## 1 Introduction  
Offshore platforms are a form of marine infrastructure; they are an important tool for understanding the ocean and for developing marine resources, and they are of great significance in strategic marine development. So far, the fixed steel structure jacket platform has become the most widely used offshore platform [1]. For example, many offshore platform jackets have been built in China's Bohai Bay, China's offshore exploration and development technology has reached the world-class level, and the continuous production increase of Bohai oil field has provided energy demand for China's rapid economic development. However, offshore structures are faced with complex marine environment, e.g., wind, waves, currents, ice, or other loads. In order to ensure the functional performance during the safe design service life, structural health monitoring (SHM) of offshore structures plays a major role in ensuring their safe operation [2]. Typical SHM methods are typically based on natural frequency or modal shape, frequency response function and modal strain energy. In recent years, the parametric methods, especially the modal strain energy -based methods, have often been applied for damage detection of marine structures [3]. Those SHM method are mainly based on the collected structural dynamic response data and feedback the changes of structural dynamic characteristics to determine the loss location and degree of offshore platform structure. However,due to the disturbance of marine environment, it is not easy to obtain accurate results [4]. Therefore, the improved SHM methods rely heavily on the accuracy of the modal analysis, some data processing techniques have been proposed to overcome the problems that arise in the identification of modal parameters, e.g., mode correction, sensitivity to noise. [PERSON] et al. [5] introduced the factors of mode correction and defined a new damage indicator based on the concept of modal strain energy to localize the damage of offshore wind turbines based on spatial incompleteness with better accuracy. [PERSON] et al. [6] introduced frequency information into the traditional Stubbs index method. The effectiveness of the improved method for damage localization was proved by the numerical example and laboratory study of jacket platforms. [PERSON] et al. [7] presented a two-step approach to capture the dynamic response of an offshore jacket platform based on the real-time kinematic global navigation satellite system (RTKGNSS), which combined a Chebyshev filter and complementary ensemble empirical mode decomposition with adaptive noise (hereinafter referred to as CF-CEEMDAN). [PERSON] et al. [8] proposed a new approach for SHM of offshore jacket platforms, which used the measured ambient vibration responses and the corresponding readable natural frequencies and mode shapes of the structural system. [PERSON] et al. [9] proposed a novel method to detect structural damages of offshore platforms based on grouping modal strain energy, which method divided the unit modal strain energy into axial tension-compression and bending. [PERSON] et al. [10] proposed an iterative noise extraction and elimination method to solve the difficulty of modal parameter identification caused by contaminated high-energy components in measured signals. [PERSON] et al. [11] proposed an improved model reduction-modal-based method for model updating and health monitoring of an offshore jacket-type platform. [PERSON] et al. [12] presented a sampling rate selection of sensors method in offshore platform SHM based on vibration. However, the complexity of the marine environment leads to the above traditional and improved SHM methods to still present challenges, e.g., incomplete and inaccurate modal information, noisy measurements. With the in-depth study of SHM for offshore platform, mathematical statistical methods have also been introduced, which is capable of damage diagnosis with limited, dispersed modal data. [PERSON] et al.