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1.
In previous work, we presented a method for estimation and correction of non-linear mathematical model structures, within a Bayesian framework, by merging uncertain knowledge about process physics with uncertain and incomplete observations of dynamical input-state-output behavior. The resulting uncertainty in the model input-state-output mapping is expressed as a weighted combination of an uncertain conceptual model prior and a data-derived probability density function, with weights depending on the conditional data density. Our algorithm is based on the use of iterative data assimilation to update a conceptual model prior using observed system data, and thereby construct a posterior estimate of the model structure (the mathematical form of the equation itself, not just its parameters) that is consistent with both physically based prior knowledge and with the information in the data. An important aspect of the approach is that it facilitates a clear differentiation between the influences of different types of uncertainties (initial condition, input, and mapping structure) on the model prediction. Further, if some prior assumptions regarding the structural (mathematical) forms of the model equations exist, the procedure can help reveal errors in those forms and how they should be corrected. This paper examines the properties of the approach by investigating two case studies in considerable detail. The results show how, and to what degree, the structure of a dynamical hydrological model can be estimated without little or no prior knowledge (or under conditions of incorrect prior information) regarding the functional forms of the storage–streamflow and storage–evapotranspiration relationships. The importance and implications of careful specification of the model prior are illustrated and discussed.  相似文献   

2.
We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first-order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis–Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first-order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible.  相似文献   

3.
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   

4.
Reinforced concrete frame structures built prior to the mid‐1970s are susceptible to brittle column failure under seismic action, potentially leading to progressive collapse of the structure. The behavior of columns susceptible to brittle shear‐axial failure has been studied previously but rarely has the interaction between damaged columns and the surrounding three‐dimensional structure been investigated experimentally and at full scale. In this study, as the second in a series of hybrid simulations, two full‐scale reinforced concrete columns of a representative pre‐1970s structure were tested at the Multi‐axial Full‐scale Substructure Testing and Simulation (MUST‐SIM) laboratory. Through the use of hybrid simulation, the interaction of the columns with the surrounding structure is studied under a severe seismic motion including vertical excitation. The computational model representing the remainder of the representative 10‐story structure is created in the computer program OpenSees. During the hybrid simulation, both physical specimens experience significant loss of shear and axial strength, and the effects of these failures on the surrounding system are described. The three‐dimensional computational model in OpenSees allowed for analytical flexural‐axial failure of a third column in the structure to occur. The effects of these multiple failures on the response of a full structural system under seismic action are quantified, and the progressive collapse resistance mechanisms are discussed. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
A method for using remotely sensed snow cover information in updating a hydrological model is developed, based on Bayes' theorem. A snow cover mass balance model structure adapted to such use of satellite data is specified, using a parametric snow depletion curve in each spatial unit to describe the subunit variability in snow storage. The snow depletion curve relates the accumulated melt depth to snow‐covered area, accumulated snowmelt runoff volume, and remaining snow water equivalent. The parametric formulation enables updating of the complete snow depletion curve, including mass balance, by satellite data on snow coverage. Each spatial unit (i.e. grid cell) in the model maintains a specific depletion curve state that is updated independently. The uncertainty associated with the variables involved is formulated in terms of a joint distribution, from which the joint expectancy (mean value) represents the model state. The Bayesian updating modifies the prior (pre‐update) joint distribution into a posterior, and the posterior joint expectancy replaces the prior as the current model state. Three updating experiments are run in a 2400 km2 mountainous region in Jotunheimen, central Norway (61°N, 9°E) using two Landsat 7 ETM+ images separately and together. At 1 km grid scale in this alpine terrain, three parameters are needed in the snow depletion curve. Despite the small amount of measured information compared with the dimensionality of the updated parameter vector, updating reduces uncertainty substantially for some state variables and parameters. Parameter adjustments resulting from using each image separately differ, but are positively correlated. For all variables, uncertainty reduction is larger with two images used in conjunction than with any single image. Where the observation is in strong conflict with the prior estimate, increased uncertainty may occur, indicating that prior uncertainty may have been underestimated. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

6.
Four widely used structural system identification methods are presented. Based on Bayesian estimation theory, two new formulae and their derivations are shown. Time domain responses of two frames when subjected to the ground motion of the El Centro earthquake are computed then transformed to the frequency domain. Frequencies and mode shapes of frames are extracted from Fourier spectra. Using these frequencies and mode shapes, a parametric study is conducted, and the system identification methods are compared and discussed. The importance of a prior analytical model on the rate of convergence of the revised parameters is investigated. Recommendations are given regarding the feasibility of each method for more accurate estimation. A model suitable for parameter identification of three-dimensional frames is presented. This model, with different identification methods, is used to estimate the parameters of a two-storey frame.  相似文献   

7.
The seismic reflection method provides high-resolution data that are especially useful for discovering mineral deposits under deep cover. A hindrance to the wider adoption of the seismic reflection method in mineral exploration is that the data are often interpreted differently and independently of other geophysical data unless common earth models are used to link the methods during geological interpretation. Model-based inversion of post-stack seismic data allows rock units with common petrophysical properties to be identified and permits increased bandwidth to enhance the spatial resolution of the acoustic-impedance model. However, as seismic reflection data are naturally bandlimited, any inversion scheme depends upon an initial model, and must deal with non-unique solutions for the inversion. Both issues can be largely overcome by using constraints and integrating prior information. We exploit the abilities of fuzzy c-means clustering to constrain and to include prior information in the inversion. The use of a clustering constraint for petrophysical values pushes the inversion process to select models that are primarily composed of several discrete rock units and the fuzzy c-means algorithm allows some properties to overlap by varying degrees. Imposing the fuzzy clustering techniques in the inversion process allows solutions that are similar to the natural geologic patterns that often have a few rock units represented by distinct combinations of petrophysical characteristics. Our tests on synthetic models, with clear and distinct boundaries, show that our methodology effectively recovers the true model. Accurate model recovery can be obtained even when the data are highly contaminated by random noise, where the initial model is homogeneous, or there is minimal prior petrophysical information available. We demonstrate the abilities of fuzzy c-means clustering to constrain and to include prior information in the acoustic-impedance inversion of a challenging magnetotelluric/seismic data set from the Carlin Gold District, USA. Using fuzzy c-means guided inversion of magnetotelluric data to create a starting model for acoustic-impedance proved important in obtaining the best result. Our inversion results correlate with borehole data and provided a better basis for geological interpretation than the seismic reflection images alone. Low values of the acoustic impedance in the basement rocks were shown to be prospective by geochemical analysis of rock cores, as would be predicted for later gold mineralization in weak, decalcified rocks.  相似文献   

8.
Acoustic emissions prior to rupture indicate precursory damage. Laboratory studies of frictional sliding on model faults feature accelerating rates of acoustic emissions prior to rupture. Precursory seismic emissions are not generally observed prior to earthquakes. To address the problem of precursory damage, we consider failure in a fiber-bundle model. We observe a clearly defined nucleation phase followed by a catastrophic rupture. The fibers are hypothesized to represent asperities on a fault. Two limiting behaviors are the equal load sharing p = 0 (stress from a failed fiber is transferred equally to all surviving fibers) and the local load sharing p = 1 (stress from a failed fiber is transferred to adjacent fibers). We show that precursory damage in the nucleation phase is greatly reduced in the local-load sharing limit. The local transfer of stress from an asperity concentrates nucleation, restricting precursory acoustic emissions (seismic activity).  相似文献   

9.
In this paper we propose a methodology to include prior information in the estimation of effective soil parameters for modelling the soil moisture content in the unsaturated zone. Laboratory measurements on undisturbed soil cores were used to estimate the moisture retention curve and hydraulic conductivity curve parameters. The soil moisture content was measured at 25 locations along three transects and at three different depths (surface, 30 and 60 cm) on an 80×20 m hillslope for the year 2001. Soil cores were collected in 84 locations situated in three profile pits along the hillslope. For the estimation of the effective soil hydraulic parameters the joint probability distribution of measured parameter values was used as prior information. A two-horizon single column 1D MIKE SHE model based on Richards' equation was set-up for nine soil moisture measurement locations along the middle transect of the hillslope. The goal of the model is to simulate the soil moisture profile at each location. The shuffled complex evolution (SCE) algorithm has been applied to estimate effective model parameters using either wide parameter ranges, referred to as the ‘no-prior’ case, or the joint probability distribution of measured parameter values as prior information (‘prior’ case). When the prior information is incorporated in the SCE optimisation the goodness-of-fit of the model predictions is only slightly worse compared to when no-prior information is incorporated. However, the effective parameter estimates are more realistic when the prior information is incorporated. For both the no-prior and prior case the generalised likelihood uncertainty estimation procedure (GLUE) was subsequently used to estimate the uncertainty bounds (UB) on the model predictions. When incorporating the prior information more parameter sets were accepted for the estimation of the predictive uncertainty and the parameter values were more realistic. Moreover, UB better enclosed the observations. Thus, incorporating prior information in GLUE reduces the amount of model evaluations needed to obtain sufficient behavioural parameter sets. The results indicate the importance of prior information in the SCE and GLUE parameter estimation strategies.  相似文献   

10.
The multi-Gaussian model is used in geostatistical applications to predict functions of a regionalized variable and to assess uncertainty by determining local (conditional to neighboring data) distributions. The model relies on the assumption that the regionalized variable can be represented by a transform of a Gaussian random field with a known mean value, which is often a strong requirement. This article presents two variations of the model to account for an uncertain mean value. In the first one, the mean of the Gaussian random field is regarded as an unknown non-random parameter. In the second model, the mean of the Gaussian field is regarded as a random variable with a very large prior variance. The properties of the proposed models are compared in the context of non-linear spatial prediction and uncertainty assessment problems. Algorithms for the conditional simulation of Gaussian random fields with an uncertain mean are also examined, and problems associated with the selection of data in a moving neighborhood are discussed.  相似文献   

11.
大地电磁测深(MT)的观测数据易受到由近地表小尺度非均匀体或地形起伏引起的电流型畸变干扰,消除或压制这种干扰对获取可靠的深部电性结构至关重要.当区域结构为二维时,电流型畸变可采用张量分解等方法予以消除或压制.当区域结构为三维时,畸变问题更加复杂和严重,传统张量分解方法往往效果不佳或无效,严重地制约了MT三维反演技术的实用性.对此,本文提出一种考虑电流型畸变的MT三维反演算法,将完整的电流型畸变参数引入到目标函数,并采用非线性共轭梯度法与电阻率参数同时反演,从而达到压制畸变的目的.该算法有两个关键点:一是通过分析实测数据所遭受畸变的分布特征,在目标函数中对其进行有效约束;二是在迭代过程中,通过自适应地调整双正则化因子保障算法的稳定和效率.理论模型测试结果显示,常规三维反演算法不能合理解释数据中的畸变成分,而只能通过引入虚假异常体强制地拟合受畸变数据,从而造成电阻率模型严重失真.与之相比,本文算法能够在反演中自动求解各测点所受到的畸变,获得更接近真实的电阻率模型.  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.
Abstract

A modelling scheme is developed for real-time flood forecasting. It is composed of (a) a rainfall forecasting model, (b) a conceptual rainfall-runoff model, and (c) a stochastic error model of the ARMA family for forecast error correction. Initialization of the rainfall-runoff model is based on running this model on a daily basis for a certain period prior to the flood onset while parameters of the error model are updated through the Recursive Least Squares algorithm. The scheme is suitable for the early stages of operation of flood forecasting systems in the presence of inadequate historical data. A validation framework is set up which simulates real-time flood forecasting conditions. Thus, the effects of the procedures for rainfall-runoff model initialization, forecast error correction and rainfall forecasting are assessed. Two well-known conceptual rainfall-runoff models (the Soil Moisture Accounting model of the US National Weather Service River Forecast Service—SMA-NWSRFS and TANK) together with data from a Greek basin are used for illustration purposes.  相似文献   

14.
Univariate and bivariate Gamma distributions are among the most widely used distributions in hydrological statistical modeling and applications. This article presents the construction of a new bivariate Gamma distribution which is generated from the functional scale parameter. The utilization of the proposed bivariate Gamma distribution for drought modeling is described by deriving the exact distribution of the inter-arrival time and the proportion of drought along with their moments, assuming that both the lengths of drought duration (X) and non-drought duration (Y) follow this bivariate Gamma distribution. The model parameters of this distribution are estimated by maximum likelihood method and an objective Bayesian analysis using Jeffreys prior and Markov Chain Monte Carlo method. These methods are applied to a real drought dataset from the State of Colorado, USA.  相似文献   

15.
A key point in the application of multi‐model Bayesian averaging techniques to assess the predictive uncertainty in groundwater modelling applications is the definition of prior model probabilities, which reflect the prior perception about the plausibility of alternative models. In this work the influence of prior knowledge and prior model probabilities on posterior model probabilities, multi‐model predictions, and conceptual model uncertainty estimations is analysed. The sensitivity to prior model probabilities is assessed using an extensive numerical analysis in which the prior probability space of a set of plausible conceptualizations is discretized to obtain a large ensemble of possible combinations of prior model probabilities. Additionally, the value of prior knowledge about alternative models in reducing conceptual model uncertainty is assessed by considering three example knowledge states, expressed as quantitative relations among the alternative models. A constrained maximum entropy approach is used to find the set of prior model probabilities that correspond to the different prior knowledge states. For illustrative purposes, a three‐dimensional hypothetical setup approximated by seven alternative conceptual models is employed. Results show that posterior model probabilities, leading moments of the predictive distributions and estimations of conceptual model uncertainty are very sensitive to prior model probabilities, indicating the relevance of selecting proper prior probabilities. Additionally, including proper prior knowledge improves the predictive performance of the multi‐model approach, expressed by reductions of the multi‐model prediction variances by up to 60% compared with a non‐informative case. However, the ratio between‐model to total variance does not substantially decrease. This suggests that the contribution of conceptual model uncertainty to the total variance cannot be further reduced based only on prior knowledge about the plausibility of alternative models. These results advocate including proper prior knowledge about alternative conceptualizations in combination with extra conditioning data to further reduce conceptual model uncertainty in groundwater modelling predictions. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

16.
The need for simplifi ed physical models representing frequency dependent soil impedances has been the motivation behind many researches throughout history. Generally, such models are generated to capture impedance functions in a wide range of excitation frequencies, which leads to relatively complex models. That is while there is just a limited range of frequencies that really in? uence the response of the structure. Here, a new methodology based on the response-matching concept is proposed, which can lead to the development of simpler discrete models. The idea is then used to upgrade an existing simple model of surface foundations to the case of embedded foundations. The applicability of the model in both frequency domain and time domain analyses of soil-structure systems with embedded foundations is discussed. Moreover, the accuracy of the results is compared with another existing discrete model for embedded foundations.  相似文献   

17.
Seismic Rock physics plays a bridge role between the rock moduli and physical properties of the hydrocarbon reservoirs. Prestack seismic inversion is an important method for the quantitative characterization of elasticity, physical properties, lithology and fluid properties of subsurface reservoirs. In this paper, a high order approximation of rock physics model for clastic rocks is established and one seismic AVO reflection equation characterized by the high order approximation(Jacobian and Hessian matrix) of rock moduli is derived. Besides, the contribution of porosity, shale content and fluid saturation to AVO reflectivity is analyzed. The feasibility of the proposed AVO equation is discussed in the direct estimation of rock physical properties. On the basis of this, one probabilistic AVO inversion based on differential evolution-Markov chain Monte Carlo stochastic model is proposed on the premise that the model parameters obey Gaussian mixture probability prior model. The stochastic model has both the global optimization characteristics of the differential evolution algorithm and the uncertainty analysis ability of Markov chain Monte Carlo model. Through the cross parallel of multiple Markov chains, multiple stochastic solutions of the model parameters can be obtained simultaneously, and the posterior probability density distribution of the model parameters can be simulated effectively. The posterior mean is treated as the optimal solution of the model to be inverted.Besides, the variance and confidence interval are utilized to evaluate the uncertainties of the estimated results, so as to realize the simultaneous estimation of reservoir elasticity, physical properties, discrete lithofacies and dry rock skeleton. The validity of the proposed approach is verified by theoretical tests and one real application case in eastern China.  相似文献   

18.
An oil droplet size model was developed for a variety of turbulent conditions based on non-dimensional analysis of disruptive and restorative forces, which is applicable to oil droplet formation under both surface breaking-wave and subsurface-blowout conditions, with or without dispersant application. This new model was calibrated and successfully validated with droplet size data obtained from controlled laboratory studies of dispersant-treated and non-treated oil in subsea dispersant tank tests and field surveys, including the Deep Spill experimental release and the Deepwater Horizon blowout oil spill. This model is an advancement over prior models, as it explicitly addresses the effects of the dispersed phase viscosity, resulting from dispersant application and constrains the maximum stable droplet size based on Rayleigh-Taylor instability that is invoked for a release from a large aperture.  相似文献   

19.
The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. & Cooley, R.L., Water Resources Research, 1987, 23(7), 1237–1250] was used to calculate nonlinear Scheffé-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km2 of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.  相似文献   

20.
Better parameterization of a hydrological model can lead to improved streamflow prediction. This is particularly important for seasonal streamflow forecasting with the use of hydrological modelling. Considering the possible effects of hydrologic non‐stationarity, this paper examined ten parameterization schemes at 12 catchments located in three different climatic zones in east Australia. These schemes are grouped into four categories according to the period when the data are used for model calibration, i.e. calibration using data: (1) from a fixed period in the historical records; (2) from different lengths of historical records prior to prediction year; (3) from different climatic analogue years in the past; and (4) data from the individual months. Parameterization schemes were evaluated according to model efficiency in both the calibration and verification period. The results show that the calibration skill changes with the different historic periods when data are used at all catchments. Comparison of model performance between the calibration schemes indicates that it is worth calibrating the model with the use of data from each individual month for the purpose of seasonal streamflow forecasting. For the catchments in the winter‐dominant rainfall region of south‐east Australia, a more significant shift in rainfall‐runoff relationships at different periods was found. For those catchments, model calibration with the use of 20 years of data prior to the prediction year leads to a more consistent performance. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

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