Spectral Peak Period Research Articles

Digital twin for rapid damage detection of a fixed net panel in the sea

The fishing net is the most important component of aquaculture net cages. Once damaged, it can cause substantial economic losses and ecological problems to the aquaculture industry. To avoid these subsequent issues caused by the damage to the fishing net, seeking a computerized, labor-saving approach and detecting damage in real time becomes the primary task of this paper. Inspired by recent development of the artificial neural networks and machine learning, this study proposes a fast and accurate approach for fishing net damage detection based on digital twin. Firstly, time-domain numerical simulations of the fishing net are conducted in a series of wave and current conditions to develop the artificial neural network-based digital twin. Then, the significant wave height, the spectral peak period, and tensions of vertical and horizontal ropes are used as input variables during the artificial neural network training; the intact and damaged states of the fishing net are considered outputs. Alongside this, the back-propagation learning algorithm is used for training to maximize damage detection performance. The results highlight that the digital twin model can effectively identify the fishing net damage using the sensor data, and the accuracy of the damage detection reaches above 93%. When the damage occurs at different net positions, the prediction accuracies of the artificial neural network model for training and testing sets are 93.97% and 93.00%, respectively. Regarding different wave-current directions, the prediction accuracies of the artificial neural network model are 99.87 % and 99.34 % for training and testing sets. Moreover, the developed digital twin can accurately detect the damage of the net even sea conditions and sensor data are not included in the training. The digital twin model proposed in the present study can potentially be used for damage detection in other aquaculture components and structures.

A spectral description for extreme sea states offshore Denmark Part II: Directional spreading function

Power spectral density and frequency-dependent directional spreading functions are developed for describing extreme sea state spectra in the Danish sector of the North Sea. The input to the spectral models are the significant wave height, the spectral peak period, the spectral second-moment period, and the circular root-mean-square spreading at the spectral peak frequency. The new spectral functions have been developed from measurements of large sea states, made with a Directional Waverider buoy, at two sites in the Danish sector of the North Sea. This paper describes the new directional spreading function; a companion paper describes the new power spectral density function. The new directional spreading function is based on a simple parameterisation of measured frequency-dependent spreading derived from the Directional Waverider buoys. It is defined in terms of the peak period and significant wave height, with different expressions depending on whether the dominant component in the spectrum is a wind-sea or a swell. A form for a combined wind-sea and swell sea state is also defined. The new spreading function is compared against measurements for the location and found to provide an accurate representation of the spreading estimated from the measurements.

A spectral description for extreme sea states offshore Denmark Part I: Power spectrum

A power spectral density function that describes extreme sea states in the Danish sector of the North Sea is developed. The power spectrum is specified in terms of the parameters: significant wave height, spectral peak period, and spectral second-moment period. The power spectral density function is a modified Torsethaugen spectrum, involving an expression for the peak enhancement factor that is dependent on the inverse of the square root of wave steepness and a high-frequency tail that decays at a rate which is dependent on the significant wave height and the ratio of the peak and second-moment periods. The new function was developed from Directional Waverider data measured at two sites in the Danish sector of the North Sea and validated with data from other sites offshore Denmark, primarily recorded with Saab WaveRadars. A companion paper describes a new directional spreading function, which together with the power spectral density function, provides a description of the complete frequency-direction spectrum of extreme sea states in the Danish sector of the North Sea.

Increasing Trends in Spectral Peak Energy and Period in a Semi-Closed Sea

Increasing Trends in Spectral Peak Energy and Period in a Semi-Closed Sea

Influence of second-order wave force and focusing position on dynamic responses of tension leg platform under a freak wave

As a semicompliant and semirigid column group structure, both second-order sum-frequency and diff-frequency wave forces and focusing positions are important for tension leg platforms (TLPs) under freak waves. The double-wave train superposition model is widely used to generate freak waves; however, multiple trials are inevitable for freak wave generation owing to the uncertainty in parameter selection, which may decrease the simulation efficiency. In this study, the effects of the energy ratio of the focused wave train, number of constituent waves, and parameters of the JONSWAP wave spectrum on the generation probability of freak waves are studied, and the generation probability of the freak wave is fitted by a Γ cumulative probability density function. The advantage of the fitted formula is that the generation probability of a freak wave is quantified, and an appropriate number of constituent waves can be determined for a given energy ratio of the focused wave to increase the simulation efficiency. Furthermore, the dynamic responses of a TLP in a freak wave considering the influences of second-order wave forces and focusing positions are simulated and discussed. Two main findings are that the second-order diff-frequency wave force may cause large-amplitude low-frequency motion in the surge direction and set-down motion in the heave direction, which are 3.71 and 4.08 times the first-order surge and heave responses, respectively, whereas the second-order sum-frequency wave force may cause high-frequency oscillation in the pitch direction, the amplitude of which is 3.9 times the amplitude of the first-order pitch response. The response of the TLP is significantly increased under the freak wave, especially when the second-order wave force is considered. The apparent focusing position of the maximum response changes with the spectral peak period owing to the nonrepeatability of the freak wave and phase difference of the columns. The maximum predicted errors of surge, heave, and pitch motion reached 42.0%, 41.1%, and 98.9%, respectively, when the freak wave acts on the front column, center of the platform, and back column, which may significantly underestimate the dynamic response. Therefore, the effects of the focusing position should be considered when calculating the response of a TLP under a freak wave.

Discussion/comments of “Parameterization of nearshore wave breaker index” by Chi Zhang, Yuan Li, Yu Cai, Jian Shi, Jinhai Zheng, Feng Cai and Hong Shuai

The purpose of these comments and discussion has been to point out that wave statistics can be incorporated in future applications of the nearshore wave breaker index formula proposed by Zhang et al. (2021). This is demonstrated by using a joint distribution of significant wave height and spectral peak period provided by Li et al. (2015).

Improving accuracy on wave height estimation through machine learning techniques

Estimation of wave agitation plays a key role in predicting natural disasters, path optimization and secure harbor operation. The Spanish agency Puertos del Estado (PdE) has several oceanographic measure networks equipped with sensors for different physical variables, and manages forecast systems involving numerical models. In recent years, there is a growing interest in wave parameter estimation by using machine learning models due to the large amount of oceanographic data available for training, as well as its proven efficacy in estimating physical variables.In this study, we propose to use machine learning techniques to improve the accuracy of the current forecast system of PdE. We have focused on four physical wave variables: spectral significant height, mean spectral period, peak period and mean direction of origin. Two different machine learning models have been explored: multilayer perceptron and gradient boosting decision trees, as well as ensemble methods that combine both models. These models reduce the error of the predictions of the numerical model by 36% on average, demonstrating the potential gains of combining machine learning and numerical models.

Quantifying wave measurement differences in historical and present wave buoy systems

An intra-measurement evaluation was undertaken, deploying a NOMAD buoy equipped with three National Data Buoy Center and two Environment and Climate Change Canada-AXYS sensor/payload packages off Monterey, California; a Datawell Directional Waverider buoy was deployed within 19 km of the NOMAD site. The six independent wave measurement systems reported hourly estimates of the frequency spectra, and when applicable, the four Fourier directional components. The integral wave parameters showed general agreement among the five sensors compared to the neighboring Datawell Directional Waverider, with the Inclinometer and the Watchman performing similarly to the more sophisticated 3DMG, HIPPY, and Triaxys sensor packages. As the Hm0 increased, all but the Inclinometer were biased low; however, even the Watchman reported reasonable wave measurements up to about 6–7 m, after which the Hm0 becomes negatively biased up to about a meter, comparable to previous studies. The parabolic fit peak spectral wave period, Tpp, results showed a large scatter, resulting from the complex nature of multiple swell wave systems compounded by local wind-sea development, exacerbated by a variable that can be considered as temporally unstable. The three directional sensors demonstrated that NOMAD buoys are capable of measuring directional wave properties along the western US coast, with biases of about 6 to 9 deg, and rms errors of approximately 30 deg. Frequency spectral evaluations found similarities in the shape, but a significant under estimation in the high frequency range. The results from slope analyses also revealed a positive bias in the rear face of the spectra, and a lack of invariance in frequency as suggested by theory.

Assessment of operational limits: Effects of uncertainties in sea state description

For operations dominated by waves, operational limits are normally expressed in terms of allowable sea state parameters, such as the significant wave height (Hs) and spectral peak period (Tp). The allowable sea states need to be assessed in the planning phase of the operations. Different sources of uncertainties (including weather forecasts, wave spectral model and numerical models) should be accounted for in the allowable sea states to provide safety margins. This study focuses on assessment of the operational limits (in terms of Hs and Tp) considering the uncertainties associated with the sea state descriptions used in the numerical analysis. The aim is to demonstrate the effects of simultaneous description of wind sea and swell sea accounting for their different directional spreading and directions of propagation. A case study using lifting operation is chosen to address these uncertainties in the allowable sea states. To illustrate the results, two types of floating crane vessels, mono-hull and semi-submersible are employed in the case study. Operability analysis by using these vessels are performed and compared using NORA10 hindcast data for a site in the Barents Sea.

Using Sentinel-2 Images to Map the Populus euphratica Distribution Based on the Spectral Difference Acquired at the Key Phenological Stage

Populus euphratica is an important tree species in desert ecosystems. The protection and restoration of natural Populus euphratica forests requires accurate positioning information. The use of Sentinel-2 images to map the Populus euphratica distribution at a large scale faces challenges associated with discriminating between Populus euphratica and Tamarix chinensis. To address this problem, this study selected the Daliyabuyi Oasis in the hinterland of the Taklimakan Desert as the study site and sought to distinguish Populus euphratica from Tamarix chinensis. First, we determined the peak spectral difference period (optimal time window) between Populus euphratica and Tamarix chinensis within monthly Sentinel-2 time-series images. Then, an appropriate vegetation index was selected to represent the spectral difference between Populus euphratica and Tamarix chinensis within the key phenological stage. Finally, the maximum entropy method was used to automatically determine the threshold to map the Populus euphratica distribution. The results indicated that the period from 22 April to 1 May was the optimal time window for mapping the Populus euphratica distribution in the Daliyabuyi Oasis. The combination of the inverted red-edge chlorophyll index (IRECI) and the maximum entropy method can effectively distinguish Populus euphratica from Tamarix chinensis. The user’s accuracy of the Populus euphratica distribution extraction from single-data Sentinel-2 images acquired within the optimal time window was 0.83, the producer’s accuracy was 0.72, and the F1-score was 0.77. This study verified the feasibility of mapping Populus euphratica distribution based on Sentinel-2 images, and analyzed the validity of exploiting spectral differences within the key phenological stage from a single-data image to distinguish between the two species. The results can be used to extract the distribution of Populus euphratica and serve as an auxiliary variable for other plant classification methods, providing a reference for the extraction and classification of desert plants.

Dynamic reliability analysis of a floating offshore wind turbine under wind-wave joint excitations via probability density evolution method

Floating offshore wind turbine (FOWT) towers are dynamically sensitive to wind and wave excitations. Since the wave tends to be harsher with the increase of wind speed, FOWT towers are likely to experience the most severe vibration operating at the cut-out wind speed. In the present study, the short-term dynamic reliability of a spar-type FOWT is evaluated based on the probability density evolution method (PDEM). For this purpose, an integrated coupled dynamics model for the FOWT is firstly established by incorporating the multibody dynamics with the finite element (FE) method. Next, the conditional joint probability distribution of the significant wave height and peak spectral wave period at the cut-out wind speed is constructed based on the copula model. Then, the stochastic dynamic response and reliability of the FOWT can be analyzed via PDEM. The numerical example of reliability analysis of a 5-MW spar-type FOWT operating at the cut-out wind speed is carried out, in which the long-term met-ocean data at a South China Sea site is utilized. Simulation results show that the reliability of the FOWT for normal operation is less than 0.2 when the acceleration at the tower top is adopted as the failure criterion.

Experimental study on hydrodynamic characteristics of a moored square cylinder under freak wave (II: Frequency-domain study)

Previous studies indicated that the occurrence of freak wave has a significant impact on the time-domain characteristics of a moored floater dynamic response. In this study, extensive investigations have been performed to figure out further dynamic response characteristics of a moored square cylinder under freak wave in frequency-domain. In the experiments, the wave sequences with and without the freak wave are defined as freak and random waves, respectively. The results show that, the freak wave parameter α1 and spectral peak period have significant impacts on the dynamic response characteristics of the moored floater in frequency-domain. The effect of freak wave on surge and mooring tension of the floater is figured out through the low frequency components (0–0.5fp) which leads to significant increase with α1. Followed the occurrence of freak wave, surge increases sharply and oscillates for longer than 20 wave periods in low frequency. Without the occurrence of freak wave, however, both amplitude and oscillating of surge is significantly weaker. The mooring tension response is subjected to surge and hence the trend of variation is similar to surge.

Application of Taylor diagram in the evaluation of joint environmental distributions' performances

Probability-based design of offshore structures usually require a joint distribution of significant wave heights and zero-up-crossing periods, or spectral peak periods, in order to describe the long-term wave scenario, and thus predict long-term extreme responses. Several joint statistical models have been proposed in the literature, often comprising environmental parameters aside from significant wave heights and zero-up-crossing or spectral peak periods, such as wind and current velocities, among others. However, since there is no theoretical environmental distribution function, the assessment of different models is done on an empirical basis for each available data set. The fitting of a joint distribution model on a set of long-term wave data, given the extensive number of available joint statistical models and the inherent extrapolations required for extreme conditions, can be extremely cumbersome. This paper proposes the application of Taylor diagram in the assessment of the fit of joint models. The aim is to find the models with the best performances through an easy and straightforward visual comparison. For simplification purposes, the joint statistical model considered comprises significant wave heights and spectral peak periods only. Results show that Taylor diagram is a useful tool for primarily evaluations of adjusted probability models. The indicatives for better model performances identified in the diagram were shown to correspond to other common identifiers, which demonstrates that the diagram can be a reliable indicator for good models. Some study cases are presented to demonstrate Taylor diagram application in joint probability distributions fittings for wave environmental parameters.

On Efficient Surrogate Model Development for the Prediction of the Long-Term Extreme Response of a Moored Floating Structure

Abstract This study focuses on the development of efficient surrogate models by polynomial chaos expansion (PCE) for the prediction of the long-term extreme surge motion of a moored floating offshore structure. The structure is subjected to first-order and second-order (difference-frequency) wave loading. Uncertainty in the long-term response arises from contrasting sea state conditions, characterized by significant wave height, Hs, and spectral peak period, Tp, and their relative likelihood of occurrence; these two variables are explicitly included in the PCE-based uncertainty quantification (UQ). In a given sea state, however, response simulations must be run for the associated Hs and Tp; in such simulations, typically, a set of random amplitudes and phases define an irregular wave train consistent with that sea state. These random amplitudes and phases for all the frequency components in the wave train introduce additional uncertainty in the simulated waves and in the response. The UQ framework treats these two sources of uncertainty—from Hs and Tp on the one hand, and the amplitude and phase vectors on the other—in a manner that efficiently yields long-term surge motion extreme predictions consistent with more expensive Monte Carlo simulations (MCS) that serve as the “truth” system. To reduce uncertainty in response extremes that result from sea states with a low likelihood of occurrence, importance sampling is employed with both MCS- and PCE-based extreme response predictions. Satisfactory performance with such efficient surrogate models can help in assessing the long-term response of various offshore structures.

Effects of a passive tuned mass damper on blade root impacts during the offshore mating process

Single-blade installation is a conventional method for installing blades on monopile-type offshore wind turbines. A jack-up crane vessel is commonly used, and individual blades are lifted to the tower top height and mated with the hub. The relative motions between the hub and blade root during the mating phase, partly due to wind-induced blade motion and partly due to wave-induced monopile motion, can induce substantial impact forces at the blade root. This can cause severe damage at the blade root connections and have a high potential to jeopardise the installation task. Mitigation measures are therefore required to limit the relative motion between the hub and the root during the mating process. In this article, we investigate the effects of a passive tuned mass damper (TMD) on the (1) impact velocities manifested between the blade root and hub during the mating phase and (2) its effect on the response-based limiting sea states. Time-domain multi-body simulations of an installation system characterising the mating operation with and without a TMD for collinear and misaligned wind and wave conditions have been performed, and the effectiveness of TMD for controlling the impact velocity is quantified. Furthermore, finite element analyses are performed to determine the threshold velocity of impact for a scenario in which a blade root with a guide pin suffers a sideways impact with the hub. It is found that the tuned mass damper can reduce the relative impact velocities by more than 40% and can substantially expand the allowable sea states and operability for the mating operation. Moreover, the effectiveness of TMD at reducing the impact velocity increases with increasing significant wave height (Hs); however, it decreases with increasing wind-wave misalignment and with shifts in the wave spectral peak period (Tp) away from the tuned frequency. The findings of the study can be utilised for planning safe and cost-efficient installation of latest-generation wind turbine blades.

Extended Environmental Contour Methods for Long-Term Extreme Response Analysis of Offshore Wind Turbines1

AbstractEnvironmental contour method is an efficient method for predicting the long-term extreme response of offshore structures. The traditional environmental contour is obtained using the joint distribution of mean wind speed, significant wave height, and spectral peak period. To improve the accuracy of traditional environmental contour method, a modified method was proposed considering the non-monotonic aerodynamic behavior of offshore wind turbines. Still, the modified method assumes constant wind turbulence intensity. In this paper, we extend the existing environmental contour methods by considering the wind turbulence intensity as a stochastic variable. The 50-year extreme responses of a monopile-based offshore wind turbine are compared using the extended environmental contour methods and the full long-term method. It is found that both the environmental contour method and the modified environmental contour method, with the wind turbulence intensity included as an individual variable, give more accurate predictions compared with those without. Using the full long-term method as a benchmark, this extended approach could reduce the nonconservatism of the environmental contour method and conservatism of the modified environmental contour method. This approach is effective under wind-dominated or combined wind-wave loading conditions, but may not be as important for wave-dominated conditions.

The effective prediction of wave-in-deck loads

The present paper concerns the extreme wave loads acting on an offshore structure; specifically the wave-in-deck loading component that arises when the height of an incident wave crest exceeds the elevation of the topside structure. In this case wave inundation occurs, the resulting loads on the topside structure represent a significant part of the total wave load. A new model for the effective prediction of this important loading component is presented. This is based upon the conservation of momentum, is formulated in a Lagrangian frame of reference, can incorporate any incident wave form, and takes due account of the porosity (or openness) of the topside structure. Comparisons between the model predictions and wide-ranging laboratory observations are shown to be in good agreement; the latter based upon deterministic focused wave events that are known to be representative of the largest waves arising in realistic sea-states. In addition, comparisons are also made with independent cfd calculations. Taken together, the proposed model is shown to accommodate changes in the spectral shape, the spectral peak period, the incident crest elevation (and hence the level of inundation), the directional spread of the incident waves, and the porosity of the topside structure. Importantly, this agreement applies to both non-breaking and breaking waves, involves no empirical calibration, and can be achieved with limited computational resources. As such, the model is ideally suited to design/re-assessment calculations in which the reliability of any offshore structure must be based upon a rigorous assessment of the long-term distribution of the total wave loads, including any wave-in-deck loading component.

Numerical Investigations on Wave Remote Sensing from Synthetic X-Band Radar Sea Clutter Images by Using Deep Convolutional Neural Networks

X-band marine radar is an effective tool for sea wave remote sensing. Conventional physical-based methods for acquiring wave parameters from radar sea clutter images use three-dimensional Fourier transform and spectral analysis. They are limited by some assumptions, empirical formulas and the calibration process while obtaining the modulation transfer function (MTF) and signal-to-noise ratio (SNR). Therefore, further improvement of wave inversion accuracy by using the physical-based method presents a challenge. Inspired by the capability of convolutional neural networks (CNN) in image characteristic processing, a deep-learning inversion method based on deep CNN is proposed. No intermediate step or parameter is needed in the CNN-based method, therefore fewer errors are introduced. Wave parameter inversion models were constructed based on CNN to inverse the wave’s spectral peak period and significant wave height. In the present paper, the numerically simulated X-band radar image data were used for a numerical investigation of wave parameters. Results of the conventional spectral analysis and CNN-based methods were compared and the CNN-based method had a higher accuracy on the same data set. The influence of training strategy on CNN-based inversion models was studied to analyze the dependence of a deep-learning inversion model on training data. Additionally, the effects of target parameters on the inversion accuracy of CNN-based models was also studied.

Improvement of the ANFIS-based wave predictor models by the Particle Swarm Optimization

In this paper, the Particle Swarm Optimization (PSO) algorithm is employed to deal with the Adaptive Network based Fuzzy Inference System (ANFIS) model drawbacks in prediction of wind –driven waves. In the ANFIS model selection of fuzzy IF-THEN rules structure and numbers is not an automatic process. In addition, in the ANFIS model extraction of fuzzy antecedent and consequent parameters is a gradient-based method which makes the answer susceptible to entrap in local optima. To cope with the ANFIS deficiencies, herein the PSO algorithm is coupled with the wave predictor FIS models in three viewpoints to optimize fuzzy subtractive clustering parameters, i.e. radii of clustering and quash factor, and the antecedent and consequent parameter of fuzzy IF-THEN rules. At first viewpoint, two PSO algorithms are used to optimize fuzzy subtractive clustering parameters and fuzzy IF-THEN rule parameters. In the second viewpoint, a PSO algorithm is used to optimize subtractive clustering parameters while the ANFIS model is used to tune the fuzzy IF-THEN rule parameters. In the third viewpoint, only a PSO algorithm is used to optimize the subtractive clustering parameters along with fuzzy IF-THEN rule parameters. Gathered data sets by National Data Buoy Center (NDBC) at Lake Michigan are used to evaluate the developed models for prediction of wave parameters including significant wave height and peak spectral period. Results indicate the efficiency of PSO algorithm to improve the ANFIS model accuracy.

Assessment of wave runup and wave rundown based on observed long-term wave conditions

The article presents an analytical method that can be applied to provide first estimates of wave runup (RU) and wave rundown (RD) on shorelines and coastal structures based on observed long-term wave statistics and is supplementary to [12] who based their results on long-term wind statistics. Some recently published wave RU and wave RD formulae are used, together with joint statistics of significant wave height and spectral peak period from the Northern North Sea. Results are exemplified for the average statistical properties of wave RU and wave RD in terms of the expected values and the standard deviations, as well as values estimated from 1-, 10- and 100-years return period contour lines.