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.     

Virtual hull monitoring of a naval vessel using hindcast data and reconstructed 2-D wave spectra

A novel virtual hull monitoring approach is assessed using full-scale measurements from a naval vessel trial to address two questions. First: Can this technique accurately reproduce stress spectra from measured strains? Second: Are responses calculated using reconstructed two-dimensional wave spectra from hindcast data more accurate than those using simpler wave representations? Stresses calculated using wave hindcast data, ship track information, and stress transfer functions compare favorably to those derived from strain gauge measurements at five structural locations. Wave conditions are represented using a spectrum model along with bulk spectral parameters (significant wave height, peak period, and primary direction) from hindcast datasets and by reconstructing two-dimensional spectra from hindcast partition data. Both approaches give good agreement with strain measurements but using the more-detailed reconstructed two-dimensional wave spectra yields better results. Results suggest that wave hindcast data are sufficient for accurate structural calculations, encouraging further study of virtual hull monitoring using wave hindcast data.     

Wave spectrum estimation conditioned on machine learning-based output using the wave buoy analogy

In this work, a hybrid approach for wave spectrum estimation is proposed. Fundamentally, the approach is based on the wave buoy analogy, processing ship response measurements, via a framework combining machine learning and a physics-based method dependent on available transfer functions. Specifically, a non-parametric (Bayesian) estimate is obtained of the directional wave spectrum conditioned on integral wave parameters established by a convolutional neural network. The developed method is assessed in a case study considering about two years of data obtained from an in-service container ship. The method produces good results, significantly improved when compared to the initial estimate made without constraints.     

舰船在三维非规则波中的航向航速优选

文章探讨了舰船在三维非规则波中，基于方向谱的六自由度摇荡及动力响应统计特征值的计算方法，并给出了计算结果和实船海试结果的对比，证实了算法是可行的，精度高于舰船在二维非规则波中基于频谱的计算结果。在此基础上，提出了舰船在三维非规则波中航向航速优选的求解模式和算例。     

Model experiment reproducing an incident of fast ferry

A model scale experiment at a new basin reproduced a phenomenon occurring for a fast ferry; large roll motion and subsequent cargo shift in a quartering sea. Wave generators surrounding the whole periphery of the basin realized a designated directional sea. A carriage system tracked a free-running model ship and a movable weight simulated the cargo shift. Measuring the directional wave field in the basin confirmed the all-around wave generator successfully reproduced the intended wave field that was estimated for the location and the time of the incident. The encounter wave spectrum analyzed using measured data agree well with the theoretically predicted one. The reproduced ship motion, triggered by a small concentrating wave, tells how the ship responded in the successive large quartering waves and the validity of the procedure to reproduce the incident. Repeated measurements of the model ship’s extreme motion confirm a high repeatability of the experiment.     

Estimation of the wave direction of ship waves generated by a small vessel using the multiple signal classification method

It is very important to estimate the waves generated by a small vessel so as to investigate their effects on floating bodies within the scope of fisheries and ocean engineering. Simplified methods for estimating the wave heights and periods of ship waves have been presented in previous studies. However, estimating the direction of ship waves is not easy. The focus of the present study is to develop an analytical technique to determine the direction of ship waves based on the measurements in field experiments. The multiple signal classification (MUSIC) method is newly proposed for determining the direction of ship waves. For high ship speeds, the directional spectrum of ship waves estimated by MUSIC resulted in a sharp monotone peak, and the estimated directions of ship waves were very similar to the results of field experiments using an actual small vessel. The proposed MUSIC method has thus been confirmed to be effective in estimating ship wave directions with high resolution.     

中国海浪方向谱的分析研究

通过比较光易型和我国规范中两种不同的方向分布函数,表明我国规范推荐的方向分布函数表现为风浪和传播距离较短的涌浪特征,并与光易型方向分布函数有很强的一致性。认为方向分布函数应与频谱联合分析,才能更好地反映天然的海浪。通过分析我国近海几个区域的方向谱特征,均反映理论分布的特点,方向集中度略小于规范推荐的情况。     

Difference in ship motion and wave load in long and short crested irregular waves北大核心CSCD

[Objective]To investigate ship motion and load responses in realistic 3D waves and overcome the limitations of the traditional 2D wave assumption, this paper develops a method for predicting ship motion and load responses in short-crested waves. [Method]The long- and short-term responses of ship motion and load in long- and short-crested waves are numerically predicted using the spectral analysis and statistical probability methods, respectively. The influence of directional function on ship response is also numerically analyzed. Moreover, tank model tests and a large-scale model sea trial are comparatively conducted to validate the difference between ship response and statistics in long- and short-crested irregular waves. [Results]The results show that when navigating against the waves in the same sea condition, the long-crested wave assumption overestimates the statistical mean value of ship load response, but underestimates extreme load in real seas. For long-crested waves, the ship motion and acceleration power spectrum is concentrated around a certain frequency band. [Conclusion]Ship motion and load responses in realistic 3D waves are significantly different from those in 2D long-crested waves. The directional function of short-crested waves also has a significant effect on ship motion and load responses. © 2023 The Author(s).     

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.     

Ocean wave spectrum estimation using measured vessel motions from an in-service container ship

This article is about the use of measured wave-induced vessel motions for estimation of ocean wave spectra by application of the wave buoy analogy. In the study, data from a larger, in-service container ship is considered. The estimation of wave spectra, equivalently sea state parameters, is based on measurements from, respectively, a gyro and two accelerometers leading to the simultaneous use of the pitching motion together with the horizontal and vertical accelerations in a position close to the forward perpendicular. The study of in-service data leads to contemplations about the vessel's advance speed, as the possible existence of sea current means that speed-over-ground (SOG) and speed-through-water (STW) will be different. The article discusses aspects related to advance speed in the context of the wave buoy analogy, and a smaller sensitivity study is conducted. Preceding to the sensitivity study, a comparison is made between sea state estimates by the wave buoy analogy and estimates obtained from a hindcast study. The article shows an acceptable agreement between the two sets of estimates. Following, the main conclusion from the sensitivity study on advance speed is that errors and uncertainties in the speed log have an effect on the estimates of the wave buoy analogy. In fact, the effect can be severe if reliable STW measurements are not available. In the final part, the article includes a few discussions about (non)stationary conditions in the context of the wave buoy analogy, and, although the effect on results is not necessarily detrimental, care must be shown when the wave buoy analogy is applied during in-service conditions.     

基于两种转换函数的真实波浪参数的统计分析（英文）

The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.     

Tuning of transfer functions for analysis of wave–ship interactions

Transfer functions are often used together with a wave spectrum for analysis of wave–ship interactions, where one application addresses the prediction of wave-induced motions or other types of global responses. This paper presents a simple and practical method which can be used to tune the transfer function of such responses to facilitate improved prediction capability. The input to the method consists of a measured response, i.e. time series sequences from a given sensor, the 2D wave spectrum characterising the seaway in which the measurements are taken, and an initial estimate of the transfer function for the response in study. The paper presents results obtained using data from an in-service container ship. The 2D wave spectra are taken from the ERA5 database, while the transfer function is computed by a simple closed-form expression. The paper shows that the application of the tuned transfer function leads to predictions which are significantly improved compared to using the transfer function without tuning.     

Calibration of response amplitude operators based on measurements of vessel motions and directional wave spectra

A vessel's response to waves is dependent on a large number of parameters, some of which are both frequency and direction dependent. To predict vessel response, these parameters are used to construct response amplitude operators (RAOs) that act as transfer functions between the directional wave spectra and the motion spectra of the vessel. In particular situations, however, vessel motions predicted using RAOs calculated with general-purpose radiation-diffraction codes and measured wave spectra are found to deviate from measured vessel responses. To address this problem, a methodology for calibrating RAOs based on measurements of the directional wave spectra and vessel motions is proposed. Use is made of a vector fitting method through which the frequency dependent hydrodynamic properties of the vessel can be approximated by a ratio of two polynomials, thus greatly reducing the number of parameters that need to be calibrated. The reduced set of parameters is subsequently related to previously identified causes of RAO inaccuracy in order to arrive at optimization algorithms for identifying more accurate RAOs from the measurements. It is shown that the RAOs can be improved with accuracy in situations where the discrepancies are caused by imprecise estimates for the vessel's radii of gyration, center of gravity, or viscous damping. When the discrepancies in the RAOs are related to the potential mass, damping and wave forces, however, the problem becomes highly non-convex and it is not possible to find a unique RAO that satisfies the data.     

Practical estimation methods of the design loads for primary structural members of tankers

Various design loads used in the strength evaluation of ship structures have been introduced currently by classification societies. As most of these design loads have been determined as the standard loads for the sake of convenience, the relationships between the design loads and the sea states actually encountered by ships seem to be weak. Accordingly, it may be difficult to refer and utilize them as the fundamental design concepts for ship designers or the operational guidelines for ship operators. To overcome these difficulties, the authors have developed practical estimation methods of the design loads having transparent and consistent backgrounds to the actual loads acting on primary structural members of tankers. In this paper, the design sea states that closely resemble the actual sea states which are considered as the most severe for hull structures are firstly proposed. Secondly, the practical estimation methods of the design sea states are proposed by parametric studies using the results of series calculation of representative tankers. Thirdly, the practical estimation methods of design regular waves resulting in the same level of stresses with that induced in irregular waves under the design sea states are proposed. Finally, the practical estimation methods of the design loads such as ship motions, accelerations, hull girder bending moments and hydrodynamic pressures that are induced under design regular waves are proposed.     

基于船舶运动信息的航行海域海浪特性预报

以船舶自身为波浪测量仪,致力于采集方便而又尽可能少的船舶运动信号以提取航行海域实时海浪特性.由于估计中不依赖原始理论计算的传递函数,不需要附带波浪采集装置,而仅利用航行中船舶运动的观测序列完成海浪谱反演,故该海浪测量方法可适应船舶自身运动参数的变化.另一方面,由于反演估计的船舶运动频率响应特性,与事先计算或以其它实验方法得到的船舶运动频率响应特性得以比较,可以深化、修正对许多不易实时测量的海浪激励状态与船舶运动响应关系的认识,并积累船舶工程研究设计所必需的相关海域海浪谱信息.     

Global wave loads on intact and damaged Ro-Ro ships in regular oblique waves

A nonlinear time-domain simulation method is presented for the prediction of dynamic global wave loads on a Ro-Ro ship at zero speed in regular oblique waves in an intact and a damaged condition. Numerical computations and model tests have been carried to investigate the structural responses of Ro-Ro ship Dextra to various wave amplitudes at three different wave headings (DTR-4.1-NEW-12.98, DEXTREMEL project BE97-4375, 1998; DTR-4.2-NEW-11.99, DEXTREMEL project BE97-4375, 1999). The results of numerical and experimental investigations for stern quartering waves are reviewed. Comparisons between predictions and measurements for global wave loads at the midship section of the intact and the damaged Ro-Ro ship show that the agreement between the theory and experiment for dynamic horizontal and vertical bending moments is excellent. On the other hand, correlation between the predictions and measurements for dynamic vertical shear force is better than that for dynamic horizontal shear force. Nevertheless, the calculated torsion moment values are higher than the measured values. As the wave amplitude is not small, the positive and negative peaks of global wave loads are no longer equal to each other as found in both the calculations and experiments. The dynamic vertical global wave loads in the damaged condition are larger than that in the intact condition.     

参数横摇下大型集装箱船外飘砰击的近似计算方法（英文）

Since the research of flare slamming prediction is seldom when parametric rolling happens, we present an efficient approximation method for flare slamming analysis of large container ships in parametric rolling conditions. We adopt a 6-DOF weakly nonlinear time domain model to predict the ship motions of parametric rolling conditions. Unlike previous flare slamming analysis, our proposed method takes roll motion into account to calculate the impact angle and relative vertical velocity between ship sections on the bow flare and wave surface. We use the Wagner model to analyze the slamming impact forces and the slamming occurrence probability. Through numerical simulations, we investigate the maximum flare slamming pressures of a container ship for different speeds and wave conditions. To further clarify the mechanism of flare slamming phenomena in parametric rolling conditions, we also conduct real-time simulations to determine the relationship between slamming pressure and 3-DOF motions, namely roll, pitch, and heave.     

船舶结构极限波浪弯矩统计特征的一致性定义

在船舶结构界可靠性方法已得到越来越广泛的应用。在进行现有船舶的可靠性分析或对新船制订可靠性设计规范时，必须要首先确定能力与载荷的统计特征。对于船舶结构来说，波浪弯矩是主要的载荷，极限波浪弯矩的统计特征对极限强度的可靠性分析十分重要。但是，通过研究发现，不同的文献中给出的用于确定极限波浪弯矩统计特征的概念和方法并不一致，这一差别可能对了随后的船舶结构可靠性分析和设计有一定的影响。本文旨在对船舶结构极限波浪弯矩统计特征的一致性定义作一些讨论，以期澄清一些概念。     

海浪扰动信号的仿真方法

给出了一种新的以遭遇频率表示的海浪遭遇谱和遭遇波倾角谱的数学表达式，介绍了建立随机海浪模型的三种仿真方法，即频率等分法、能量等分法和有理谱法，并采用能量等分法进行了海浪模型的仿真和分析。它对于研究船舶装备、船舶行业机器人、海上作业平台和船舶的运动控制具有重要意义。     

规则迎浪中船舶参数横摇的三维时域预报方法研究

参数横摇是船舶因复原特性改变而引起的典型非线性现象。文章采用三维时域方法预报规则迎浪中船舶的参数横摇运动。该方法引入匹配面将流域分为内域和外域,内域中采用Rankine源来满足物面条件和线性自由面条件,而外域中应用时域格林函数来满足线性自由面条件和远场辐射条件。数值方法中,Froude-Krylov力和恢复力是通过对船舶瞬时湿表面积积分获得,同时考虑了横摇、垂荡和纵摇三自由度之间的耦合作用,以及非线性横摇阻尼的影响。数值结果与试验结果吻合很好,说明该方法可以有效地预报参数横摇。