共查询到20条相似文献，搜索用时 78 毫秒
1.
Allan D. Woodbury Tadeusz J. Ulrych 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(5):317-358
The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic
inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the
theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the
similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions
for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution.
The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the
constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number
of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy
formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds
if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with
a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior
probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities.
In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results
of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing
MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model
and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source
problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may
show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the
prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined
case with a uniform prior. 相似文献
2.
根据贝叶斯理论给出了对含噪声地球物理数据处理的具体流程和方法,主要包括似然函数估计和后验概率计算.我们将数据向量的概念扩展为数据向量的集合,通过引入数据空间内的信赖度,把数据噪声转移到模型空间的概率密度函数上,即获得了反映数据本身的不确定性的似然函数.该方法由于避免了处理阶段数据空间内的人工干预,因而可以保证模型空间中的概率密度单纯反映数据噪声,具有信息保真度高、保留可行解的优点.为了得到加入先验信息的后验分布,本文提出了使用加权矩阵的概率分析法,该方法在模型空间直接引入地质信息,对噪声引起的反演多解性有很强的约束效果.整个处理流程均以大地电磁反演为例进行了展示. 相似文献
3.
The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic
inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the
theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the
similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions
for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution.
The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the
constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number
of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy
formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds
if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with
a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior
probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities.
In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results
of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing
MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model
and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source
problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may
show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the
prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined
case with a uniform prior. 相似文献
4.
Uncertainty Analysis in Atmospheric Dispersion Modeling 总被引：1，自引：0，他引：1
The concentration of a pollutant in the atmosphere is a random variable that cannot be predicted accurately, but can be described using quantities such as ensemble mean, variance, and probability distribution. There is growing recognition that the modeled concentrations of hazardous contaminants in the atmosphere should be described in a probabilistic framework. This paper discusses the various types of uncertainties in atmospheric dispersion models, and reviews sensitivity/uncertainty analysis methods to characterize and/or reduce them. Evaluation and quantification of the range of uncertainties in predictions yield a deeper insight into the capabilities and limitations of atmospheric dispersion models, and increase our confidence in decision-making based on models. 相似文献
5.
Compositional Bayesian indicator estimation 总被引：1，自引：1，他引：0
Carolina Guardiola-Albert Eulogio Pardo-Ig��zquiza 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(6):835-849
Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions
of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution
function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator
kriging provides an estimation variance that, although not often used in applications, should be taken into account as it
assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this
alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described
in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according
to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution,
point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the
posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate
being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus
in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty.
On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple
kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of
definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation
and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability
of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its
user guides are public domain and freely available. 相似文献
6.
Simultaneous identification of the pollutant release history and the source location in groundwater by means of a geostatistical approach 总被引：4，自引：1，他引：3
Ilaria Butera Maria Giovanna Tanda Andrea Zanini 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1269-1280
This paper describes an innovative procedure that is able to simultaneously identify the release history and the source location of a pollutant injection in a groundwater aquifer (simultaneous release function and source location identification, SRSI). The methodology follows a geostatistical approach: it develops starting from a data set and a reliable numerical flow and transport model of the aquifer. Observations can be concentration data detected at a given time in multiple locations or a time series of concentration measurements collected at multiple locations. The methodology requires a preliminary delineation of a probably source area and results in the identification of both the sub-area where the pollutant injection has most likely originated, and in the contaminant release history. Some weak hypotheses have to be defined about the statistical structure of the unknown release function such as the probability density function and correlation structure. Three case studies are discussed concerning two-dimensional, confined aquifers with strongly non-uniform flow fields. A transfer function approach has been adopted for the numerical definition of the sensitivity matrix and the recent step input function procedure has been successfully applied. 相似文献
7.
Despite their apparent high dimensionality, spatially distributed hydraulic properties of geologic formations can often be compactly (sparsely) described in a properly designed basis. Hence, the estimation of high-dimensional subsurface flow properties from dynamic performance and monitoring data can be formulated and solved as a sparse reconstruction inverse problem. Recent advances in statistical signal processing, formalized under the compressed sensing paradigm, provide important guidelines on formulating and solving sparse inverse problems, primarily for linear models and using a deterministic framework. Given the uncertainty in describing subsurface physical properties, even after integration of the dynamic data, it is important to develop a practical sparse Bayesian inversion approach to enable uncertainty quantification. In this paper, we use sparse geologic dictionaries to compactly represent uncertain subsurface flow properties and develop a practical sparse Bayesian method for effective data integration and uncertainty quantification. The multi-Gaussian assumption that is widely used in classical probabilistic inverse theory is not appropriate for representing sparse prior models. Following the results presented by the compressed sensing paradigm, the Laplace (or double exponential) probability distribution is found to be more suitable for representing sparse parameters. However, combining Laplace priors with the frequently used Gaussian likelihood functions leads to neither a Laplace nor a Gaussian posterior distribution, which complicates the analytical characterization of the posterior. Here, we first express the form of the Maximum A-Posteriori (MAP) estimate for Laplace priors and then use the Monte-Carlo-based Randomize Maximum Likelihood (RML) method to generate approximate samples from the posterior distribution. The proposed Sparse RML (SpRML) approximate sampling approach can be used to assess the uncertainty in the calibrated model with a relatively modest computational complexity. We demonstrate the suitability and effectiveness of the SpRML formulation using a series of numerical experiments of two-phase flow systems in both Gaussian and non-Gaussian property distributions in petroleum reservoirs and successfully apply the method to an adapted version of the PUNQ-S3 benchmark reservoir model. 相似文献
8.
Studies on environmental dispersion are essential for applications as water management. The two-scale perturbation analysis is applied in this paper to deduce the environmental dispersion model for the typical case of contaminant transport in two-layer wetland flows. The analysis follows the established theoretical framework on the basis of phase average and the concept of Taylor dispersion. By the obtained flow velocity distribution for the two-layer flow, the analytical expression for the environmental dispersivity is deduced and shown to be consistent with previous results by the concentration moment method, while with much simplifications on the expression for ignoring the less concerned time-dependent stage of the dispersivity. 相似文献
9.
Benjamin Renard Michel Lang Philippe Bois 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,21(2):97-112
Statistical analysis of extremes currently assumes that data arise from a stationary process, although such an hypothesis is not easily assessable and should therefore be considered as an uncertainty. The aim of this paper is to describe a Bayesian framework for this purpose, considering several probabilistic models (stationary, step-change and linear trend models) and four extreme values distributions (exponential, generalized Pareto, Gumbel and GEV). Prior distributions are specified by using regional prior knowledge about quantiles. Posterior distributions are used to estimate parameters, quantify the probability of models and derive a realistic frequency analysis, which takes into account estimation, distribution and stationarity uncertainties. MCMC methods are needed for this purpose, and are described in the article. Finally, an application to a POT discharge series is presented, with an analysis of both occurrence process and peak distribution. 相似文献
10.
Bayesian approach to contaminant source characterization in water distribution systems: adaptive sampling framework 总被引：1，自引：1，他引：0
Hui Wang Kenneth W. Harrison 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(8):1921-1928
Bayesian analysis can yield a probabilistic contaminant source characterization conditioned on available sensor data and accounting for system stochastic processes. This paper is based on a previously proposed Markov chain Monte Carlo (MCMC) approach tailored for water distribution systems and incorporating stochastic water demands. The observations can include those from fixed sensors and, the focus of this paper, mobile sensors. Decision makers, such as utility managers, need not wait until new observations are available from an existing sparse network of fixed sensors. This paper addresses a key research question: where is the best location in the network to gather additional measurements so as to maximize the reduction in the source uncertainty? Although this has been done in groundwater management, it has not been well addressed in water distribution networks. In this study, an adaptive framework is proposed to guide the strategic placement of mobile sensors to complement the fixed sensor network. MCMC is the core component of the proposed adaptive framework, while several other pieces are indispensable: Bayesian preposterior analysis, value of information criterion and the search strategy for identifying an optimal location. Such a framework is demonstrated with an illustrative example, where four candidate sampling locations in the small water distribution network are investigated. Use of different value-of-information criteria reveals that while each may lead to different outcomes, they share some common characteristics. The results demonstrate the potential of Bayesian analysis and the MCMC method for contaminant event management. 相似文献
11.
Improved performance‐based seismic assessment of buildings by utilizing Bayesian statistics 
下载免费PDF全文
下载免费PDF全文 This paper addresses two important issues of concern to practicing engineers and researchers alike in application of performance‐based seismic assessment (PBSA) methodology on buildings: (i) the number of ground motion records required to exercise PBSA—current practice (FEMA P‐58‐1) requires eleven or more pairs of motions for this purpose, and (ii) the time and effort associated with performing the number of nonlinear response history analyses required to exercise PBSA. We present a method for exercising of PBSA that employs classical linear modal analysis to develop a first estimate (i.e., a priori) of probability distribution of loss, followed by utilizing Bayesian statistics to update this estimate using estimates of loss obtained by utilizing a small number of nonlinear response history analyses of a detailed model of the building (i.e., posterior). The proposed technique is used to assess the distribution of monetary loss of two case studies, a 4‐story reinforced concrete moment‐resisting frame building and a 20‐story steel moment‐resisting frame building, both located in Los Angeles, for a ground motion hazard with 10% probability of exceedance in 50 years. The efficiency of the proposed PBSA method is demonstrated by showing the similarity between the distribution of monetary loss at each story of case study buildings obtained from the traditional/sophisticated PBSA methodology and the proposed PBSA method in this study. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
12.
A macroscopic transport model is developed, following the Taylor shear dispersion analysis procedure, for a 2D laminar shear flow between parallel plates possessing a constant specified concentration. This idealized geometry models flow with contaminant dissolution at pore-scale in a contaminant source zone and flow in a rock fracture with dissolving walls. We upscale a macroscopic transient transport model with effective transport coefficients of mean velocity, macroscopic dispersion, and first-order mass transfer rate. To validate the macroscopic model the mean concentration, covariance, and wall concentration gradient are compared to the results of numerical simulations of the advection–diffusion equation and the Graetz solution. Results indicate that in the presence of local-scale variations and constant concentration boundaries, the upscaled mean velocity and macrodispersion coefficient differ from those of the Taylor–Aris dispersion, and the mass transfer flux described by the first-order mass transfer model is larger than the diffusive mass flux from the constant wall. In addition, the upscaled first-order mass transfer coefficient in the macroscopic model depends only on the plate gap and diffusion coefficient. Therefore, the upscaled first-order mass transfer coefficient is independent of the mean velocity and travel distance, leading to a constant pore-scale Sherwood number of 12. By contrast, the effective Sherwood number determined by the diffusive mass flux is a function of the Peclet number for small Peclet number, and approaches a constant of 10.3 for large Peclet number. 相似文献
13.
Probabilistic-fuzzy health risk modeling 总被引：3，自引：2，他引：1
Health risk analysis of multi-pathway exposure to contaminated water involves the use of mechanistic models that include many uncertain and highly variable parameters. Currently, the uncertainties in these models are treated using statistical approaches. However, not all uncertainties in data or model parameters are due to randomness. Other sources of imprecision that may lead to uncertainty include scarce or incomplete data, measurement error, data obtained from expert judgment, or subjective interpretation of available information. These kinds of uncertainties and also the non-random uncertainty cannot be treated solely by statistical methods. In this paper we propose the use of fuzzy set theory together with probability theory to incorporate uncertainties into the health risk analysis. We identify this approach as probabilistic-fuzzy risk assessment (PFRA). Based on the form of available information, fuzzy set theory, probability theory, or a combination of both can be used to incorporate parameter uncertainty and variability into mechanistic risk assessment models. In this study, tap water concentration is used as the source of contamination in the human exposure model. Ingestion, inhalation and dermal contact are considered as multiple exposure pathways. The tap water concentration of the contaminant and cancer potency factors for ingestion, inhalation and dermal contact are treated as fuzzy variables while the remaining model parameters are treated using probability density functions. Combined utilization of fuzzy and random variables produces membership functions of risk to individuals at different fractiles of risk as well as probability distributions of risk for various alpha-cut levels of the membership function. The proposed method provides a robust approach in evaluating human health risk to exposure when there is both uncertainty and variability in model parameters. PFRA allows utilization of certain types of information which have not been used directly in existing risk assessment methods. 相似文献
14.
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
15.
储层物性参数是储层描述的重要参数,常规的基于贝叶斯理论的储层物性参数反演方法大多是通过反演获得的弹性参数进一步转换而获得物性参数,本文提出一种基于弹性阻抗数据预测储层物性参数的反演方法.该方法主要通过建立可以表征弹性阻抗与储层物性参数之间关系的统计岩石物理模型,联合蒙特卡罗仿真模拟技术,在贝叶斯理论框架的指导下,应用期望最大化算法估计物性参数的后验概率分布,最终实现储层物性参数反演.经过模型测试和实际资料的处理,其结果表明本文提出的方法具有预测精度高,稳定性强,横向连续性好等优点. 相似文献
16.
为了提高AVO(amplitude versus offset)反演结果的精度和横向连续性,本文提出了一种新的AVO反演约束方法,该方法结合贝叶斯原理和卡尔曼滤波算法实现了对反演参数纵向和横向的同时约束.文章首先结合反演参数的纵向贝叶斯先验概率约束和反演参数的横向连续性假设建立了与卡尔曼滤波算法对应的AVO反演系统的数学模型,然后将该数学模型代入卡尔曼滤波算法框架,利用卡尔曼滤波算法实现了双向约束AVO反演.二维模型测试和实际数据测试结果表明,相对于单纯的纵向贝叶斯先验概率约束,双向约束能更准确地刻画参数的横向变化,得到更准确、横向连续性更好的反演结果. 相似文献
17.
重力异常对地壳横向密度变化敏感,而无约束重力反演得到的密度模型其垂向分辨能力往往不理想.为了改善反演结果的垂向分辨率,本文参考已有先验分层模型,基于贝叶斯原理,提出了一种重震联合反演的新策略,可实现多种参考模型和复杂加权参数条件下的最大后验概率估计.理论模型测试结果表明,对于深度加权、多参考模型约束等多种问题,本文提出的新方法都可以稳健地获得最优化的模型参数.本文同时以中国地震科学台阵在龙门山地区及周边的一维接收函数分层模型和地震层析成像结果为参考,通过此方法对该区的重力异常进行反演,获得了该区的高精度三维密度结构,其水平分辨率优于10 km,垂直分辨率优于5 km.结合四条通过汶川和芦山地震震中的剖面进行分析后发现,反演得到的密度结构模型在过强震震源区位置横向变形显著,其揭示的分层地壳结构和变形模式与地表已知断裂构造具有相关性.本文提出的重震联合反演新策略,可为研究潜在强震风险源区的地壳结构和物性特征提供有效的科技方法支撑. 相似文献
18.
Identification of contaminant point source in surface waters based on backward location probability density function method 总被引：2，自引：0，他引：2
A backward location probability density function (BL-PDF) method capable of identifying location of point sources in surface waters is presented in this paper. The relation of forward location probability density function (FL-PDF) and backward location probability density, based on adjoint analysis, is validated using depth-averaged free-surface flow and mass transport models and several surface water test cases. The solutions of the backward location PDF transport equation agreed well to the forward location PDF computed using the pollutant concentration at the monitoring points. Using this relation and the distribution of the concentration detected at the monitoring points, an effective point source identification method is established. The numerical error of the backward location PDF simulation is found to be sensitive to the irregularity of the computational meshes, diffusivity, and velocity gradients. The performance of identification method is evaluated regarding the random error and number of observed values. In addition to hypothetical cases, a real case was studied to identify the source location where a dye tracer was instantaneously injected into a stream. The study indicated the proposed source identification method is effective, robust, and quite efficient in surface waters; the number of advection–diffusion equations needed to solve is equal to the number of observations. 相似文献
19.
Simultaneous identification of a single pollution point-source location and contamination time under known flow field conditions 总被引：3，自引：0，他引：3
A theoretical framework is presented that allows direct identification of a single point-source pollution location and time in heterogeneous multidimensional systems under known flow field conditions. Based on the concept of the transfer function theory, it is shown that an observed pollution plume contains all the necessary information to predict the concentration at the unknown pollution source when a reversed flow field transport simulation is performed. This target concentration C0 is obtained from a quadratic integral of the observed pollution plume itself. Backwards simulation of the pollution plume leads to shrinkage of the C0-contour due to dispersion. When the C0-contour reduces to a singular point, i.e. becomes a concentration maximum, the position of the pollution source is identified and the backward simulation time indicates the time elapsed since the contaminant release. The theoretical basis of the method is first developed for the ideal case that the pollution plume is entirely known and is illustrated using a synthetic heterogeneous 2D example where all the hydro-dispersive parameters are known. The same example is then used to illustrate the procedure for a more realistic case, i.e. where only few observation points exist. 相似文献
20.
The estimation of site intensity occurrence probabilities in low seismic activity regions has been studied from different points of view. However, no method has been definitively established because several problems arise when macroseismic historical data are incomplete and the active zones are not well determined. The purpose of this paper is to present a method that estimates site occurrence probabilities and at the same time measures the uncertainties inherent in these probabilities in low activity regions. The region to be studied is divided into very broad seismic zones. An exponential intensity probability law is adjusted for each zone and the degree of uncertainty in the assumed incompleteness of the catalogue is evaluated for each intensity. These probabilities are used to establish what may be termed ‘prior site occurrence models’. A Bayesian method is used to improve ‘prior models’ and to obtain the ‘posterior site occurrence models’. Epicentre locations are used to recover spatial information lost in the prior broad zoning. This Bayesian correction permits the use of specific attenuation for different events and may take into account, by means of conservative criteria, epicentre location errors. Following Bayesian methods, probabilities are assumed to be random variables and their distribution may be used to estimate the degree of uncertainty arising from (a) the statistical variance of estimators, (b) catalogue incompleteness and (c) mismatch of data to prior assumptions such as Poisson distribution for events and exponential distribution for intensities. The results are maps of probability and uncertainty for each intensity. These maps exhibit better spatial definition than those obtained by means of simple, broad zones. Some results for Catalonia (NE of Iberian Peninsula) are shown. 相似文献