Sequential Gaussian simulation for geosystems modeling: A machine learning approach

Sequential Gaussian Simulation(SGSIM)as a stochastic method has been developed to avoid the smoothing effect produced in deterministic methods by generating various stochastic realizations.One of the main issues of this technique is,however,an intensive computation related to the inverse operation in solving the Kriging system,which significantly limits its application when several realizations need to be produced for uncertainty quantification.In this paper,a physics-informed machine learning(PIML)model is proposed to improve the computational efficiency of the SGSIM.To this end,only a small amount of data produced by SGSIM are used as the training dataset based on which the model can discover the spatial correlations between available data and unsampled points.To achieve this,the governing equations of the SGSIM algorithm are incorporated into our proposed network.The quality of realizations produced by the PIML model is compared for both 2D and 3D cases,visually and quantitatively.Furthermore,computational performance is evaluated on different grid sizes.Our results demonstrate that the proposed PIML model can reduce the computational time of SGSIM by several orders of magnitude while similar results can be produced in a matter of seconds.     

Ultrasonic prediction of crack density using machine learning:A numerical investigation

Cracks are accounted as the most destructive discontinuity in rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems. The most well-known mechanical parameter for such an evaluation is wave velocity through which one can qualitatively or quantitatively characterize the porous media. In small scales, such information is obtained using the ultrasonic pulse velocity(UPV) technique as a non-destructive test. In large-scale geo-systems, however, it is inverted from seismic data. In this paper, we take advantage of the recent advancements in machine learning(ML) for analyzing wave signals and predict rock properties such as crack density(CD) – the number of cracks per unit volume. To this end, we designed numerical models with different CDs and, using the rotated staggered finite-difference grid(RSG) technique, simulated wave propagation. Two ML networks, namely Convolutional Neural Networks(CNN) and Long Short-Term Memory(LSTM), are then used to predict CD values. Results show that, by selecting an optimum value for wavelength to crack length ratio, the accuracy of predictions of test data can reach R2> 96% with mean square error(MSE) < 25e-4(normalized values). Overall, we found that:(i) performance of both CNN and LSTM is highly promising,(ii) accuracy of the transmitted signals is slightly higher than the reflected signals,(iii) accuracy of 2D signals is marginally higher than 1D signals,(iv)accuracy of horizontal and vertical component signals are comparable,(v) accuracy of coda signals is less when the whole signals are used. Our results, thus, reveal that the ML methods can provide rapid solutions and estimations for crack density, without the necessity of further modeling.     

Nonlinear joint flexibility element for the modeling of jacket-type offshore platforms

A new nonlinear two-dimensional tubular joint element is developed in this study on the basis of flexibility equations and the interaction between the axial force and the in-plane bending moment in the joint. Empirical equations are used to define the joint yielding in the axial direction and the in-plane rotation. An elastic-perfectly plastic yield function is adopted to include the combined effects of axial loads and bending moments on the yielding of the joint. The element formulation is straightforward, and it can readily be implemented in nonlinear finite element programs. Verification studies are carried out for the element to prove its suitability for the modeling of tubular joints of offshore jacket structures. It is concluded that the nonlinear joint model that has been developed produces accurate results, verified against experimental data as well as against sophisticated multi-axial finite element joint models.     

Comparing Training-Image Based Algorithms Using an Analysis of Distance

As additional multiple-point statistical (MPS) algorithms are developed, there is an increased need for scientific ways for comparison beyond the usual visual comparison or simple metrics, such as connectivity measures. In this paper, we start from the general observation that any (not just MPS) geostatistical simulation algorithm represents two types of variability: (1) the within-realization variability, namely, that realizations reproduce a spatial continuity model (variogram, Boolean, or training-image based), (2) the between-realization variability representing a model of spatial uncertainty. In this paper, it is argued that any comparison of algorithms needs, at a minimum, to be based on these two randomizations. In fact, for certain MPS algorithms, it is illustrated with different examples that there is often a trade-off: Increased pattern reproduction entails reduced spatial uncertainty. In this paper, the subjective choice that the best algorithm maximizes pattern reproduction is made while at the same time maximizes spatial uncertainty. The discussion is also limited to fairly standard multiple-point algorithms and that our method does not necessarily apply to more recent or possibly future developments. In order to render these fundamental principles quantitative, this paper relies on a distance-based measure for both within-realization variability (pattern reproduction) and between-realization variability (spatial uncertainty). It is illustrated in this paper that this method is efficient and effective for two-dimensional, three-dimensional, continuous, and discrete training images.