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The utilization of neural operators in a digital twin model of an offshore floating structure holds the potential for a significant shift in the prediction of structural responses and health monitoring, offering valuable real-time control insights. In this work, we investigate the effectiveness of three neural operators, namely the deep operator network (DeepONet), the Fourier neural operator (FNO), and the Wavelet neural operator (WNO), to accurately capture the responses of a floating structure under six different sea state codes (3 − 8) based on the wave characteristics described by the World Meteorological Organization (WMO). To further enhance the accuracy of the vanilla architecture of the neural operators, novel extensions, such as wavelet-DeepONet and self-adaptive WNO, are proposed in this paper. The results demonstrate that these high-precision neural operators can deliver structural responses more efficiently, up to two orders of magnitude faster than a dynamic analysis using conventional numerical solvers. Additionally, compared to gated recurrent units (GRUs), a commonly used recurrent neural network for time-series estimation, neural operators are both more accurate and efficient, especially in situations with limited data availability. Taken together, our study shows that FNO outperforms all other operators for approximating the mapping of one input functional space to the output space as well as for responses that have small bandwidth of the frequency spectrum. Conversely, DeepONet, with historical states, proves most accurate in learning the mapping of multiple input functions to the output space and capturing responses within a broad frequency spectrum. • Assess neural operators' performance to predict offshore structure response to waves. • Introduced Wavelet DeepONet for improved signal decomposition in wavelet space. • Introduced self-adaptive WNO for balancing loss function components automatically. • Neural operators compute responses up to two times faster than numerical solvers. [ABSTRACT FROM AUTHOR]

Offshore structures have inherently uncertain structure characteristics, which lead to the uncertainty of barrier levels. Although the uncertainty of barrier levels may affect the uncertainty of structural failures, there is no guidance on how to conduct an analysis due to a lack of efficient methods, particularly related to the random nature of both barrier levels and seismic motions. This article contributes to the development of an efficient method to compute the probability density function (PDF) of the first passage probability of offshore structures with an uncertain barrier level under random seismic motion. By establishing a transformation relationship between the barrier level and the first passage probability through the curve fitting operation, an explicit PDF of the first passage probability is simplified to the product of the transformation relationship and the PDF of the barrier level. Once the transformation relationship is obtained, the proposed method can quickly calculate the PDF of the first passage probability of structures with an arbitrary PDF of the barrier level. In the numerical studies, a monopile offshore wind turbine subjected to two types of random seismic motions is studied. Three kinds of PDFs of the uncertain barrier level are chosen for each case. The high accuracy and efficiency of the proposed method are validated by comparing with Monte Carlo simulations. Numerical studies confirm that a small uncertainty of the barrier level leads to a very large uncertainty of the first passage probability. It indicates that the first passage probability computed by traditional deterministic methods might be far from the true failure probability. The quantitative calculation of the uncertainty of failure probability is recommended in design to improve the safety and economy of structures. • Consider uncertain barrier level of OWTs came from uncertain structure features. • Derive the probability distribution of first passage probability (FPP) for OWTs. • Small uncertainty in barrier level generates large uncertainty in FPP. • Verify the proposed method by Monte Carlo simulations. • Apply to arbitrary probability density function of the barrier level. [ABSTRACT FROM AUTHOR]

Fixed offshore structures under stochastic loadings usually have time-dependent reliability due to time-varying statistics of nonstationary load effects. Since closed-form solutions for such time-varying statistics are difficult to obtain, traditional methods cannot analytically evaluate reliability of structures. In this paper: (1) the explicit closed-form solutions for variances of nonstationary load effects at arbitrary time of linear structures are derived by a pole-residue method; and (2) the explicit solution of a time-dependent reliability index of the structure is then established. For computing displacement variances of offshore structures to waves using the pole-residue method in step (1), an innovative approach of writing the wave force power spectral density into its pole-residue form is developed. To verify the efficiency of the proposed method, a numerical example studies the time-dependent reliability index of the monopile foundation of offshore wind turbines under random waves. Furthermore, a hybrid numerical–experimental study of a jacket platform model to ground motions is conducted. The results indicate that reliability of structures at the nonstationary part is significantly smaller than that at the stationary part. This study provides a reference and advocates attention to structural failures generated by nonstationary responses to extreme loads, e.g., earthquakes. [ABSTRACT FROM AUTHOR]

This paper explores the use of physics-informed neural networks (PINNs) to estimate motion and identify system parameters of a moored buoy under three different sea states. PINNs are a deep learning architecture that incorporates physical information to provide an interpretable and physically-meaningful neural network model, making it well-suited for modeling offshore moored structures with high nonlinearity. The moored buoy is modeled as a nonlinear ordinary differential equation (ODE), and the general formulation of PINN for the system of ODEs is established. Two new metrics for motion estimation and system identification are proposed to evaluate the accuracy and efficiency of the implementation of PINN. The results demonstrate that PINN can accurately estimate motion and identify system parameters by choosing appropriate hyperparameters (HPs). This paper also investigates the effects of the number of layers, nodes, and learning rate on motion estimation and system identification to provide a benchmark for selecting optimal HPs. This study finds that hyperparameter optimization can reduce the relative error of identified parameters by up to two thousand times compared to no optimization. Motion estimation prefers large neural networks for all sea states, while at least three layers of neural networks are needed for accurate parameter identification. The paper also provides a look-up table to investigate further implementing PINN on moored floating offshore structures. Proper selection of HPs is crucial as it can incur up to three orders of magnitude PINN loss and exceedingly-high identification error. Overall, this study highlights the applicability of PINN in modeling complex offshore structures and provides insights into selecting optimal HPs for accurate and efficient estimation of motion and system parameters. [ABSTRACT FROM AUTHOR]