## 5 Noise Robustness and Excitation Adaptability
### Robustness Analysis  
The measured dynamic response inevitably introduces noise due to environmental noise or equipment limitations. How to accurately detect the damage locations in noisy (or even high noise) conditions is a key issue that must be addressed in the field of structural damage identification [40]. In order to test the noise immunity of the CWT-SSSM feature-based method, the strain response is superimposed with Gaussian white noise, and the response signal containing noise is used for the damage identification study. The noise level \(\gamma\) can be expressed as the following formula:  
\[\gamma=\frac{RMS(\varepsilon_{noise})}{RMS(\varepsilon_{signal})}\times 100\% \tag{40}\]  
where, \(RMS(\varepsilon_{noise})\) and \(RMS(\varepsilon_{signal})\) denote the root mean square of white noise and noiseless strain response, respectively, and if the value of \(\gamma\) is larger, it means that the noise intensity is also larger. Take the strain response of measurement point 70 under scenario I as an example, and add the Gaussian white noise of \(\gamma=5\%\), \(10\%\) to the strain response, respectively, and the strain response of measurement point 70 after adding the noise is shown in Figure 16.  
Figure 16: Strain response after adding noise at measurement point 70 under scenario I: (**a**) \(\gamma=5\%\); (**b**) \(\gamma=10\%\). Figure 15: Damage identification results under scenario II: (**a**) \(\overline{CS}(b,s)\); (**b**) Damage index \(SSSM_{DI}\). The crack detection of cantilever beams using a strain response containing noise was investigated. Figures 17-20 show the identification results of scenarios I and II under the noise conditions of \(\gamma=5\%\) and \(\gamma=10\%\). It can be seen that \(SSSM_{DI}\) accurately indicates the crack location in both \(\gamma=5\%\) and \(\gamma=10\%\) noise conditions, and the value of \(SSSM_{DI}\) at the non-destructive location is 0. Figures 17-20 show the identification results of the once-noise test, which is not representative. In order to quantitatively analyze the noise immunity based on the CWT-SSSM feature method in different noise environments, a noise immunity index (_NII_) is defined according to the Monte Carlo simulation, and the formula of _NII_ is shown as follows:  
\[NII=(1-MRR)\times(1-FRR)\times 100\% \tag{41}\]  
where \(MRR\) is the missing report rate, which represents the probability of missing the actual damage location in \(N\) tests. \(FRR\) is the missing report rate, which represents the probability of misreporting the actual damage location in the \(N\) tests. The essence of _NII_ is the probability of identifying the damage without missing and false reports. The larger the _NII_, the higher the accuracy of the proposed method in identifying the actual damage location under noisy conditions, and the better the noise immunity. In this paper, 5000 tests were conducted in \(\gamma=\{5\%,\ 10\%,\ 15\%,\ 20\%,\ 25\%,\ 30\%,\ 35\%\}\) noise conditions, and Table 2 shows the results of noise immunity analysis based on the CWT-SSSM feature method in different noise conditions. It can be seen from Table 2 that each _NII_ value of \(SSSM_{DI}\) is greater than \(80\%\) in a \(\gamma\leq 20\%\) noise condition under slight damage (scenario I). Each _NII_ value of \(SSSM_{DI}\) is greater than \(90\%\) in a \(\gamma\leq 35\%\) noise condition under scenario II. In summary, the CWT-SSSM feature-based baseline-free damage identification method possesses high resistance to noise. Without additional noise reduction algorithms, \(SSSM_{DI}\) can identify multiple damage locations of the cracked beams in noisy or even high-noise (\(\gamma=20\%\)) conditions. number of modal frequencies. A theoretically applied impulsive load can also meet the application requirements of the method in this paper. To verify the applicability of the proposed method to the approximate uniform spectral excitation, an impulsive load of 1000 \(N\) is applied to the right end of the breathing cracked cantilever beam.