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1.
受工程勘察成本及试验场地限制,可获得的试验数据通常有限,基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是,目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布,似然函数为多维正态分布,这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型,以一个不排水黏土边坡为例,采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响,选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险,选用对数正态分布获得的边坡可靠度计算结果居中。相比之下,似然函数的影响更加显著。与其他类型似然函数相比,由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时,获得与场地信息更为吻合的计算结果。另外,构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。 相似文献
2.
A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ad hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric semivariogram to the data under the transformed coordinates. We propose a Bayesian methodology which simultaneously estimates the linear transformation and the other semivariogram parameters. In addition, the Bayesian paradigm allows full inference for any characteristic of the geometrically anisotropic model rather than merely providing a point estimate. Our work is motivated by a dataset of scallop catches in the Atlantic Ocean in 1990 and also in 1993. The 1990 data provide useful prior information about the nature of the anisotropy of the process. Exploratory data analysis (EDA) techniques such as directional empirical semivariograms and the rose diagram are widely used by practitioners. We recommend a suitable contour plot to detect departures from isotropy. We then present a fully Bayesian analysis of the 1993 scallop data, demonstrating the range of inferential possibilities. 相似文献
3.
大地电磁法的1D无偏差贝叶斯反演 总被引：2，自引：0，他引：2
应用贝叶斯理论对一维(1D)大地电磁反演问题进行无偏差不确定度分析。在贝叶斯理论中,测量数据和先验信息包含在后验概率密度函数(PPD)中,它可以解释成模型的单点估计和不确定度等贝叶斯推断,这些信息的获取需要对反演问题进行优化求最优模型和在高维模型空间中对PPD进行采样积分。采样的完全、彻底和效率,对反演结果有着重要的影响。为了使采样更有效、更完全,数值积分采用主分量参数空间的Metropolis Hastings采样,并采用了不同的采样温度。在反演中,同时采用了欠参数化和超参数化方法,数据误差和正则化因子被当成随机变量。反演结果得到各参数的不确定度、参数间的相关关系和不同深度模型的不确定度分布。COPROD1数据的反演结果表明模型空间中存在双峰结构。非地电参数在反演中得到了约束,说明数据本身不仅包含地球物理模型信息(电导率等),还包含了这些非地电参数的信息。 相似文献
4.
Maria Navarro Olivier P. Le Maître Ibrahim Hoteit David L. George Kyle T. Mandli Omar M. Knio 《Computational Geosciences》2018,22(6):1447-1463
This work tackles the problem of calibrating the unknown parameters of a debris flow model with the drawback that the information regarding the experimental data treatment and processing is not available. In particular, we focus on the evolution over time of the flow thickness of the debris with dam-break initial conditions. The proposed methodology consists of establishing an approximation of the numerical model using a polynomial chaos expansion that is used in place of the original model, saving computational burden. The values of the parameters are then inferred through a Bayesian approach with a particular focus on inference discrepancies that some of the important features predicted by the model exhibit. We build the model approximation using a preconditioned non-intrusive method and show that a suitable prior parameter distribution is critical to the construction of an accurate surrogate model. The results of the Bayesian inference suggest that utilizing directly the available experimental data could lead to incorrect conclusions, including the over-determination of parameters. To avoid such drawbacks, we propose to base the inference on few significant features extracted from the original data. Our experiments confirm the validity of this approach, and show that it does not lead to significant loss of information. It is further computationally more efficient than the direct approach, and can avoid the construction of an elaborate error model. 相似文献
5.
George A. Griffiths 《Mathematical Geology》1982,14(1):65-75
Bayesian inference modeling may be applied to empirical stochastic prediction in geomorphology where outcomes of geomorphic processes can be expressed by probability density functions. Natural variations in process outputs are accommodated by the probability model. Uncertainty in the values of model parameters is reduced by considering statistically independent prior information on long-term, parameter behavior. Formal combination of model and parameter information yields a Bayesian probability distribution that accounts for parameter uncertainty, but not for model uncertainty or systematic error which is ignored herein. Prior information is determined by ordinary objective or subjective methods of geomorphic investigation. Examples involving simple stochastic models are given, as applied to the prediction of shifts in river courses, alpine rock avalanches, and fluctuating river bed levels. Bayesian inference models may be applied spatially and temporally as well as to functions of a random variable. They provide technically superior forecasts, for a given shortterm data set, to those of extrapolation or stochastic simulation models. In applications the contribution of the field geomorphologist is of fundamental quantitative importance. 相似文献
6.
7.
Lawrence D. Stone 《Mathematical Geology》1990,22(3):309-332
This paper presents a Bayesian version of the classical model of Kaufman et al. for the order of discovery of hydrocarbon pools and the distribution of their sizes in a geologically homogeneous area. Using the model, a Bayesian method is developed for estimating the distribution of the size of the undiscovered pools using the information from the discovery record. This method avoids most of the arbitrary choices required by the modified maximum likelihood method developed by Lee and Wang. As an example, this method is applied to the same Bashaw reef data on which Lee and Wang demonstrated their approach. For this case, the Bayesian approach produces sharly lower estimates of undiscovered resources. 相似文献
8.
Allan D. Woodbury 《Mathematical Geology》1989,21(3):285-308
Bayesian updating methods provide an alternate philosophy to the characterization of the input variables of a stochastic mathematical model. Here, a priori values of statistical parameters are assumed on subjective grounds or by analysis of a data base from a geologically similar area. As measurements become available during site investigations, updated estimates of parameters characterizing spatial variability are generated. However, in solving the traditional updating equations, an updated covariance matrix may be generated that is not positive-definite, particularly when observed data errors are small. In addition, measurements may indicate that initial estimates of the statistical parameters are poor. The traditional procedure does not have a facility to revise the parameter estimates before the update is carried out. alternatively, Bayesian updating can be viewed as a linear inverse problem that minimizes a weighted combination of solution simplicity and data misfit. Depending on the weight given to the a priori information, a different solution is generated. A Bayesian updating procedure for log-conductivity interpolation that uses a singular value decomposition (SVD) is presented. An efficient and stable algorithm is outlined that computes the updated log-conductivity field and the a posteriori covariance of the estimated values (estimation errors). In addition, an information density matrix is constructed that indicates how well predicted data match observations. Analysis of this matrix indicates the relative importance of the observed data. The SVD updating procedure is used to interpolate the log-conductivity fields of a series of hypothetical aquifers to demonstrate pitfalls and possibilities of the method. 相似文献
9.
Allan D. Woodbury 《Mathematical Geosciences》1989,21(3):285-308
Bayesian updating methods provide an alternate philosophy to the characterization of the input variables of a stochastic mathematical model. Here, a priori values of statistical parameters are assumed on subjective grounds or by analysis of a data base from a geologically similar area. As measurements become available during site investigations, updated estimates of parameters characterizing spatial variability are generated. However, in solving the traditional updating equations, an updated covariance matrix may be generated that is not positive-definite, particularly when observed data errors are small. In addition, measurements may indicate that initial estimates of the statistical parameters are poor. The traditional procedure does not have a facility to revise the parameter estimates before the update is carried out. alternatively, Bayesian updating can be viewed as a linear inverse problem that minimizes a weighted combination of solution simplicity and data misfit. Depending on the weight given to the a priori information, a different solution is generated. A Bayesian updating procedure for log-conductivity interpolation that uses a singular value decomposition (SVD) is presented. An efficient and stable algorithm is outlined that computes the updated log-conductivity field and the a posteriori covariance of the estimated values (estimation errors). In addition, an information density matrix is constructed that indicates how well predicted data match observations. Analysis of this matrix indicates the relative importance of the observed data. The SVD updating procedure is used to interpolate the log-conductivity fields of a series of hypothetical aquifers to demonstrate pitfalls and possibilities of the method. 相似文献
10.
Spatial data are often sparse by nature. However, in many instances, information may exist in the form of soft data, such as expert opinion. Scientists in the field often have a good understanding of the phenomenon under study and may be able to provide valuable information on its likely behavior. It is thus useful to have a sensible mechanism that incorporates expert opinion in inference. The Bayesian paradigm suffers from an inherent subjectivity that is unacceptable to many scientists. Aside from this philosophical problem, elicitation of prior distributions is a difficult task. Moreover, an intentionally misleading expert can have substantial influence on Bayesian inference. In our experience, eliciting data is much more natural to the experts than eliciting prior distributions on the parameters of a probability model that is a purely statistical construct. In this paper we elicit data, i.e., guess values for the realization of the process, from the experts. Utilizing a hierarchical modeling framework, we combine elicited data and actual observed data for inferential purposes. A distinguishing feature of this approach is that even an intentionally misleading expert proves to be useful. Theoretical results and simulations illustrate that incorporating expert opinion via elicited data substantially improves the estimation, prediction, and design aspects of statistical inference for spatial data. 相似文献
11.
Erik Rüttener Juan José Egozcue Dieter Mayer-Rosa Stephan Mueller 《Natural Hazards》1996,14(2-3):165-178
Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law. 相似文献
12.
《国际地质力学数值与分析法杂志》2018,42(15):1765-1784
In this paper a fully probabilistic approach based on the Bayesian statistical method is presented to predict ground settlements in both transverse and longitudinal directions during gradual excavation of a tunnel. To that end, the convergence confinement method is adopted to give estimates of ground deformation numerically. Together with in situ measurements of the evolution of vertical deflections at selected points along the tunnel line, it allows for the construction of a likelihood function and consequently in the framework of Bayesian inference to provide posterior improved knowledge of model parameters entering the numerical analysis. In this regard, the Bayesian updating is first exploited in the material identification step and next used to yield predictions of ground settlement in sections along the tunnel line ahead of the tunnel face. This methodology thus makes it possible to improve original designs by utilizing an increasing number of data (measurements) collected in the course of tunnel construction. 相似文献
13.
地基沉降修正系数的Bayes概率推断 总被引：2，自引：0，他引：2
通过分析常规方法在沉降修正系数的选取中具有的定值性和随意性,引入建立在过去信息和现在样本信息之上的Bayes理论,结合某客运专线红黏土路基工程,提出用后验分布得到修正系数的取值范围。实例研究表明,用以往经验综合样本信息,估计修正系数的先验概率在某一区间上服从均匀分布。由现场载荷试验实测沉降量与理论计算沉降量分析所得的修正系数,将现场量测的沉降变形信息与先验信息结合起来,利用Bayes统计理论,由小样本试验数据推算得到修正系数的后验概率服从正态分布。对后验分布所得参数进行区间估计,得到该区域红黏土地基沉降修正系数的取值优化区间为 [1.0, 1.7],分析了不同荷载作用条件下沉降修正系数的概率分布模型。 相似文献
14.
Analysis of human risks due to dam break floods—part 2: application to Tangjiashan landslide dam failure 总被引：1，自引：1，他引：0
The Tangjiashan landslide dam was formed during the Ms8.0 Wenchuan earthquake in 2008 and posed high risks to 1.2?million people downstream the dam. A human risk analysis model (HURAM) reported in the companion paper is applied to evaluate the human risk in the Tangjiashan landslide dam failure. The characteristics of this landslide dam are introduced first. The breaching parameters in two cases (i.e., the actual case and a high erodibility case) are predicted with a physically based model, and the flood routing processes in these two cases are simulated using numerical analysis. The population at risk downstream of the landslide dam is then obtained based on the results of the flood routing simulations. Subsequently, the human risks are analyzed with HURAM using Bayesian networks. Fourteen influence parameters and their interrelationships are considered in a systematic structure in the case study. A change in anyone of them may affect the other parameters and leads to loss of life. HURAM allows not only cause-to-result inference, but also result-to-cause inference by updating the Bayesian network with specific information from the study case. The uncertainties of the parameters and their relationships are studied both at the global level using multiple sources of information and at the local level by updating the prior probabilities. 相似文献
15.
Hystad Grethe Eleish Ahmed Hazen Robert M. Morrison Shaunna M. Downs Robert T. 《Mathematical Geosciences》2019,51(4):401-417
Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.
相似文献16.
Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties
such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task.
Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to
overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable
before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference
have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering.
In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of
them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most
common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal
densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational
cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of
the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally,
a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared
with the ones computed by the maximum likelihood estimation approach. 相似文献
17.
《地学前缘(英文版)》2021,12(5)
Rock mechanical parameters and their uncertainties are critical to rock stability analysis, engineering design, and safe construction in rock mechanics and engineering. The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass, but this does not consider the uncertainty. This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data, then integrating the monitored data, prior knowledge of geotechnical parameters,and a mechanical model of a rock tunnel using Markov chain Monte Carlo(MCMC) simulation. The proposed approach is illustrated by a circular tunnel with an analytical solution, which was then applied to an experimental tunnel in Goupitan Hydropower Station, China. The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables. The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements. It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically. Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data. Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering. 相似文献
18.
A Bayesian procedure for Probabilistic Tsunami Hazard Assessment 总被引：1，自引：1，他引：0
In this paper, a Bayesian procedure is implemented for the Probability Tsunami Hazard Assessment (PTHA). The approach is general
and modular incorporating all significant information relevant for the hazard assessment, such as theoretical and empirical
background, analytical or numerical models, instrumental and historical data. The procedure provides the posterior probability distribution that integrates the prior probability distribution based on the physical knowledge of the process
and the likelihood based on the historical data. Also, the method deals with aleatory and epistemic uncertainties incorporating
in a formal way all sources of relevant uncertainty, from the tsunami generation process to the wave propagation and impact
on the coasts. The modular structure of the procedure is flexible and easy to modify and/or update as long as new models and/or
information are available. Finally, the procedure is applied to an hypothetical region, Neverland, to clarify the PTHA evaluation in a realistic case. 相似文献
19.
We present a new Bayesian framework for the validation of models for subsurface flows. We use a compositional model to simulate CO2 storage in saline aquifers, comparing simulated saturations to observed saturations, together with a Bayesian analysis, to refine the permeability field. At the laboratory scale, we consider a core that is initially fully saturated with brine in a drainage experiment performed at aquifer conditions. Two types of data are incorporated in the framework: the porosity field in the entire core and CO2 saturation values at equally spaced core slices for several values of time. These parameters are directly measured with a computed tomography scanner. We then find permeability fields that (1) are consistent with the measured parameters and, at the same time, (2) allow one to predict future fluid flow. We combine high performance computing, Bayesian inference, and a Markov chain Monte Carlo (McMC) method for characterizing the posterior distribution of the permeability field conditioned on the available dynamic measurements (saturation values at slices). We assess the quality of our characterization procedure by Monte Carlo predictive simulations, using permeability fields sampled from the posterior distribution. In our characterization step, we solve a compositional two-phase flow model for each permeability proposal and compare the solution of the model with the measured data. To establish the feasibility of the proposed framework, we present computational experiments involving a synthetic permeability field known in detail. The experiments show that the framework captures almost all the information about the heterogeneity of the permeability field of the core. We then apply the framework to real cores, using data measured in the laboratory. 相似文献
20.
《地学前缘(英文版)》2018,9(6):1665-1677
Determining soilewater characteristic curve(SWCC) at a site is an essential step for implementing unsaturated soil mechanics in geotechnical engineering practice, which can be measured directly through various in-situ and/or laboratory tests. Such direct measurements are, however, costly and timeconsuming due to high standards for equipment and procedural control and limits in testing apparatus. As a result, only a limited number of data points(e.g., volumetric water content vs. matric suction)on SWCC at some values of matric suction are obtained in practice. How to use a limited number of data points to estimate the site-specific SWCC and to quantify the uncertainty(or degrees-of-belief) in the estimated SWCC remains a challenging task. This paper proposes a Bayesian approach to determine a site-specific SWCC based on a limited number of test data and prior knowledge(e.g., engineering experience and judgment). The proposed Bayesian approach quantifies the degrees-of-belief on the estimated SWCC according to site-specific test data and prior knowledge, and simultaneously selects a suitable SWCC model from a number of candidates based on the probability logic. To address computational issues involved in Bayesian analyses, Markov Chain Monte Carlo Simulation(MCMCS), specifically Metropolis-Hastings(M-H) algorithm, is used to solve the posterior distribution of SWCC model parameters, and Gaussian copula is applied to evaluating model evidence based on MCMCS samples for selecting the most probable SWCC model from a pool of candidates. This removes one key limitation of the M-H algorithm, making it feasible in Bayesian model selection problems. The proposed approach is illustrated using real data in Unsaturated Soil Database(UNSODA) developed by U.S. Department of Agriculture. It is shown that the proposed approach properly estimates the SWCC based on a limited number of site-specific test data and prior knowledge, and reflects the degrees-of-belief on the estimated SWCC in a rational and quantitative manner. 相似文献