## 3 Crack Identification Based on COSMO
### Experimental Measurement  
A specimen made of Q235 (See Table 1) with dimensions 800 mm \(\times\) 250 mm \(\times\) 20 mm was used in the experimental measurement, as shown in Figure 5. Four sections embedded with cracks with average depth of 6 mm, 2 mm, 1 mm, and 0.5 mm were manufactured in the specimen, mainly located at 150 mm, 300 mm, 450 mm, and 600 mm, respectively, denoted by B, C, D and E. Additionally, Section A and F represented as undamaged regions located in the two ends of the specimens. A portable TOFD ultrasonic detector (PXUT-920, Nantong Union Digital Tech., China) was used to excite a narrow-pulse acoustic signal with 200 ns in width and stored the echo signals from inspected cracked region. Scanning was manually carried out by a scanner unit with one pair of 5 MHz normal transducer, i.e., the transmitter and the receiver, with 60\({}^{\circ}\) wedges for longitudinal waves. Two transducers, spaced 62 mm apart, were located at equidistant over the crack region center, and scanning was done by moving the scanner in the length direction of steel plate parallel to the crack region. The echo signal sampled by the detector, containing 1496 points, was acquired every 0.5 mm along the length direction. After a scanning, a total of 1600 echo signals (A-scan) were obtained and stored in the ultrasonic detector.  
COSMO method was applied to analyze this dataset of echo-signal recorded by TOFD ultrasonic detector. Firstly, the Hellinger distance matrix D was constructed using Equation (1), and the row with minimum sum was chosen in the metric D so that the \(z\)-score could be determined using Equation (2). Figure 6a shows the \(z\)-score distribution for 30 scanning. It is shown that the \(z\)-score in undamaged sections is much larger than those in the region with cracks. For example, the \(z\)-score for positions A and F are about 0.4-1, while those for positions B, C, D and E are below 0.4. The results suggest that the \(z\)-score is closely related to cracks of specimen, just as the simulated results.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Grade**} & \multicolumn{4}{c}{**Elements (\%)**} & \multicolumn{4}{c}{**Yield Strength**} & **Tensile Strength** & **Elongation** \\ \cline{2-7}  & **C** & **Mn** & **Si** & **P** & **S** & **(MPa)** & **(MPa)** & **(\%)** \\ \hline Q235A & 0.14–0.22 & 0.30–0.65 & 0.30 & 0.045 & 0.030 & 235 & 375–460 & 21–26 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical characteristics of Q235 carbon steel. (Provided by HBO Windpower Equipment Co., Ltd, Nantong, China).  
Figure 5: (**a**) A specimen with four cracks with average depth of (**b**) 6 mm, (**c**) 2 mm, (**d**) 1 mm, and 0.5 mm located at Section B, C, D, E, respectively. Section A and F without cracks.  
By using Equations (1)-(4) and (5), the deviation level T-Value is calculated to make a significant analysis. It can be observed from Figure 6b that the T-value at B, C, D and E are of high level compared to those in uncracks region. For instance, the T-value at x = 150 up to 13, and T- value at x = 600 sharply increasing from 0 to 7, but T-value of sections without cracks almost equal to 0, far less than T-value at crack region. In addition, T-value increase almost linearly with the depth of cracks. The relationship curve between the peaks of T-value and crack depth is plotted in Figure 7. It is shown that the peak of T value increases with crack growth from 0 to1.5 mm quickly up to 5, which is exactly in stage I. When the crack depth is larger than 2, the slope of curve go slow but still faster than the simulated results. It is worth noting that the change of slope is not distinct enough to easily recognize stage II or III when depth of crack exceeding 1.5 mm, different from the simulated curve, which might attributed to the result of multi-physical mechanisms.