# Guided Wave-Based Monitoring of Evolution of Fatigue Damage in Glass Fiber/Epoxy Composites
## 5 Experimental Results  
With the aforementioned WPT-based signal processing and multivariate feature extraction method, the wave signals obtained under different fatigue states are analyzed. The mother wavelet function of Daubechies wavelet 'db1' is used to decompose each of the wave signals into sub-components, and a 4-level decomposition is performed with \(2^{4}=16\) components in total. Figure 6 shows the WP component energies of the baseline wave signals for specimens S_A and S_B at zero cycle, i.e., without fatigue damage. It can be seen that the WP component energies mainly concentrate on the first several components. For both specimens, the sums of energies in the first five components exceed 98% of the total energies of the wave signals, thus the first five energies form the energy vector as the multivariate signal features for characterizing the fatigue damage in this study. Figure 7 shows the evolution of the first five WP component energies of the wave signals with the increase of fatigue cycles. It can be seen that, in general, with the increase of fatigue cycles, the energies for each WP component decay quickly at the initial stage and then slow down. This trend is very similar to that of the decay of stiffness. Figure 6: \(Cont.\)  
Figure 6: Wavelet packet (WP) component energies for the baseline wave signal: (**a**) specimen S_A and (**b**) specimen S_B. Figure 7: Variations of WP component energies of wave signals with fatigue cycles: (**a**) specimen S_A and (**b**) specimen S_B. As aforementioned, to construct a suitable mean vector and a covariance matrix for outlier analysis, the guided wave signals in pristine state are copied 500 times and each copy is subsequently corrupted with amplitude fluctuation and measurement noise, as described in Equation (10). Two contamination levels are considered: (I) Level 1: the fluctuation factor \(e\) comes from uniform distribution [\(-\)0.05 0.05] and the SNR of measurement noise is 20 dB. (II) Level 2: The fluctuation factor \(e\) comes from uniform distribution [\(-\)0.1 0.1] and the SNR of measurement noise is 10 dB. Figure 8a,b illustrates the contaminated baseline signals with different levels for specimen S_A. Similar contaminated signals can be obtained through Equation (10) for baseline signal for specimen S_B. Then for each set of contaminated 500 baseline copies, mean vector and covariance matrix are constructed and baseline MSDs are calculated according to Equation (9). To set an appropriate threshold value, statistical analysis is performed and lognormal distribution is used to fit the probability density function (PDF) for baseline MSDs. As illustrated in Figure 9a, for wave signals from specimen S_A with Level 1 contamination, threshold is determined by taking the value corresponding to 99.9% confidence of the fitted lognormal distribution, which is 19.3. To test whether the wave signals after a certain fatigue cycles are outlier or not, the wave signals are copied 100 times and the same contamination levels for the baseline signals are applied. The corresponding MSDs for different sets of contaminated wave signals can be also calculated by Equation (9) and compared with the threshold value. If the MSDs are less than the threshold value, it can be considered that the change of guided wave features compared to the baseline set is caused by environmental conditions or measurement noise; otherwise it is caused by damage in the structure, i.e., fatigue damage in our case. It can be seen from Figure 9b, the calculated MSDs after different fatigue cycles all exceed the threshold value, and with the increase of fatigue cycles, the MSDs have a general increased trend. The means of the MSDs increase almost monotonically with the fatigue cycles. This may because only matrix cracks increasingly accumulate in specimen S_A before 10,000 fatigue cycles. It demonstrates that MSD can be used as a measure to integrate the multivariate signal features to detect and characterize fatigue damage in composites.