# A Novel Optimization Framework to Replicate the Vibro-Acoustics Response of an Aircraft Fuselage
## 4 Optimization Process
### Global Optimization Method  
DEVOL was selected as the global optimization method to guarantee complete coverage of the design space even if its computational burden can represent a drawback. This was not the case for our problem as the evaluation of hundreds of candidate points on the surrogate models was executed in sub-second time. Other algorithms were tested (like Simulated Annealing) achieving comparable results; the accuracy of the RSM was significantly more relevant than the algorithm itself. Subsequently, a proximity check was performed to avoid oversampling of the same design region and/or \"corned\" RSMs, (measuring the distance between the proposed optimal point and the existing experiments). Differences in design variables ranges were removed through a normalization of the design space. The distance was determined using the design variable only, not the results of the simulation. Candidate points within an arbitrary threshold were moved by a limited, random offset to preserve the general location but avoid duplicated samples, as would happen when the solver is trapped in a local minimum. The random offset reduces but does not solve entirely, the potential oversampling problem, thus resulting in new experiments still focused on a specific region of the domain. To address this limitation, a dedicated space-filling was performed; this improved the overall RSM and reduced the chances of local minima traps [16] by setting up one experiment in the less explored region of the design space. The resulting continuous MaxMin optimization problem was replaced with a discretized version, based on a dense, support LHD [17]. The identification of the design point that has the maximum, minimum distance from all the existing ones requires the evaluation of the distance of all the points in the support from all the previous experiments. L1 norm was used both to reduce the effort and due to its representativeness in higher dimensions [18]. MaxMin and discrete space-filling offer comparable solutions (provided a dense enough support) for single-point applications, whereas if multiple experiments had to be added, the discrete space-fillingresults were sub-optimal. This limitation has been considered acceptable due to the nature of the envisioned optimization method. As a final step, the FEM simulations for both candidate and space-filling points were performed, and the results included in the DOE dataset used in the following iterations. From the operative point of view, running two experiments in a single batch was more efficient than 2 separated experiments. The adopted termination criterion was the total number of analyses, whereas the implementation of a convergence check was postponed to a later stage. The simulation workflow illustrated in Figure 10 was constructed in Optimus to run the MDO process. This optimization strategy made the structure flexible since the DOE results were independent of the chosen function for the metrics, i.e., the target function; the latter was defined in a python script loaded in the software when calculating the metrics (see Figure 10). The separation between the outputs generated by the simulations and the post processing allowed for different metrics to be tested preserving the experiments database. The choice of the metric function was a key point of the work in order to get the most appropriate comparison between RC and SC data. Different functions were tested and the current choice (this aspect is still under study) is reported in Equation (1): it represents a normalized percentage difference among the AI values for each microphone:  
\[\text{Normalized metric}=\frac{\sum_{\text{i=1}}^{\text{n}}\left|\frac{ \Delta\text{I}^{\text{RC}}-\Delta\text{I}^{\text{SC}}_{\text{i}}}{\Delta\text {I}^{\text{RC}}_{\text{i}}}\right|}{\text{n}}=\frac{\text{metric}}{\text{n}} \tag{1}\]  
where n is the number of microphones, AIRC is the acoustic intensity array for the RC, and AISC is the acoustic intensity array calculated for each iteration.