## 1 Introduction  
It is of great importance to utilize ocean space and marine renewable energy, as land-based resources are increasingly depleted [1]. Offshore steel jacket platforms play an important role in oil and gas exploration, drilling operations, and transportation in ocean environments [2]. The jacket platform is a type of bottom-fixed offshore structure with many advantages. A jacket platform is often composed of slender tubular members, making the structure less exposed to ocean wave loads and relatively robust in adverse environments [3]. However, some natural phenomena such as earthquakes, wind, and currents can arise in the working environments [3; 4; 5; 6]. A few catastrophic accidents of offshore jacket platforms occurred in the past years. For example, in 1964, hurricane Hilda, with wave height of 13 m and wind gusts up to 89 m/s, destroyed 13 platforms. The next year, hurricane Betsy destroyed three platforms and damaged many others [7]. The degradation of materials due to fatigue and corrosion may cause serious damage to the structural elements during their useful life [8], and the damage probability increases under adverse environments. Therefore, effective damage identification methods are desired by the industry [9], and research has been carried out in this area. [PERSON] et al. [10] presented a method of damage identification for jacket platforms using the frequency variation approach. [PERSON] et al. [11] noted that the change of modal response amplitude can reflect the structural damage. Besides the damage identification method based on dynamic results, the damage identification methods based on model updating are focused on by many researchers. For example, [PERSON] et al. [12] presented a method for model updating using the cross-modal method and the Guyan scheme method. [PERSON] et al. [13] studied a consistent regularization of nonlinear model updating for damage identification which can avoid unrealistic results due to inherent measurement errors. [PERSON] et al. [14] studied the performance of the two different model updating techniques to localize and quantify the damage. [PERSON] et al. [15] solved the identification problem with the OMAX approach. [PERSON] et al. [16] proposed a substructure approach to extract the substructure dynamic flexibility matrices from the measured modal properties of the global structure and updated directly using the traditional model updating method. [PERSON] et al. [17] improved the model updating method using response surfaces and performed damage identification. [PERSON] et al. [18] proposed a probability-based damage detection procedure using model updating. [PERSON] et al. [19] performed damage assessment using model updating with uncertainty. [PERSON] et al. [20] improved the updating method using the Bayesian approach. [PERSON] et al. [21] proposed an automated model updating method considering multiple crack effects. [PERSON] et al. [22] introduced the power spectral density to model updating of damage identification. [PERSON] et al. [23] studied the effects of variability in ambient vibration measurements on model updating and performed damage identification. [PERSON] et al. [24] proposed a sensitivity-based finite element model updating approach to identify the local damages in the axially functionally graded beams. [PERSON] et al. [25] proposed a process to mitigate the effects of modeling errors during model updating. [PERSON] et al. [7] proposed a methodology for damage identification using the damage submatrices method. In addition, [PERSON] et al. [26] presented a new approach for structural health monitoring of offshore jacket platforms using inverse vibration technique. Generally, damage detection is a type of inverse problem, and one needs to determine structural parameters based on given structural responses. Because artificial neural networks (ANNs) have a strong ability to solve inverse problems that cannot be described in terms of explicit mathematical formulae, they have been used to solve many different kinds of problems.