Nonstationary Field Research Articles

A CNN-LSTM model for predicting wind speed in non-stationary wind fields in mountainous areas based on wavelet transform and adaptive programming

A CNN-LSTM model for predicting wind speed in non-stationary wind fields in mountainous areas based on wavelet transform and adaptive programming

Analytical solution to the problem of injection or reduction of the formation pressure in the reservoir with a fracture

The problem of injection of Newtonian fluid at a constant flow rate through an injection well into an initially undisturbed infinite reservoir with an erosive vertical main fracture of constant width is considered. Using the Laplace transform method, analytical solutions are obtained for the pressure fields in the fracture and reservoir, the flow velocity in the fracture, as well as the equations for fluid trajectories in the reservoir and in the main fracture are derived. The solutions obtained are also applicable to the problem of fluid withdrawal into a production well intersected by a vertical main fracture. Nonstationary two-dimensional pressure fields in the reservoir, as well as the pressure and velocity fields in the fracture, are constructed.

Thermal stresses in bimetallic plate under induction heating by nonstationary electromagnetic field

A thermomechanical problem is formulated for a bimetallic plate subjected to induction heating by a nonstationary electromagnetic field. As the object of the study, a plate with layers made of stainless steel and copper is selected. The stress intensities in the constituent layers of the plate are numerically analyzed on its external surfaces and at the contact interface of the constituent layers. The analysis is conducted based on the amplitude-frequency characteristics and the duration of the nonstationary electromagnetic action. The research is carried out for two cases of electromagnetic carrier wave frequencies including those equal to the first resonance frequency and those extending outside the resonance frequency range of the electromagnetic field.

Probabilistic stability analysis of small-angle marine slopes considering hydrate decomposition and seismic excitation

The submarine massive mud transports of several seas around the world, including the Shenhu Sea, are thought to relate with hydrate decomposition, which occur even at small gradients. This article investigates the stability and reliability of marine slopes considering three factors related to hydrate decomposition and earthquake, namely decrease in sediment strength, increase in excess pore pressure, and activation by external seismic force. Taking the SH2 hole, implemented by the first Chinese offshore hydrate drilling mission (GMGS-1), as an example, the impacts of three factors mentioned above on marine slopes stability are analyzed with infinite slope theory. In addition, the space distribution of physical and mechanical parameters in hydrate deposits is under consideration. The cohesion, friction angle and buoyant unit weight in a non-stationary random field are treated as spatial random variables, where the means of the first two increase linearly with depth. Variation characteristics of the failure probability for various slope angles are analyzed under different scenarios. The outcomes reveal that the safety factor of the slopes at 30% potential for damage is around 1.25 within a given variant characterization. The proposed integrated stability and reliability analysis can effectively provide early warning for collapse of marine hydrate-bearing slopes.

Stability analysis of tunnel heading in clay with nonstationary random fields of undrained shear strength

The stability problem of a tunnel heading in clay remains a significant challenge in geotechnical engineering. Specifically, when considering the spatial variability of the soil, the stability factor may be influenced by geographically random fields. This study investigates the effect of random fields on a probabilistic analysis of a tunnel heading in undrained clay. The study assumes that the undrained shear strength of the clay increases linearly with depth due to a strength gradient factor. The random adaptive finite element limit analysis is employed to calculate the stability numbers for tunnel headings. Nonstationary random fields with varying vertical correlation lengths are simulated using Monte Carlo simulation technique. The stability analysis takes into account geometry parameters (i.e., cover depth ratio) and nonstationary random field of undrained shear strength parameters. (i.e., strength gradient, coefficient of variation, and vertical correlation length). The results of tunnel face stability using random adaptive finite element limit analysis have also been utilised to assess the probability of design failure over a practical range of deterministic factors of safety. In the context of probabilistic failure analysis, the failure mechanism resulting from varying vertical correlation lengths could influence the probability of design failure. The findings of this study can be of significant interest to tunnel engineering practitioners during the design phase of tunnel heading projects.

Modified RNN for Solving Comprehensive Sylvester Equation With TDOA Application.

The augmented Sylvester equation, as a comprehensive equation, is of great significance and its special cases (e.g., Lyapunov equation, Sylvester equation, Stein equation) are frequently encountered in various fields. It is worth pointing out that the current research on simultaneously eliminating the lagging error and handling noises in the nonstationary complex-valued field is rather rare. Therefore, this article focuses on solving a nonstationary complex-valued augmented Sylvester equation (NCASE) in real time and proposes two modified recurrent neural network (RNN) models. The first proposed modified RNN model possesses gradient search and velocity compensation, termed as RNN-GV model. The superiority of the proposed RNN-GV model to traditional algorithms including the complex-valued gradient-based RNN (GRNN) model lies in completely eliminating the lagging error when employed in the nonstationary problem. The second model named complex-valued integration enhanced RNN-GV with the nonlinear acceleration (IERNN-GVN) model is proposed to adapt to a noisy environment and accelerate the convergence process. Besides, the convergence and robustness of these two proposed models are proved via theoretical analysis. Simulative results on an illustrative example and an application to the moving source localization coincide with the theoretical analysis and illustrate the excellent performance of the proposed models.

Reconstruction of nonstationary sound field based on group sparsity time domain equivalent source method

To improve the accuracy and stability of reconstruction of nonstationary sound field, a novel time domain equivalent source method based on non-convex overlapping group sparsity (NOGS-TESM) is proposed. In the proposed NOGS-TESM, the time-varying pressure in the near field is first modeled by a set of equivalent sources positioned inside the vibrating structure. Then, the NOGS regularization is applied for solving the inverse problem, and a novel algorithm derived on the basis of Majorize-Minimization theory is utilized to obtain the optimal solution of equivalent sources strengths. Finally, the optimal equivalent sources strengths at all times are substituted into a time-domain convolution to calculate the time-varying pressure of reconstruction surface. The proposed NOGS-TESM enriches the prior information by considering the group sparsity of spatial pressure distribution, and enhances the accuracy of estimated equivalent sources strength via its alternative calculation of l0−norm. A vibrating plate to produce a nonstationary sound field, which is designed as a numerical simulation, and the time-varying pressures of measurement surface are input into the proposed NOGS-TESM. The quantitative and qualitative comparisons confirm that the proposed NOGS-TESM can greatly reconstruct the non-stationary sound field in time–space domains, and its reconstruction accuracy is higher than that of TESM with Tikhonov regularization (TR-TESM). Meanwhile, several parameters, for example, the noise and position of equivalent source surface, are discussed in detail, and the superiorities of the proposed NOGS-TESM in terms of stability and robustness are proved by comparing to TR-TESM. The predominance of the proposed NOGS-TESM is further validated by conducting one experiment on the vibrating steel plate.

Digital technologies for signal radio vision and radio monitoring

Objectives. Radiophysical processes involving the electrodynamic formation of signal radio images diffusely scattered by the signature of small-sized objects or induced by the near field of radio devices are relevant for identifying radiogenomic (cumulant) features of objects in the microwave range in the development of neuroimaging ultra-short pulse (USP) signal radio vision systems, telemonitoring, and near-radio detection. The paper sets out to develop methods and algorithms for vector analysis of radio wave deformation of nonstationary fields forming a signal radio image based on radiophysical and topological characteristics of small-sized objects; to develop software and hardware for registration and neural network recognition of signal radio images, including methods for the synthesis and extraction of signal radiogenomes using digital twins of objects obtained through vector electrodynamic modeling; and to analyze signal radio images induced by elements of printed topology of electronic devices.Methods. The study is based on statistical radiophysics methods, time-frequency approaches for wavelet transformation of USP radio images, numerical electrodynamic methods for creating digital twins of small-sized objects, as well as neural network authentication algorithms based on the cumulant theory of pole-genetic and resonant physically unclonable functions used in identifying signal radio images.Results. The results of fundamental research on electrodynamic effects of vector-wave deformation of nonstationary fields of sub-nanosecond configuration are presented as a means of identifying and authenticating signal radio images. Neural network techniques for cumulant formation of radio genomes of signal radio images are proposed on the basis of pole-genetic and resonant functions.Conclusions. A radiogenome, representing the unique authenticator of a radio image, is shown to be formed on the basis of physically unclonable functions determined by the structure and set of radiophysical parameters of the image. Cumulant features of signal radio images identified on the basis of pole-genetic and physically unclonable resonant functions of small-sized objects are revealed.

Undrained HM bearing capacity of hybrid foundations in spatially variable soils

This paper investigates the probabilistic capacity of hybrid foundations (HF) for offshore structures in spatially variable marine sediments under horizontal (H) and moment (M) combined loading. Non-stationary random fields are used to model the spatially varying undrained shear strength that linearly increases with depth. The results indicate that using hybrid foundations, with peripheral and two internal skirts of identical length (i.e. d/D = 1) is almost similar to simple skirted (SS) foundations for both deterministic and stochastic approaches. Increasing length of internal skirts to twice that of peripheral ones with d/D = 2, results however in significant increase of foundations capacity, mainly under HM combined loading.

Simulating non-stationary and non-Gaussian cross-correlated fields using multivariate Karhunen–Loève expansion and L-moments-based Hermite polynomial model

In practical engineering, cross-correlated random fields are often used to model structural materials or random loads containing multiple correlations. Effective and accurate simulation of these cross-correlation fields is an important prerequisite for subsequent reliability analysis and uncertainty quantification of complex systems. Therefore, this paper proposes a new simulation method for non-stationary non-Gaussian cross-correlated random fields to satisfy realistic engineering requirements. In this new method, L-moments-based Hermite polynomials model (LHPM) is extended to non-stationary non-Gaussian cross-correlated fields. Then, a transformation model from non-stationary non-Gaussian correlation matrix function (CMF) to the underlying Gaussian CMF is explicitly given. Multivariate K-L expansion is further used to approximate the underlying Gaussian cross-correlated fields, where the eigenvalue and eigenfunctions are estimated via the Nyström method with uniform weights. The approximation permits the application of few random variables to characterize the entire Gaussian cross-correlated fields. Ultimately, the simulated underlying Gaussian cross-correlated fields are mapped back to the target non-stationary non-Gaussian cross-correlated fields based on LHPM. Three typical examples, including exponential kernel, Wiener process kernel and spatially varying non-Gaussian and nonstationary seismic ground motions, are used to validate the effectiveness of the proposed method. The source code is readily available at: https://github.com/zhaozhao23/Simulation-of-non-stationary-and-non-Gaussian-cross-correlated-fields.

Full inference for the anisotropic fractional Brownian field

The anisotropic fractional Brownian field (AFBF) is a non-stationary Gaussian random field which has been used for the modeling of textured images. In this paper, we address the open issue of estimating the functional parameters of this field, namely the topothesy and Hurst functions. We propose an original method which fits the empirical semi-variogram of an image to the semi-variogram of a turning-band field that approximates the AFBF. Expressing the fitting criterion in terms of a separable non-linear least square criterion, we design a minimization algorithm inspired by the variable projection approach. This algorithm also includes a coarse-to-fine multigrid strategy based on approximations of functional parameters. Compared to existing methods, the new method enables to estimate both functional parameters on their whole definition domain. On simulated textures, we show that it has a low estimation error, even when the parameters are approximated with a high precision. We also apply the method to characterize mammograms and sample images with synthetic parenchymal patterns.

Joint Scattering Environment Sensing and Channel Estimation Based on Non-Stationary Markov Random Field

Joint Scattering Environment Sensing and Channel Estimation Based on Non-Stationary Markov Random Field

Time-domain sound field reconstruction using a rigid spherical microphone array.

A time-domain approach for interior spherical near-field acoustic holography is proposed to achieve the low-delay reconstruction of time-domain sound fields using a rigid spherical microphone array. This reconstruction encompasses the incident pressure field, the incident radial particle velocity field, and the total pressure field, which includes scattering. The proposed approach derives time-domain radial propagators through the inverse Fourier transform of their frequency-domain counterparts. These propagators are then applied to the array measurements to obtain the time-domain spherical harmonic coefficients of the interior sound field. Given the fact that the time-domain radial propagators possess finite-time support and exhibit significant high-frequency attenuation characteristics, they can be efficiently implemented using finite impulse response (FIR) filters. The proposed approach processes the signal sample-by-sample through these FIR filters, avoiding a series of issues associated with time-frequency transformations in frequency-domain methods. As a result, the approach offers higher accuracy and lower latency in reconstructing non-stationary sound fields compared to its frequency-domain counterpart and thus holds greater potential for real-time applications. Additionally, owing to the scattering effect of the rigid sphere, the approach avoids the impact of spherical Bessel function nulls and does not require the measurement of particle velocities, which renders the measurements cost effective.

The Convincing Cosmic Energy Gravitational Genesis of the Strongest Geomagnatic Anomalies of the Magnetic Field of the Earth

The author presents convincing evidence of the cosmic (planetary and solar) energy gravitational origin (related to the maximal and minimal combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth) of the maximal temporal intensifications of the global magnetic processes of the Earth. In fairly good agreement with the calculated date 2007.416666666 AD (of the local minimal planetary and solar integral energy gravitational influence on the internal rigid core), it was observed the very rapid changes of the geomagnetic field near the date March 2007 AD (corresponding approximately to 19-20 April 2007 AD). This fairly good agreement gives the additional convincing argument that the date March 2007 AD can be considered as the possible beginning of the geomagnetic reversal during the evaluated range (2007÷2216) AD. The strong magnetic anomaly occurred on 6 January 2020 AD in perfect agreement with the calculated date 2020.016666667 AD (corresponding to 6 January 2020 AD) related to the local maximal planetary and solar integral energy gravitational influence on the internal rigid core. In fairly good agreement with the calculated date 2023.26666666 AD (corresponding approximately to 7 April 2023 AD) of the local maximal planetary and solar integral energy gravitational influence on the internal rigid core, it was observed the strongest (during the last 6 years) magnetic anomaly on 23 March 2023 AD. These convincing agreements demonstrate the physical validity of the established global prediction thermohydrogravidynamic principles, which can be considered as the proven physical basis for the development of the general unified geophysical theory (describing the possible geomagnetic reversal during the evaluated range (2007 ÷ 2216) AD) combining the Special Theory of Relativity, the relativistic electrodynamics and the relativistic theory of the non-stationary gravitation, which can be developed based on the established physical analogy between the established relation for the energy flux (of the gravitational energy) and the Lorentz’s calibration condition (for the vector potential related with the scalar potential of the non-stationary electromagnetic field).

Nonstationary optics: tutorial.

Over the past several decades, nonstationary optics has risen as a key enabling technology for a multitude of novel applications. These include areas of research such as micromachining and ultrafast optics, as well as the Nobel awarded research in femtochemistry, optical frequency combs, and attosecond physics. This tutorial aims to present some of the main concepts required to analyze nonstationary fields, with an emphasis on pulsed beams. The work begins from the fundamental building blocks of such fields, and builds up to some of their main properties. The spatiotemporal properties and stability of such fields are discussed in length, and some common measurement schemes are reviewed.

Investigation on wave-induced responses of heterogeneous seabed around a buried pipeline based on nonstationary random field model

The instability of the seabed poses a threat to the structural integrity and functionality of submarine pipelines. This numerical study investigates wave-induced responses in a heterogeneous seabed around a buried pipeline, considering spatial variability in soil properties through nonstationary random field models. Three scenarios of spatial variability for soil parameters changing with depth are simulated using both stationary and nonstationary random field models via the Karhunen-Loève expansion method. The discrete random fields are validated in terms of correlation structures and statistical characteristics. The stochastic finite element method, incorporating random fields and a poroelastic seabed model through a LiveLink code, is employed to examine probabilistic outcomes of dynamic soil responses and liquefaction zone distributions within a probabilistic framework. Contrastive analyses are conducted for seabed models with different random field scenarios, in addition to deterministic analyses. The results of the stochastic analysis show that the increasing trend of soil strength with depth has significant effects on the seabed responses and transient liquefaction characteristics around a pipeline.

Heat flow in the Eurasian, North American and Atlantic regions

The article is a presentation of the research results of the next stage of complex geophysical control of models of deep processes in the tectonosphere of continents and oceans, built by geological theory. Models of the crust and upper mantle are located along a system of profiles encircling the northern hemisphere of the Earth, which have are DSS sections (in some places fragmentary, especially in the oceans). In the first stage, control was performed for density models. It is shown that the gravitational field can always be explained without fitting by calculated effects with discrepancies corresponding to the errors. The second stage focused on thermal models, the effects of which were compared with the observed heat flow (HF) distribution through the surface. Solving the problem is complicated by many features of the manifestation of a nonstationary thermal field. Some of them can be considered as nearsurface interference that needs to be eliminated (but usually this is not done). The work done covered the regions of Eurasia and North America, the Atlantic Ocean, a peripheral fragment of the Pacific Ocean, and transition zones between continents and oceans. Activated and nonactivated platforms, Phanerozoic geosynclines, and rifts were studied on the continents. In transition zones, there are depressions with recent oceanisation, island arcs, and deep9sea trenches. In the oceans, there are basins and the mid9ocean ridge (MOR). In the MOR and some other areas of the World Ocean, the intensity of interference does not allow the use of observed HF for routine monitoring. In other regions, the result was achieved, although often after smoothing out the heat flow field. On the continents, the cases are better, although there are also situations where significant parts of the profiles should simply be excluded from consideration due to an unacceptable level of error. However, here it was possible to confidently demonstrate the correspondence of thermal models of deep processes to experimental HF within the limits of observation and calculation errors.

КОЭФФИЦИЕНТЫ ДИФФУЗИИ И АКТИВНОСТЬ КОМПОНЕНТОВ ВОДНОСПИРТОВЫХ СМЕСЕЙ В ПОЛИУРЕТАНОВЫХ ПЛЕНКАХ НА ОСНОВЕ АМИНОЭФИРОВ БОРНОЙ И ОРТОФОСФОРНОЙ КИСЛОТ

The work carried out studies to determine the diffusion coefficients and activities of water, isopropyl and ethyl alcohols in polymer polyurethane films based on amino esters of boric and orthophosphoric acids at temperatures of 22, 40 and 60 °C. To determine the diffusion coefficients, we used data on the dynamics of sorption of low molecular weight components in the polymers under study, presented in our previous study. To describe the process of swelling of a polymer film, the Fick differential equation was used; the process was represented as unsteady diffusion in a flat plate. The initial condition was the absence of a component in the polymer at the initial moment of time; the solution to the differential equation was the non-stationary field of concentrations of the component in the film. The experimental dependences of changes in the volume-mass concentration of components in the polymer were described using the Heaviside switching function; due to the presence of a maximum in the swelling curve, it is associated with a restructuring of the polymer structure that occurs due to possible relaxation processes. By minimizing the discrepancies between the calculated and experimental values of the concentration versus time dependence, the diffusion coefficients of pure components in AEPA and AEBA films were determined. Based on data on the diffusion of components through polymer films, the separation characteristics of polymers were assessed for their use as a selective layer of pervaporation membranes. Based on swelling data over long periods of time for water-alcohol mixtures of various compositions, the parameters of the Flory-Huggins model were determined for calculating the activities of components in the polymer. It was shown that among the solvents under study, water has the highest diffusion coefficient, and isopropyl alcohol has the lowest, regardless of the type of film (AEPA/AEBA). For all films, there is a tendency for the diffusion coefficient to increase with increasing temperature, regardless of the solvent.

Solution of the Heat and Mass Transfer Problem for Soil Radiant Heating Conditions Using the Error Function

Achieving high yields of agricultural crops requires the ability to predict soil temperature and moisture regimes, taking into account soil heating technology. The object of study is soil heated by a ceiling infrared emitter. The subject of study is one-dimensional non-stationary fields of soil moisture content and temperature. The objective of the study is to predict soil temperature and moisture regimes under radiant heating conditions. Research methods: analytical methods for solving differential equations of heat and mass transfer using the error function. Research results: the top 5 mm layer of milled peat with an initial moisture content of 3.7 kg/kg will reach a final moisture content of 1.0 kg/kg in about 6 hours during infrared drying. As a result of radiant heating, the soil will heat up from an initial temperature of 5 ℃ to a final temperature of 20 ℃ in approximately 3 hours. The analytical solution of the mass transfer differential equation can be used for theoretical studies of drying of capillary-porous materials, for example, to determine the drying period or the thickness of the material layer that will dry to a given final moisture content. The analytical solution of the heat transfer differential equation can be used to control the operating mode of the infrared radiation source, for example, to determine the periods of its operation and switching off in case the soil surface temperature reaches the maximum (critical) value. The mathematical solutions considered in the article do not take into account the cross processes of heat and mass transfer, which is a promising direction for further scientific research.

Comparative analysis of computational schemes for FEM modeling of 3D time-domain geoelectromagnetic fields excited by a horizontal grounded-wire source

Two mathematical formulations are considered for calculating the time-domain electromagnetic fields excited by a horizontal grounded-wire source in a 3D geological medium. The first of them is formulated for a vector potential (A-formulation), the second one is formulated for the electric field strength (E-formulation). Both formulations are also considered when using the primary-secondary field approach (PSFA), where the primary field is calculated in a horizontally layered medium. The calculation of 3D non-stationary fields is performed using the vector finite element method (FEM). For time discretization, both two-point and three-point implicit schemes are considered. As the initial field, we used the stationary field of the direct current, the corresponding mathematical formulations are also presented using the PSFA. To verify computational schemes, a comparison with the results of other authors is given. For the problems of marine electrical exploration, we present a comparison of two formulations, analyze the effectiveness of PSFA and the use of a three-point implicit scheme instead of a two-point one. The results of computational experiments have shown that when using both formulations, the use of PSFA and the three-point implicit scheme “with backward overstepping” (instead of the two-point implicit scheme) can reduce computational costs by more than an order. In this case, both formulations give solutions that are close to each other in accuracy and computational costs. However, the implementation of the E-formulation using the PSFA requires certain thoroughness and in some cases can lead to a sharp deterioration in the numerical solution accuracy at late times. This is due to the fact that when using the vector FEM, the numerical solution can lead to a nonzero constant field, which is the gradient of some scalar function.