## 4 Conclusions  
Numerical and experimental validation confirmed that the proposed SER approach is an effective method of damage identification. In the novel approach, the difference between the expanded and measured strains is used for damage identification. In the intact structure, the expanded strain is consistent with the measured strain. An increase in the severity of damage to the structure results in an increased difference between the expanded and measured strains. We defined \(D\) to quantify the difference in strain and determined _DI_ to identify damage. A large value of _DI_ indicated high severity of damage in the structure. For the structure with one slat possessing merely 0.5% damage zone, the calculated index is increased by 259% of the intact case. When the damage zone was doubled, the index increases significantly by 467% of the intact case. The difference of _DI_s between different DL1 and DL2 damage scenarios is up to 58% to determine the damage severity. By categorizing the _DI_ levels, the severity of damage can be classified in future applications.  
Moreover, numerical simulation confirmed that the novel damage identification method can be applied to an OWT jacket substructure to identify multiple damage sites in both the same pipe and different pipes. The _DI_ values are extremely high (>10) for identifying the sites. Even if the severity at multiple damage sites is different, damages and their severity can still be discerned with distinct _DI_s. Thus, the proposed method is promising, can determine damage severity, and can provide information  
Figure 7: Simulation results of Case 3-1 at Location 1 under (**a**) wind loading and (**b**) wave loading; \(e\) and \(m\) denote expanded and measured strains, respectively. We eliminated the first 5 s of simulation results, which were calculated as the preloading step.  
to enable a suitable solution to be found. The application of this method is expected to be extended to complicated situations. Besides, the results for the governing loading verified that our proposed method can be effectively employed not only under normal operating conditions but also when the wind speed is sufficiently high. By identifying the damage at an early stage, the method can reduce maintenance costs and even extend the service life of an OWT jacket substructure.  
Conceptualization, H.-H.H.; methodology, [PERSON]-H.H., [PERSON]-P.L. and [PERSON]-H.H.; software, [PERSON]-H.H. and D.-P.L.; validation, [PERSON]-H.H. and D.-P.L.; formal analysis, [PERSON]-H.H. and D.-[PERSON]; investigation, [PERSON] and [PERSON]; data curation, [PERSON] and [PERSON]; writing--original draft preparation, [PERSON] and [PERSON]; writing--review and editing, [PERSON], [PERSON] and [PERSON]; visualization, [PERSON] and [PERSON]; supervision, [PERSON] and [PERSON]; funding acquisition, [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Ministry of Science and Technology (MOST), Taiwan [grant No. 108-2628-E-002-007-MY3]; Bureau of Energy, Ministry of Economic Affairs (MOEA), Taiwan [grant No. 109-D0106]; and National Taiwan University, Taipei, Taiwan [grant Nos. NTU-CDP-109L7725].  
The authors declare no conflict of interest.