Stochastic Sea Research Articles

The Safety Assessment of Civil Ships against Capsizing Based on the Probability Analysis of Multiple Threshold-crossings of Stochastic Sea Waves

Abstract This paper investigates the impact of threshold-crossing events on ship capsizing through a probabilistic model that predicts random wave heights. Utilizing statistical data from wave height observations, this paper proposes that random waves can be approximated and modeled using the Wiener process, employing autocorrelation function identification and probabilistic statistical verification methods. The threshold-crossing duration of a random wave is just the period of the wave exceeds a given threshold, which can reflect the frequency property of the stochastic sea waves. And the probability distribution of the period can theoretically be determined using the derived probability density function for the time interval between any two adjacent crossings of the Wiener process and a threshold. Based on the above theories, the capsizing probabilities of a civil ship sailing in different wave areas are analyzed under different safety thresholds considering certain ratios of the ship's intrinsic period and wave period. The research results can provide a reference for the anti-overturning design of the ships under the action of random waves.

A stepwise scheme for the optimization implementation of lazy wave dynamic cables

The dynamic cables are usually designed to present a complex layout to improve service life and safety in commercial scale floating applications. It is urgent to establish consistent design philosophy and analysis methodologies to provide cost-efficient design requirement. A stepwise scheme for the optimization implementation of lazy wave dynamic cables is proposed and performed with a mass-damping equivalence model. A complicated multi-objective optimal procedure is implemented progressively under hydrostatic state, regular wave state and stochastic sea state. It is validated through a lazy wave dynamic cable (LWDC) from a cylindrical FPSO system under extreme conditions. Stepwise upgraded calibrations based on the coupling of multi-objective optimization modular NSGA-II and lumped mass FEM are applied to assess every sub-objective in defined steps. It is shown that the result is far beyond expectation than initial design after the application of the progressive solution system.

Modulation Instability and Convergence of the Random-Phase Approximation for Stochastic Sea States

The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power spectrum using the random-phase approximation, and periodized on an interval of length L. It is known that most realistic ocean waves power spectra do not exhibit modulation instability, but the most severe ones do; it is thus a natural question to ask whether the periodized random-phase approximation has the correct stability properties. In this work, we specify a random-phase approximation scaling, so that, in the limit of L→∞,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L\\rightarrow \\infty ,$$\\end{document} the stability properties of the periodized problem are identical to those of the continuous power spectrum on the infinite line. Moreover, it is seen through concrete examples that using a too short computational domain can completely suppress the modulation instability.

Adaptive neural network asymptotic path-following control of underactuated ships with stochastic sea loads

This paper investigates the high-precision path following of underactuated ships suffering from stochastic sea loads, where a novel adaptive neural network asymptotic control framework is fabricated. Based on the nonlinear 3-degree-of-freedom (3-DOF) motion model of the underactuated ship, the stochastic ship motion model is established by involving both unknown deterministic and stochastic disturbances, which is chosen as the control objective. To transform path following to tracking control, a novel virtual ship guidance approach is fabricated with generating smooth reference signals. Through the control scheme, the radial-basis-function neural networks (RBF NNs) are employed to approximate the total marine uncertainties. By introducing integral-bounded functions to control laws and adaptive laws, the asymptotic convergence of positional tracking errors is guaranteed with the aid of adaptive backstepping control. To ensure the computational simplicity, the adaptive laws are fabricated with the minimum learning parameters (MLPs). Via the important inequality of the neural basis function, the “algebraic loop” problem is successfully solved, such that the control logicality is guaranteed. Finally, the numerical experiments validate the high-precision tracking performance of the proposed scheme.

Wave episode based Gaussian process regression for extreme event statistics in ship dynamics: Between the Scylla of Karhunen–Loève convergence and the Charybdis of transient features

For a number of structural and fatigue problems in marine science, engineers need accurate statistics for kinematic and dynamical quantities, such as displacements and bending moments. For many such problems the response statistics depend nonlinearly on input stochastic processes, such as sea surface elevation. Nonlinearity prevents the use of standard linear methods, leading to the adoption of expensive experiments and time-consuming numerical simulations. In order to avoid this cost we present a machine learning framework to minimize the training set requirements. This framework consists of two parts. First, we use the Karhunen–Loève theorem to represent stochastic sea states with finite-time wave episodes, which have low dimensionality that nonetheless captures the features important to hydrodynamics and structural mechanics. However, the choice of the wave episode duration is ‘caught’ between the Scylla of slow Karhunen–Loève series convergence for long time durations and the Charybdis of missing transient behaviors when the interval is short. To combat this dilemma, we propose a division into a region, designed for parametric interpolation and machine learning, and a stochastic prelude region, designed to probabilistically model transients. The second part of the framework consists of a Gaussian Process Regression (GPR) model designed to learn the mapping from wave episodes to structural outputs. GPR is able to take advantage of the low dimensional parametric representation of the sea state in order to converge with reasonably-sized training sets (on the order n≈100). At the same time, we use a low-dimensional representation in order to represent the stochastic response time series. The principal advantages of the Gaussian process surrogate are the blazing speed of evaluation – ten thousand times faster than the direct method – and the built in uncertainty quantification. Taken together, we can reconstruct the statistics of the responses by sampling sea states via the Karhunen–Loève construction, estimating the corresponding model outputs using the trained GPR, and estimating statistics of interest through Monte-Carlo calculation on the surrogate model. Finally the developed framework allows for trivial computation of the statistics for different sea spectra, i.e. without the need to retrain the Gaussian Process Regression scheme.

Deep Learning-Enabled Road Segmentation and Edge-Centerline Extraction from High-Resolution Remote Sensing Images

Nowadays, precise and up-to-date maps of road are of great significance in an extensive series of applications. However, it automatically extracts the road surfaces from high-resolution remote sensed images which will remain as a demanding issue owing to the occlusion of buildings, trees, and intricate backgrounds. In order to address these issues, a robust Gradient Descent Sea Lion Optimization-based U-Net (GDSLO-based U-Net) is developed in this research work for road outward extraction from High Resolution (HR) sensing images. The developed GDSLO algorithm is newly devised by the incorporation of Stochastic Gradient Descent (SGD) and Sea Lion Optimization Algorithm (SLnO) algorithm. Input image is pre-processed and U-Net is employed in road segmentation phase for extracting the road surfaces. Meanwhile, training data of U-Net has to be done by using the GDSLO optimization algorithm. Once road segmentation is done, road edge detection and road centerline detection is performed using Fully Convolutional Network (FCN). However, the developed GDSLO-based U-Net method achieved superior performance by containing the estimation criteria, including precision, recall, and F1-measure through highest rate of 0.887, 0.930, and 0.809, respectively.

Protection of qubits by nonlinear resonances

We show that quantized superconducting circuits are non-integrable at the classical level of description, adorned by nonlinear resonances amidst stochastic sea. The stable (elliptic) and unstable (hyperbolic) points occur in a way that by choosing the parameters of a system close to elliptic points, the dynamics is stable. Quantum mechanically, any disturbance has to tunnel the separatrix to reach the elliptic point. Thus, nonlinearity of the system provides protection. Based on these fundamental considerations from the Kolmogorov–Arnold–Moser theorem, we propose criteria for protection of qubits from any disturbance.

Ship Steering Adaptive CGS Control Based on EKF Identification Method

In recent years, marine autonomous surface vessels (MASS) have grown into a ship research issue to increase the level of autonomy of ship behavior decision-making and control while sailing at sea. This paper focuses on the MASS motion control module design that aims to improve the accuracy and reliability of ship steering control systems. Nevertheless, the stochastic sea and wind environment have led to the extensive use of filters and state observers for estimating the ship-motion-related parameters, which are important for ship steering control systems. In particular, the ship maneuverability Nomoto index, which primarily determines the designed ship steering controller’s performance, cannot be observed directly due to the model errors and the external environment disturbance in the process of sailing. Hence, an adaptive robust ship steering controller based on a closed-loop gain shaping (CGS) scheme and an extended Kalman filter (EKF) on-line identification method is explored in this paper. To verify the effectiveness of the proposed steering controller design scheme, the motor vessel YUKUN was taken as the control plant and a series of simulation experiments were carried out. The results show the advantages of the dynamic response performance of the proposed steering controller compared with the classical PD and traditional CGS controllers. Therefore, the proposed adaptive CGS steering controller would be a good solution for MASS motion control module design.

WIFF1.0: a hybrid machine-learning-based parameterization of wave-induced sea ice floe fracture

Abstract. Ocean surface waves play an important role in maintaining the marginal ice zone, a heterogenous region occupied by sea ice floes with variable horizontal sizes. The location, width, and evolution of the marginal ice zone are determined by the mutual interaction of ocean waves and floes, as waves propagate into the ice, bend it, and fracture it. In previous work, we developed a one-dimensional “superparameterized” scheme to simulate the interaction between the stochastic ocean surface wave field and sea ice. As this method is computationally expensive and not bitwise reproducible, here we use a pair of neural networks to accelerate this parameterization, delivering an adaptable, computationally inexpensive, reproducible approach for simulating stochastic wave–ice interactions. Implemented in the sea ice model CICE, this accelerated code reproduces global statistics resulting from the full wave fracture code without increasing computational overheads. The combined model, Wave-Induced Floe Fracture (WIFF v1.0), is publicly available and may be incorporated into climate models that seek to represent the effect of waves fracturing sea ice.

The nonlinear ship rolling and safe basin erosion in stochastic beam seas

A short number of steep breaking waves hitting a ship from the side may affect its dynamic behaviour and determine extreme roll angles and, eventually, capsizing. Even the capsize is a rare event, its consequences for the ship and crew are often fatal. Generally, the ship rolling in regular or stochastic beam seas could be described by a second-order non-linear differential equation with the roll angle as dependent variable. Non-linearity comes from the restoring and damping moments, which are usually represented by polynomials of roll angle or of its time derivative. In the paper, we used such a model equation to estimate the ship rolling and capsizing in a stochastic beam sea. The sea action was simulated by a harmonic function with random frequency and phase. The roll equation was solved using a simple, fast and accurate iterative scheme based on Taylor expansion which proved to be very competitive in terms of accuracy with more elaborate methods and which allowed a substantial reduction of the CPU time. Due to these properties of the scheme, we were able to conduct an extensive investigation on fractal erosion of safe basins and to represent the boundaries between capsizing and non-capsizing regions in wave frequency – wave amplitude plane and normalized integrity curves for different combinations of random wave parameters. The restoring and damping coefficients corresponded to a vehicle ferry model, considered to be either with or without bilge keels.

Hull-form stochastic optimization via computational-cost reduction methods

The paper shows how cost-reduction methods can be synergistically combined to enable high-fidelity hull-form optimization under stochastic conditions. Specifically, a multi-objective hull-form optimization is presented, where (a) physics-informed design-space dimensionality reduction, (b) adaptive metamodeling, (c) uncertainty quantification (UQ) methods, and (d) global multi-objective algorithm are efficiently and effectively combined to achieve high-fidelity simulation-based design optimization (SBDO) solutions. The application pertains to the multi-objective optimization for resistance and seakeeping (operational efficiency and effectiveness) of a destroyer-type vessel. Two hierarchical multi-objective SBDO problems are presented, with a level of complexity decreasing from the most general (stochastic sea state, heading, and speed) to the least general (deterministic regular wave, at fixed sea state, heading, and speed). Design-space dimensionality reduction is based on a generalized Karhunen-Loeve expansion of the shape modification vector combined with low-fidelity-based physical variables. A multi-objective deterministic particle swarm optimization algorithm is applied to a stochastic radial-basis-function metamodel that provides objective predictions. UQ methods include Gaussian quadrature and metamodel-based importance sampling. Numerical simulations are based on unsteady Reynolds-averaged Navier–Stokes and potential flow solvers. The paper shows and discusses the joint effort of computational-cost reduction methods in enabling high-fidelity SBDO, providing guidelines for future research directions in this area.

Statistical properties for compositions of standard maps with increasing coefficient

The Chirikov standard map is a prototypical example of a one-parameter family of volume-preserving maps for which one anticipates chaotic behavior on a non-negligible (positive-volume) subset of phase space for a large set of parameters. Rigorous analysis is notoriously difficult and it remains an open question whether this chaotic region, the stochastic sea, has positive Lebesgue measure for any parameter value. Here we study a problem of intermediate difficulty: compositions of standard maps with increasing coefficient. When the coefficients increase to infinity at a sufficiently fast polynomial rate, we obtain a strong law, a central limit theorem, and quantitative mixing estimates for Holder observables. The methods used are not specific to the standard map and apply to a class of compositions of ‘prototypical’ two-dimensional maps with hyperbolicity on ‘most’ of phase space.

Analysis of Offshore Structures Based on Response Spectrum of Ice Force

With the development of large-scale offshore projects, sea ice is a potential threat to the safety of offshore structures. The main forms of damage to bottom-fixed offshore structures under sea ice are crushing failure and bending failure. Referred to as the concept of seismic response spectrums, the design response spectrum of offshore structures induced by the crushing and bending ice failure is presented. Selecting the Bohai Sea in China as an example, the sea areas were divided into different ice zones due to the different sea ice parameters. Based on the crushing and bending failure power spectral densities of ice force, a large amount of ice force time-history samples are firstly generated for each ice zone. The time-history of the maximum responses of a series of single degree of freedom systems with different natural frequencies under the ice force are calculated and subsequently, a response spectrum curve is obtained. Finally, by fitting all the response spectrum curves from different samples, the design response spectrum is generated for each ice zone. The ice force influence coefficients for crushing and bending failure are obtained, which can be used to estimate the stochastic sea ice force acting on a structure conveniently in a static way. A comparison of the proposed response spectrum method with the Monte Carlo method by a numerical example shows good agreement.

On the Development of an Efficient Surrogate Model for Predicting Long-Term Extreme Loads on a Wave Energy Converter

Accurate prediction of long-term extreme loads is essential for the design of wave energy converters (WECs), but it is also computationally demanding due to the low probabilities associated with their occurrence. Although a full long-term probabilistic analysis using integration over all sea states or Monte Carlo simulation (MCS) may be used, these methods can be prohibitively expensive when individual response simulations are complex and time-consuming. The application of polynomial chaos expansion (PCE) schemes to allow the propagation of uncertainty from the environment through the stochastic sea surface elevation process and ultimately to WEC extreme load response prediction is the focus in this study. A novel approach that recognizes the role of long-term ocean climate uncertainty (in sea state variables such as significant wave height and spectral peak period) as well as short-term response uncertainty arising from the unique random phasing in irregular wave trains is presented and applied to a single-body point-absorber WEC device model. Stochastic simulation results in time series realizations of various response processes for the case-study WEC. We employ environmental data from a possible deployment site in Northern California (NDBC 46022) to assess long-term loads. MCS computations are also performed and represent the “truth” system against which the efficiency and accuracy of the PCE surrogate model are assessed. Results suggest that the PCE approach requires significantly less effort to obtain comparable estimates to MCS.

A Stochastic Extreme Sea Level Model for the German Baltic Sea Coast

AbstractThis paper describes a framework in which artificial extreme sea levels (ESLs) can be generated for use in flood risk analyses. Such analyses require large numbers of events to accurately assess the risk associated with certain return water levels and quantify uncertainties surrounding the temporal variability of ESL events. Stochastic models satisfy this requirement as they are computationally inexpensive, and thus, many thousands of events may be generated over a very short period of time. As a case study, we have developed a stochastic model for the German Baltic Sea coast capable of simulating the temporal behavior of ESLs. To do this, high‐resolution water level data from 45 tide‐gauges have been used as model input. At each location, observed ESLs are identified and parameterized. Artificial ESLs are generated using Monte Carlo simulations based on the parametric distribution functions fitted to the parameterized observed ESLs. We show that the method outlined here provides an accurate representation of ESLs at all tide‐gauges tested. However, the model is limited by the availability, length, and quality of high‐resolution water level data. Due to the rarity of ESLs in the German Baltic Sea, including historical measurements into the stochastic procedure allows for the generation of artificial ESLs more in‐line with past extremes.

Wave-induced flexural response of idealized non-uniform hull girder in random seas

The aim is to analyze the wave-induced vertical vibration of a non-prismatic mathematical hull in a stochastic sea, by normal mode analysis. The hull has been generated mathematically, to represent two distinct Indian merchant vessels: DS (Tanker) and SCIM (Containership). The body-plan, deck waterline, bow and stern profiles, have been modeled as semi-superellipses. These render non-uniform distributions of mass and stiffness over the ship-length. The energy-based Rayleigh–Ritz method has been used to analyze the idealized hull girder natural frequencies and modeshapes. The non-uniform beam modeshape is a weighted series sum of prismatic beam-free vibration modeshapes. The 2D added mass of superelliptic sections is formulated, solving the radiation boundary value problem by the constant strength source distribution method. The hull girder is subject to the Pierson–Moskowitz sea spectrum in fully loaded condition. The diffraction force is formulated through the Khaskind’s relations. The flexural response of the girder is evaluated by the modal superposition method. The response spectra have been generated for various sea states and ship speeds. The magnitudes of the maximum flexural/shear stress for each vessel are generated. The probability of shear/tensile failure is also estimated, giving insights into the hull structural design.

The Influence of Oceanic Stochastic Forcing on the Atmospheric Response to Midlatitude North Pacific SST Anomalies

AbstractThe stochastic sea surface temperature (SST) anomalies are always present because of the internal oceanic variability due to small‐scale SST variability and based on a set of ensemble experiments forced by Pacific Decadal Oscillation‐related midlatitude North Pacific SST anomalies with and without oceanic stochastic forcing, their influences on atmospheric variability in coarse‐resolution models are investigated in this study. Comparisons of experiment results show that oceanic stochastic forcing can improve the simulated atmospheric response by generating more organized atmospheric transient eddies through the increases of both thermal activity and atmospheric baroclinicity, similar to the high‐resolution observations and simulations. Dynamic diagnostics further reveal the dominant contributions of corresponding transient eddy vorticity forcing to the significantly enhanced westerly wind with equivalent barotropic structure. It suggests that the oceanic stochastic forcing is important and nonnegligible for the understanding and theory of oceanic feedback to the atmosphere in the midlatitudes.

Wave and Current Effects on Floating Fish Farms

The paper is partly a review on hydrodynamic and structural aspects offish farms. In addition, new numerical results are presented on the stochasticbehavior of bending stresses in the floater of a realistic net cage in extreme waveconditions. The behavior of traditional-type fish farms with net cages and closedfish farms in waves and currents is discussed. Hydroelasticity can play asignificant role for net cages and closed membrane-type fish farms. The many meshesin a net cage make CFD and complete structural modeling impracticable. As anexample, a hydrodynamic screen model and structural truss elements are instead usedto represent the hydrodynamic loading and the structural deformation of the net. Inaddition, the wake inside the net due to current plays an important role. Thedescribed simplified numerical method has been validated by comparing with modeltests of mooring loads on a single net cage with two circular elastic floaters andbottom weight ring in waves and currents. It is discussed which parts of thecomplete system play the most important roles in accurately determining the mooringloads. Many realizations of a sea state are needed to obtain reliable estimates ofextreme values in a stochastic sea. In reality, many net cages operate in closevicinity, which raises questions about spatial variations of the current and waveenvironment as well as hydrodynamic interaction between the net cages. Live fishtouching the netting can have a non-negligible influence on the mooring loads. It isdemonstrated by numerical calculations in waves and currents that a well boat at anet cage can have a significant influence on the mooring loads and the bendingstresses in the floater. The latter results provide a rational way to obtainoperational limits for a well boat at a fish farm. Sloshing has to be accounted forin describing the behavior of a closed fish farm when important wave frequencies arein the vicinity of natural sloshing frequencies. The structural flexibility has tobe considered in determining the natural sloshing frequencies for a membrane-typeclosed fish farm. Free-surface non-linearities can matter for sloshing and can, forinstance, result in swirling in a certain frequency domain for a closed cage with avertical symmetry axis.

Wash wave effects on ships moored in ports

A ship moored in a port is subjected to both the sea waves and the wash waves produced by nearby passing ships. A hybrid numerical model is proposed to estimate the transient response of a moored ship exposed to the two types of waves. The hybrid method is based on the combination of 3-D Rankine source method and impulse response theory. The 3-D Rankine source method is applied to address the wash waves and the wave-structure interactions. The transient response is subsequently simulated in time-domain with the impulse response theory. The transient effect produced by the wash wave impact loads is found to be dependent on the sea waves induced response. The transient effect becomes less significant when the sea waves induced response is strong and vice versa. Besides, the propagation distance of wash waves has a limited influence on the transient response due to the dissipation feature of the divergent wash waves. The transient response in stochastic sea waves is also investigated, which is dominated by the resonant frequency, the sea wave frequency and the wash wave varying frequency.

Chaos analysis of ship rolling motion in stochastic beam seas

In this paper, the chaotic motion of ship roll in stochastic beam seas, which is regarded as a bounded noise is investigated in detail. The stochastic Melnikov approach is applied to the model and the criterion for the chaos in the mean-square sense is derived. The chaotic thresholds of noise parameters obtained by means of the stochastic Melnikov process are verified by the numerical safe basin. Besides of the factors of noise disturbances, the effects of the other parameters in the system on safe basin are also discussed systematically. The varieties of coefficients of the restoring moment can also induce the erosion of safe basin and lead to the occurrence of the chaos. On the other hand, the increase of damping coefficients can enhance the safe domain of ship sailing.