## 3 Model Complexity and Space Reduction Techniques for System-Level Optimization
### Parameter Criticality Assessment
#### 3.2.1 Sensitivity Analysis  
The sensitivity analysis approach is aimed at classifying the parameters intended for optimization based on how small variations in these parameters influence system performance. These variations may arise from inherent material imperfections, manufacturing  
Figure 8: Basic structure of an artificial neural network. The three primary layers—input, hidden, and output—are illustrated. defects, or constraints introduced by tolerances during the manufacturing process [53]. Essentially, this method allows the designer to eliminate parameters that have minimal or no impact and focus solely on optimizing the critical ones, thereby reducing the parameter space. Indicative methods include One-at-a-Time (OAT), Pearson correlation coefficient, regression-based sensitivity analysis, variance-based decomposition (VBD), and the Sobol method. The latter two are particularly widespread due to their ability to account for model non-linearities and higher-order interactions among parameters, whereas the former methods are limited in capturing such complexities unless combined with complementary techniques such as DoE. Based on the above discussion, and the illustration in Figure 9, the most critical parameter is \(x_{1}\), while \(x_{2}\) appears to be the least influential for the output variables, \(y\), as indicated by the qualitative \"sensitivity\" metric. In the studies [14; 37; 38; 39; 40; 50] analyzed previously, a sensitivity analysis served as the fundamental pillar for further analysis. In [54], a study was conducted utilizing the magnetic parameter design methodology, which is based on the non-linear properties of magnetic materials combined with analytical equations. Variance-based sensitivity analysis is performed to determine the criticality of various parameters and capture their non-linearities and higher-order dependencies. Following this, the analysis identifies the turn-on, \(\theta_{on}\), angle as the critical parameter for the controller and the number of turns, N, as the critical parameter for the motor, optimizing both simultaneously. The proposed method is applied to the following three SRM topologies: five-phase 10/8, nine-phase 18/20, and three-phase 12/8. The results are compared with the FEM analysis, leading to the conclusion that minor errors exist but are justified. Reference [55] serves as a continuation of [26], where the proposed method is experimentally validated. Additionally, a form of sensitivity analysis is employed, utilizing a systematic down-selection process to determine the parameters for optimization. As a result, although the number of design parameters increased from six in [26] to eleven in [55], only the most critical parameters are selected at each iteration for further optimization. The study further compares the results obtained from the voltage-fed analytical equations and the FEM-based simulations under dynamic conditions. The findings indicate that the dis  
Figure 9: Sensitivity analysis of the output variables, \(y\), based on the input parameters, \(x\). crepancies between the two approaches remain within an acceptable range. Experimental validation is carried out using a scaled 5 hp SRM prototype tested on a dynamometer setup, where voltage, current, and torque waveforms closely match simulation results, with minor deviations attributed to practical factors. In [56], the authors focus on the design of an External Rotor Switched Reluctance Motor (ERSRM) by implementing a sensitivity analysis through the Pearson correlation coefficient, Latin hypercube sampling to extract candidate models, and an improved version of the NSGA-II algorithm, referred to as CD-NSGA-II. This enhanced optimizer incorporates the chi-square distance metric in contrast to the standard NSGA-II and is applied through MATLAB/Simulink and ANSYS. The sensitivity analysis identifies the critical parameters as the \(\theta_{on}\) and \(\theta_{off}\) angles, along with key geometric parameters of the motor.