with the ARMAX models. Therefore, the MIMO PIP closed-loop control strategy based on the MIMO NMMS models performs better than those built on the MIMO ARMAX models of the MIMO chiller plant, as is proved in [12, 13].

Taking advantage of the considerable advances in modeling, identification, and control systems developed in the field of literature, thanks to the latest achievements in artificial intelligence, statistics and machine learning, deep learning, signal process analysis, our research objectives diversify with new approaches. The most recent results in modeling and identification for various industrial applications reported in the literature field motivate us to investigate attractive new modeling approaches.

Then remains to adapt these approaches to our research topic of developing new Li-ion battery models. Furthermore, the proposed Li-ion battery SOC estimator for a Rint SAFT model of 6 Ah and 11 V nominal voltage in the selected case study is expected to perform much better in terms of accuracy and robustness of the battery SOC estimates for different operating conditions [7]. For simulation and comparison results purposes, as a case study of Li-ion battery, a third-order resistor-capacitor (RC) equivalent circuit model (ECM) (in abbreviated notation 3RC ECM) is considered. It combines three parallel polarization circuits R-C connected in series with the battery's internal resistance (Rint) and voltage source, i.e., as a similar 3RC ECM battery model developed in [7]. The model selection is suggested due to its simplicity and ability to describe the static and dynamic behavior of the Li-ion battery accurately.

Since the proposed Li-ion battery's open-circuit voltage (OCV) has highly nonlinear dependence on the battery SOC, as an alternative block model developed in [7], it is an adaptive neuro-fuzzy inference system (ANFIS) model. It is a hybrid neuro-fuzzy technique that brings the learning capabilities of neural networks to fuzzy inference systems. The learning algorithm tunes the membership functions of a Sugeno-type fuzzy inference system using the training input/output data [14]. More precisely, the learning algorithm teaches the ANFIS to map the input (current driving cycle profile) to the Li-ion battery SOC and terminal voltage through training. At the end of the training, the trained ANFIS network would have learned the input-output map and be ready to be deployed into the Kalman filter SOC estimator solution. The architecture, design, and implementation of the proposed ANFIS battery model are developed in an attractive MATLAB R2021b simulation environment [14–16]. This new battery model adjusts the design techniques and guidelines inspired from [14–33] to the selected model adopted in the case study from [7]. The accuracy of the ANFIS battery model has a significant impact on the SOC Li-ion battery Kalman Filter estimator accuracy performance built on this model. Its effectiveness is proved through extensive simulations and comparisons conducted on the same MATLAB platform. In this research, our motivation for using adaptive neuro-fuzzy training of Sugano-type fuzzy inference system (ANFIS) modeling comes from the preliminary results obtained for similar investigations on the impact of nonlinearities and uncertainties actuators [18]. The ANFIS modeling is well documented in the most recent MATLAB release versions that use the fuzzy logic toolbox and fuzzy inference tuning procedure [14–16]. Handy tutorials of using ANFIS modeling architectures are presented in [14–17]. For MATLAB implementation and simulation intent, as well as "proof concept" in this research, the accuracy of the Li-ion battery ANFIS model is tested for a battery urban dynamometer driving schedule (UDDS) input current profile.

In the proposed case study, for both ARX and ANFIS models an adaptive EKF (AEKF) SOC estimator is adopted attached to Li-ion battery used for creating fault detection and isolation (FDI) control strategies in [12], preferred for its simplicity, SOC accuracy, real-time implementation capability, and robustness. Its robustness is tested for four different scenarios, such as to changes in SOC initial values (guess values), ranging 70–40%, 20, 90, and 100%, to federal test procedure for 75 F (FTP-75) degree Fahrenheit driving cycle profile test, changes in measurement-level noise (from 0.001 to 0.01), to changes in the battery capacity value from 6 Ah to 4.8 Ah due to aging effects, and changes in internal resistance due to temperature effects, and also for simultaneous changes [7, 29]. Based on a rigorous performance *Investigations of Using an Intelligent ANFIS Modeling Approach for a Li-Ion Battery… DOI: http://dx.doi.org/10.5772/intechopen.105529*

analysis of SOC residual error compared with the similar results reported in the literature with a typically 2% error, in some situations, the AEKF estimator SOC residual error reached values smaller than 1%, such as shown in [29]. Since of the lack of data in the literature field for similar situations developed in our research for Li-ion battery, it is not easy to make a state-of-the-art analysis of the results reported in the literature related to Li-ion battery SAFT 6 Ah and 11 V nominal voltage AEKF SOC estimators based on ANFIS models analysis. The overall ANFIS battery model consists of two ANFIS models, the first one attached to the battery Rint-3RC active part and the second to OCV(SOC) nonlinear block. The SOC and terminal voltages accuracy of the overall battery ANFIS model and AEKF SOC estimators, as well as their robustness to changes in the initial values of the battery SOC from 70 to 40%, are proved in this research paper based on extensive simulations conducted on MATLAB R2021b platform.
