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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]

The stabilities, mechanical and electronic properties of TiC x N 4- x are calculated and discussed in this paper. Using the first principle calculations, the influence of C/N ratio on mechanical properties and stability are investigated in detail. Notably, calculations show that the Pbcn TiC 2 N 2 structure is thermodynamic, mechanical and dynamic at ambient condition, due to the fact that the strong interaction between C–N bonds is beneficial to improving the stability, combined with the results of density of state and the charge density difference. Analysis of mechanical properties indicates that the hardness of TiC x N 4 -x will increase with the C/N ratio increasing, instead material ductility reduces. Herein, the new 1:4 stoichiometry for Ti-based structure is predicted to pave the way to facility the future application of Titanium carbonitride materials. • Using first-principle calculation to predict a new 1:4 stoichiometry for Titanium Carbonitride, TiC x N 4- x. • Armchair C–N chains consisting of alternating carbon and nitrogen within Titanium Carbonitride are stable at ambient pressure. [ABSTRACT FROM AUTHOR]

The dynamic behaviour of monopile offshore wind turbines (OWTs) equipped with viscoelastic dampers (VE dampers) modelled by a fractional Kelvin–Voigt model is governed by a fractional differential equation. Most available methods to solve this kind of equation are limited to single-degree-of-freedom systems or simple deterministic loadings. Considering an OWT under either complex deterministic or random loadings, this work develops an efficient pole-residue method to evaluate its vibration. The key of the proposed method is to express the impulse response function with fractional derivatives into a pole-residue form. Then, the dynamic response time history and the response evolutionary power spectrum (EPS) are transformed into explicit solutions. In numerical studies, a monopile OWT with a VE damper subjected to irregular wind-wave loadings and nonstationary random earthquakes is investigated. Direct Duhamel integral and Monte Carlo simulations are utilized to verify their accuracy. After adding the VE damper, the deterministic response and the random EPS are significantly reduced. By conducting sensitivity analysis, we find that the growth of the fractional order of VE dampers leads to larger damping ratios of the OWT. Increasing the damping coefficient of the VE damper results in larger natural frequencies. • Introduce viscoelastic dampers modelled by a fractional model to monopile OWTs. • Propose an efficient pole-residue method to solve a fractional differential equation. • Deal with both deterministic and random excitation. • Derive the response and response evolutionary power spectrum in closed-form. [ABSTRACT FROM AUTHOR]

At present, the vast majority of offshore wind turbines (OWTs) have been the monopile type. Although design standards recommend seismic assessments be included in their designs, there has been no guidance on how to conduct an analysis due in part to a lack of efficient methods, particularly related to the nonstationary nature of seismic motions. This article contributes to the development of an efficient pole-residue method operated in the Laplace domain to analytically compute response statistics, including the response evolutionary power spectrum (EPS) and time-varying mean square values. While the nonstationary seismic motions are treated as a uniformly modulated random process, both exponential and gamma models are considered for the modulating function. Furthermore, a fully nonstationary seismic motion with multiple independent modulated subprocesses is also studied. In the numerical studies, a 5 MW monopile OWT subjected to nonstationary stochastic seismic motion is studied; Monte Carlo simulations are employed to verify the correctness of the analytical solutions. Numerical studies confirm that the response EPS at the tower top is contributed mainly by the OWT's first bending mode. While applying the linear superposition principle, the proposed method can also be extended to the situation that an OWT is subjected to fully nonstationary earthquake and stationary wave loadings simultaneously. • Develop an efficient analytical method for OWTs to nonstationary seismic motion. • Derive the response evolutionary power spectrum (EPS) in closed-form. • Treat the seismic motion as a fully nonstationary random process. • Verify the derived analytical solutions by Monte Carlo simulations. [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]

In this study, the viability of MgGa 2 O 4 as a pigment for thermal control coatings is discussed. Notably, the MgGa 2 O 4 based coating exhibited excellent initial optical properties and irradiation stability. After irradiation with 40 keV proton at a dose of 1.4 × 1014 P/cm2, the optical performance of the coating remained essentially unchanged, while the solar absorption of the coating is still maintained below 0.10 after irradiation with 40 keV electron at a dose of 1.6 × 1016 e/cm2. Further, the mechanism of the optical changes induced by electron irradiation was elucidated through experimental and computational methods. In MgGa 2 O 4 lattice, two different types of oxygen vacancies and a transition process of them were found. This process was accompanied by the leakage of some oxygen atoms from the lattice, leading to an increased number of color centers and the change in optical properties. Despite the solar absorption raised after electron irradiation, the MgGa 2 O 4 based thermal control coating showed minimal change and low end-of-irradiation-life values, which suggests that they have excellent stability and promising applications. [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]

A novel structural dynamic model for free standing hybrid riser (FSHR) is established based on the absolute nodal coordinate formulation (ANCF) in the present study. The position and slope coordinates are used in global framework to avoid coordinate transformation, and an accurate geometric relationship is introduced to describe geometric nonlinearity. The current loads on the risers and buoyancy can are simulated by Morrison equation and wake oscillator, respectively. After case validations, the vortex-induced motion (VIM) regimes of the buoyancy can and the phase dynamics of the riser and jumper in a FSHR system, subjected to the ocean current and vessel motion, is numerically investigated. It is found that the VIM of the buoyancy can experiences multiple motion switches among the periodic, quasiperiodic, multiple periodic, transition I and transition II regimes under different vessel motions. The y -motion of the jumper and both x - and y -motions of the riser present the phase trapping phenomenon along the structures. The phase trapping and locking, phase drifting and slipping, and other states are observed for x -motion of the jumper, which form a shape of "fish head" with opening mouth towards lower amplitude or higher period of vessel motion in regime map. • A novel structural dynamic model for FSHR system is established based on the ANCF. • Periodic, quasiperiodic, multiple periodic, transition I and II regimes of VIM are found under different vessel motions. • Three transition and multiple periodic bands are interspersed in the quasiperiodic regime of VIM. • The phase trapping and locking, drifting and slipping, and other states are captured for in-line motion along the jumper. • The phase dynamics of the jumper form a shape of "fish head" in the regime map. [ABSTRACT FROM AUTHOR]