A reliability analysis framework coupled with statistical uncertainty characterization for geotechnical engineering

Deep Markov models of multidimensional random fields

The paper considers a quasiprobable and a maximum probable algorithm of area estimation with regard to possible absence of an image in an observed realization of a random field. Exact expressions for characteristics of the area estimation algorithms are derived.

Frequency domain analysis is used to examine estimates from linear smoothers operating on realizations of random fields over space and/or time. The estimates are expressed in terms of the Fourier transforms of the dependent variable and of the smoother weights. The latter is referred to as the equivalent transfer function. The data do not need to be evenly spaced to perform this analysis. The modulus of the equivalent transfer function characterizes the spectral content of an estimate and may reveal subtle sampling properties of the design. Frequency domain bias calculations are useful for comparing different smoothers and for assessing the resolution capabilities of a data set. These methods are used to compare six one-dimensional smoothers and analyze a complex three-dimensional example using data from a satellite altimeter.

Summary Here a mathematical approach which can be used for comparison of three methods for modeling Gaussian random fields is developed. Namely, the known methods of Sequential Gaussian Simulation and Spectral Modeling as well as new method based of Fourier transform and spectral modeling random fields of Fourier coefficients are considered. We show that these methods give equivalent result when specific Gaussian fields are modeled. Also we discuss advantages and limitations of these methods, their applicability in practice problems, computational complexity and ways for their effective realizations.

In recent years, spatial variability modeling of geotechnical parameters using random field theory is gaining strength in the reliability based analysis of geotechnical problems. Slope stability analysis of highly weathered rock slope requires proper modeling of geotechnical parameters with due consideration of extent of weathering and overburden pressure. The present study demonstrates the approach for spatial variation modeling of geotechnical parameters and reliability analysis based stability assessment of highly weathered rock slope by considering a typical case of height = 5.0 m and slope angle of 30°. Commercially available software FLAC 5.0, via inbuilt FISH function, has been utilized for the numerical analysis purpose with the assumption that highly weathered rock mass can be analyzed within the framework of the concept of equivalent continuum model. A parametric study is performed to investigate the following: (i) influence of coefficients of variation of geotechnical parameters and (ii) auto-correlation distances on the reliability analysis results. For the reliability analysis, information on mean and variance of output parameter, i.e., factor of safety of the given rock slope is obtained from 2000 Monte Carlo simulations and results are utilized with first order reliability method to obtain reliability index values. The results of the analysis clearly demonstrated that numerical modeling of spatially varying geotechnical parameters gives more realistic treatment to the property variation of a natural material and stability assessment in reliability analysis framework is more comprehensive than conventional limit equilibrium based factor of safety approach.

In the past few years, random field theory has been increasingly used to model the inherent soil variability. The scale of fluctuation is one of the important parameters describing a stationary random field. In this study, the factors affecting an accurate estimation of the scale of fluctuation were studied with numerical experiments to show how a proper sampling strategy can help improve the estimate of scale of fluctuation. Hypothetical data sets were generated from random field theory. Data were then sampled for different sampling strategies. The scale of fluctuation estimated from the sampling programs were compared with the predefined scale of fluctuation. The accuracy with which one can estimate scale of fluctuation depends on both the sampling intensity and extent of the sampling range. For the numerical example in this study, the sampling interval should be close enough such that 10 samples are measured within one scale of fluctuation, and the distance covered by the sampling should cover at least 100 scales of fluctuation.

This paper examines the interaction between the spatial variations in binder concentration (i.e. cement slurry concentration) and in situ water content, in cement-mixed soil, using field and model data as well as statistical analysis and random field simulation. The field data are first analysed to shed light on the spatial variation in the in situ water content, including its scale of fluctuation. A statistical model is then developed which takes into account the variation in binder concentration and in situ water content. This leads to a two-parameter model for the prediction of the mean, variance and probability distribution function of the strength of the cement-treated soil. The scale of fluctuation for the variation in binder concentration arising from imperfect mixing within a cement-mixed column is then examined using centrifuge model data. This indicates that the scale of fluctuation in binder concentration is much shorter in range than that of the in situ water content. The combined effect of these two scales of fluctuation is then studied by simulating the resulting random field using Monte-Carlo simulations. This indicates that the size of the sampling region has a significant effect on the scale of fluctuation that is captured. If the sampling region is of a similar size to the column diameter, the measured scale of fluctuation reflects that of the binder concentration. As the size of the sampling region increases, so does the measured scale of fluctuation. This explains the wide range of scales of fluctuation that have been reported for cement-treated soil. To capture both scales of fluctuation in core sampling, some boreholes should be sunk at close spacings of less than a column diameter, in order to capture short-range variation.

The unconfined compressive strength (UCS) of rocks is a crucial factor in geotechnical engineering, assuming a central role in various civil engineering undertakings, including tunnel construction, mining operations, and the design of foundations. The precision in forecasting UCS holds paramount importance in upholding the security and steadfastness of these endeavors. This article introduces a fresh methodology for UCS prognostication by amalgamating Gaussian process regression (GPR) with two pioneering optimization techniques: sand cat swarm optimization (SCSO) and the equilibrium slime mould algorithm (ESMA). Conventional techniques for UCS prediction frequently encounter obstacles like gradual convergence and the potential for becoming ensnared in local minima. In this investigation, GPR is the foundational predictive model due to its adeptness in managing nonlinear associations within the dataset. The fusion of GPR with cutting-edge optimizers is envisioned to elevate the precision and expeditiousness of UCS prognostications.An extensive collection of rock samples, each accompanied by UCS measurements, is harnessed to assess the suggested methodology. The efficacy of the GPSC and GPES models is juxtaposed with the conventional GPR technique. The findings reveal that incorporating SCSO and ESMA optimizers into GPR brings about a noteworthy enhancement in UCS prediction accuracy and expedites convergence. Notably, the GPSC models exhibit exceptional performance, evidenced by an exceptional R2 value of 0.995 and an impressively minimal RMSE value of 1.913. These findings emphasize the GPSC model’s potential as an exceedingly auspicious tool for experts in the realms of engineering and geology. It presents a sturdy and dependable method for UCS prediction, a resource of immense value in augmenting the security and efficiency of civil engineering endeavors.

Numerous applications-including optical communications, directed energy, remote sensing, and optical tweezing-utilize the principles of statistical optics and optical coherence theory. Simulation of these phenomena is, therefore, critical in the design of new technologies for these and other such applications. For this reason, this tutorial describes how to generate random electromagnetic field instances or realizations consistent with a given or desired cross-spectral density matrix for use in wave optics simulations. This tutorial assumes that the reader has knowledge of the fundamental principles of statistical optics and optical coherence theory. An extensive reference list is provided where the necessary background information can be found. We begin this tutorial with a brief summary of the coherent-mode representation and the superposition rule of stochastic electromagnetic fields as these foundational ideas form the basis of all known synthesis techniques. We then present optical field expressions that apply these concepts before discussing proper sampling and discretization. We finally compare and contrast coherent-mode- and superposition-rule-based synthesis approaches, discussing the pros and cons of each. As an example, we simulate the synthesis and propagation of an electromagnetic partially coherent field from the literature. We compare simulated or sample statistics to theory to verify that we have successfully produced the desired field and are capturing its propagation behaviors. All computer programs, including detailed explanations of the source code, are provided with this tutorial. We conclude with a brief summary.

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

There is not abstract.

Speckle suppression in PolSAR images is an important step for the extraction of meaningful information from PolSAR images, especially for homogeneous extended targets. It has been shown that insufficient noise filtering resulting in low equivalent number of look (ENL) values will increase bias on incoherent polarimetric parameters such as the Cloude-Pottier parameters. In addition, meaningful high-frequency information, such as edges and point targets must be preserved. Adaptive filters have been the most successful in reaching a good compromise between noise suppression and detail preservation. A large set of artificial PolSAR images, which ground truth are realizations of Markov random fields, has been generated. Performance metrics are focusing on speckle suppression (ENL), edge preservation, relative errors on polarimetric parameters and point target preservation.

Estimating a covariance model for kriging purposes is traditionally done using semivariogram analyses, where an empirical semivariogram is calculated, and a chosen semivariogram model, usually defined by a sill and a range, is fitted. We demonstrate that a convolutional neural network can estimate such a semivariogram model with comparable accuracy and precision by training it to recognise the relationship between realisations of Gaussian random fields and the sill and range values that define it, for a Gaussian type semivariance model. We do this by training the network with synthetic data consisting of many such realisations with the sill and range as the target variables. Because training takes time, the method is best suited for cases where many models need to be estimated since the actual estimation itself is about 70 times faster with the neural network than with the traditional approach. We demonstrate the viability of the method in three ways: (1) we test the model’s performance on the validation data, (2) we do a test where we compare the model to the traditional approach and (3) we show an example of an actual application of the method using the Danish national hydrostratigraphic model.

Inverse problems in geophysics require the introduction of complex a priori information and are solved using computationally expensive Monte Carlo techniques (where large portions of the model space are explored). The geostatistical method allows for fast integration of complex a priori information in the form of covariance functions and training images. We combine geostatistical methods and inverse problem theory to generate realizations of the posterior probability density function of any Gaussian linear inverse problem, honoring a priori information in the form of a covariance function describing the spatial connectivity of the model space parameters. This is achieved using sequential Gaussian simulation, a well-known, noniterative geostatisticalmethod for generating samples of a Gaussian random field with a given covariance function. This work is a contribution to both linear inverse problem theory and geostatistics. Our main result is an efficient method to generate realizations, actual solutions rather than the conventional least-squares-based approach, to any Gaussian linear inverse problem using a noniterative method. The sequential approach to solving linear and weakly nonlinear problems is computationally efficient compared with traditional least-squares-based inversion. The sequential approach also allows one to solve the inverse problem in only a small part of the model space while conditioned to all available data. From a geostatistical point of view, the method can be used to condition realizations of Gaussian random fields to the possibly noisy linear average observations of the model space.

We construct a new numerical modeling for two-phase immiscible flow in a strongly heterogeneous deformable carbonate underneath a rock salt composed by halite and anhydrite displaying creep behavior with the viscous strain ruled by a nonlinear constitutive law of power-law type. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and transient porosity input fields for the transport problem for the water saturation. Such transport equation is decomposed within an operator splitting technique based on a predictor-corrector scheme with the predictor step discretized by a higher-order non-oscillatory finite volume central scheme. Numerical simulations of a water-flooding problem in secondary oil recovery are presented for different realizations of the input random fields (permeability, Young modulus and initial porosity). Comparisons between the accuracies of the proposed approach and the traditional one-way coupled hydro-geomechanical formulation are presented. In addition, simulations including the viscoelastic behavior of the overburden rock salt are performed showing the effects of salt stiffness and irreversible deformation upon finger grow and breakthrough curves. A notable feature of the formulation proposed herein is the accurate prediction of the influence of geomechanical effects upon the unstable movement of the water front, whose evolution is dictated by carbonate heterogeneity, unfavorable viscosity ratio and geomechanical effects without deteriorating the local conservative character of the numerical schemes.