Experimental Parameter Identification Techniques

Accurate fitting of the battery model with experimental data is not the focus of this paper, so the authors rely on the existing techniques. Instead, the focus is parameterizing the model once the battery is in the usage phase and eventually at EoL (discussed in Section 3.3). Experimental parameter identification is naturally the first step to model development.

ECM or DFN model development requires the human and hardware effort to set up the experiments and perform the necessary tests followed by the subsequent calculation of the battery parameters and its state [47]. The state of the art method of optimizing the parameter set consists of: (1) initially solving the model for a given set of model parameters; and (2) finding the parameter set that minimizes the sum of squared error between the simulated voltage response of the cell and the experimentally observed voltage for a specific drive cycle [48]. It is worth noting that, many techniques have been proposed to identify the necessary parameters for electrical models, but a lower number of identification techniques are available in the literature for electrochemical and aging models.

The term **parameter** refers to the characteristic of the battery, including chemical (solidphase conductivity, diffusion coefficients, etc.) and electric quantities (internal resistance, capacitance, etc.), while the term **state** refers to the variables which illustrate the behavior of the battery such as SOC and SOH.

In the conventional battery model parameter identification methods, experimental data is used to reference the model parameters, which are then brought closer to the experimental results using the following methods: Kalman filter (KF) method, the gradient method, and the gradient-free method. KF approach is usually applied in the parameter estimation of ECMs due to its recursive computation process, while gradient and gradientfree methods are often employed for a DFN model. Evolutionary computation-based identification methods such as particle swarm optimization (PSO) and genetic algorithm (GA) are gradient-free methods, immune to local minimum traps and are usually used to solve the cell's governing equations faster.

The objective or fitness function for parameter identification via GA, PSO, DE, and KF algorithms is defined by Equation (1) [49–52]:

$$L^2 = \frac{1}{N} \min \sum\_{i=1}^{N} \left[ V\_{\exp}(t\_i) - V\_{\text{sim}}(\theta\_\prime t\_i) \right]^2 \tag{1}$$

where, *Vexp* and *Vsim* are the experimental and simulated cell output voltage with the same input current, *N* is the total number of input current data samples, and *i* is the time index, *L* is a representation of the RMS error.

However, the estimations done using these methods may deviate from the actual values due to the fact that the degradation physics caused by SEI (solid electrolyte interphase) layer or lithium plating is not included. Moreover, the variations of the concentrationdependent parameters are usually ignored or assumed as the constant values, which makes the battery state estimation deviate further from reality.
