Random Waves Research Articles

Seismic responses analysis of monopile offshore wind turbines in clays considering the long-term cyclic degradation effect

In marine environment, the monopile offshore wind turbines (MOWTs) are subjected to long-term horizontal cyclic loads caused by wind, waves and currents, which will lead to the stiffness degradation and plastic cumulative deformation of clays. The decrease of clays bearing capacity caused by long-term cyclic degradation effect is a threat to the safe use of MOWTs in earthquake-prone countries (such as some countries in the circum-Pacific seismic belt). A three-dimensional finite element model is established to research the seismic response analysis of MOWT in clays considering the long-term cyclic degradation effect. The cumulative deformation of pile-soil system after long-term cycle are obtained by adopting the stiffness degradation of clays through the USDFLD subroutine. On this basis, the dynamic response analysis of MOWT system under the combined action of seismic and environmental loads is carried out. The influence of long-term horizontal cyclic load number, long-term horizontal cyclic load amplitude, seismic intensity, soil strength, environmental loads and cyclic degradation parameter on the dynamic response of MOWT is analyzed. In the seismic design of MOWTs, the effects of long-term degradation and random wind, waves and other environmental loads should be considered.

UFO‐Shaped Integrated Triboelectric Nanogenerator for Water Wave Energy Harvesting

AbstractThe triboelectric nanogenerator (TENG), which is suitable for low‐frequency and high‐entropy mechanical energy harvesting, has great advantages in ocean energy collection and potential blue energy applications. The rational structural design can ensure the best working state of TENG in complex marine environment. Herein, an unidentified flying object (UFO) shaped integrated triboelectric energy harvester (U‐TENG) is proposed for complex and random ocean wave energy harvesting. The U‐TENG is assembled in a vertical structure by combining a coping TENG in a rotational structure and a bottom TENG in a rolling‐ball design. The proposed vertically integrated TENG structure can increase the efficiency of space utilization and improve the entirety output performance compared with the single device structure. A sophisticated auxiliary facility has also been pioneerily designed to simulate the ocean waving during the experiment tests. The prepared U‐TENG can easily light up dozens of light emitting diodes and power a commercial hygrothermograph at a low operating frequency. This work provides a highly efficient means to the development of high‐performance and robust TENG for ocean energy harvesting.

Research on second level of vulnerability criteria of parametric rolling with stochastic stability theory

The second level of vulnerability criteria of parametric rolling proposed by the International Maritime Organization (IMO) is aimed to evaluate the probability of roll instability and large roll motion of ships in the designated sea areas. Compared with the numerical simulation in random waves, the stability boundary derived from the criteria has large errors. Some additional checks are required in the key region. A new method is proposed to assess ship parametric roll in the designed sea area based on stochastic stability theory. A nonlinear system has the same stability properties as its equivalent linear system. Therefore, the nonlinear parametric rolling motion equation is linearized in order to study its stochastic stability in random waves. Based on the top Lyapunov exponent and the stochastic averaging theory, the expressions for parametric rolling stability boundary are given. The accuracy of these stability boundaries is verified by comparison with numerical simulation. The new method with the stochastic stability boundary can quickly and accurately evaluate the probability of large roll motion of ships in the designated sea areas which illustrates the possibility of improvement to a certain extent.

Wave Transmission over Rubble-Mound Submerged Breakwaters

This study focuses on the prediction of technical efficiency of narrow-crested submerged permeable rubble-mound breakwaters, in terms of wave attenuation. A number of existing formulae for estimating wave transmission coefficient for submerged breakwaters can be found in the literature, whereas in this work further improvement for that estimation has been achieved mainly through physical modelling. A series of 2D experiments under scale were conducted for regular and random waves providing data on wave transmission coefficient and respective wave breaking characteristics. A Boussinesq-type wave model capable of simulating wave propagation for regular waves over porous submerged breakwaters was also used in order to provide additional wave transmission information. Data analysis showed that wave breaking mechanism significantly affects wave energy dissipation and, therefore, wave breaking occurrence and type can be directly linked to wave transmission coefficient for a given structure’s geometry and sea state. The result of this work is the proposal of a set of simple semi-empirical equations for predicting wave transmission coefficient over small profile porous submerged breakwaters in relevance to the parameterization of the expected dominant wave breaking mechanism.

On the Evolution Equations of Nonlinearly Permissible, Coherent Hole Structures Propagating Persistently in Collisionless Plasmas

AbstractA fundamental study describing nonlinear plasma wave propagation is presented. Elementary linear wave theory describes small‐amplitude random waves, but lacks information about coherent structures. This improved wave model arises from the fact that structure formation is inevitably associated with particle trapping, which can only be properly addressed by the pseudo‐potential method instead of Bernstein, Greene, and Kruskal (BGK) ‐ likemethods. Only by using this method can legitimate nonlinear dispersion relations be obtained and reconciled with trapping scenarios. This privilege is used to derive evolution equations for five structures, the derivation being simplified by the acoustic nature of the permitted modes. The focus is on a special structure, the solitary electron hole of negative polarity, with which it can explain a spacecraft observation for the first time. Furthermore, it is shown that an intrinsically nonlinear structure can become macroscopically linear and thus harmonic by suitably adjusting the trapping scenario. An example is the monochromatic ion acoustic wave that propagates at ion sound velocity without dispersion. In this literature research, it also takes a critical look at a recently awarded work.

Energy management strategy for hybrid power ships based on nonlinear model predictive control

How to achieve energy saving and emissions reduction is a critical issue of great concern to all countries. The development of marine hybrid power technology provides a new research direction for rational energy distribution and utilization. In this paper, an energy management strategy for real-time regulation of internal combustion engines and motor torque is designed to solve the optimal energy management problem of parallel hybrid power ships. A nonlinear model predictive control method is used as the core, aided by a machine learning technique and an unscented Kalman filter. Machine learning techniques are used to extract representative test cycles and apply them to the testing and evaluation of design strategies. The effect of random waves on propeller load torque is observed using an unscented Kalman filter, which is used as a disturbance variable to participate in establishing the prediction model. Furthermore, a trade-off coefficient is designed to further demonstrate the balance between fuel consumption and carbon emission optimization. To verify the performance of the designed energy management strategy, NMPC is compared with the conventional intelligent optimization algorithm and dynamic programming algorithm, and the fuel consumption and carbon emission trade-off parameterization of the strategy is investigated. The results show that the strategy can resist random wave disturbances and follow the reference data of the ship’s internal combustion engine speed extracted by machine learning. The energy distribution is also performed according to the variation of the trade-off coefficients to achieve the optimal trade-off energy management under the required constraints.

The vibration mitigation of jacket offshore platform based on inerter nonlinear energy sink

The application of the traditional passive vibration control system is limited by the demand for large mass. To ameliorate this situation, the inerter nonlinear energy sink (NES) is introduced and applied, as the substitute for the traditional passive vibration control system, to vibration mitigation of jacket offshore platform under random wave loading, since it has the clear advantage of obtaining apparent vibration control effect through low amounts of added mass. For one thing, the equation of jacket offshore platform including inerter NES is developed considering wave loads. For another, the optimal parameters of inerter NES are obtained through Particle Swarm Optimization (PSO) using numerical simulations. Both analytical and numerical results strongly support that the inerter NES contributes greatly to vibration suppression, compared with traditionally tuned mass dampers (TMD). To explore more practical benefits, further comparison between the vibration mitigation of inerter NES and the optimal TMD system, considering different masses and stiffness, is made right after, which verifies the effectiveness and robustness of inerter NES. Based on the above study and results, it proves valid to conclude that the inerter NES system allows practical application of vibration mitigation for marine structures.

Comparison of schlieren-based techniques for measurements of a turbulent and wavy free surface

The free surface at an air–water interface can provide information regarding bathymetric complexities, as well as the subsurface flow. We present a comparison of the performance of two recent advances in light-based optical techniques for free surface measurements, total internal reflection-deflectometry and moon-glade background-oriented schlieren, with the more established method of free surface synthetic schlieren. We make use of an optical flow algorithm over the more traditional digital image correlation, in order to obtain higher spatial resolution data across the imaged free surface domain. The optical flow algorithm presents additional benefits, such as computational efficiency and robustness in capturing large displacements and straining of tracked features. The three optical techniques are assembled in synchronization to image two free surface conditions: (1) a free surface being impinged upon by an underlying turbulent, free-shear flow and (2) a random and irregular wave field induced by a free jet. Using the high-resolution measurements, we provide insight on the emergence of multiple free surface dynamics for a turbulent free surface. We present a comprehensive discussion on the benefits and drawbacks of each technique, including suggestions on the suitability of each technique for several experimental constraints.Graphical abstract

Study of Wave Parameters in the West side of Java Sea using Wave Spectral Analysis and Zero Up-Crossing Methods

Waves in the sea have a random shape, where the height, length, and direction of the waves change during the observation time. Due to the unpredictable nature of the waves with certain patterns, a statistical and probability approach is needed in analyzing waves. Before carrying out statistical and probability analysis, it is necessary to extract the wave parameters from the random wave data. There are two methods commonly used to extract wave parameters: the first is the individual wave analysis method, using a zero up/down-crossing technique. The second method is the wave spectral analysis method. In this study, both methods will be applied to observation data from the Pabelokan station [1] in the West Java Sea for a six-day. From this study, it was found that the significant wave height parameter generated by the spectral analysis technique and the zero up-crossing technique showed a positive correlation, which the correlation coefficient is 0.9891. In the study of the wave period investigation, both of method have a positive correlation, but the value of the wave period is very likely to be different. The correlation coefficient values for the average wave period are 0.5848 for Tm01 and 0.5757 for Tm02 .

Inter-Story Drift Ratio Detection of High-Rise Buildings Based on Ambient Noise Recordings

The inter-story drift ratio (IDR) is a crucial parameter in structural health monitoring to judge the safety, stability, and serviceability of buildings. Real-time, continuous, and widely applicable detection on IDRs is essential. However, the current methods present some challenges in conducting such detection, including adverse effects from weather, the requirement for large amounts of space, and fragile instruments. This study proposes an alternative method to overcome these defects to measure IDRs and evaluate the structural conditions using ambient noise recordings. Ambient noise is a random and continuous wave signal with various sources and is modified by its propagating medium. Taking the Zhonghe Building on the campus of Tongji University, Shanghai, China, as an example, 24 three-component seismometers were deployed to capture and record the ambient noise continuously from 20 November 2021 to 9 December 2021. Using analysis of the polarization parameters of ambient noise during the building’s most dangerous time and ordinary time, a deflection curve, IDRs, and harmful IDRs of the Zhonghe Building during the most dangerous time were calculated. The computed maximum drift was 0.06 m, the maximum IDR was 1.140×10−3, and the maximum harmful IDR was −2.573×10−4. These results were compared with the relevant specifications in China, and it was found that the structure was in good condition. The study proposes an alternative method to measure IDRs with high applicability and continuity in real time and underscores the need for further research to achieve a localized and real-time structural health monitoring system.

Study on the energy capture spectrum (ECS) of a multi-DoF buoy under random waves

Energy Capture Spectrum (ECS) and Wave Height Take-Off (WHTO) are two methods for evaluating the energy extraction of a wave energy converter (WEC) by treating energy capture as equivalent wave or wave height loss. This paper demonstrates the relationship between the two in the real sea state and proposed the concept of WHTO under random waves, which is helpful in improving the energy capture evaluation system of WECs. To design and optimize WECs in the preliminary stage, a new ECS calculation method based on potential flow theory is also presented. A case study of a multi-DOF (degree of freedom) buoy was carried out on this method to analyze its ECS characteristics in three main energy-capture DOFs (heave, surge, and pitch). Physical model tests were conducted to measure the initial load and validate the accuracy of the mathematic model. Based on the case study, the characteristics of ECS of the buoy in different DoFs with PTO change were presented and discussed. This paper aims to provide new methods and ideas for the design and optimization of WECs in the real sea state.

Hydrodynamic behaviour of composite bucket foundation with random waves

In real sea conditions, the effect of nonlinear phenomena, such as wave run-up and wave pressure, on the foundations of offshore wind structures may threaten the safety of the platforms. This study investigated the hydrodynamic behaviour of a composite bucket foundation (CBF) under random waves. A hydrodynamic simulation model of the interaction between random waves and the CBF was developed using the renormalisation group (RNG) k-ε model, which was verified through experiments. The relationship between wave run-up and wave parameters was studied, and the distributions of wave pressure around the CBF was described. The flow field and velocity vector distribution characteristics around the CBF were analysed. The results show that two types of wave fields appear around the CBF. The maximum run-up value of the CBF is 100%–150% higher than the minimum value, and the run-up value at the back side is 50%–70% higher than the minimum value. A larger wave steepness parameter leads to a smaller wave run-up value at the location of the smallest wave run-up value. The results can provide a reference for the practical application of a CBF.

New fractal–fractional parametric inequalities with applications

In the present paper, we first establish a general parameterized identity for local fractional twice differentiable functions involving extended fractal–fractional integral operators. Thus by employing generalized convexity on differentiable mappings along with Yang’s Power-mean, Hölder’s and improved fractal integral inequalities lead us to develop variety of new fractal–fractional parameterized inequalities. Several examples are provided with graphical illustrations to prove the validity of new results. We give error analysis of improved bounds numerically and also by 2D, 3D graphical representations. Finally, we show that our main results recapture fractal variants of trapezoid, midpoint, Simpson and Bullen-type inequalities. Some related applications to the fractal means, moment of random variables and wave equations are given as well.

First passage times for nonlinear ship dynamics using Gaussian random fields and effective waves

It is important to know the mean time until critical roll motion occurs in various operating and sea conditions, in order to determine and ensure the safety of ship designs and operating ships. Since typical ocean waves are irregular, the forcing and roll response of the ship is considered to be a stochastic process of colored noise type. However, the simulation of the corresponding first passage times is very time consuming. Therefore, an approach for the determination of mean first passage times of critical roll motion of ships is proposed in this paper which needs much less computation time. This approach is based on explicit formulas for the roll energy of the ship. These formulas are used to determine the mean first passage times based on integral expressions, which were previously obtained. The resulting integral expressions can be computed very fast using standard quadrature formulas. Moreover, the underlying model for ship dynamics is extended by introducing a new effective wave for short-crested sea states. This is an extension to the improved Grim’s effective wave concept.

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).

Experimental Study on Hydrodynamic Characteristics of a Submerged Floating Tunnel under Freak Waves (I: Time-Domain Study)

The dynamic response characteristics of a two-dimensional submerged floating tunnel (SFT) under random and freak waves were investigated in the present study. The results demonstrate that (1) the dynamic responses of the SFT under the freak wave are significantly larger than those under the largest wave in the wave train excluding the freak wave, particularly for the motion response. The maximum values of the motion responses induced by the freak wave were several times larger than those induced by the largest wave in the wave train excluding the freak wave, far exceeding the proportion of the corresponding wave height. (2) The freak wave parameter α1 has a significant effect on the amplification coefficients of surge, heave and pitch; all increase nonlinearly as α1 increases. Within α1 = 1.90~2.59, the amplification coefficients of the surge, heave and pitch vary in the ranges of 1.91~6.46, 1.53~3.87 and 1.73~5.32, respectively. (3) Amplification coefficients of tension increase almost linearly as α1 increases. Additionally, the amplification effect of the freak wave on the mooring tension is much smaller than that on motion responses. Within α1 = 1.90~2.59, the amplification coefficients of tension vary from 1.15 to 1.35. (4) Generalised amplification coefficients of motion responses increase as α1 increases and are all greater than 1.0, indicating that growth rates for motion responses under the freak wave exceed the growth rates for maximum wave height. Moreover, motion responses show a significantly nonlinear growth as maximum wave height increases. The generalised amplification coefficients of the mooring tension decrease as α1 increases, and are all less than 1.0, indicating that the dynamic amplification effect of the freak wave on the mooring tension is much smaller than that on motions. On the other hand, growth rates of the mooring tension under freak waves are smaller than the linear growth rate of the height of freak waves.

Experimental Study of the Hydrodynamic Characteristics of a Submerged Floating Tunnel under Freak Wave (II: Time-Frequency Domain Study)

A freak wave is a spike in a random wave series and hence the local characteristics in the time-domain are of key importance. When freak waves act on moored floating structures, the dynamic responses of the structures in the time and frequency domains change interdependently in a short period of time. It is difficult to comprehensively and accurately describe this physical process using a single-dimensional analysis method, such as time-domain statistical analysis or frequency-domain spectral analysis. The wavelet analysis method, which can simultaneously provide the time-domain and frequency-domain joint information of the physical process, is used to discuss the time-frequency joint variation characteristics of the dynamic responses of a two-dimensional submerged floating tunnel under a freak wave. The time-frequency characteristics of the dynamic responses induced by the freak wave and the differences from the action under random waves are investigated, with a particular emphasis on the ‘convex variation’ characteristics of the dynamic responses under a freak wave. The results show that: (1) The wavelet analysis method can effectively describe the basic characteristics of the dynamic responses of the SFT under a freak wave and clearly distinguish the differences in dynamic responses under freak and random waves. (2) Freak waves have dynamic amplification effects, which are related to the freak wave parameter α1, on a two-dimensional SFT. Following the action of freak waves on a two-dimensional SFT, significant energy concentration occurs in the time-frequency spectrum of the dynamic response in a certain time and frequency range. The degree of energy concentration increases nonlinearly with an increase in α1, and a certain high-frequency energy appears in the time-frequency spectrum of the motion response. The maximum values of the time-frequency spectra of the dynamic responses under a freak wave are much larger than those under a random wave with the identical wave spectrum. (3) Following the action of a freak wave on a two-dimensional SFT, the generalised energy spectra of surge, heave, pitch, and mooring tensions have convex peak values, which occur simultaneous with the occurrence of the freak wave, and the convex parts significantly increase as α1. (4) The time lengths of the influence of a freak wave on the dynamic responses exceeded the freak wave period. With an increase in α1, the time ranges of the large values of the time-frequency spectra of surge, heave, pitch, and mooring tensions increase nearly linearly.

Baroclinic interaction of forced shock waves with random thermal gradients

Density gradients aligned at an angle to pressure gradients result in baroclinic torque in fluid flows, generating vorticity. In this work, we study the vorticity generated by the baroclinic torque exerted by the interaction of pressure jumps across random two-dimensional shock waves with density gradients. A field of random two-dimensional shock waves has acoustic spectral energy scaling as Êk∼ε2/3ℓ−1/3k−2, where k is the wavenumber, ε is the energy dissipation, and ℓ is the integral length scale of the field. Since the acoustic energy is broadband, pressure and velocity gradients exist in a wide range of length scales. We study the interaction of these broadband gradients with isobaric thermal gradients localized at a length scale in the spectral space. We show that the method of generating shock waves or injection of wave energy in the system governs the baroclinic interactions. For stochastically forced shock waves, baroclinic terms are negligible. Broadband vorticity with energy at least two orders of magnitude smaller is generated due to continuous variation in curvature of shock waves caused by stochastic forcing. On the other hand, shock waves maintained by energy rescaling result in the generation of coherent vorticity. We also discuss the relative magnitude of the baroclinic torque generated due to total density gradients compared to the one generated due to non-isentropic density gradients within the shock waves interacting with the pressure gradients.

Development of a real-time wave energy control with consideration of control latency

In order to enhance the power capture of wave energy converters in random ocean waves, real-time control is commonly implemented. Despite the developments of various control algorithms, many of them assume that the control is implemented instantly, which may not be consistent with the real situation. The research aims to develop a control algorithm that can model control latency and investigate its effect on control effectiveness in enhancing wave power capture. The control algorithm developed replaces the traditional instant control model with a differential formula that considers the time-varying control behavior. The study found that the developed time-varying control algorithm is effective in enhancing wave power capture even with consideration of latency. However, when compared to traditional instant control theory, the present control method becomes less effective due to the residual control force caused by latency. The residual control force has a negative impact on the optimization of control commands and, consequently, wave power capture. Furthermore, it is found that the effect of latency on the control algorithm is sensitive to the wave period. The latency effect becomes less significant as the wave period increases.

Seismic response analysis of subway station structure under random excitation based on probability density evolution method

The subway station structure mainly faces the uncertainty of ground motion and surrounding soil mass. Comprehensive analysis of the seismic response of subway station structures under random excitation is the key to ensuring the safety of urban people's lives and property. In this paper, the random shear wave velocity profile model and the random ground motion model characterizing uncertainty are established. Using a high-dimensional space optimization point selection strategy significantly reduces the number of sample points and computational costs of nonlinear time history analysis (NLTHA). Combining the probability density evolution method (PDEM) with finite element analysis, the stochastic seismic response analysis of the subway station structure under dual random excitations is realized. In addition, statistical methods are used to analyze the distribution characteristics of the most unfavorable seismic responses of the subway station structure. The research results show that when random excitation is not considered, the adverse seismic damage risk of subway station structures will be ignored. The evolution of the seismic dynamic response of subway station structures is mainly controlled by the amplitude of random ground motion acceleration. Additional random shear wave velocities can increase the lateral deformation range of the subway station structure, leading to a decrease in the dynamic reliability of the structure. PDEM can conduct stochastic seismic response analysis of the subway station structure from both time and response dimensions. The proposed method provides strong support for a comprehensive analysis of the seismic response of underground structures.