Random Wave Model Research Articles

Modeling and simulation analysis of ship 6-dof simulation swing platform based on matlab

In this paper, the kinematics and dynamics model of the ship’s six-degree-of-freedom simulation swing platform were studied. Then, a random wave and ship motion response model was established, and a six-degree-of-freedom motion model of DP ship in four-level sea state was established and studied by using the open source MSS toolbox, which lays a foundation for the subsequent simulation and control strategy research. The ordinary PID controller and fuzzy PID controller were designed and simulated, and the results were compared to verify the effect of fuzzy PID controller.

Fluctuations of polyspectra in spherical and Euclidean random wave models

Fluctuations of polyspectra in spherical and Euclidean random wave models

Research on dynamic responses of mooring line system of semi-submersible platforms in Vietnam sea conditions using random model

Recently, due to the nearshore oil fields in Vietnam were nearly exhausted, oil and gas extraction proceeds to deeper water areas using the mooring floating offshore structures. Therefore, the durability of the mooring system in deep water should be studied through determining the dynamic tension of the mooring line system using random wave models. However, full stochastic dynamics analysis for mooring line system takes up a lot of time and requires large computing resources. This paper is going to study the hydrodynamic interaction of random waves onto a semi-submersible platform, thereby analysing the dynamic responses in time domain of the mooring system using the “time window” method to optimize computational time and computing resources. This method performs the dynamic simulations around the maximum quasi-dynamic tension values to determine the dynamic tension and the dynamic amplification factor (DAF) of a maximum load-bearing mooring line, thereby evaluating the dynamic responses for the whole mooring system. The method is applied to calculate for a semi-submersible platform in Dai Hung field in Vietnam Sea.

Local repulsion of planar Gaussian critical points

We study the local repulsion between critical points of a stationary isotropic smooth planar Gaussian field. We show that the critical points can experience a soft repulsion which is maximal in the case of the random planar wave model, or a soft attraction of arbitrary high order. If the type of critical points is specified (extremum, saddle point), the points experience a hard local repulsion, that we quantify with the precise magnitude of the second factorial moment of the number of points in a small ball.

Functional Convergence of Berry’s Nodal Lengths: Approximate Tightness and Total Disorder

We consider Berry’s random planar wave model (J Phys A 10(12):2083–2092, 1977), and prove spatial functional limit theorems—in the high-energy limit—for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular domains. Our analysis is crucially based on a detailed study of the projection of nodal lengths onto the so-called second Wiener chaos, whose high-energy fluctuations are given by a Gaussian total disorder field indexed by polygonal curves. Such an exact characterization is then combined with moment estimates for suprema of stationary Gaussian random fields, and with a tightness criterion by Davydov and Zitikis (Ann Inst Stat Math 60(2):345–365, 2008).

Quantum entanglement and the growth of Laplacian eigenfunctions

We study the growth of Laplacian eigenfunctions on compact manifolds (M, g). Hörmander proved sharp polynomial bounds on which are attained on the sphere. On a “generic” manifold, the behavior seems to be different: both numerics and Berry’s random wave model suggest as the typical behavior. We propose a mechanism, centered around an analog of the spectral projector, for explaining the slow growth in the generic case: for to be large, it is necessary that either (1) several of the first n eigenfunctions were large in x 0 or (2) that is strongly correlated with a suitable linear combination of the first n eigenfunctions on most of the manifold or (3) both. An interesting byproduct is quantum entanglement for Laplacian eigenfunctions: the existence of two distinct points such that the sequences and do not behave like independent random variables. The existence of such points is not to be expected for generic manifolds but common for the classical manifolds and subtly intertwined with eigenfunction concentration.

Almost-sure asymptotics for Riemannian random waves

We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for large and small band models, the process properly rescaled and evaluated at an independently and uniformly chosen point X on the manifold, converges in distribution under the sole randomness of X towards an universal Gaussian field as the frequency tends to infinity. This result extends the celebrated central limit Theorem of Salem–Zygmund for trigonometric polynomials series to the more general framework of compact Riemannian manifolds. We then deduce from the above convergence the almost-sure asymptotics of the nodal volume associated with the random wave. To the best of our knowledge, in the real Riemannian case, these asymptotics were only known in expectation and not in the almost sure sense due to the lack of sufficiently accurate variance estimates. This in particular addresses a question of S. Zelditch regarding the almost sure equidistribution of nodal volume.

ACTIVE CONTROL OF VERTICAL ACCELERATION WITH T-FOIL AND TRIM TAB SYSTEMS IN A FAST FERRY

This study is concerned with the active T-foil placed near the bow on the keel line of the fast ferry and two active trim tab controls placed at the stern to improve the maritime performance of a fast ferry, whilst improving the comfort and safety of passengers and crew. In the scope of the study, the vertical direction of the fast ferry under the random head waves, heave and pitch motions were taken into account. For the control of T-foil and trim Tabs, PID and LQR control methods were used. The purpose of these controllers is to reduce the acceleration of the heave and pitch motions of the fast ferry by changing the operating angles of the T-foil and trim tab wings. A random wave model was created using the Pierson-Moskowitz model, and simulations were done assuming that the fast ferry was subjected to random head waves. Finally, in order to see the effect of vertical acceleration on passengers, the rate of seasickness (MSI) change of the fast ferry in uncontrolled and controlled states was examined. Mathematical models of fast ferry, T-foil and trim tab and their simulations were carried out in MATLAB / Simulink environment. The simulation results show that T-foil and trim tab Active systems can effectively reduce vertical acceleration by improving heave and pitch motions.

Small Scale CLTs for the Nodal Length of Monochromatic Waves

We consider Berry's random planar wave model (1977) for a positive Laplace eigenvalue $E>0$, both in the real and complex case, and prove limit theorems for the nodal statistics associated with a smooth compact domain, in the high-energy limit ($E\to \infty$). Our main result is that both the nodal length (real case) and the number of nodal intersections (complex case) verify a Central Limit Theorem, which is in sharp contrast with the non-Gaussian behaviour observed for real and complex arithmetic random waves on the flat $2$-torus, see Marinucci et al. (2016) and Dalmao et al. (2016). Our findings can be naturally reformulated in terms of the nodal statistics of a single random wave restricted to a compact domain diverging to the whole plane. As such, they can be fruitfully combined with the recent results by Canzani and Hanin (2016), in order to show that, at any point of isotropic scaling and for energy levels diverging sufficently fast, the nodal length of any Gaussian pullback monochromatic wave verifies a central limit theorem with the same scaling as Berry's model. As a remarkable byproduct of our analysis, we rigorously confirm the asymptotic behaviour for the variances of the nodal length and of the number of nodal intersections of isotropic random waves, as derived in Berry (2002).

Nodal set of monochromatic waves satisfying the Random Wave Model

We construct deterministic solutions to the Helmholtz equation in Rm which behave accordingly to the Random Wave Model. We then find the number of their nodal domains, their nodal volume and the topologies and nesting trees of their nodal set in growing balls around the origin. The proof of the pseudo-random behaviour of the functions under consideration hinges on a de-randomisation technique pioneered by Bourgain and proceeds via computing their Lp-norms. The study of their nodal set relies on its stability properties and on the evaluation of their doubling index, in an average sense.

Fractional order adaptive sliding mode control for nonlinear anti-roll of ship

Objectives In order to solve the problem of ship nonlinear rolling control, a fractional order adaptive sliding mode control (FOASMC) algorithm is proposed. Methods First, the spectral density of random waves, spectral density of wave inclination and spectrum of waves acting on ships are calculated using a random wave model with long peak waves. The rolling angle tracking error of the system is then verified on the basis of Lyapunov stability theory. Moreover, the switching function is designed to make the system robust to uncertainties and external disturbances. Finally, the effects of fractional order, control law gain and sliding surface mode gain are analyzed. Results The results show that the mean rolling angle and standard deviation of FOASMC are smaller than those of basic sliding mode control (SMC) for various speeds and wave directions. For example, when the ship's speed is 10 m/s and the encountering wave direction is five degrees, the average rolling angle is 25.89% of the basic SMC, and the mean square deviation is 14.32% of the basic SMC. Conclusions It is proven that the proposed control algorithm has good stabilization effectiveness at various navigation speeds and encountering wave directions, as well as such advantages as strong robustness, continuous control input and no high gain.

A second order random wave model for predicting the power performances of a wave energy converter

A second order random wave model for predicting the power performances of a wave energy converter

A Numerical Study on the Evolution of Random Seas With the Occurrence of Rogue Waves

Abstract Numerous numerical and experimental investigations show that rogue waves present much larger probabilities of occurrence than predicted by the linear random wave model, i.e., Gaussian distributed waves. The deviation from normal statistical events excites a continuous concern about rogue wave research. In this study, rogue waves under long-crested and narrow-banded wave trains are checked using the high-order spectral (HOS)-NST model. The JONSWAP wave spectra with random phases are selected as the initial state of the incoming wave trains. Different values of spectral parameters are chosen to reproduce different random sea states with different Benjamin–Feir index (BFI). Numerical results are compared with the classical experimental study and show good agreements. Statistical properties of rogue waves are recounted again within the analysis of exceedance distribution function (EDF) of wave heights and wave crests. Spectral changes are examined, and the monotonic increases with BFI are stressed. However, no bifurcations are observed for BFI near 1. For large BFI, quasi-resonance interactions dominate the wave nonlinearities, and the resulted dynamic excess kurtosis involves initially monotonic enhancement along with space, peaking at around 20–30 wavelengths, but stays at stably high-level values. The quasi-steady-state of dynamic excess kurtosis after full interaction of wave nonlinearities in time and space demonstrates a continuous emergence of rogue waves much more frequent than normality. The changes of excess kurtosis along x are complicated where BFI near 1 and the occurrence of rogue waves might be enhanced even for BFI slightly inferior to 1.

On 3-dimensional Berry’s model

This work aims to study the dislocation or nodal lines of 3D Berry's random wave model. Their expected length is computed both in the isotropic and anisotropic cases, being them compared. Afterwards, in the isotropic case the asymptotic variance and distribution of the length are obtained as the domain grows to the whole space. Under some integrability condition on the covariance function, a central limit theorem is established. The study includes the Berry's monochromatic random waves, the Bargmann-Fock model and the Black-Body radiation as well as a power law model that exhibits an unusual asymptotic behaviour and yields a non-central limit theorem.

A Stochastic Green’s Function for Solution of Wave Propagation in Wave-Chaotic Environments

We present a statistical, mathematical, and computational model for prediction and analysis of wave propagation through complex, wave-chaotic environments. These are generally enclosed environments that are many wavelengths in extent and are such that, in the geometric optics limit, ray trajectories diverge from each other exponentially with distance traveled. The wave equation solution is expressed in terms of a novel stochastic Green's function that includes both coherent coupling due to direct path propagation and incoherent coupling due to propagation through multiple paths of the scattering environment. The statistically fluctuating portion of the Green's function is characterized by random wave model and random matrix theory. Built upon the stochastic Green's function, we have derived a stochastic integral equation method, and a hybrid formulation to incorporate the component-specific attributes. The proposed model is evaluated and validated through representative experiments.

Ranking uncertainty: Wave climate variability versus model uncertainty in probabilistic assessment of coastline change

Sand nourishments are increasingly applied as adaptive coastal protection measures. Predictions of the evolution of these nourishments and their impact on the surrounding coastline contain many uncertainties. The sources that add to this uncertainty can be delineated between intrinsic and epistemic uncertainty, i.e. inevitably in the system or related to knowledge limitations. Effects of intrinsic uncertainty (e.g. due to wave climate variability) on coastal evolution can be significant. In studying these effects, it has often been assumed that intrinsic uncertainty is dominant over epistemic uncertainty (e.g. introduced by the model), yet the magnitude of both contributions have not been explicitly quantified to assess the validity of this assumption. This paper examines the relative importance of intrinsic and epistemic uncertainty in coastline modeling of a large-scale nourishment. It uses a probabilistic framework in which sediment transport is considered to be a function of random wave forcing (intrinsic) and model (epistemic) uncertainty, calculating transport using a one-line model. The test case for this analysis is the mega-nourishment, the Sand Engine, located in the Netherlands. The applied wave climate variability is obtained from long term wave observations, whereas model uncertainty is quantified using the Generalized Likelihood Uncertainty Estimation (GLUE) method relying on monthly observations. We find that the confidence intervals on predicted volume losses increase substantially when including both intrinsic and epistemic sources of uncertainty. A global sensitivity analysis shows that ignoring model uncertainty would underestimate the variance by at least 50% after a 2.5-year simulation period for the Sand Engine, hence producing significant overconfidence in the results. These findings imply that for coastal modeling purposes a dual approach should be considered, evaluating both epistemic and intrinsic uncertainties.

A generic linear non-causal optimal control framework integrated with wave excitation force prediction for multi-mode wave energy converters with application to M4

The multi-float multi-mode wave energy converter (M-WEC) M4 has essentially linear hydrodynamics characteristics in operational and even extreme waves. This is in contrast to point-absorber and most raft-type devices where nonlinear effects and associated losses are significant. The control problem now involves a large number of degrees of freedom. Energy maximizing control of wave energy converters (WECs) is a non-causal control problem. This paper aims to propose a complete self-contained non-causal optimal control framework by combining a linear non-causal optimal control (LNOC) algorithm with an autoregressive (AR) model as the wave excitation force predictor and a Kalman Filter with random walk wave model (KFRW) as the wave excitation force estimator. The efficacy of the proposed framework together with its enabling components is demonstrated numerically using irregular waves. The proposed framework has low computational load, which enables its real-time implementation on standard computational hardware. Furthermore, the wave force prediction does not require deployment and maintenance of expensive hardware, which helps to reduce the unit cost of the generated electricity.

Gaussian Random Measures Generated by Berry’s Nodal Sets

We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry's random wave model to a finite collection of (possibly overlapping) smooth compact subsets of $\mathbb{R}^2$. Our main result shows that, as the energy diverges to infinity and after an adequate normalisation, these random elements converge in distribution to a Gaussian vector, whose covariance structure reproduces that of a homogeneous independently scattered random measure. A by-product of our analysis is that, when restricted to rectangles, the dominant chaotic projection of the nodal length field weakly converges to a standard Wiener sheet, in the Banach space of real-valued continuous mappings over a fixed compact set. An analogous study is performed for complex-valued random waves, in which case the nodal set is a locally finite collection of random points.

Towing Motion Characteristics of Composite Bucket Foundation for Offshore Wind Turbines

Composite bucket foundation (CBF) is an environmentally friendly form of offshore wind power foundation. By virtue of the air-floating subdivision structure in the bucket, the foundation has a self-floating characteristic and can allow for long-distance air-floating towing and transport. In this study, first, a numerical analysis was performed on the towing motion characteristics of CBF, and the formula for foundation stability was deduced; then, we probed into the variation rules of the natural period of the foundation with draft and analyzed the response amplitude operator (RAO) responses, added mass coefficients, radiation damping coefficients, and exciting forces (moments) of the composite bucket foundation under different drafts and different wave directions. Finally, we clarified the basic hydrodynamic characteristics of the composite bucket foundation in the frequency domain and adopted multiple random wave models to investigate the effects of different wave heights, periods, and spectral peak factors on the towing motion characteristics of composite bucket foundation.

Nodal Statistics of Planar Random Waves

We consider Berry's random planar wave model (1977) for a positive Laplace eigenvalue $$E > 0$$ , both in the real and complex case, and prove limit theorems for the nodal statistics associated with a smooth compact domain, in the high-energy limit ( $$E \rightarrow \infty$$ ). Our main result is that both the nodal length (real case) and the number of nodal intersections (complex case) verify a Central Limit Theorem, which is in sharp contrast with the non-Gaussian behaviour observed for real and complex arithmetic random waves on the flat 2-torus, see Marinucci et al. (2016) and Dalmao et al. (2016). Our findings can be naturally reformulated in terms of the nodal statistics of a single random wave restricted to a compact domain diverging to the whole plane. As such, they can be fruitfully combined with the recent results by Canzani and Hanin (2016), in order to show that, at any point of isotropic scaling and for energy levels diverging sufficently fast, the nodal length of any Gaussian pullback monochromatic wave verifies a central limit theorem with the same scaling as Berry's model. As a remarkable byproduct of our analysis, we rigorously confirm the asymptotic behaviour for the variances of the nodal length and of the number of nodal intersections of isotropic random waves, as derived in Berry (2002).