Estimation Of Directional Wave Spectra Research Articles

Improvement in the Post-Processing of Wave Buoy Data Driven by the Needs of a National Coast and Sea Monitoring Agency

Technological development in terms of the power requirement for data acquisition and processing opens new perspectives in the field of environmental monitoring. Near real-time data flow about the sea condition and a possible direct interface with applications and services devoted to marine weather networks would have a significant impact on several aspects, such as, for example, safety and efficiency. In this scenario, the needs of buoy networks have been analyzed, and the estimation of directional wave spectra from buoys’ data has been deeply investigated. Two methods have been implemented, namely the truncated Fourier series and the weighted truncated Fourier series, and they have been tested by both simulated and real experimental data, representative of typical Mediterranean Sea conditions. From simulation, the second method proved to be more efficient. From the application to real case studies, it emerged that it works effectively in real conditions, as confirmed by parallel meteorological observations. The estimation of the main propagation direction was possible with a small uncertainty of a few degrees, yet the method exhibits a limited directional resolution, which suggests the need for undertaking further studies, briefly addressed in the conclusions.

Directional wave spectrum estimation with ship motion responses using adversarial networks

The external environmental conditions around a vessel are essential for efficient and safe ship operation, among which the sea state is of key importance. Considering the ship as a large wave buoy, the sea state can be estimated from motion responses without extra sensors installed. This is a challenging task since the relationships between the waves and the ship motions are hard to describe accurately. Machine learning approaches can learn these mapping without an explicit model, which is promising for sea state estimation. Current machine learning approaches represent the sea state as a set of categories or a number of wave parameters while neglecting the 2D wave spectrum. This paper proposes a sea state estimation network that estimates the 2D wave spectrum along with a discrimination network. The discrimination network can detect and correct high-order inconsistencies of the spectrum. Simulation studies are performed to show that the proposed method can provide wave spectrum estimation with high accuracy.

Estimation of directional wave spectra and hull structural responses based on measured hull data on 14,000 TEU large container ships

To ensure hull structural strength of container ships in association with their increase in size, it is very important to grasp the hull stress histories all over the hull structure in actual sea state. However, ordinary hull stress monitoring systems are insufficient for this purpose because of the small number of stress sensors actually practicable. Therefore, in this paper, we discuss an approach to reproduce the hull stress responses which are not measured based on the estimated wave spectrum from the limited measurement data. To achieve this, we introduce a new model to estimate directional wave spectra based on measured ship stress responses and ship response functions, and further we estimate other ship responses using the model. To model an arbitrarily shaped directional wave distribution, the 360° direction is discretized into 36 directions of 10-degree intervals instead of using a directional distribution function, and in each direction, the wave spectrum is represented using the Ochi (3P) spectrum with three parameters (average wave period, significant wave height, and kurtosis). The authors discuss the evaluation results based on two stress response combinations, and a comparison is made between the sea state estimates made by the proposed method and the ocean wave hindcast database (JWA). Furthermore, by comparing the significant values and the spectra of the measured response of the ship with the estimated response based on both the estimated sea state by the proposed method and the hindcast sea state, the accuracies of the proposed method and the hindcast method are discussed in terms of ship stress estimation at non-instrumented locations.

Sea state estimation based on vessel motion responses: Improved smoothness and robustness using Bézier surface and L1 optimization

Floating structures oscillate in waves, where these wave-induced motions may be critical for various marine operations. An important consideration is thereby given to the sea states at the planning and operating stages for an offshore project. The most important information extracted from a sea state is the directional wave spectrum, indicating wave direction, significant wave height, and wave spectrum peak period. Among several available methods of measuring and estimating the directional wave spectrum, the wave buoy analogy technique based on vessel motion responses is an in situ and almost real-time solution without extra costs of devices. If the forms of the wave spectra are not predefined in the estimation, the method is called a nonparametric approach. Its most remarkable advantage is the flexible form, but the smoothness should be regulated. After the discrete Fourier transform has been applied to the measured vessel motions, smoothing is necessary. However, this process results in disturbed vessel cross-spectra and a lowpass characteristic of the windowing function. This paper presents a nonparametric approach for directional wave spectrum estimation based on vessel motion responses. It introduces novel smoothness constraints using Bézier surface and includes a more robust estimate using L1 optimization. Both techniques are applied to the wave buoy analogy for the first time. Numerical simulations are conducted to verify the proposed algorithm.

Full-scale identification of the wave forces exerted on a floating bridge using inverse methods and directional wave spectrum estimation

Abstract The dynamic behaviour of long-span bridges is governed by stochastic loads from typically ambient excitation sources. In real life, these loads cannot be measured directly at full scale. However, inverse methods can be utilised to identify these unknown forces using response measurements together with a numerical model of the relevant structure. This paper presents a case study of full-scale identification of the wave forces on the Bgsoysund bridge, a long-span pontoon bridge that has been monitored since 2013. First, a numerical model of the structure is formed, resulting in a reduced-order state-space model that takes into account the frequency-dependent hydrodynamic mass and damping from the fluid, based on fitting of rational transfer functions. Using acceleration data of the structure measured during several events of moderate and strong seas, the wave forces are identified using stochastic-deterministic methods for combined state and input estimation. In addition, a separate frequency-domain assessment of the wave forces is performed, in which the spectral density of the first-order wave forces is constructed from an estimated directional wave field model driven by wave elevation data. When compared in the frequency domain, the force estimates from the two approaches are of comparable magnitude. However, uncertainties in the assumptions and models behind the force estimates from the two approaches still play a significant role.

Directional Wave Spectra from Video Images Data and SWAN Model

In this paper, analysis of directional wave spectra in shallow water area estimated by video images data has been compared with numerical model of SWAN. Estimation of directional wave spectra from video images is based on the Bayesian Directional Method using a group of pixels brightness on the image. For this study, the pixels can be considered equivalent to fixed instruments as wave probe sensor after rectification process. The results show that there is a good agreement between directional wave spectra estimated by video images data and the SWAN model. Both methods estimate similar shape of directional wave spectra in the shallow water. In addition, the energy distribution of directional wave spectra in shallow water is concentrated significantly in frequency and direction.

VERIFICATION OF A MODIFIED BAYESIAN METHOD FOR ESTIMATING DIRECTIONAL WAVE SPECTRA FROM HF RADAR

A Modified Bayesian Method (MBM) for estimating directional wave spectra from Doppler spectra obtained by HF radar is examined using field data which were employed in the verification of Bayesian Method (BM). Applicability, validity and accuracy of the MBM are demonstrated compared with the directional wave spectra estimated by BM and observed by buoy acquired from the reliable field data obtained from Surface Current and Wave Variability Experiments (SCAWVEX) project. The necessary conditions of the Doppler spectral components to be used to estimate a reliable directional spectrum are correspondingly estimated by BM. The results clearly demonstrate that directional wave spectra can be estimated by MBM on the basis of Doppler spectra. In addition, though BM shows very time consuming in computations, BM is more robust against the presence of noise than MBM.
 
 
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 Lukijanto, Hashimoto, N., and Yamashiro, M. (2009b). An improvement of Modified Bayesian Method for estimating directional wave spectra from HF radar backscatter. Proceedings of 5 th APAC (Asian and Pacific Coasts), 105-111.
 
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 Wyatt, L. R. Gurgel, K.W., Peters, H.C., Prandle, D., Krogstad, H.E., Haug, O., Gerritsen, H., Wensink, G.J. (1997b). The SCAWVEX Project. Proceedings of WAVES97, ASCE.

非定常船体動揺データを用いた方向波スペクトルのリアルタイム推定について

The Bayesian modeling procedure is modified for real-time estimation of directional wave spectra using non-stationary ship motion data. The assumption of stationary stochastic processes is applied to the seaway, but not to ship response because it also depends on ship maneuvers. Ship response is strongly affected by changes in the encounter angle and frequency of waves. Therefore, it is need to be a real-time algorithm that can deal with non-stationary stochastic processes and estimate the directional wave spectra. In the proposed algorithm, the iterative calculations of the non-linear equations were optimized and the convergence was not achieved at every time step, but was achieved gradually over several time steps. In order to examine the reliability of the proposed method, real-time estimation was conducted by using the data of onboard experiments. Comparisons between the results of the proposed algorithm and a wave monitoring radar system show good agreements.Copyright © 2009 by ASME

Estimating directional wave spectrum based on stationary ship motion measurements

Useful information can be derived from on-board estimation of the directional wave spectrum of the sea, especially concerning feed forward control of dynamically positioned systems. This work discusses the feasibility of using stationary ship motion measurements for in-site directional wave spectrum estimation, focusing on the particular problems that may arise in the application of adapted estimation methods to this kind of system. Load variations, operational trim and other disturbances frequently occur, modifying the ship response to incident waves. Since the methodology depends on previous knowledge about the amplitude response operators, these errors may cause some degradation in the estimated spectrum. Furthermore, due to the large inertia of the ship, high frequency wave components are filtered, reducing the frequency range of the spectrum that can be estimated. These drawbacks are analyzed and their influence in final estimation is quantified. Roll motion of the ship presents non-linear and resonant behavior and is extremely sensitive to load variations. For this reason, sway motion was used instead of roll one, differently from common directional buoys algorithms that take into account the three motions in the vertical plane (heave, roll and pitch). A parametric estimation method, normally used for directional buoys measurements, was adapted to the case and tested. Exhaustive numerical trials were carried out using a tanker in two loading conditions (full and ballasted) and a pipe-laying barge, under typical wave spectra of Brazil's Campos Basin, either in unimodal or bimodal cases. Small-scale towing-tank results were also used as a first experimental validation concerning unimodal unidirectional sea states. Spectral estimations based on experimental results were also compared to those obtained by means of a Bayesian estimation method presented in literature, for the sake of comparison. Parametric Method presented best accuracy in all tested cases.

逐次型Bayes法による方向波スペクトルのオンライン推定

The ship motions in waves are regarded as a nonstationary random process because of the ship maneuvers, such as changes of the course and the speed, even on the assumption that the seaway can be considered as stationary stochastic process. In this paper, the recursive type of Bayesian modeling procedure is proposed and applied to online estimation of directional wave spectra based on ship motion data, which are pitch angle, roll angle and vertical acceleration. In the proposed method, the convergence of the estimates is not achieved every time step, but gradually achieved with time steps by using the ship motion cross spectra. To cope with the nonstationarity included in the time history data, instantaneous cross spectrum analysis based on T-VVAR (Time Varying Coefficient Vector Auto Regressive) modeling procedure is adopted. The T-VVAR model is transformed into the state space model and the time varying coefficients can be evaluated by using the Kalman Filter algorithm. Using the estimated time varying coefficients, the instantaneous ship motion cross spectra can be calculated every moment. Moreover, in order to estimate the directional wave spectra stably, a new constraint condition, which is based on the observed significant wave height data, is introduced into the Bayesian modeling procedure. To examine the reliability of the proposed procedure, onboard tests were carried out on nonstationary conditions. It is shown that the statistical values derived by integration of the estimated directional wave spectra agree well with the observed one.

Study on Online Bayesian Estimation of Directional Wave Spectra

Bayesian modeling procedure is applied to online analysis to estimate directional wave spectra based on ship motion data. The proposed method can deal with the nonstationarity of ship responses that comes from the ship maneuvers such as changes of the course and speed. In order to cope with the nonstationarity included in the time history data, instantaneous cross spectrum analysis based on T-VVAR (Time Varying Coefficient Vector Auto Regressive) modeling procedure is introduced. Moreover, Bayesian modeling procedure is transformed into an online algorithm. Some numerical experiments were carried out to examine the proposed method. Using an array of wave probes, measurements of time varying directional wave spectra were simulated. It is shown that the estimated directional wave spectra agree well with the incident wave spectrum and the proposed method can cope with the nonstationarity.

Bayesian estimation of directional wave spectra based on ship motions

New techniques are introduced into the Bayesian modeling procedure to estimate directional wave spectra based on ship motion data. In the proposed method, the triple-valued function problem in following seas is strictly taken into account and the optimum solution is obtained from the stochastic viewpoint. In order to examine the reliability of the proposed method, towing tank experiments and onboard experiments were carried out. Using the proposed method, it is shown that the directional wave spectra can be estimated from the vector-valued time series recorded on a running ship even in following seas.

A Bayesian Approach for Estimation of Directional Wave Spectra with HF Radar

A new method for estimating directional wave spectra from the Doppler spectra by HF radar is proposed. This method is developed by introducing a Bayesian approach, previously proposed by one of the authors (Hashimoto et al., 1987), as one of the most accurate and reliable methods for estimating directional wave spectra for in situ measurements. The principal advantage of the new method is that it can be applied without introducing empirical weighting coefficients. Applicability, validity and accuracy of the proposed method axe demonstrated with numerically simulated data for various wave conditions.

Bayesian Estimation of Directional Wave Spectra Based on Ship Motions

An experimental study on estimation of directional wave spectra is proposed. Based on Bayesian modeling procedure, a stochastic procedure is introduced. Using this procedure, directonal wave spectra can be estimated by using the ship motion data which were recorded during the ship is underway. The prior distribution in this procedure consists of two parts. The one is a stochastic constraint so called Gaussian smoothness prior distribution. And the other one is addopted to avoid excessive estimation for the directional wave spectra. Furthermore, the encounter frequencies are transformed into the true wave frequencies even in following seas. In order to examine the reliability of the proposed procedure, the onboard tests were carried out. And, the possibility of this procedure can be shown and problems encountered on applying are reported.

A practical method for the estimation of directional wave spectra in reflective wave fields

A practical method is presented for the computation of directional spectra in presence of phase locked reflections (e.g., close to coastal structures). Existing modified directional analysis methods (e.g., The Modified Bayesian Method and the Modified Maximum Likelihood Method MMLM) require an input of the effective reflection line distance. In practice the position of the reflection line is often ambiguous leading to large errors in the directional spectrum. This paper presents a refinement of Isobe and Kondo's MMLM [Isobe, Kondo, K., 1984. Methods for estimating directional wave spectrum in incident and reflected wave field. Proc. 19th Conf. on Coastal Eng., Am. Soc. of Civil Eng., New York, pp. 467–483] which includes the reflection line position as an additional free parameter. The method presented here is based on minimising an error function which characterises the difference between the predicted and observed surface elevation variance observed at a number of spatially separated gauges. The new method is tested rigorously with both synthetic time-series and field data. Results indicate that the method is robust in a variety of incident wave conditions, in the presence of added noise and with only four transducers, providing the array is in close proximity to the shore. The new method of directional analysis when applied to field data produced frequency dependent reflection estimates which compared closely to those obtained by using the 2-dimensional approach of Gaillard et al. (1980) [Gaillard, P., Gauthier, M., Holly, F., 1980. Method of analysis of random wave experiments with reflecting coastal structures. Proc. 17th Conf. on Coastal Eng., ASCE, New York, pp. 204–220].

Bayesian Estimation of Directional Wave Spectra Based on Ship Motions (2nd Report)

Based on Bayesian modeling procedure, a stochastic procedure is introduced. Using this procedure, directional wave spectra can be estimated by using the ship motion data which were recorded during the ship underway. The prior distribution in this procedure consists of two parts. The one is a stochastic constraint so called Gaussian smoothness prior distribution. And the other one is adopted to avoid excessive estimation for the directional wave spectra. Furthermore, the encounter frequencies are transformed into the true wave frequencies even in following seas.In order to examine the reliability of the proposed procedure, the onboard tests were carried out. And, the possibility of this procedure can be shown and problems encountered on applying are reported.

Bayesian Estimation of Directional Wave Spectra Based on Ship Motions

In this paper, the authors carried out model tests to estimate directional wave spectra from only a set of simultaneous records of ship motions. Based on the assumption of linearity between the waves and the ship motions, many studies which estimate the wave power spectra by using only data of ship motions have been done. However, there are few results for estimation of directional wave spectra based on only information of ship motions. The estimating calculation in this paper consists of three steps. The first step is a calculation of cross spectra of ship motions by a stochastic approach using a multidimensional auto regressive model. The second one is a theoretical calculation of frequency response functions of the ship from the waves by New Strip Method. And, the last one is an estimation of directional wave spectra by using Bayesian Model. In order to discuss the quantitative accuracy of this method, some results were compared with the ones estimated from the observing data in an array of wave height sensors. Successful agreement between measured and estimated directional wave spectra was obtained. And the power spectra which were obtained by integration of the estimated directional wave spectra also agreed quantitatively with the measured ones.

船体運動データからの方向波スペクトルの推定について

In this paper, the authors carried out on board experiments to estimate directional wave spectra from only a set of simultaneous records of ship motions. The estimating calculation consists of three steps. The first step is a calculation of cross spectra of ship motions by a stochastic approach using a multi-dimensional auto regressive model. The second one is a theoretical calculation of frequency transfer functions of the ship by New Strip Method. And, the last one is an estimation of directional wave spectra by using so called Extended Maximum Likelihood Method. The direction in which an estimated directional wave spectrum takes maximum value is compared with a wave direction measured by the observer. Successful agreement between measured and estimated wave directions were obtained, when the actual wave was regarded as a long-crested irregular wave. And the power spectra which were obtained by integration of the estimated directional wave spectra also agreed qualitatively with the measured ones with a ship-borne wave recorder.

Maximum entropy estimation of directional wave spectra from an array of wave probes

A procedure for estimating directional wave spectra from an array of wave probes based on the Maximum Entropy Method (MEM) is developed in the present paper. The MEM approach yields an angular spreading function at each frequency band consistent with the input cross-spectral density matrix. The method is evaluated using numerical simulations of directional sea states. The MEM is also used to analyze data obtained from the three-dimensional wave basin of the Hydraulics Laboratory, National Research Council of Canada. Finally, the MEM is compared with the Maximum Likelihood Method (MLM) and is shown to be a powerful tool for directional wave analysis.

High-Resolution Directional Wave Spectra from Horizontally Mounted Acoustic Doppler Current Meters

Abstract The paper discusses the estimation of directional wave spectra by the Iterative Maximum Likelihood Method. The performance of the estimate is illustrated using data obtained by an Acoustic Doppler Current Meter in the CUrrent Measurement EXperiment (CUMEX) in the Norwegian Sea.