Search

Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction. Nonetheless, under these methods, the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area. This assumption, known as spatial stationarity, is very questionable in real-world situations due to the influence of contextual factors. Therefore, allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable. However, existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself. Moreover, under these techniques, local machine learning models are effectively built using only fewer observations, which can lead to well-known issues such as over-fitting and the curse of dimensionality. This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered. The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset. The proposed method's effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data. In the synthetic (resp. real) case study, the proposed method's predictive accuracy, as indicated by the Root Mean Square Error (RMSE) on the test set, is 17% (resp. 7%) better than that of popular machine learning methods dealing with the response variable's spatial auto-correlation. Additionally, this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space, and it can even be used to investigate the local significance of predictor variables. [ABSTRACT FROM AUTHOR]

We introduce two algorithms for generating from the bimodal generalized von Mises-Fisher distribution on the sphere. This generalization of the von Mises-Fisher distribution is more flexible, in particular by allowing for multimodality, and it preserves many of the theoretical properties of the von Mises-Fisher. The first proposed generation algorithm is obtained from conditional simulation and acceptance-rejection. The second one is the Metropolis-Hastings with mixture of von Mises-Fisher as jumping or instrumental distribution. These two algorithms are compared through density estimations of generated polar angles. [ABSTRACT FROM AUTHOR]

Markov chain geostatistics is a methodology for simulating categorical fields. Its fundamental model for conditional simulation is the Markov chain random field (MCRF) model, with the transiogram serving as its basic spatial correlation measure. There are different methods to obtain transiogram models for MCRF simulation based on sample data and expert knowledge: linear interpolation, mathematical model joint-fitting, and a mixed approach combining both. This study aims to explore the sensitivity of the MCRF model to different transiogram jointing modeling methods. Two case studies were conducted to examine how simulated results, including optimal prediction maps and simulated realization maps, vary with different sets of transiogram models. The results indicate that all three transiogram joint modeling methods are applicable, and the MCRF model exhibits a general insensitivity to transiogram models produced by different methods, particularly when sample data are sufficient to generate reliable experimental transiograms. The variations in overall simulation accuracies based on different sets of transiogram models are not significant. However, notable improvements in simulation accuracy for minor classes were observed when theoretical transiogram models (generated by mathematical model fitting with expert knowledge) were utilized. This study suggests that methods for deriving transiogram models from experimental transiograms perform well in conditional simulations of categorical soil variables when meaningful experimental transiograms can be estimated. Employing mathematical models for transiogram modeling of minor classes provides a way to incorporate expert knowledge and improve the simulation accuracy of minor classes. [ABSTRACT FROM AUTHOR]

Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction. Nonetheless, under these methods, the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area. This assumption, known as spatial stationarity, is very questionable in real-world situations due to the influence of contextual factors. Therefore, allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable. However, existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself. Moreover, under these techniques, local machine learning models are effectively built using only fewer observations, which can lead to well-known issues such as over-fitting and the curse of dimensionality. This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered. The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset. The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data. In the synthetic (resp. real) case study, the proposed method’s predictive accuracy, as indicated by the Root Mean Square Error (RMSE) on the test set, is 17% (resp. 7%) better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation. Additionally, this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space, and it can even be used to investigate the local significance of predictor variables.

For regional hazard analysis or engineering applications, it is necessary to simulate a group of correlated ground motions containing information from given recordings. A new method is presented to conditionally generate ground motions at unobserved points using actual recordings in this localized region. This method is based on an extension of the traditional conditional simulation using a wavelet packet. Utilizing the advantages of wavelet-packet transformation, the time and frequency characteristics of ground motions are effectively identified. Besides by decomposing the signal into non-overlapping sub-frequency bands, it is possible to conditionally simulating stationary, space-time, and Gaussian random fields. These simulated motions are consistent with the actual recordings in terms of temporal variations in the frequency domain and its design spectrum, and their coherence functions satisfy the target coherence values. Two numerical examples have been provided to illustrate the capability of the proposed method: the simulation of ensembles of earthquake accelerograms using actual recordings and blind tests in SMART-1 array. [ABSTRACT FROM AUTHOR]

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

Increased availability and quality of surface and subsurface observations provide the chance to improve the perception of hydrological phenomena. An important factor that hinders our understanding of hydrological structures is the characterization of heterogeneous patterns with continuous attributes inside the structures (e.g., porosity, permeability, fluid saturation, etc.). Unlike categorical attributes, continuous attributes convey more realistic characteristics but require more computational resources to characterize such complex earth systems. In this work, we propose a novel deep learning approach for the characterization of complex hydrological realism with continuous attributes based on generative adversarial networks (GANs) and self‐attention mechanism, named SA‐RelayGANs. To address the complexity of heterogeneous hydrological structures, we divide the modeling process into two stages: facies construction stage and property reconstruction stage. In the first stage, we employ an improved GAN with self‐attention mechanism to construct the heterogeneous structures while adhering to hard conditioning constraints. In the second stage, we utilize another GAN with an attribute enhancement term to reconstruct realizations based on the constructed structures and observations. SA‐RelayGANs can successfully predict the statistical distributions of heterogeneous structures with continuous attributes by using limited observations. This study highlights the effectiveness of using GANs to characterize the heterogeneous patterns of hydrological realism and the application over large geoscience fields. Key Points: A novel deep learning approach is proposed for the characterization of complex hydrological structures with continuous attributesThe two relaying generative adversarial networks (GANs) are dedicated to facies construction and property reconstruction respectivelySA‐RelayGANs makes it possible to accurate characterize the subsurface realism from sparse observations [ABSTRACT FROM AUTHOR]

Reservoir characterization is one of the main engineering components to ensure the optimum exploration and development of oil and gas. Deep-learning-based approaches are effective and widely used in reservoir modeling in recent years. In this work, a novel reservoir characterization method based on variational auto-encoder and selective attention mechanism (SA-VAE) is proposed. We construct a new network architecture and improved loss functions to achieve conditional reservoir modeling. To improve the ability of extracting connectivity characteristics of variational auto-encoder, the selective attention mechanism is also applied in the proposed SA-VAE model. Besides, to accurate describe the spatial characteristics of connected structures, an innovative strategy by reconstructing the whole structures step by step according to the corresponding structure connectivity is used in SA-VAE. We validate the performance of SA-VAE by using both 2D and 3D datasets with different reservoir structures. The experimental results indicate that our method can reproduce geological structures accurately under the constraints of conditioning data both in morphology and geostatistics. These prove that SA-VAE is able to characterize heterogeneous reservoir structures effectively. [ABSTRACT FROM AUTHOR]

A new method is presented that simulates nonstationary multipoint earthquake accelerograms at local field points, when the observed ground motions are specified at several locations. This process effectively avoids the stochastic decomposition of the spectral matrix. In addition, it does not use the target spectrum and spatial coherence function to define the information of each point. First, the observed ground motions are reconstructed using an autoregressive model. Second, a new cross-regressive model is proposed based on the formulation of the auto-regressive model. The cross-regressive model can reconstruct different observed ground motions by using recordings from any nearby area. To consider the nonstationary characteristics and spatial coherence, the ground motions of unobserved points between two observed points can be generated using an interpolation algorithm. This new method simulates the ground motions of target points in the Chiba array using partially observed earthquake accelerograms. The simulated earthquake accelerograms satisfy the nonstationary characteristics and spatial coherence of the Chiba array. This study is promising for engineering applications and hazard analyses. [ABSTRACT FROM AUTHOR]

The only source of revenue for mining is the sale of its reserves. Therefore, a particular quantity of reserves and a specific selling price will generate a certain income. However, these income determinants are very unpredictable. Theoretically, real options (RO) substitute the discounted cash flow (DCF) approach to account for this uncertainty. Generally, RO quantify the uncertainty particularly related to price volatility. However, owing to its mathematical intricacy and application, the utility of RO is minimal. In addition, historical data analysis cannot be applied for spatial uncertainty related to grade uncertainty. Conventional RO approaches, such as the Black–Scholes method and lattice valuation technique, cannot measure a project with multiple uncertainties. In addition, these methods are mathematically complex and not sufficiently flexible for practical adaptation. This study proposes originality on simulation technique called stratified state aggregation (SSA) development that combined price and grade uncertainties in estimating the value of mining projects. For case study, a tin mining project of PT Timah Tbk in Indonesia was undertaken, specifically for short-term mine planning in underwater mining operations at two mining locations. We utilized the historical data natural logarithmic analysis to determine price uncertainty and conditional simulation to evaluate grade uncertainty. Our results indicated that mining uncertainties might be modeled using RO and value-added through SSA can be used to assess multi-uncertainty and multi-stage mining (rainbow option). The SSA decision aligned with the DCF method with improvement in uncertainty assessment. In addition, incorporating management flexibility may aid in alleviating concerns regarding the continuation or termination of a project. [ABSTRACT FROM AUTHOR]

Training images are important input parameters for multipoint geostatistical modeling, and training images that can portray 3D spatial correlations are required to construct 3D models. The 3D training images are usually obtained by unconditional simulation using algorithms such as object-based algorithms, and in some cases, it is difficult to obtain the 3D training images directly, so a series of modeling methods based on 2D training images for constructing 3D models has been formed. In this paper, a new modeling method is proposed by synthesizing the advantages of the previous methods. Taking the fluvial reservoir modeling of the P oilfield in the Bohai area as an example, a comparative study based on 2D and 3D training images was carried out. By comparing the variance function, horizontal and vertical connectivity in x-, y-, and z-directions, and style similarity, the study shows that based on several mutually perpendicular 2D training images, the modeling method proposed in this paper can achieve an effect similar to that based on 3D training images directly. In the case that it is difficult to obtain 3D training images, the modeling method proposed in this paper has suitable application prospects. [ABSTRACT FROM AUTHOR]

Understanding the dependence relationship of credit spreads of corporate bonds is important for risk management. Vine copula models with tail dependence are used to analyze a credit spread dataset of Chinese corporate bonds, understand the dependence among different sectors, and perform conditional inferences. It is shown how the effect of tail dependence affects risk transfer, or the conditional distributions given one variable is extreme. Vine copula models also provide more accurate cross prediction results compared with linear regressions. These conditional inference techniques are a statistical contribution for analysis of bond credit spreads of investment portfolios consisting of corporate bonds from various sectors. [ABSTRACT FROM AUTHOR]

Abstract Non-stationary spatially variable ground motions (SVGMs) are commonly modelled as multivariate oscillatory processes based on evolutionary power spectral density (EPSD) functions. The existing conditional simulation algorithms require the known EPSD functions. The EPSD functions are usually assumed to be identical for all locations, which is unreasonable for long-span bridges because variable soil conditions are practically observed at different bridge piers. This paper proposes a conditional simulation algorithm for non-stationary SVGMs in consideration of non-uniform site conditions. The spatial interpolation tool, termed inverse-distance-weighted (IDW) interpolation, is introduced to estimate the EPSD functions at sites without ground motion measurement. Subsequently, the covariance matrix of the random Fourier coefficients of the multivariate oscillatory processes can be calculated. The Kriging estimation is adopted to obtain the unknown random Fourier coefficients, from which the time histories of the non-stationary SVGMs can be conditionally simulated. The proposed conditional simulation algorithm is first validated through a numerical example, in which the EPSD functions of non-uniform sites are represented by a non-stationary Kanai-Tajimi spectrum with different soil parameters. Then, the algorithm is applied to the Jiuzhou Channel Bridge, a navigation channel bridge of the Hong Kong-Zhuhai-Macau Bridge (HZMB), with complex soil and water conditions. Based on the limited in-situ seismic measurement data, the site characteristics in the bridge area are analysed, and the ground motion time histories at all piers can be generated.

Evidence‐based studies in the environmental sciences frequently rely on the presence of spatially dense climatological data. However, such data are often available only at a fixed set of locations that may be regularly or irregularly arranged across a region. Spatial interpolation enables the approximation of variables of interest at locations between those sites. When conducting interpolation in collaboration with an end user or in interdisciplinary research, mutual knowledge exchange allows for greater insight on what is required of an interpolation method since each may have different pros and cons. We outline and discuss several key considerations one should make in an interpolation study, such as the purpose of the variable and the goals of the end user, including how the variable is used to inform decisions. This process is then illustrated via case study within a wildland fire weather context. For the province of Ontario, Canada, we contrast several methods for interpolating the Fire Weather Index (FWI), comparing them quantitatively via metrics and qualitatively using a proposed categorical gradients visualization scheme. Conditional simulations and a spatial ensemble are also investigated. This work is in collaboration with the Ontario Ministry of Natural Resources and Forestry. [ABSTRACT FROM AUTHOR]

Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution of the ocean environment and for wave–structure interaction, EVA provides a basis for full probabilistic design analysis. Alternatively, environmental contours provide an approximate approach to estimating structural integrity, without requiring structural knowledge. These contour methods also exploit statistical models, including EVA, but avoid the need for structural modelling by making what are believed to be conservative assumptions about the shape of the structural failure boundary in the environment space. These assumptions, however, may not always be appropriate, or may lead to unnecessary wasted resources from over design. We demonstrate a methodology for efficient fully probabilistic analysis of structural failure. From this, we estimate the joint conditional probability density of the environment (CDE), given the occurrence of an extreme structural response. We use CDE as a diagnostic to highlight the deficiencies of environmental contour methods for design; none of the IFORM environmental contours considered characterise CDE well for three example structures. • Methodology for full probabilistic analysis of fluid loading presented with linear kinematics. • Methodology incorporates conditional simulation of time series and importance sampling. • Conditional density of environment (CDE) given extreme loading estimated for simple structures. • Performance of different environmental contour methods in characterising CDE quantified. • Parametric form underlying IFORM-type methods shown to be important source of variability. [ABSTRACT FROM AUTHOR]

A variogram-based two-point geostatistical approach was applied to generate a geological model of a petroleum reservoir. The geology consists of a sandstone formation with uniformly inclined rock strata of equal dip angle structurally trapped by surrounding faults. Data exploration of electrical well logs using univariate/bivariate statistical tests and data transformation tools demonstrated the data to be statistically suitable for ordinary kriging and sequential Gaussian simulation. Three directions were defined as part of the variogram and the data were interpolated resulting in a 3D subsurface representation. Validation included performing a leave-one-out cross-validation for each well and statistical comparison of multiple realizations generated from a computed stochastic model. The results display a reliable geological model which indicate a direct causation of the continuity trends from the bedding attitude of the regional fault trap.

Computing an ensemble of random fields using conditional simulation is an ideal method for retrieving accurate estimates of a field conditioned on available data and for quantifying the uncertainty of these realizations. Methods for generating random realizations, however, are computationally demanding, especially when the estimates are conditioned on numerous observed data and for large domains. In this article, a new, approximate conditional simulation approach is applied that builds on circulant embedding (CE), a fast method for simulating stationary Gaussian processes. The standard CE is restricted to simulating stationary Gaussian processes (possibly anisotropic) on regularly spaced grids. In this work, we explore two possible algorithms, namely, local Kriging and approximate grid embedding, that extend CE for irregularly spaced data points. We establish the accuracy of these methods to be suitable for practical inference and the speedup in computation allows for generating conditional fields close to an interactive time frame. The methods are motivated by the U.S. Geological Survey's software ShakeMap, which provides near real-time maps of shaking intensity after the occurrence of a significant earthquake. An example for the 2019 event in Ridgecrest, California, is used to illustrate our method. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) models of orebodies and deposits can provide strong support for quantitative evaluation of mineral resources. However, 3D modeling of ore deposits based on limited mineral exploration data remains a challenge due to the non-stationarity of the spatial distribution of orebodies and the uncertainty of data and models. Stochastic methods based on multiple-point geostatistics (MPS) have shown promise in automatic 3D characterization of complex geological structures (e.g., minerals, rocks, facies). However, as an essential element of MPS methods, a credible training image is difficult to obtain in real 3D applications. The spatial distribution of orebodies is critically non-stationary because the formation and evolution of a deposit are complex and its shape and distribution are controlled by faults, surrounding rock and other structures. In this work, we propose a feature-enhanced MPS-based approach, namely FE-3DRCS, by combining the characteristics of geological exploration data distribution following a MPS method called 3DRCS. To reduce the influence of non-stationarity of orebodies, a spatial stationarity enhancement strategy is presented. Besides, the artifact elimination strategy of spatial features and the adaptive optimization strategy based on an iterative mechanism are integrated in our approach. By performing FE-3DRCS on the geological exploration data in the Luodang Cu deposit, southwestern China, a set of 3D deposit models and Cu grade models were built. A series of morphological comparisons and statistical analyses were followed to evaluate the spatial distribution characteristics of orebodies. The Cu reserve was also evaluated based on the built 3D grade models. The real application confirms that FE-3DRCS can be applied effectively in the fields of 3D characterization and quantitative evaluation of mineral resources. [ABSTRACT FROM AUTHOR]

One of the main issues in the application of statistical‐learning‐based methods to the characterization of hydrological phenomena is the complex parameterization of the high‐quality reconstruction. The difficulty of obtaining enough training data and generating multiple‐scale structures hinder the applications of deep‐learning‐based methods in hydrogeological modeling. Hydrogeological modeling problems can be regarded as stochastic processes, and we propose a novel hydrogeological modeling approach based on convolutional conditional neural processes (GM‐ConvCNPs), a meta‐learning approach for dealing with stochastic processes. In this work, GM‐ConvCNP is used to reconstruct the entire spatial structures of subsurface hydrological attributes and channels from a limited amount of conditioning data. To achieve 3‐D characterization of subsurface structures, 3‐D GM‐ConvCNP is proposed according to the spatial distribution characteristics of 3‐D conditioning data. Compared to other deep‐learning‐based methods, we use a small amount of training data and obtain positive model generalization capabilities. Four data sets of categorical and continuous hydrogeological structures are exploited in the experiments. Various validation tests including variograms, connectivity functions, and multi‐dimensional scaling (MDS) map are used to evaluate the quality of generated realizations. The proposed approach is able to significantly reduce training consumption and improve the performance of realizations compared to a set of different benchmark tests. The experiments confirm that the GM‐ConvCNP model can extract heterogeneous patterns by using meta‐learning from limited training data and reconstruct multiple‐scale hydrogeological structures. A case study demonstrates that our method can be applied to characterize multiple‐source hydrological variables. Plain Language Summary: Characterization of realistic subsurface structures can provide a prior reference for understanding geosystem behavior in spatial scale. Hydrogeological modeling is a well‐established method of describing the structure of subsurface spaces. One of the main issues in the application of statistical‐learning‐based methods to the characterization of hydrological phenomena is the complex parameterization of the high‐quality reconstruction. Insufficient amount of training data has become a hindrance to the application of deep‐learning‐based hydrogeological modeling methods. In this work, we propose a novel method to reconstruct the entire spatial structures of subsurface hydrogeological attributes and channels from a limited amount of conditioning data, named geological modeling method with convolutional conditional neural process (GM‐ConvCNP). The proposed approach is able to significantly reduce training consumption and improve the performance of realizations compared to a set of different benchmark tests. Experimental results confirm that the GM‐ConvCNP model can extract heterogeneous patterns by using meta‐learning from limited training data and reconstruct multiple‐scale hydrogeological structures. We show that can be applied to characterize multiple‐source hydrological variables. Key Points: A meta‐learning‐based geological modeling method with convolutional conditional neural process is proposed to characterize various 2‐D and 3‐D hydrogeological structuresMultiple‐scale realizations can be obtained by using the same trained model with single‐scale training dataThe proposed method can reproduce realizations with both categorical facies and continuous variables [ABSTRACT FROM AUTHOR]

The stability of the retaining system under seismic conditions is an important aspect of safe design in earthquake-prone areas. In addition, this stability is highly dependent on soil uncertainty and failure mode contribution. On the other hand, imaging the borehole data directly into the analysis section and ignoring the known data by using unconditional simulation can lead to unrealistic results. Against this background, the current study presents a reliability analysis by incorporating geostatistical conditional simulations and a pseudostatic approach into the Finite-Element Method (FEM) MATLAB code to address the aforementioned issues. Then, the Sequential Compounding Method (SCM) is implemented to calculate the overall system reliability from a combination of the individual subsystem. Reliability analysis of a real case study reveals that compared with the Unconditional Random Finite-Element Method (URFEM), utilizing the Conditional Random Finite-Element Method (CRFEM) helps improve the mean value of the Factor of Safety (FS) against all failure modes by 7%–30%, while reducing the related standard deviation by 12%–43%. The results of system reliability show that bending moment and lateral displacement are the fundamental mechanisms in the static and seismic states. Moreover, implementing conditional simulation in seismic stability analysis offers a 16% and 43% reduction in the mean value and standard deviation of an unsafe distance from the excavation edge, accounting for less uncertainty in the slip surface location. Besides, according to the Coefficient of Variation (COV) of the failure modes, it is concluded that the FS against lateral displacement is chiefly affected by the soil heterogeneity compared with others, while shear force failure mode is less affected. Soldier piles are widely used in urban and industrial areas as a temporary or permanent retaining system for constructing underground structures. The stability of the retaining system under seismic conditions is an important aspect of safe design in earthquake-prone areas. In addition, the inherent variability of the soil properties dictates that stability problems are probabilistic rather than deterministic. In the current study, a real case with three boreholes of 22.5 m depth was considered and the soil parameters were estimated via field and laboratory tests. Then, the FS distribution and reliability indices of different failure modes were obtained for both static and seismic states by considering the seismic coefficient and efficient soil properties as stochastic parameters. These curves provided the essential data for structural design based on the target performance level. Next, the variation of the slip surface was determined, which could be used for determining the unsafe zone adjacent to the excavation. The responses of soldier piles indicated that by taking the seismic coefficient into account, the mean value of lateral displacement, maximum shear force, and maximum bending moment increased by 80%, 16%, and 37%, respectively. Moreover, considering different failure modes separately led to an overestimation of the reliability indices by three times. [ABSTRACT FROM AUTHOR]

This paper presents a framework for the conditional simulation of a 3D nonstationary wind field for super-long sea-crossing bridges based on wind speed time histories measured by limited anemometers on site. The variations of wind characteristics along the bridge deck with multi-elements are considered in this framework. The wind characteristics, including mean wind speeds, mean wind directions, turbulence intensities, turbulence integral scales, evolutionary wind spectra and spectral parameters, coherence functions and function parameters, at the measurement points are first obtained by analyzing the measured wind speed time histories. The wind characteristics are then extended over all the simulation points along the deck of the sea-crossing bridge using the spatial interpolation method and considering the variation of deck height above the sea level using the profiles of mean wind speeds, turbulence intensities and turbulence integral scales estimated from the measured wind speed time histories. After working out wind cross correlation functions, wind speed time histories at all simulation points over the sea-crossing bridge can be conditionally simulated. The proposed framework is finally applied to a real 22.9 km sea-crossing bridge under Typhoon Higos. The conditionally simulated wind speed time histories at all simulation points of the bridge are acceptable and consist a complete wind field which can be used for the buffeting analysis of the bridge. [ABSTRACT FROM AUTHOR]

Non-stationary spatially variable ground motions (SVGMs) are commonly modelled as multivariate oscillatory processes based on evolutionary power spectral density (EPSD) functions. The existing conditional simulation algorithms require the known EPSD functions. The EPSD functions are usually assumed to be identical for all locations, which is unreasonable for long-span bridges because variable soil conditions are practically observed at different bridge piers. This paper proposes a conditional simulation algorithm for non-stationary SVGMs in consideration of non-uniform site conditions. The spatial interpolation tool, termed inverse-distance-weighted (IDW) interpolation, is introduced to estimate the EPSD functions at sites without ground motion measurement. Subsequently, the covariance matrix of the random Fourier coefficients of the multivariate oscillatory processes can be calculated. The Kriging estimation is adopted to obtain the unknown random Fourier coefficients, from which the time histories of the non-stationary SVGMs can be conditionally simulated. The proposed conditional simulation algorithm is first validated through a numerical example, in which the EPSD functions of non-uniform sites are represented by a non-stationary Kanai-Tajimi spectrum with different soil parameters. Then, the algorithm is applied to the Jiuzhou Channel Bridge, a navigation channel bridge of the Hong Kong-Zhuhai-Macau Bridge (HZMB), with complex soil and water conditions. Based on the limited in-situ seismic measurement data, the site characteristics in the bridge area are analysed, and the ground motion time histories at all piers can be generated. [ABSTRACT FROM AUTHOR]

[Display omitted] • Predicted tunnel settlement can be characterized using log-normal distributions. • Geotechnical uncertainties result in large errors in tunnel settlement prediction. • Reducing measurement errors can effectively improve settlement prediction. • Conditional simulation notably enhances settlement prediction at tunnel junctions. Inherent soil variability, measurement error, statistical uncertainty, and transformation uncertainty constitute the four main sources of geotechnical uncertainties. This paper presents a systematic probabilistic analysis framework, through a case study, to assess the influence of geotechnical uncertainty on the existing shield tunnel settlement due to new tunneling underneath. Within this framework, various sources of geotechnical uncertainties are quantified using available Cone Penetration Test data (cone tip resistance) in the studied area, and three scenarios (i.e., pessimistic, neutral, and optimistic scenarios) are considered to incorporate different magnitudes of measurement errors. Through a random field-based 3D numerical simulation, the existing tunnel settlement by construction of a new tunnel is evaluated under the three scenarios. The errors in the settlement prediction are quantified using the monitored settlement data in a probabilistic manner with the assistance of Monte Carlo simulations. Two types of errors in predicting the existing tunnel settlement are identified (positive error, which occurs when the predicted settlements exceed the monitored settlement; and negative error, which occurs when the predicted settlements are smaller than the monitored settlement), and a conditional random field-based numerical simulation is performed. The results indicate that the conditional random field-based numerical simulation significantly reduces the positive error at the junction of the two tunnels, with the largest accuracy improvement of 48% for the pessimistic scenario. [ABSTRACT FROM AUTHOR]

Training images are important input parameters for multipoint geostatistical modeling, and training images that can portray 3D spatial correlations are required to construct 3D models. The 3D training images are usually obtained by unconditional simulation using algorithms such as object-based algorithms, and in some cases, it is difficult to obtain the 3D training images directly, so a series of modeling methods based on 2D training images for constructing 3D models has been formed. In this paper, a new modeling method is proposed by synthesizing the advantages of the previous methods. Taking the fluvial reservoir modeling of the P oilfield in the Bohai area as an example, a comparative study based on 2D and 3D training images was carried out. By comparing the variance function, horizontal and vertical connectivity in x-, y-, and z-directions, and style similarity, the study shows that based on several mutually perpendicular 2D training images, the modeling method proposed in this paper can achieve an effect similar to that based on 3D training images directly. In the case that it is difficult to obtain 3D training images, the modeling method proposed in this paper has suitable application prospects.

Ground motions could be modelled as amplitude and frequency modulated process. The frequency modulation through a time transformation results in the modelled motions in the new timescale being a stationary process except for the amplitude modulation. The assessment of power spectral density (PSD) and the lagged coherence in the transformed timescale is presented in this study. It is shown theoretically and numerically that the PSD functions obtained through time transformation in the original timescale should not be used as an amplitude modulation function, and that the lagged coherence in the new or auxiliary timescale differs from that in the original timescale. [ABSTRACT FROM AUTHOR]

We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic susceptible-infectious-recovered model, to describe the interplay between the dynamics of the disease spread and the contact network underlying the epidemic. A Markov chain Monte Carlo framework is developed for likelihood-based inference from partial epidemic observations, with a novel data augmentation algorithm specifically designed to deal with missing individual recovery times under the dynamic network setting. Through a series of simulation experiments, we demonstrate the validity and flexibility of the model as well as the efficacy and efficiency of the data augmentation inference scheme. The model is also applied to a recent real-world dataset on influenza-like-illness transmission with high-resolution social contact tracking records. for this article are available online. [ABSTRACT FROM AUTHOR]

We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g. from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algorithm in terms of a mixing procedure that consists of generating a $1+1$ -dimensional field $u(t,\xi)$ , where each Gaussian component $u_\xi(t)$ is synthesized with identical underlying noise but different covariance function $C_\xi(t,s)$ parameterized by a log-normally distributed parameter ξ . Due to the Gaussianity of each component $u_\xi(t)$ , we can exploit standard sampling algorithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture u ( t ) is then initialized by assigning each point in time t a $\xi(t)$ and therefore a specific value from $u(t,\xi)$ , where the time-dependent parameter $\xi(t)$ follows a log-normal process with a large correlation time scale compared to the correlation time of $u(t,\xi)$ . We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical approximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets.

In order to prioritize the exhumation of the most informative reference relatives to increase the statistical power of a reference group, a conditional simulation approach for missing person identification that combines both exclusion and inclusion power in reference families has been previously developed. The aim of this study is to empirically validate this approach by comparing its predicted theoretical prioritization model with the observed changes in statistical power in real cases of our laboratory, in which new relatives had already been added. We conclude that this approach is a reliable tool to choose the most appropriate reference relatives to complete a family group and improve the identification power of a Missing Person (MP). [ABSTRACT FROM AUTHOR]

There are a number of ways to test for the absence/presence of a spatial signal in a completely observed fine-resolution image. One of these is a powerful nonparametric procedure called enhanced false discovery rate (EFDR). A drawback of EFDR is that it requires the data to be defined on regular pixels in a rectangular spatial domain. Here, we develop an EFDR procedure for possibly incomplete data defined on irregular small areas. Motivated by statistical learning, we use conditional simulation (CS) to condition on the available data and simulate the full rectangular image at its finest resolution many times (M, say). EFDR is then applied to each of these simulations resulting in M estimates of the signal and M statistically dependent p-values. Averaging over these estimates yields a single, combined estimate of a possible signal, but inference is needed to determine whether there really is a signal present. We test the original null hypothesis of no signal by combining the M p -values into a single p-value using copulas and a composite likelihood. If the null hypothesis of no signal is rejected, we use the combined estimate. We call this new procedure EFDR-CS and, to demonstrate its effectiveness, we show results from a simulation study; an experiment where we introduce aggregation and incompleteness into temperature-change data in the Asia-Pacific; and an application to total-column carbon dioxide from satellite remote sensing data over a region of the Middle East, Afghanistan, and the western part of Pakistan. for this article are available online. [ABSTRACT FROM AUTHOR]

The conditional simulation of non-Gaussian excitations utilizing records from the monitoring system is of great significance for hazard mitigation. To this end, this paper proposes a novel conditional non-Gaussian simulation method. In this method, the Unified Hermite Polynomial Model (UHPM) is used to describe the transformation relationship between recorded and unrecorded non-Gaussian processes and their underlying Gaussian counterparts. Meanwhile, an explicit transformation model between their correlation functions is also provided. Then, the covariance matrix of Fourier coefficients of the underlying Gaussian processes is constructed. Based on this covariance matrix, the conditional samples of Fourier coefficients are generated and substituted into the Spectral Representation Method (SRM) to perform the conditional simulation of the underlying Gaussian processes. Finally, the conditionally simulated samples of the underlying Gaussian processes are transformed into the non-Gaussian samples by the UHPM. To showcase the precision and efficacy of the proposed method, two numerical examples involving the conditional simulations of non-Gaussian ground motions and non-Gaussian wind pressure coefficients are provided. [ABSTRACT FROM AUTHOR]

Simulating a depositional (or stratigraphic) sequence conditionally on borehole data is a long-standing problem in hydrogeology and in petroleum geostatistics. This paper presents a new rule-based approach for simulating depositional sequences of surfaces conditionally on lithofacies thickness data. The thickness of each layer is modeled by a transformed latent Gaussian random field allowing for null thickness thanks to a truncation process. Layers are sequentially stacked above each other following the regional stratigraphic sequence. By choosing adequately the variograms of these random fields, the simulated surfaces separating two layers can be continuous and smooth. Borehole information is often incomplete in the sense that it does not provide direct information about the exact layer that some observed thickness belongs to. The latent Gaussian model proposed in this paper offers a natural solution to this problem by means of a Bayesian setting with a Markov chain Monte Carlo (MCMC) algorithm that can explore all possible configurations that are compatible with the data. The model and the associated MCMC algorithm are validated on synthetic data and then applied to a subsoil in the Venetian Plain with a moderately dense network of cored boreholes. [ABSTRACT FROM AUTHOR]

This paper considers the problem of conditional stochastic simulation in geostatistics. A new type of conditioning method that generalizes the well-known two-step conditioning approach is introduced. The distinctive feature of the new method is that it solves the modeling problem for multiple stochastic fields in a general setup. A generalized kriging procedure is developed in the paper, using linear combinations of the simulated fields as input data instead of the commonly used separate fields' values. Although the new conditioning method was developed initially in the framework of a particular approach to geostatistical simulation (the spectral method), it can be applied in many more general settings of conditional simulation of stationary stochastic fields of arbitrary dimension. The workings of the method and its applicability are illustrated with the results of several numerical experiments, including simulation on real oil field data. [ABSTRACT FROM AUTHOR]

This study revisits the conditional bias that can be observed with spatial estimators such as kriging. In the geostatistical literature, the term "conditional bias" has been used to describe two different effects: underestimation of high values and overestimation of low values, or the opposite, viz. overestimation of high values and underestimation of low values. To add to the confusion, the smoothing effect of the estimator is always indicated to be the culprit. It seems that geostatisticians have been debating conditional bias since the birth of geostatistics. Is less or more smoothing required to alleviate conditional bias, and which one? This paradox is actually resolved when one considers the different distribution partitions on which conditional expectation can be calculated. Depending on the partitions of the bivariate distribution of true versus estimated values, conditional expectation can be calculated on conditional or marginal distributions. These lead to different types of conditional bias, and smoothing affects them differently. The type based on conditional distributions is smoothing friendly, while the type based on marginal distributions is smoothing adverse. The same estimator can display under- and overestimation, depending on whether a conditional or marginal distribution is considered. It is also observed that all conditional biases, regardless of the bivariate distribution partitions, are greatly affected by the variance of the conditioning data and vary with the sampling. A simple estimator correction can be applied to exactly remove the smoothing-friendly conditional bias in the sample as measured by the slope of the linear regression between the true and estimated values in cross-validation. Over many samplings, it is observed that this cross-validation measure is itself conditionally biased, depending on the variance of the data. On the other hand, the smoothing-adverse type of conditional bias can be corrected by conditional simulation that reproduces the distribution of the data. The results are also biased, depending on the variance of the conditioning data. Correcting for the smoothing-adverse type will worsen the smoothing-friendly type, and vice versa. Both types of conditional bias can be corrected by averaging statistics, or averaging estimates, over multiple samplings. [ABSTRACT FROM AUTHOR]

The complex topological characteristics of network-like structural systems, such as lattice structures, cellular metamaterials, and mass transport networks, pose a great challenge for uncertainty qualification (UQ). Various UQ approaches have been developed to quantify parametric uncertainties or high dimensional random quantities distributed in a simply connected space (e.g., line section, rectangular area, etc.), but it is still challenging to consider the topological characteristics of the spatial domain for uncertainty representation and quantification. To resolve this issue, a network distance-based Gaussian random process uncertainty representation approach is proposed. By representing the topological input space as a node-edge network, the network distance is employed to replace the Euclidean distance in characterizing the spatial correlations. Furthermore, a conditional simulation-based sampling approach is proposed for generating realizations from the uncertainty representation model. Network node values are modeled by a multivariate Gaussian distribution, and the network edge values are simulated conditionally on the node values and the known network edge values. The effectiveness of the proposed approach is demonstrated on two engineering case studies: thermal conduction analysis of 3D lattice structures with stochastic properties and characterization of the distortion patterns of additively manufactured cellular structures. [ABSTRACT FROM AUTHOR]

This paper introduces a method to generate conditional categorical simulations, given an ensemble of partially conditioned (or unconditional) categorical simulations derived from any simulation process. The proposed conditioning method relies on implicit functions (signed distance functions) for representing the categorical spatial variable of interest. Thus, the conditioning problem is reformulated in terms of signed distance functions. The proposed approach combines aspects of principal component analysis and Gibbs sampling to achieve the conditioning of the unconditional categorical realizations to the data. It is applied to synthetic and real-world datasets and compared to the traditional sequential indicator simulation. It appears that the proposed simulation technique is an effective method to generate conditional categorical simulations from a set of unconditional categorical simulations. [ABSTRACT FROM AUTHOR]

Abstract Risk or uncertainty assessment in the reservoir flow modeling, especially in real field-scale evaluation, is essential to make a trustful decision regarding the future development plans. This paper presents an efficient uncertainty assessment workflow of geological and production data through the cyclic $$\text{CO}_2$$ CO2 -assisted gravity drainage (GAGD) process in South Rumaila oil field in Southern Iraq. First, the sequential Gaussian simulation created a large number of reservoir stochastic realizations that capture the entire geological uncertainty space. Second, ranking was applied to select the quartiles $$(\text{P}10, \text{P}20,\ldots ,\text{P}90)$$ (P10,P20,…,P90) of reservoir permeability and anisotropy ratio to quantify the geological uncertainty. Next, the equation of state-compositional flow model was constructed to evaluate these realizations by calculating the reservoir flow response. Then, 81 designed simulations were created by factorial design considering the combined realizations of permeability and anisotropy ratio. In a successive step, the most-likely model was considered for the uncertainty quantification of the operational decision parameters through the cyclic GAGD process to restrict the uncertainty space, which leads to obtain the true optimal scenario. The cyclic GAGD operational parameters include durations of injection, soaking, and production and the minimum bottom hole pressure in production wells. The compositional reservoir flow model was again used to evaluate the multiple simulations created by the proxy-based Box–Behnken design and Monte Carlo simulation. The combined geological and production uncertainty workflow gave an idea about the uncertainty or risk space of the predicted reservoir flow response in the future cyclic GAGD process performance.