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1.
Jose A. Carnicero M. Concepción Ausín Michael P. Wiper 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(8):1991-2002
This paper proposes a nonparametric approach to estimating the dependence relationships between circular variables and other circular or linear variables using copulas. The proposed method is based on the use of Bernstein copulas which are a very flexible class of non-parametric copulas which allows for the approximation of any kind of dependence structure, including non symmetric relationships. In particular, we present a simple procedure to adapt Bernstein copulas to the circular framework and guarantee that the constructed bivariate distributions are strictly continuous. We provide two illustrative case studies, the first on the relation between wind direction and quantity of rainfall in the North of Spain and the second on the dependence between the wind directions in two nearby buoys at the Atlantic ocean. 相似文献
2.
实验数据表明土体参数具有很大的空间变异性,而随机场理论为模拟土体参数空间变异性提供了有效途径。因为传统的谱表示法(SRM)无法正确模拟多维多元随机场参数间的互相关性,提出支持向量机法(SVM)与SRM耦合的方法。SVM是基于统计学习理论和结构风险最小化原理基础上的通用机器学习方法,它在解决小样本、非线性和高维模式识别问题中表现出诸多优势。以土体抗剪强度参数:黏聚力c和内摩擦角φ为例,通过实验证明二者之间存在天然负相关性,即为二维二元随机场。结果表明,在样本数量较少的条件下,基于耦合算法模拟随机场不仅能有效地描述变量的自相关性,而且能够准确地描述变量间的互相关性,为解决小样本条件下模拟多维多元随机场提供了一种有效的方法。 相似文献
3.
A multivariate spatial sampling design that uses spatial vine copulas is presented that aims to simultaneously reduce the prediction uncertainty of multiple variables by selecting additional sampling locations based on the multivariate relationship between variables, the spatial configuration of existing locations and the values of the observations at those locations. Novel aspects of the methodology include the development of optimal designs that use spatial vine copulas to estimate prediction uncertainty and, additionally, use transformation methods for dimension reduction to model multivariate spatial dependence. Spatial vine copulas capture non-linear spatial dependence within variables, whilst a chained transformation that uses non-linear principal component analysis captures the non-linear multivariate dependence between variables. The proposed design methodology is applied to two environmental case studies. Performance of the proposed methodology is evaluated through partial redesigns of the original spatial designs. The first application is a soil contamination example that demonstrates the ability of the proposed methodology to address spatial non-linearity in the data. The second application is a forest biomass study that highlights the strength of the methodology in incorporating non-linear multivariate dependence into the design. 相似文献
4.
In this paper a new procedure to derive flood hazard maps incorporating uncertainty concepts is presented. The layout of the procedure can be resumed as follows: (1) stochastic input of flood hydrograph modelled through a direct Monte-Carlo simulation based on flood recorded data. Generation of flood peaks and flow volumes has been obtained via copulas, which describe and model the correlation between these two variables independently of the marginal laws involved. The shape of hydrograph has been generated on the basis of a historical significant flood events, via cluster analysis; (2) modelling of flood propagation using a hyperbolic finite element model based on the DSV equations; (3) definition of global hazard indexes based on hydro-dynamic variables (i.e., water depth and flow velocities). The GLUE methodology has been applied in order to account for parameter uncertainty. The procedure has been tested on a flood prone area located in the southern part of Sicily, Italy. Three hazard maps have been obtained and then compared. 相似文献
5.
AbstractGiven that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radar-based rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.
Editor D. Koutsoyiannis; Associate editor S. Grimaldi 相似文献
6.
The coherence method is always used to describe the discontinuity and heterogeneity of seismic data. In traditional coherence methods, a linear correlation coefficient is always used to measure the relationship between two random variables (i.e., between two seismic traces). However, mathematically speaking, a linear correlation coefficient cannot be applied to describe nonlinear relationships between variables. In order to overcome this limitation of liner correlation coefficient. We proposed an improved concordance measurement algorithm based on Kendall’s tau. That mainly concern the sensitivity of the liner correlation coefficient and concordance measurements on the waveform. Using two designed numerical models tests sensitivity of waveform similarity affected by these two factors. The analysis of both the numerical model results and real seismic data processing suggest that the proposed method, combining information divergence measurement, can not only precisely characterize the variations of waveform and the heterogeneity of an underground geological body, but also does so with high resolution. In addition, we verified its effectiveness by the actual application of real seismic data from the north of China. 相似文献
7.
The estimation of flood frequency is vital for the flood control strategies and hydraulic structure design. Generating synthetic flood events according to statistical properties of observations is one of plausible methods to analyze the flood frequency. Due to the statistical dependence among the flood event variables (i.e. the flood peak, volume and duration), a multidimensional joint probability estimation is required. Recently, the copula method is widely used for multivariable dependent structure construction, however, the copula family should be chosen before application and the choice process is sometimes rather subjective. The entropy copula, a new copula family, employed in this research proposed a way to avoid the relatively subjective process by combining the theories of copula and entropy. The analysis shows the effectiveness of the entropy copula for probabilistic modelling the flood events of two hydrological gauges, and a comparison of accuracy with the popular copulas was made. The Gibbs sampling technique was applied for trivariate flood events simulation in order to mitigate the calculation difficulties of extending to three dimension directly. The simulation results indicate that the entropy copula is a simple and effective copula family for trivariate flood simulation. 相似文献
8.
Songbai Song Vijay P. Singh 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(3):425-444
This study aims to model the joint probability distribution of periodic hydrologic data using meta-elliptical copulas. Monthly
precipitation data from a gauging station (410120) in Texas, US, was used to illustrate parameter estimation and goodness-of-fit
for univariate drought distributions using chi-square test, Kolmogorov–Smirnov test, Cramer-von Mises statistic, Anderson-Darling
statistic, modified weighted Watson statistic, and Liao and Shimokawa statistic. Pearson’s classical correlation coefficient
r
n
, Spearman’s ρ
n, Kendall’s τ, Chi-Plots, and K-Plots were employed to assess the dependence of drought variables. Several meta-elliptical copulas and
Gumbel-Hougaard, Ali-Mikhail-Haq, Frank and Clayton copulas were tested to determine the best-fit copula. Based on the root
mean square error and the Akaike information criterion, meta-Gaussian and t copulas gave a better fit. A bootstrap version
based on Rosenblatt’s transformation was employed to test the goodness-of-fit for meta-Gaussian and t copulas. It was found
that none of meta-Gaussian and t copulas considered could be rejected at the given significance level. The meta-Gaussian copula
was employed to model the dependence, and these results were found satisfactory. 相似文献
9.
Response uncertainty evaluation and dynamic reliability analysis corresponding to classical stochastic dynamic analysis are usually restricted to the uncertainties of the excitation. The inclusion of the parameter uncertainties contained in structural properties and excitation characteristics has become an increasingly important problem in many areas of dynamics. In the present paper, a point estimate procedure is proposed for the evaluation of stochastic response uncertainty, and a response surface approach procedure in standard normal space is proposed for analysis of time-variant reliability analysis for hysteretic MDF structures having parameter uncertainties. Using the proposed procedures, the response uncertainties and time-variant reliability can be easily obtained by several repetitions of stochastic response analysis under given parameters without conducting sensitivity analysis, which is considered to be one of the primary difficulties associated with conventional methods. In the time-variant reliability analysis, the failure probability can be readily obtained by improving the accuracy of the first-order reliability method using the empirical second-order reliability index. The random variables are divided into two groups, those with CDF and those without CDF. The latter are included via the high-order moment standardization technique. A numerical example of a 15F hysteretic MDF structure that takes into account uncertainties of four structural parameters and three excitation characteristics is performed, based on which the proposed procedures are investigated and the effects of parameter uncertainties are discussed. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
10.
Multivariate drought characteristics using trivariate Gaussian and Student t copulas 总被引：4，自引：0，他引：4
This study aims to investigate the changing properties of drought events in Weihe River basin, China, by modeling the multivariate joint distribution of drought duration, severity and peak using trivariate Gaussian and Student t copulas. Monthly precipitations of Xi'an gauge are used to illustrate the meta‐elliptical copula‐based methodology for a single‐station application. Gaussian and Student t copulas are found to produce a better fit comparing with other six symmetrical and asymmetrical Archimedean copulas, and, checked by the goodness‐of‐fit tests based on a modified bootstrap version of Rosenblatt's transformation, both of them are acceptable to model the multivariate joint distribution of drought variables. Gaussian copula, the best fitting, is employed to construct the dependence structures of positively associated drought variables so as to obtain the multivariate joint and conditional probabilities of droughts. A Kendall's return period (KRP) introduced by Salvadori and De Michele (2010) is then adopted to assess the multivariate recurrent properties of drought events, and its spatial distributions indicate that prolonged droughts are likely to break out with rather short recurrence intervals in the whole region, while drought status in the southeast seems to be severer than the northwest. The study is of some merits in terms of multivariate drought modeling using a preferable copula‐based method, the results of which could serve as a reference for regional drought defense and water resources management. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
Copula-based geostatistical modeling of continuous and discrete data including covariates 总被引：4，自引：3，他引：1
Hannes Kazianka Jürgen Pilz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(5):661-673
It is common in geostatistics to use the variogram to describe the spatial dependence structure and to use kriging as the spatial prediction methodology. Both methods are sensitive to outlying observations and are strongly influenced by the marginal distribution of the underlying random field. Hence, they lead to unreliable results when applied to extreme value or multimodal data. As an alternative to traditional spatial modeling and interpolation we consider the use of copula functions. This paper extends existing copula-based geostatistical models. We show how location dependent covariates e.g. a spatial trend can be accounted for in spatial copula models. Furthermore, we introduce geostatistical copula-based models that are able to deal with random fields having discrete marginal distributions. We propose three different copula-based spatial interpolation methods. By exploiting the relationship between bivariate copulas and indicator covariances, we present indicator kriging and disjunctive kriging. As a second method we present simple kriging of the rank-transformed data. The third method is a plug-in prediction and generalizes the frequently applied trans-Gaussian kriging. Finally, we report on the results obtained for the so-called Helicopter data set which contains extreme radioactivity measurements. 相似文献
12.
Quantification of the environmental structural risk with spoiling ties: is randomization worthwhile?
Many recent works show that copulas turn out to be useful in a variety of different applications, especially in environmental sciences. Here the variables of interest are usually continuous, being times, lengths, weights, and so on. Unfortunately, the corresponding observations may suffer from (instrumental) adjustments and truncations, and eventually may show several repeated values (i.e., ties). In turn, on the one hand, a tricky issue of identifiability of the model arises, and, on the other hand, the assessment of the risk may be adversely affected. A possible remedy is to adopt suitable randomization procedures: here three different strategies are outlined. The goal of the work is to carry out a simulation study in order to evaluate the effects of the randomization of multivariate observations when ties are present. In particular, it is investigated whether, how, and to what extent, the randomization may change the estimation of the structural risk: for this purpose, a coastal engineering example will be used, as archetypical of a broad class of models and problems in engineering applications. Practical advices and warnings about the use of randomization techniques are hence given. 相似文献
13.
Macarena Zegpi 《水文科学杂志》2013,58(7):1123-1136
Abstract A model based on analytical development and numerical solution is presented for estimating the cumulative distribution function (cdf) of the runoff volume and peak discharge rate of urban floods using the joint probability density function (pdf) of rainfall volume and duration together with information about the catchment's physical characteristics. The joint pdf of rainfall event volume and duration is derived using the theory of copulas. Four families of Archimedean copulas are tested in order to select the most appropriate to reproduce the dependence structure of those variables. Frequency distributions of runoff event volume and peak discharge rate are obtained following the derived probability distribution theory, using the functional relationship given by the rainfall–runoff process. The model is tested in two urban catchments located in the cities of Chillán and Santiago, Chile. The results are compared with the outcomes of continuous simulation in the Storm Water Management Model (SWMM) and with those from another analytical model that assumes storm event duration and volume to be statistically independent exponentially distributed variables. Citation Zegpi, M. & Fernández, B. (2010) Hydrological model for urban catchments – analytical development using copulas and numerical solution. Hydrol. Sci. J. 55(7), 1123–1136. 相似文献
14.
M. Janga Reddy Vijay P. Singh 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(3):475-489
This study investigated the utility of two meta-heuristic algorithms to estimate parameters of copula models and for derivation of drought severity–duration–frequency (S–D–F) curves. Drought is a natural event, which has huge impact on both the society and the natural environment. Drought events are mainly characterized by their severity, duration and intensity. The study adopts standardized precipitation index for drought characterization, and copula method for multivariate risk analysis of droughts. For accurate estimation of copula model parameters, two meta-heuristic methods namely genetic algorithm and particle swarm optimization are applied. The proposed methodology is applied to a case study in Trans Pecos, an arid region in Texas, USA. First, drought severity and duration are separately modeled by various probability distribution functions and then the best fitted models are selected for copula modeling. For modeling the joint dependence of drought variables, different classes of copulas, namely, extreme value copulas, Plackett and Student’s t copulas are employed and their performance is evaluated using standard performance measures. It is found that for the study region, the Gumbel–Hougaard copula is the best fitted copula model as compared to the others and is used for the development of drought S–D–F curves. Results of the study suggest that the meta-heuristic methods have greater utility in copula-based multivariate risk assessment of droughts. 相似文献
15.
M. Paul Mosley 《地球表面变化过程与地形》1981,6(2):127-137
Data to describe the morphologic, hydrologic and sedimentologic characteristics of 72 South Island, New Zealand, rivers were collected and analysed. Nearly 70 per cent of variation in channel morphology is accounted for by differences in cross-sectional area, slope, and cross-section shape; only 53 per cent of the morphologic variability could be statistically ‘explained’ by the hydrologic and sediment variables used. The level of explanation varied for different morphologic variables; nearly 90 per cent of the variability in cross-sectional area could be explained, but aspect ratio (maximum depth divided by hydraulic radius) was completely independent. Apart from the inadequacy of the measured variables as indices of the true underlying controlling factors, and the imperfect measurement and sampling procedures, the low level of explanation is probably due to the influence of factors such as floodplain vegetation, high quasi-random variability in bark sediment character, boundary effects imposed by bedrock bluffs, and the precise sequence of flood events, none of which are easily quantified. In addition, observations indicate that there is a large random variation in channel form which cannot be related to any factor. An attempt to relate channel morphology to flow variability, using simple indices of the latter, was unsuccessful. 相似文献
16.
The authors present a statistical procedure to estimate the probability distributions of storm characteristics. The approach uses recent advances in stochastic hydrological modeling. The temporal dynamics of rainfall are modeled via a reward alternating renewal process that describes wet and dry phases of storms. In particular, the wet phase is modeled as a rectangular pulse process with dependent random duration and intensity; the global dependence structure is described using multidimensional copulas. The marginal distributions are described by Generalized Pareto laws. The authors derive both the storm volume statistics and the rainfall volume distribution within a fixed temporal window preceding a storm. Based on these results, they calculate the antecedent moisture conditions. The paper includes a thorough discussion of the validity of the assumptions and approximations introduced, and an application to actual rainfall data. The models presented here have important implications for improved design procedures of water resources and hydrologic systems. 相似文献
17.
The causal and physically realizable Biot hysteretic model proves to be the simplest linear model able to describe the nearly rate‐independent behaviour of engineering materials. In this paper, the performance of the Biot hysteretic model is analysed and compared with those of the ideal and causal hysteretic models. The Laguerre polynomial approximation (LPA) method, recently proposed for the time‐domain analysis of linear viscoelastic systems, is then summarized and applied to the prediction of the dynamic response of linear hysteretic systems to deterministic and random excitations. The parameters of the LPA model generally need to be computed through numerical integrals; however, when this model is used to approximate the Biot hysteretic model, closed‐form expressions can be found. Effective step‐by‐step procedures are also provided in the paper, which prove to be accurate also for high levels of damping. Finally, the method is applied to the dynamic analysis of a highway embankment excited by deterministic and random ground motions. The results show that in some cases the inaccuracy associated with the use of an equivalent viscous damping model is too large. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
18.
Izuru Takewaki 《地震工程与结构动力学》2001,30(4):519-535
Since earthquake ground motions are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new non‐stationary random critical excitation method is proposed. In contrast to the conventional critical excitation methods, a stochastic response index is treated as the objective function to be maximized. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. It is shown that the original idea for stationary random inputs can be utilized effectively in the procedure for finding a critical excitation for non‐stationary random inputs. The key for finding the new non‐stationary random critical excitation is the exchange of the order of the double maximization procedures with respect to time and to the power spectral density function. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
19.
Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches.In this paper,different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions,i.e.,the stochastic diffusion process,stochastic jump process,and stochastic jump diffusion process.While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows,the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows.An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment.In this paper,the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process（i.e.the time lag between the flow particle and the sediment particle in extreme flows is considered negligible）.In the proposed particle tracking models,a random term mainly caused by fluid eddy motions is modeled as a Wiener process,while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process.The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement.The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations.The ensemble mean and variance of particle velocity are verified with available data.Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed. 相似文献
20.
J. T. Shiau 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(1-2):42-57
Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate
distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it
requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most
common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either
separate single random variables or two joint random variables. In the latter case, the return periods can be defined using
one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another
magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain
magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model
extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily
streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical
models and observed flood data.
The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this
work. 相似文献