# Parameter Identification of Lithium Battery Model Based on Chaotic Quantum Sparrow Search Algorithm
###### Abstract
It was found that the FOM with one CPE is equivalent to an integer-order model (IOM) which has five RC networks [17]. To further improve the accuracy, a Warburg component (W) was added in series with the polarization resistor [18] or the internal ohmic resistor [19] to describe the battery dynamic characteristics more properly. Moreover, [PERSON] et al. [20] proposed an FOM with two CPEs, which exhibited more robustness to uncertainties. In addition to the accurate modeling of the battery, another key challenge is model parameter identification. In general, precise model parameters are not only crucial for \(SOC\) estimation but they can also reflect the battery SOH which is usually defined by the internal resistance or the capacity. For the IOMs of ECM, a typical method is offline identification based on the HPPC test which, however, has poor accuracy under dynamic operating conditions. Therefore, plenty of online parameter identification algorithms have been put forward, such as the recursive least squares (RLS) [21], RLS with forgetting factors (FFRLS) [22], extended Kalman filters (EKF) [23] and universal adaptive stabilizers (UAS) [24]. Moreover, some researchers have designed an online parameter identification method considering multiple time scales according to the fast and slow change characteristics of the model parameters [25]. Nevertheless, these methods are not adequate for FOM models. A heuristic optimization algorithm is one feasible solution. For example, the genetic algorithm (GA) was adopted to obtain the order of the fractional element and other model parameters [26; 27; 28]. Moreover, [PERSON] et al. [29] used the particle swarm optimization (PSO) algorithm to identify the parameters of a fractional-order two-RC circuit model. [PERSON] et al. [30] proposed a time-frequency-domain-based fractional-order model parameter identification method using a genetic particle swarm optimization algorithm. However, the naive forms of these algorithms are prone to fall into local optimal solutions. To account for this weakness, quantum behavior has been combined with intelligent algorithms, such as the PSO [31], artificial bee colony algorithm [32] and bacterial foraging algorithm [33]. Recently, to further improve the solution accuracy, a sparrow search algorithm (SSA) was proposed [34]. However, like PSO and GA, it may also be trapped into local optimum although the global search ability is excellent. In addition, the SSA converges slowly because a random wandering strategy is adopted when there are no neighboring peers around an individual sparrow. To address these issues, many studies have been carried out. [PERSON] et al. [35] proposed an improved SSA which applied the logistic chaotic mapping and adaptive parameters to the sparrow position initialization and update and obtained good configuration parameters. [PERSON] et al. [36] added an adaptive learning rate to accelerate the process and avoid the inefficient random wandering. Furthermore, levy flight strategies [37; 38] and Gaussian variation strategies [39] have been applied to improve the ability of avoiding getting stuck in a local optimal solution. In this study, we adopt a fractional-order model with two CPEs as a battery model and formulate the model parameter identification problem as an optimization problem. The chaotic mapping and quantum behavior strategies are combined with the SSA to minimize the sum of squared errors (SSE) between the measured and estimated voltages of the model. Experiments are performed under three different operating conditions, namely, the hybrid pulsed power characteristic test (HPPC), pulsed discharge test (PULSE) and urban dynamometer driving schedule test (UDDS). Compared with PSO, GA, GWO [40], DOA [41] and SSA, the proposed chaotic quantum sparrow search algorithm (CQSSA) exhibits superior performance in accuracy and adaptability. The main contributions of this study are as follows:  
1.