## 4 Experimental Validation
### Results and Discussion
#### 4.2.2 Network Training  
The proposed method was implemented with the open-source PyTorch machine learning framework. The detailed architectures of the proposed Generator and Discriminator are described in Table 2. The first 60% of healthy data (325 recorded AE signals) are used for training the convolutional GAN, and the \(EHI\) of each training sample is calculated by Equation (17). Then, a fault alarm threshold can be obtained according to Equation (18). Figure 9: Representative time–frequency spectral decompositions of AE signals corresponding to different stages of damage propagation. We assess the performance of HIs from the following aspects: (1) the ability to reflect the breakpoint between the healthy stage and the onset of defects; (2) the ability to characterize the waveform change of the signal; since failure is an irreversible process, (3) HI is expected to be continuous and monotonic. Figure 11 shows the obtained \(EHI\) of all of the 2471 AE data files. Observations show that the \(EHI\) successfully characterizes the evolution of the recorded AE waveforms from the following aspects. Firstly, the \(EHI\) value shows rapid growth at the stage of the 0.5 mm crack, and a breakpoint between the healthy and fault stage is easily observed. Secondly, the IEPF value captures the initiation of the continuous AE transient bursts at the intersection of the 1 mm crack and 1.5 mm crack. Additionally, the \(EHI\) presents excellent monotonicity. In order to evaluate the proposed method and highlight its superiority over existing conventional procedures, the following techniques are introduced and compared with each other. **Statistical parameters**: (1) Mean; (2) Variance; (3) Root Mean Square (RMS); (4) Skewness; (5) Kurtosis; (6) Shape Factor; (7) Crest Factor; (8) Impulse Factor; (9) Margin Factor; (10) Information Entropy (IE); (11) Energy Entropy; (12) Mean Frequency (MeanFreq); (13) RMS Frequency (RMSF); (14) Root Variance Frequency (RVF); (15) Median Frequency (Med-Freq). **Machine learning models**: (16) One-Class SVM (17) Local Outlier Factor (LOF); (18) Isolation Forest (iForest); (19) Autoencoder. The samples are fed into the probed models sequentially. The streaming accuracy (SA) is used as a metric to quantify the performance of each model, which is expressed as  
\[SA_{t}=n_{t}/N_{t} \tag{22}\]  
where \(N_{t}\) denotes the total number of samples from the start to time \(t\); \(n_{t}\) denotes the number of the correctly classified samples until time \(t\). \(SA_{t}\) shows the performance of the probed methods against the acquisition time of each AE signal, and their results are compared in Figure 12, while the average accuracy is plotted in Figure 13. It can be seen that the superiority of the proposed method becomes gradually more and more obvious during the 1 mm crack growth stage, where the developed ensembled convolutional GAN shows the highest average accuracy among all probed contenders. Figure 11: The generated \(EHI\) of the acquired AE signals. Finally, we investigate the influence of the ensemble parameters on the model performance. The ensemble model performance is impacted by the two ensemble parameters \(\theta_{1}\) and \(\theta_{2}\), and the model training epoch \(S\). To facilitate the analysis, we set the parameter \(\theta_{2}\) at 1, and examine the influence of \(\theta_{1}\) and the training epochs at fixed base model numbers. With fixed \(\theta_{2}\) and training epochs, the ensemble parameter \(\theta_{1}\) is defined as \(S-n\), where \(S\) denotes the current training epoch, and \(n\) represents the base model number. Figure 14 shows the experimental results with different training epochs ranging from 50 to 500. The black line presents the average accuracy of the convolutional GAN, while the red lines show the ensembled model accuracy with different base model numbers ranging from 5 to 30. Figure 15 represents the result of the quantitative analysis of the accuracy improvement of the model after applying the HSE procedure.