## 1 Introduction and Related Work
Temperature estimation is made by solving a set of equations representing all nodes, using numerical techniques. \[C_{i}\frac{dT_{i}}{dt}=\lambda_{i}^{cond}+\lambda_{i}^{conv}+\lambda_{i}^{rad}+P _{i} \tag{1}\]  
where C\({}_{i}\) is the thermal capacitance of node i, T\({}_{i}\) is the temperature of node i, \(\lambda_{i}^{cond}\) is the conductance thermal resistance between node i and its environment, \(\lambda_{i}^{conv}\) is the convection thermal resistance between node i and its environment, \(\lambda_{i}^{rad}\) is the radiation thermal resistance between node i and its environment, and P\({}_{i}\) is the heat source of node i. The accuracy of an LPTN-model temperature estimation depends on the number of chosen nodes in the network. Typically, LPTN models are categorized as white box (100-200 nodes) and grey box (2-15 nodes) models. In the white box LPTN-model approach, the significant details of the motor geometry and heat transfer characteristics are included. Though computationally efficient compared to FEA or CFD analysis as it requires solving a large set of differential algebraic equations, it is considered unsuitable for online deployment in the controller system [8]. In a reduced-order LPTN model, the heat transfer pathways are abstracted and thus can be represented with fewer nodes. They can be further classified as light grey (with 5-15 nodes) or dark grey (with 2-5 nodes) models and potentially are computationally lightweight. The representative thermal parameters in a grey-box model are not well known or possible to calculate using analytical equations [9; 10]. For example, the heat transfer coefficients in the airgap and the end-cap regionsare nonlinearly dependent on the motor speed and the ambient temperature. Similarly, the heat transfer coefficient in the stator frame varies as per the ambient temperature. This makes the thermal parameters non-constant and linearly time-varying. The loss components such as winding loss, which are input to the LPTN model, can be calculated from the measured current and winding resistance data; however, the resistance values are temperature-dependent, which is a variable state in the thermal matrix. Furthermore, the core loss is not measurable. Therefore, the estimation of the core loss is made based on FEA methods or by subtracting the winding losses from the measured total losses. Hence, all errors in the determination of total and winding losses directly add up to an error in the iron loss values. In the above backdrop, empirically-based parametrization is a crucial step in these studies [9; 10; 11; 12; 13; 14; 15]. The parameter identification procedure can be stated as an optimization problem in which the values are varied until the used LPTN model gives the same results as the experimental ones. Several gradient-based and non-gradient-based optimization methods have been explored in the past for identifying thermal parameters. [PERSON] et al. [9] employed a calibration procedure based on a sequential quadratic programming iterative method for obtaining the uncertain thermal parameters in the LPTN. However, the computational cost of such tuning procedures is high due to the time-variant nature of the parameters. Hence, to improve computational efficiency, the dependence of the state matrix on the phase current is approximated with polynomial approximation. In the work presented by the authors [11], the parameter identification is conducted by using two determinist methods, the Gauss-Newton method and the Levenberg-Marquardt method, and one stochastic method, the Genetic Algorithm method. The results show good accuracy in predicting the temperature; however, the authors concluded that stochastic methods are more precise for a real-time model operation. [PERSON] et al. [13] used particle swarm optimization (PSO) for the temperature estimation, minimizing the error against the empirical measurements.