共查询到20条相似文献，搜索用时 421 毫秒
1.
The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. In an identifiable case, the posterior probability density function (PDF) of the uncertain model parameters for given measured data can be approximated by a weighted sum of Gaussian distributions centered at a number of discrete optimal values of the parameters at which some positive measure‐of‐fit function is minimized. The present paper focuses on the problem of model updating in the general unidentifiable case for which certain simplifying assumptions available for identifiable cases are not valid. In this case, the PDF is distributed in the neighbourhood of an extended and usually highly complex manifold of the parameter space that cannot be calculated explicitly. The computational difficulties associated with calculating the highly complex posterior PDF are discussed and a new adaptive algorithm, referred to as the tangential‐projection (TP) algorithm, allowing for an efficient approximate representation of the above manifold and the posterior PDF is presented. Using this approximation, expressions for calculating the uncertain predictive response are established. A numerical example involving noisy data is presented to demonstrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
2.
The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian spectral density approach (BSDA) for modal updating is presented which uses the statistical properties of a spectral density estimator to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties by calculating the posterior joint probability distribution of these parameters. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite element model based on modal estimates. It is found that the updated PDF of the modal parameters can be well approximated by a Gaussian distribution centred at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
3.
随机地震反演关键参数优选和效果分析(英文) 总被引：2，自引：0，他引：2
随机地震反演技术是将地质统计理论和地震反演相结合的反演方法,它将地震资料、测井资料和地质统计学信息融合为地下模型的后验概率分布,利用马尔科夫链蒙特卡洛(MCMC)方法对该后验概率分布采样,通过综合分析多个采样结果来研究后验概率分布的性质,进而认识地下情况。本文首先介绍了随机地震反演的原理,然后对影响随机地震反演效果的四个关键参数,即地震资料信噪比、变差函数、后验概率分布的样本个数和井网密度进行分析并给出其优化原则。资料分析表明地震资料信噪比控制地震资料和地质统计规律对反演结果的约束程度,变差函数影响反演结果的平滑程度,后验概率分布的样本个数决定样本统计特征的可靠性,而参与反演的井网密度则影响反演的不确定性。最后通过对比试验工区随机地震反演和基于模型的确定性地震反演结果,指出随机地震反演可以给出更符合地下实际情况的模型。 相似文献
4.
提出了各向异性页岩储层统计岩石物理反演方法.通过统计岩石物理模型建立储层物性参数与弹性参数的定量关系，使用测井数据及井中岩石物理反演结果作为先验信息，将地震阻抗数据定量解释为储层物性参数、各向异性参数的空间分布.反演过程在贝叶斯框架下求得储层参数的后验概率密度函数，并从中得到参数的最优估计值及其不确定性的定量描述.在此过程中综合考虑了岩石物理模型对复杂地下介质的描述偏差和地震数据中噪声对反演不确定性的影响.在求取最大后验概率过程中使用模拟退火优化粒子群算法以提高收敛速度和计算准确性.将统计岩石物理技术应用于龙马溪组页岩气储层，得到储层泥质含量、压实指数、孔隙度、裂缝密度等物性，以及各向异性参数的空间分布及相应的不确定性估计，为页岩气储层的定量描述提供依据. 相似文献
5.
Z. T. Yucel R. H. Shumway 《Stochastic Environmental Research and Risk Assessment (SERRA)》1996,10(2):107-126
This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems.A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters.We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data. 相似文献
6.
The moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation‐based methods and other approximations. 相似文献
7.
The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging. 相似文献
8.
This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discussed. 相似文献
9.
Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function
Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function (FRF). The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete frame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location. 相似文献
10.
We present a methodology for determining the elastic properties of the shallow crust from inversion of surface wave dispersion characteristics through a fully nonlinear procedure. Using volcanic tremor data recorded by a small-aperture seismic array on Mount Etna, we measured the surface waves dispersion curves with the multiple signal classification technique. The large number of measurements allows the determination of an a priori probability density function without the need of making any assumption about the uncertainties on the observations. Using this information, we successively conducted the inversion of phase velocities using a probabilistic approach. Using a wave-number integration method, we calculated the predicted dispersion function for thousands of 1-D models through a systematic grid search investigation of shear-wave velocities in individual layers. We joined this set of theoretical dispersion curves to the experimental probability density function (PDF), thus obtaining the desired structural model in terms of an a posteriori PDF of model parameters. This process allowed the representation of the objective function, showing the non-uniqueness of the solutions and providing a quantitative view of the uncertainties associated with the estimation of each parameter. We then compared the solution with the surface wave group velocities derived from diffuse noise Green’s functions calculated at pairs of widely spaced (~5–10 km) stations. In their gross features, results from the two different approaches are comparable, and are in turn consistent with the models presented in several earlier studies. 相似文献
11.
A reliable computational model is necessary for evaluating the state and predicting the future performance of existing structures, especially after exposure to damaging effects such as an earthquake. A major problem with the existing iterative‐based model updating methods is that the search might be trapped in local optima. The genetic algorithms (GAs) offer a desirable alternative because of their ability in performing a robust search for the global optimal solution. This paper presents a GA‐based model updating approach using a real‐coding scheme for global model updating based on dynamic measurement data. An eigensensitivity method is employed to further fine‐tune the GA updated results in case the sensitivity problem arises due to restricted measurement information. The application on shear‐type frames reveals that with a limited amount of modal data, namely the lowest three natural frequencies and the first mode shape, it is possible to achieve satisfactory updating by the GA alone for cases involving a limited number of parameters (storey stiffness herein). With the incorporation of the eigensensitivity algorithm, the updating capability is extended to a sufficiently large number of parameters. In case the modal data contain errors, the GA is also shown to be able to update the model to a satisfactory accuracy, provided the required amount of modal data is available. An example is given in which a 6‐DOF stick model for an actual six‐storey RC frame is updated using the measured dynamic properties. The effectiveness of the updating is evaluated by comparing the measured and predicted seismic response using the updated model. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
12.
In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian-distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non-linear forward operators and mixed discrete-continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho-fluid facies from pre-stack seismic data in case of non-parametric mixture prior distributions and non-linear forward modellings. The first strategy is a two-dimensional target-oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single-interface full Zoeppritz equations. The second is an interval-oriented approach that inverts the pre-stack seismic responses along a given time interval using a one-dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P-wave velocity, S-wave velocity and density. The distribution of the elastic properties at each common-mid-point location (for the target-oriented approach) or at each time-sample position (for the time-interval approach) is assumed to be multimodal with as many modes as the number of litho-fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian-mixture-distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort. 相似文献
13.
This paper proposes a new orientation to address the problem of hydrological model calibration in ungauged basin. Satellite radar altimetric observations of river water level at basin outlet are used to calibrate the model, as a surrogate of streamflow data. To shift the calibration objective, the hydrological model is coupled with a hydraulic model describing the relation between streamflow and water stage. The methodology is illustrated by a case study in the Upper Mississippi Basin using TOPEX/Poseidon (T/P) satellite data. The generalized likelihood uncertainty estimation (GLUE) is employed for model calibration and uncertainty analysis. We found that even without any streamflow information for regulating model behavior, the calibrated hydrological model can make fairly reasonable streamflow estimation. In order to illustrate the degree of additional uncertainty associated with shifting calibration objective and identifying its sources, the posterior distributions of hydrological parameters derived from calibration based on T/P data, streamflow data and T/P data with fixed hydraulic parameters are compared. The results show that the main source is the model parameter uncertainty. And the contribution of remote sensing data uncertainty is minor. Furthermore, the influence of removing high error satellite observations on streamflow estimation is also examined. Under the precondition of sufficient temporal coverage of calibration data, such data screening can eliminate some unrealistic parameter sets from the behavioral group. The study contributes to improve streamflow estimation in ungauged basin and evaluate the value of remote sensing in hydrological modeling. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
14.
长波长假设条件下，各向同性背景地层中发育一组平行排列的垂直裂缝可等效为具有水平对称轴的横向各向同性（HTI）介质.基于不同观测方位的岩石地震响应特征变化，宽方位地震数据不仅可实现裂缝岩石弹性参数与各向异性参数的预测，同时也蕴含着丰富的孔隙度等储层物性参数信息.本文结合实际地震资料提出了贝叶斯框架下岩石物理驱动的储层裂缝参数与物性参数概率地震联合反演方法，首先基于AVAZ反演裂缝岩石的弹性参数与各向异性参数，并在此基础上通过统计岩石物理模型表征孔隙度、裂缝密度等各向异性介质储层参数与裂缝岩石参数的相互关联，并采用马尔科夫链蒙特卡洛（MCMC）抽样方法进行大量样本的随机模拟，使用期望最大化（EM）算法估计后验条件概率分布，最终寻找最大后验条件概率对应的孔隙度、裂缝密度等HTI裂缝介质储层参数即为反演结果.测井及实际地震数据处理表明，该方法能够稳定合理地从方位地震资料中获取裂缝岩石弹性参数与各向异性参数，并提供了一种较为可靠的孔隙度、裂缝密度等裂缝介质储层参数概率地震反演方法. 相似文献
15.
In the analysis of the unsaturated zone, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the porous media. Adaptative multi-scale parameterization consists in solving the problem through successive approximations by refining the parameter at the next finer scale all over the domain and stopping the process when the refinement does not induce significant decrease of the objective function any more. In this context, the refinement indicators algorithm provides an adaptive parameterization technique that opens the degrees of freedom in an iterative way driven at first order by the model to locate the discontinuities of the sought parameters. We present a refinement indicators algorithm for adaptive multi-scale parameterization that is applicable to the estimation of multi-dimensional hydraulic parameters in unsaturated soil water flow. Numerical examples are presented which show the efficiency of the algorithm in case of noisy data and missing data. 相似文献
16.
Monica Riva Alberto Guadagnini Shlomo P. Neuman Emanuela Bianchi Janetti Bwalya Malama 《Advances in water resources》2009
We present a nonlinear stochastic inverse algorithm that allows conditioning estimates of transient hydraulic heads, fluxes and their associated uncertainty on information about hydraulic conductivity (K) and hydraulic head (h ) data collected in a randomly heterogeneous confined aquifer. Our algorithm is based on Laplace-transformed recursive finite-element approximations of exact nonlocal first and second conditional stochastic moment equations of transient flow. It makes it possible to estimate jointly spatial variations in natural log-conductivity (Y=lnK), the parameters of its underlying variogram, and the variance–covariance of these estimates. Log-conductivity is parameterized geostatistically based on measured values at discrete locations and unknown values at discrete “pilot points”. Whereas prior values of Y at pilot point are obtained by generalized kriging, posterior estimates at pilot points are obtained through a maximum likelihood fit of computed and measured transient heads. These posterior estimates are then projected onto the computational grid by kriging. Optionally, the maximum likelihood function may include a regularization term reflecting prior information about Y. The relative weight assigned to this term is evaluated separately from other model parameters to avoid bias and instability. We illustrate and explore our algorithm by means of a synthetic example involving a pumping well. We find that whereas Y and h can be reproduced quite well with parameters estimated on the basis of zero-order mean flow equations, all model quality criteria identify the second-order results as being superior to zero-order results. Identifying the weight of the regularization term and variogram parameters can be done with much lesser ambiguity based on second- than on zero-order results. A second-order model is required to compute predictive error variances of hydraulic head (and flux) a posteriori. Conditioning the inversion jointly on conductivity and hydraulic head data results in lesser predictive uncertainty than conditioning on conductivity or head data alone. 相似文献
17.
Application of distributed hydrological models for predictions in ungauged basins: a method to quantify predictive uncertainty 
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下载免费PDF全文 Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub‐basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub‐basins and is applied for simulation in the other sub‐basin considered as pseudo‐ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo‐ungauged basins. The results are subsequently compared with the measured stream flow from the sub‐basins. It is observed that the measured stream flow in the pseudo‐ungauged basin lies well within the estimated confidence band of predicted stream flow. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
Yi Zhang Jasmine Siu Lee Lam 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(6):1615-1636
The analysis and design of offshore structures necessitates the consideration of environmental loads. Realistic modeling of the environmental loads is particularly important to ensure reliable performance of these structures. In this paper, structural reliability analysis of offshore structures subjected to a time varying environment is investigated. In this work, an extreme value statistical model for the wave height is adopted as a basis for the performance assessment of a jacket structure. Due to the changing environment, the model parameters are modeled to be time varying. To deal with this issue, two segmentation algorithms are proposed and applied to the observed data in order to derive piecewise stationary processes for a statistical analysis. The investigation includes the extreme value modeling of the wave height in the characterization of the sea load. The implementation of the segmentation algorithms in the original data eventually leads to approximations of the safety quality of the existing structure within different time interval. The computed result is developed to reflect the time varying effects in the failure probability of structures. The results are compared with the traditional extreme values approach in view of the accuracy and information content. The investigation is also extended to a case where the design of the structure ignores the time varying property. 相似文献
19.
Sensitivity analysis of the probability distribution of groundwater level series based on information entropy 总被引：2，自引：2，他引：0
Xiankui Zeng Dong Wang Jichun Wu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(3):345-356
Information entropy is an effective method to analyze uncertainty in various processes. The principle of maximum entropy (POME)
provides a guide line for the parameter estimation of probability density function (PDF). Mutual entropy analysis is well
qualified for delineating the nonlinear and complex multivariable relationship. The probability distribution of model output
is the element of model uncertainty analysis. In this paper, a synthetic groundwater flow field is build to produce groundwater
level series (GLS). The probability distribution of GLS is obtained by the frequency analysis method based on POME and Chi-Squared
test. The important uncertainty factors that affect the parameters of PDF of GLS are assessed by the sensitivity analysis
methods, which include stepwise regression analysis and mutual entropy analysis. Results of this analysis indicate that most
of the GLS follow normal distribution (or log-normal distribution), while a few obey others. The mean and variance of normal
GLS are affected differently by the input variables of groundwater model. Mutual entropy analysis is more competitive and
appropriate for delineating the nonlinear and nonmonotonic multivariable relationship than stepwise regression analysis. 相似文献
20.
研究了利用背向散射脉冲传播时间统计特性反演随机界面参数的问题.首先扩展了Fuks & Godin关于随机界面背向散射脉冲传播时间统计特性理论,给出了当随机界面高度-斜率统计相关情形下,最早返回的两个脉冲传播时间及其时延的概率密度函数（PDF）表达式.进而提出了一种基于背向散射脉冲传播时间统计特性的随机界面参数反演算法：采用遗传算法匹配前两个背向散射脉冲传播时间及其时延的PDF实现随机界面高度—斜率相关系数的绝对值|ρ|和无量纲参数T的反演.最后利用参数的后验概率分析反演结果的不确定性.数值模拟结果表明：该算法可有效反演随机界面的参数,参数|ρ|相对于T反演精度较高;|ρ|和T之间存在较强的参数耦合.与前人认为可忽略高度—斜率相关性（|ρ|）的观点不同：此类反演问题中应同时考虑|ρ|和T. 相似文献