Uncertainty analysis on extreme value analysis of significant wave height at eastern coast of Korea

In this study, we considered the problem of estimating long-term predictions of design wave height based on the observation data collected over 10–15 years along the eastern-coast of the Korean peninsula. We adopted a method that combines Bayesian method and extreme value theory. The conventional frequency analysis methods must be reconsidered in two ways. First, the conventional probability distributions used in the frequency analysis should be evaluated to determine whether they can accurately model the variation in extreme values. Second, the uncertainty in the frequency analysis should also be quantified. Therefore, we performed a comparative study of the Gumbel distribution and GEV distribution to show the higher efficiency of the latter. Further, we compared the Bayesian MCMC (Markov Chain Monte Carlo) scheme and the MLE (Maximum Likelihood Estimation) with asymptotic normal approximation for parameter estimation to confirm the advantage of the Bayesian MCMC with respect to uncertainty analysis.     

A New Probability of Detection Model for Updating Crack Distribution of Offshore Structures

1 .IntroductionNondestructiveinspection (NDI)isveryimportantforensuringthereliabilityofoffshorestructuresintheirservicelives (Lauraetal.,1 996 ) .Itiswellknownthatdetectionofflawsinvolvesconsider ablestatisticaluncertainties.Asaresult,theprobabilityofdetection (POD)forallflawsofagivensizehasbeenusedintheliteraturetodefinethecapabilityofaparticularNDItechniqueinagivenen vironment.SincethedataofPODusuallyscatterlargely ,itisdifficulttodeterminewhichmodelfitstheavailabledatabest.Thismodelun…     

Bayesian geoacoustic inversion for the Inversion Techniques 2001 Workshop

This paper applies a Bayesian formulation to range-dependent geoacoustic inverse problems. Two inversion methods, a hybrid optimization algorithm and a Bayesian sampling algorithm, are applied to some of the 2001 Inversion Techniques Workshop benchmark data. The hybrid inversion combines the local (gradient-based) method of downhill simplex with the global search method of simulated annealing in an adaptive algorithm. The Bayesian inversion algorithm uses a Gibbs sampler to estimate properties of the posterior probability density, such as mean and maximum a posteriori parameter estimates, marginal probability distributions, highest-probability density intervals, and the model covariance matrix. The methods are applied to noise-free and noisy benchmark data from shallow ocean environments with range-dependent geophysical and geometric properties. An under-parameterized approach is applied to determine the optimal model parameterization consistent with the resolving power of the acoustic data. The Bayesian inversion method provides a complete solution including quantitative uncertainty estimates and correlations, while the hybrid inversion method provides parameter estimates in a fraction of the computation time.     

不确定海洋环境中基于贝叶斯理论的多声源定位算法

环境参数失配导致定位性能大幅度下降是匹配场定位所面临的难题之一。应用贝叶斯理论对环境聚焦,是当前解决该难题的研究热点。环境聚焦方法的实质是将未知环境参数和声源位置联合优化估计,当出现多个目标时,估计的参数会随着声源个数成倍增加,因此不得不利用有限的观测信息来实现众多参数的估计。本文采用最大似然比方法,获得信号源谱和误差项的最大似然估计,实现这些敏感性较弱参数的间接反演,有效降低了反演参数维数和定位算法复杂度。针对遗传算法的早熟和稳定性差的问题,改进了似然函数的经验表达式。将多维后验概率密度在参数起伏变化范围内积分,得到反演参数的一维边缘概率分布,求解最优值的同时进行反演结果的不确定性分析。本文仿真了位于相同距离、不同深度的两个声源,使用仿真实验验证了提出算法的有效性。     

Failure Statistics Analysis Based on Bayesian Theory: A Study of FPSO Internal Turret Leakage

The load and corrosion caused by the harsh marine environment lead to the severe degradation of offshore equipment and to their compromised security and reliability. In the quantitative risk analysis, the failure models are difficult to establish through traditional statistical methods. Hence, the calculation of the occurrence probability of small sample events is often met with great uncertainty. In this study, the Bayesian statistical method is implemented to analyze the oil and gas leakages of FPSO internal turret, which is a typical small sample risk but could lead to severe losses.According to the corresponding failure mechanism, two Bayesian statistical models using the Weibull distribution and logarithmic normal distribution as the population distribution are established, and the posterior distribution of the corresponding parameters is calculated. The optimal Bayesian statistical model is determined according to the Bayesian information criterion and Akaike criterion. On the basis of the determined optimal model, the corresponding reliability index is solved to provide basic data for the subsequent risk assessments of FPSO systems.     

Estimating geoacoustic parameters using matched-field inversion methods

In this paper, we use matched-field inversion methods to estimate the geoacoustic parameters for three synthetic test cases from the Geoacoustic Inversion Techniques Workshop held in May 2001 in Gulfport, MS. The objective of this work is to use a sparse acoustic data set to obtain estimates of the parameters as well as an indication of their uncertainties. The unknown parameters include the geoacoustic properties of the sea bed (i.e., number of layers, layer thickness, density, compressional speed, and attenuation) and the bathymetry for simplified range-dependent acoustic environments. The acoustic data used to solve the problems are restricted to five frequencies for a single vertical line array of receivers located at one range from the source. Matched-field inversion using simplex simulated annealing optimization is initially used to find a maximum-likelihood (ML) estimate. However, the ML estimate provides no information on the uncertainties or covariance associated with the model parameters. To estimate uncertainties, a Bayesian formulation of matched-field inversion is used to generate posterior probability density distributions for the parameters. The mean, covariance, and marginal distributions are determined using a Gibbs importance sampler based on the cascaded Metropolis algorithm. In most cases, excellent results were obtained for relatively sensitive parameters such as wave speed, layer thickness, and water depth. The variance of the estimates increase for relatively insensitive parameters such as density and wave attenuation, especially when noise is added to the data.     

Geoacoustic Uncertainties From Viscoelastic Inversion of Seabed Reflection Data

This paper applies nonlinear Bayesian inversion to seabed reflection data to estimate viscoelastic parameters of the upper sediments. The inversion provides maximum a posteriori probability (MAP) parameter estimates with uncertainties quantified in terms of marginal probability distributions, variances, and credibility intervals; interparameter relationships are quantified by correlations and joint marginal distributions. The inversion is applied to high-resolution reflectivity data from two sites in the Strait of Sicily. One site is characterized by low-speed sediments, resulting in data with a well-defined angle of intromission; the second is characterized by high-speed sediments, resulting in a critical angle. Data uncertainties are quantified using several approaches, including maximum-likelihood (ML) estimation, treating uncertainties as nuisance parameters in the inversion, and analysis of experimental errors. Statistical tests are applied to the data residuals to validate the assumed uncertainty distributions. Excellent results (i.e., small uncertainties) are obtained for sediment compressional-wave speed, compressional attenuation, and density; shear parameters are less well determined although low shear-wave speeds are indicated. The Bayesian analysis provides a quantitative comparison of inversion results for the two sites in terms of the resolution of specific geoacoustic parameters, and indicates that the geoacoustic information content is significantly higher for intromission data     

Geoacoustic Information Content of Horizontal Line Array Data

This paper examines the effectiveness of horizontal line arrays (HLAs) for matched-field inversion (MFI) by quantifying geoacoustic information content for a variety of experiment and array factors, including array length and number of sensors, source range and bearing, source-frequency content, and signal-to-noise ratio (SNR). Emphasis is on bottom-moored arrays, while towed arrays are also considered, and a comparison with vertical line array (VLA) performance is made. The geoacoustic information content is quantified in terms of marginal posterior probability distributions (PPDs) for model parameters estimated using a fast Gibbs sampler approach to Bayesian inversion. This produces an absolute, quantitative estimate of the geoacoustic parameter uncertainties which can be directly compared for various experiment and array factors.     

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R² = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.     

A Bayesian state-space model for mixed-stock migrations,with application to Northeast Atlantic mackerel Scomber scombrus

Management of fisheries that exploit mixed-stock populations relies on assumptions made concerning stock structure and mixing in different areas. To address the problems of accounting for uncertainty when formulating scientific advice for the management of highly migratory fish stocks, management decisions need to be based upon assessment models that represent plausible alternative hypotheses for stock structure and migration patterns of the exploited populations. We present a multi-stock, multi-fleet, multi-area, seasonally structured Bayesian state-space model in which different stocks spawn in spatially different areas and the mixing of these stocks is explicitly accounted for in the absence of sufficient tagging data with which to estimate migration rates. The model is applied to the Northeast Atlantic mackerel Scomber scombrus population, accounting for the annual spawning-feeding-overwintering migration patterns of the three spawning components, together with uncertainty in the extent to which the southern component migrates north to feed and overwinter, and consequently the extent to which it mixes with the other components and is subject to exploitation. The model allows the effect of exploitation on the individual components to be assessed, and the results suggest that the fishing mortality of southern spawning adults was insensitive to the extent to which they migrated north.     

Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables

A key factor for computing environmental contours is the appropriate modeling of the dependence structure among the environmental variables. It is known that all the information on the dependence structure of a set of random variables is contained in the copulas that define their multivariate probability distribution. Provided that copula parameters are estimated by means of statistical inference using observations, recordings, numerical or historical data, uncertainty is unavoidably introduced in their estimates. Parametric uncertainty in the copulas parameters then introduces uncertainty in the environmental contours. This study deals with the assessment of uncertainty in environmental contours due to parametric uncertainty in the copula models that define the dependence structure of the environmental variables. A point estimation approach is adopted to estimate the statistics of the uncertain coordinates of the environmental contours considering they are given in terms of inverse functions of conditional copulas. A case study is reported using copulas models estimated from storm hindcast data for the Gulf of Mexico. Uncertainty in environmental contours of significant wave height, peak period and wind speed is assessed. The accuracy of the point estimation of the mean and variance of the contour coordinates is validated based on Monte Carlo simulations. A parametric study shows the manner in which greater parametric uncertainty induces larger variability in the environmental contours. The influence of parametric uncertainty for different degrees of association is also analyzed. The results indicate that variability between contours considering parametric uncertainty can be meaningful.     

Estimation of Transmission Loss in the Presence of Geoacoustic Inversion Uncertainty

A common problem in sonar system prediction is that the ocean environment is not well known. Utilizing probabilistic based results from geoacoustic inversions we characterize parameters relevant to sonar performance. This paper describes the estimation of transmission loss and its statistical properties based on posterior parameter probabilities obtained from inversion of ocean acoustic array data. This problem is solved by first finding an ensemble of relevant environmental model parameters and the associated posterior probability using a likelihood based inversion of the acoustic array data. In a second step, each realization of these model parameters is weighted with their posterior probability to map into the transmission loss domain. This approach is illustrated using vertical-array data from a recent benchmark data set and from data acquired during the Asian Seas International Acoustics Experiment (ASIAEX) 2001 in the East China Sea. The environmental parameters are first estimated using a probabilistic-based geoacoustic inversion technique. Based on the posterior probability that each of these environmental models fits the ocean acoustic array data, each model is mapped into transmission loss. This enables us to compute a full probability distribution for the transmission loss at selected frequencies, ranges, and depths, which potentially could be used for sonar performance prediction.     

基于Schaefer模型的东南太平洋茎柔鱼资源评估和管理

东南太平洋茎柔鱼(Dosidicus gigas)是世界范围内最重要的经济头足类之一,也是我国鱿钓渔船的重要捕捞对象。本文根据2003—2012年中国大陆的渔业数据和FAO统计的东南太平洋茎柔鱼产量数据,利用Schaefer模型,基于贝叶斯统计方法,分基准方案和敏感性分析方案对东南太平洋茎柔鱼资源进行评估,并对其管理策略做了风险分析。结果表明,年渔获量和CPUE数据为贝叶斯资源评估模型提供了足够多的信息。2003—2012年捕捞死亡率低于目标参考点F0.1,渔获量小于最大可持续产量,资源量大于目标参考点Bmsy,资源状况良好,未遭受过度捕捞。在基准方案下,最大可持续产量为142.9万吨,维持最大可持续产量的资源量为214.7万吨,此时的捕捞死亡率为0.682;在敏感性分析方案下,最大的可持续产量为152.5万吨,维持最大可持续产量的资源量为229.6万吨,此时的捕捞死亡率为0.691。决策分析和风险分析表明,当捕获率设定为0.3以下时,资源能够得到较好的养护,资源崩溃的可能性很低。将捕获率设定在0.3左右是最适的管理策略,此时的持续产量为99万吨左右。     

Blind marine seismic deconvolution using statistical MCMC methods

In order to improve the resolution of seismic images, a blind deconvolution of seismic traces is necessary, since the source wavelet is not known and cannot be considered as a stationary signal. The reflectivity sequence is modeled as a Gaussian mixture, depending on three parameters (high and low reflector variances and reflector density), on the wavelet impulse response, and on the observation noise variance. These parameters are unknown and must be estimated from the recorded trace, which is the reflectivity convolved with the wavelet, plus noise. Two methods are compared in this paper for the parameter estimation. Since we are considering an incomplete data problem, we first consider maximum likelihood estimation by means of a stochastic expectation maximization (SEM) method. Alternatively, proper prior distributions can be specified for all unknown quantities. Then, a Bayesian strategy is applied, based on a Monte Carlo Markov Chain (MCMC) method. Having estimated the parameters, one can proceed to the deconvolution. A maximum posterior mode (MPM) criterion is optimized by means of an MCMC method. The deconvolution capability of these procedures is checked first on synthetic signals and then on the seismic data of the IFREMER ESSR4 campaign, where the wavelet duration blurs the reflectivity, and on the SMAVH high-resolution marine seismic data.     

建立海洋平台管节点PSN曲线的贝叶斯方法

针对管节点疲劳试验的小样本特点,探讨了建立ＰＳＮ 曲线的贝叶斯方法。在贝叶斯方法中,ＰＳＮ曲线的统计参数作为随机变量处理,首先根据贝叶斯定理求出参数向量的后验概率密度,然后建立ＰＳＮ曲线的贝叶斯方程,最后再编程计算。算例表明,与传统的ＰＳＮ 曲线相比,贝叶斯ＰＳＮ 曲线更加安全可靠     

Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models

Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.     

Development of Bayesian stock assessment methods for Namibian orange roughy Hoplostethus atlanticus

Bayesian methods are useful in fisheries stock assessment because they provide a conceptually elegant and statistically rigorous approach to making decisions under uncertainty. The application of Bayesian stock assessment methods in the management of Namibian orange roughy Hoplosthethus atlanticus within the 200 mile EEZ of Namibia is reviewed. Time-series of relative abundance are short and their reliability in indicating abundance trends is uncertain. The development of informative prior probability density functions (pdfs) for the constants of proportionality (q) for hydro-acoustic, commercial trawl swept area, and research trawl swept area indices produced statistically consistent prior estimates of absolute abundance for each of the three grounds where more than one index of abundance was available. The posterior pdfs for stock assessment model parameters were used to account for uncertainty in evaluations of the potential consequences of alternative harvesting policies under a stock reduction model in which catch removals were assumed to account for any declines. It appears that all orange roughy stocks off Namibia have been depleted below the limit reference point (50% of long-term unfished biomass). However, the stock reduction model could not easily account for the large declines in indices on the four fishing grounds over the period from 1995 until 1999 when the informative priors for q were applied. In the 2000 stock assessment, the Bayesian procedure was updated to account formally for uncertainty in model structures that could explain the decline in abundance. The possibility of very low stock abundance could still not be discounted when these uncertainties were accounted for. Although this most recent methodology applies more statistical rigour, its complexity has hindered its acceptance in Namibia. However, if it is worth quantifying risks and uncertainties in future stock assessments for the provision of precautionary management advice, it is proposed that the assessment protocols adopted be probabilistic to account for uncertainty in model parameters, that careful attention be given to subjective judgements about their inputs and the representation of uncertainty within them, and that, where appropriate, alternative hypotheses about stock abundance and mechanisms for catchability and stock decline be taken into account.     

Effect of surge uncertainty on probabilistically computed dune erosion

To assess the flood protection capacity of dunes in The Netherlands, a semi-probabilistic dune-erosion prediction method is currently in use in which uncertainties in input parameters of an empirical dune erosion model were taken into account, with the exception of the uncertainty in the extreme surge distribution. Previous research has shown that the surge is by far the most influential parameter affecting erosion in the currently used erosion model, which is due both to the influence of the surge level itself and to the conditional dependence of the wave height and period on the surge level in the probabilistic model used for the assessment. Furthermore, the distribution of extreme surge levels has been shown to contain large statistical uncertainty. The inclusion of uncertainty in input variables into probabilistic models results in more extreme events (in this case erosion) for the same exceedance probability, largely due to the incorporation of higher values of the input variables. The goal of the research described in this paper was to determine the impact of the inclusion of uncertainty in the extreme surge distribution on the estimate of critical erosion (erosion associated with an exceedance frequency of 10^− 5 per year). The uncertainty in the surge distributions was estimated and parameterized, and was incorporated into the probabilistic model. A reduction in uncertainty was subsequently imposed to estimate what value a reduction in uncertainty can offer, in terms of the impact on critical erosion. The probabilistic technique first-order reliability method (FORM) was applied to determine the relative contribution of the uncertainty in the surge distribution (as well as the remaining stochastic variables) to the critical erosion. The impact of the inclusion of uncertainty in the surge distribution on the critical retreat distance was found to be substantial with increases ranging from 34% to 93% of the original estimate at five locations along the Dutch coast. The reduced uncertainty showed a more subtle impact, with increases in critical retreat distance ranging from 10% to 26% of the original estimate. The relative importance analysis showed that the uncertainty in the surge distribution has a strong influence, with the relative importance ranging from 10% to 23% for an exceedance frequency of 10^− 5 per year.     

Quantifying data information content in geoacoustic inversion

This paper examines the information content in matched-field geoacoustic inverse problems as a function of a variety of experiment factors, with the aim of guiding data collection and processing to achieve the best possible inversion results. The information content of the unknown geoacoustic parameters is quantified in terms of their marginal posterior probability distributions, which define the accuracy expected in inversion. Marginal distributions are estimated using a fast Gibbs sampler approach to Bayesian inversion, which provides an efficient, unbiased sampling of the multi-dimensional posterior probability density. When sampled to convergence, the marginal distributions are found to have simple, smooth shapes that facilitate straightforward comparisons. The approach is general; the specific examples considered here include factors such as the number of sensors in the receiving array, array length, source-receiver range, source frequency, number of frequencies, source bandwidth, and signal-to-noise ratio     

基于贝叶斯网络的朝鲜海峡大气能见度推理模型及实验

针对当前海上贸易航道通航风险评估工作中存在的能见度数据缺失等问题,提出基于贝叶斯网络的能见度数据推理技术。通过研究海域的确定、节点因子的选取、样本数据集的生成、推理模型的构建及参数学习和推理计算等流程,构建了基于贝叶斯网络技术的能见度数据推理模型,并以朝鲜海峡海域为例展开试验分析。结果表明:能见度具有年变化和年际变化特征规律,利用多年某月的数据作为训练样本推理该月的能见度等级具有较高的准确性,且相同样本形式下样本数据数量与推理结果准确性呈正相关。