## 3 Results and Discussion
### Fault Classification Results
Table 5 shows that for faulty operating mode 1 (\(C_{1}\)), the ANN classifier recognizes 2863 observations out of 3000 (true positive) observations. For this scenario, the detection precision is 94.05 percent, the recall is 95.43 percent, and the misclassification rate is equal to 4.57%. For \(Fault_{2}\), designated to class C2, the precision is equal to 94.44%, the recall is 98.66%, and the misclassification rate is equal to 1.34%. The Precision for \(Fault_{3}\) is 90.01%, the recall is 95.26%, and there is a 4.74% misclassification. The misclassification is therefore 8.17% for \(Fault_{4}\), 1.87% for faulty operating mode5, 6.8% for \(Fault_{6}\), 2.64% for \(Fault_{7}\), 6% for \(Fault_{8}\), 4.24% for faulty operating mode9, 5.97% for \(Fault_{10}\),9.93% for \(Fault_{11}\), 14.07% for \(Fault_{12}\), 1.37% for \(Fault_{13}\), 23.74% for \(Fault_{14}\), 8.3% for \(Fault_{15}\), 2.27% for \(Fault_{16}\), 8.07% for \(Fault_{17}\),6.14% for \(Fault_{18}\), 2.37% for \(Fault_{19}\), 2.6% for \(Fault_{20}\),and 9.27% for \(Fault_{21}\). In Table 6, the misclassification is 9.04% for the healthy case, 4.87% for \(Fault_{1}\), 1.6% for \(Fault_{2}\), 1.67% for \(Fault_{3}\), 2.84% for faulty operating mode4, 2.87% for \(Fault_{5}\), 4.1% for \(Fault_{6}\), 7.8% for \(Fault_{7}\), 9.3% for \(Fault_{8}\), 6.07% for \(Fault_{9}\), 9.34% for \(Fault_{10}\), 6.24% for \(Fault_{11}\), 10.24% for \(Fault_{12}\), 3.6% for \(Fault_{13}\), 9.94% for \(Fault_{14}\), 9.3% for \(Fault_{15}\), 2.5% for \(Fault_{16}\), 5.97% for \(Fault_{17}\), 5.47% for \(Fault_{18}\), 2.94% for \(Fault_{19}\), 4.14% for \(Fault_{20}\), and 8% for \(Fault_{21}\). In Table 7, the misclassification is 29.54% for the healthy case, 4.2% for \(Fault_{1}\), 4.64% for \(Fault_{2}\), 10.47% for \(Fault_{3}\), 8.3% for faulty operating mode4, 0.64% for \(Fault_{5}\), 10.5% for \(Fault_{6}\), 5.84% for \(Fault_{7}\), 10.54% for \(Fault_{8}\), 32.64% for \(Fault_{9}\), 98.24% for \(Fault_{10}\), 6.44% for \(Fault_{11}\), 3.77% for \(Fault_{12}\), 3.44% for \(Fault_{13}\), 9.24% for \(Fault_{14}\), 8.44% for \(Fault_{15}\), 2.6% for \(Fault_{16}\), 12.77% for \(Fault_{17}\), 38.57% for \(Fault_{18}\), 33.6% for \(Fault_{19}\), 14.84% for \(Fault_{20}\), and 11.17% for \(Fault_{21}\). Despite the fact that the introduced faults are numerous, similar, and close, the developed technique, which merges the benefits of multiscale representation and the PCA technique, shows significant efficiency in detecting and diagnosing such frequent failures. Therefore, overall results show that the evolved approach can improve the performance of a variety of existing techniques, not only in terms of recall, precision, and accuracy but also by significantly reducing computation time and storage space requirements. One can conclude that denoising variables, eliminating stochastic samples, removing irrelevant and correlated samples, and selecting and extracting only informative statistical features using an MSPCA tool are crucial to reducing the misclassification rate and thereby achieving the higher accuracy and reliability of FDD-based techniques.