## 2 Numerical Model Development and Experimental Validation
### Numerical Model Validation
#### 2.3.2 Machine Learning  
The objective of this machine learning algorithm is to analyze the correlation between the experimental and simulated data and determine if the simulations can be used as stand-ins for experimental tests and what are their limitations. With all the data correctly organized and divided, the machine learning method of choice was a Feed Forward Neural Network (FFNN) due to its simplicity and ease of use. It was also chosen due to its suitability as a regression model, thus the damage can be detected more precisely without the need for classes. The chosen batch size was 16 and the number of data points/input data used was 500 from the total 1700 obtained during the interpolation process of the time-series previously acquired. On the other hand, the output data used were, for the simulated data, [PERSON]'s modulus of the damaged area, and for the experimental, an approximation of [PERSON]'s modulus obtained from the tensile test was used. This small number of 500 points out of 1700 from the time-series was used as they possessed a portion of the initial vibration without a large influence of the reflections. This shows that the simulation is lacking in the reflections when compared to the experimental cases and thus there is a fine-tuning between too few data points and where the reflections start to heavily influence the data. The mean absolute error (MAE) was chosen both as a loss function and as an evaluation metric, while for the optimization the ADAM method was used. Finally, a total of 100 epochs was selected as previous analysis showed that there was no need for more iterations and the overall training times were in the accepted range. The overall structure of the FFNN can be seen in Figure 9, with a total of five layers, one input, three hidden, and one output layer. The input consisted of the 500 data points of one signal and the subsequent layers had several nodes that were tested empirically until the best results were achieved. Figure 9: Overall structure of the chosen FFNN with five layers, each one with a different kernel size. The first test conducted was to determine what signal direction from the simulation should be used. To do this, five tests for each direction were conducted, whose results are listed in Table 1.  
The average of the five combinations of directions was taken for each case. Finally, the average of these results was obtained. It is possible to see that the direction U2 has the lowest average value, with a total of 240 MPa of average error. Finally, when analyzing the complete dataset obtained from the five cases, U2 was the only case where there was no complete error case and where the algorithm obtained the wrong result by at least the maximum analysis range. The use of U2 also makes sense when analyzing the simulated specimen, as U2 is the direction in which the sensor is from the actuator, thus it is the shortest path and has fewer cases of reflections when compared with the other Cartesian directions. With the chosen vibrational direction, it is possible to determine the influence of the simulated data when combined with the experimental. This was done following the previous test but instead of the vibrational direction, the number of experimental cases was altered in comparison to the simulated. For each case, a total of five tests were conducted and the average can be seen in Table 2.  
In Table 2, the previously mentioned results can be seen and it is possible to conclude two things:  
* A few experimental cases constantly have bad results. This is probably because the tests had some form of inconsistency during the experimental setup and thus can be considered faulty. * The average values are always lower when simulated values are used, showing their reliability as a form of simple data augmentation. * The validation cases cannot be correctly determined when testing and training are done only with simulated values, showing that there is still a need for a few experimental cases to create a correlation between the experimental and simulated data.