Stochastic Field Model Research Articles

Statistical Analysis of Ice Load on Icebreaker Ship Based on Stochastic Ice Fields

Accurately assessing ice loads is a fundamental issue in the field of structural design for ships in ice-covered regions. In this paper, we conducted research on extreme ice load estimation for icebreaking ships, combining stochastic theory with numerical simulation. Firstly, using sea ice data from the Arctic region of the United States National Snow and Ice Data Center, a stochastic ice field model was established under Arctic sea ice conditions using non-parametric estimation and the rejection sampling method, and ice field data were generated stochastically. Then, based on the stochastic ice field data, a three-dimensional numerical model of the interaction between the ice field and the ship hull was established, and the reliability of the numerical model was verified by experimental results. Finally, based on the numerical model of the interaction between the ice field and the ship hull, asymptotic methods were used to study the extreme ice load estimation in different parts of the ship hull, revealing the variation law of the extreme ice load in different parts of the ship hull. This study provides basic theory and technical support for the structural design of ships in polar regions and has engineering application value.

Data-driven parameter estimation in stochastic dynamic neural fields by state-space approach and continuous-discrete extended Kalman filtering

This work examines the state and parameter estimation problems for Stochastic Dynamic Neural Field (SDNF) models. Unlike other studies, we suggest a general approach based on the Galerkin method that reduces the SDNF model to a standard state-space representation. This naturally yields nonlinear continuous-discrete stochastic systems with complicated nonlinear dynamics and linear measurements of a high dimension because of a spatial approximation. This in turn paves a systematic way for a strong integration of nonlinear Bayesian filtering methods into mathematical neuroscience. Because of a high resolution utilized to keep an accurate spatial approximation, a key aspect of nonlinear filters to be derived for the SDNF models is their computational budgets. In this paper, we derive the sequential Itô-Taylor-based continuous-discrete Extended Kalman filter for state and parameter estimation of the SDNF models. The novel method processes each measurement vector in a component-like manner and, hence, avoids an inversion of a large matrix. Thus, the newly-derived sequential estimator is faster and, additionally, more numerically stable compared to the previously developed SDNF-oriented estimators. Besides, the novel filter is an adaptive method, i.e. it solves both problems, which are the state and parameter estimation, in parallel. Finally, the proposed method is applied to numerical examples to provide the comparative study and to show the effectiveness of our result.

Geometric imperfections in CFS structural members, Part II: Data-driven modeling and probabilistic validation

This paper is the second part in a two-part series that examines the role of geometric imperfections in load–displacement response and collapse behavior of cold-formed steel (CFS) structural members. In part I (Farzanian et al., 2023) a review of the basics and a summary of efforts geared towards modeling geometric imperfections was provided. This included the ingredients needed for systematic identification of elastic buckling mode shapes, due to their frequent use in approximating geometric imperfections, and the development of high fidelity shell finite element (FE) nonlinear collapse analysis of CFS members seeded with different geometric imperfection models. Part II is the companion to the analysis in part I that revealed a noticeable variability in the collapse behavior and load carrying capacity of CFS members as a result of adopting different imperfection modeling strategies. In this part we provide the necessary steps to build a probabilistic framework that rests on machine learning, polynomial approximation, and parametric and non-parametric statistical inference and uses imperfection data to build a consistent stochastic field model of geometric imperfections. This data-driven model is then used to generate the much needed realizations of geometric imperfections that are faithful to the underlying statistics of measured data and therefore can be seeded, directly, in nonlinear collapse analysis of CFS members. Nonlinear shell FE analysis, within a stochastic simulation framework, is finally used to (statistically) quantify the impact of geometric imperfections and to enable probabilistic validation of geometric imperfection models.

Primordial black holes induced stochastic axion-photon oscillations in primordial magnetic field

Primordial black holes (PBHs) can be produced in the very early Universe due to the large density fluctuations. The cosmic background of axion-like particles (ALPs) could be non-thermally generated by PBHs. In this paper, we investigate the ALPs emitted by ultra-light PBHs with the mass range 10g ≲ M PBH ≲ 109 g, in which PBHs would have completely evaporated before the start of Big Bang Nucleosynthesis (BBN) and can therefore not be directly constrained. In this case, the minimal scenario that ALPs could interact only with photons is supposed. We study the stochastic oscillations between the ALPs and photons in the cosmic magnetic field in detail. The primordial magnetic field (PMF) can be modelled as the stochastic background field model with the completely non-homogeneous component of the cosmic plasma. Using the latest stringent limits on PMF, we show the numerical results of ALP-photon oscillation probability distributions with the homogeneous and stochastic magnetic field scenarios. The PBH-induced stochastic ALP-photon oscillations in the PMF may have the effects on some further phenomena, such as the cosmic microwave background (CMB), the cosmic X-ray background (CXB), and the extragalactic gamma-ray background (EGB).

Magnetic field evolution in cosmic filaments with LOFAR data

ABSTRACT Measuring the magnetic field in cosmic filaments reveals how the Universe is magnetized and the process that magnetized it. Using the Rotation Measures (RM) at 144 MHz from the LoTSS DR2 data, we analyse the rms of the RM extragalactic component as a function of redshift to investigate the evolution with redshift of the magnetic field in filaments. From previous results, we find that the extragalactic term of the RM rms at 144 MHz is dominated by the contribution from filaments (more than 90 per cent). Including an error term to account for the minor contribution local to the sources, we fit the data with a model of the physical filament magnetic field, evolving as $B_f = B_{f,0}\, (1+z)^\alpha$ and with a density drawn from cosmological simulations of five magnetogenesis scenarios. We find that the best-fitting slope is in the range α = [ − 0.2, 0.1] with uncertainty of σα = 0.4–0.5, which is consistent with no evolution. The comoving field decreases with redshift with a slope of γ = α − 2 = [ − 2.2, −1.9]. The mean field strength at z = 0 is in the range Bf, 0 = 39–84 nG. For a typical filament gas overdensity of δg = 10 the filament field strength at z = 0 is in the range $B_{f,0}^{10}=8$–26 nG. A primordial stochastic magnetic field model with initial comoving field of BMpc = 0.04–0.11 nG is favoured. The primordial uniform field model is rejected.

Self-organized criticality in a mesoscopic model of excitatory-inhibitory neuronal populations by short-term and long-term synaptic plasticity.

Dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT) bifurcation point can generate the observed scale-free avalanches at the population level and the highly variable spike patterns of individual neurons. These characteristics match experimental findings for spontaneous intrinsic activity in the brain. In this paper, we address the mechanisms causing the system to get and remain near this BT point. We propose an effective stochastic neural field model which captures the dynamics of the mean-field model. We show how the network tunes itself through local long-term synaptic plasticity by STDP and short-term synaptic depression to be close to this bifurcation point. The mesoscopic model that we derive matches the directed percolation model at the absorbing state phase transition.

Superstatistical Wind Fields from Pointwise Atmospheric Turbulence Measurements

Accurate models of turbulent wind fields have become increasingly important in the atmospheric sciences, e.g., for the determination of spatiotemporal correlations in wind parks, the estimation of individual loads on turbine rotor and blades, or the modeling of particle-turbulence interaction in atmospheric clouds or pollutant distributions in urban settings. Because of the difficult task of resolving the fields across a broad range of scales, one oftentimes has to invoke stochastic wind field models that fulfill specific, empirically observed, properties. Whereas commonly used Gaussian random field models solely control second-order statistics (i.e., velocity correlation tensors or kinetic energy spectra), we explicitly show that our extended model emulates the effects of higher-order statistics as well. Most importantly, the empirically observed phenomenon of small-scale intermittency, which can be regarded as one of the key features of atmospheric turbulent flows, is reproduced with a very high level of accuracy and at considerably low computational cost. Our method is based on a multipoint statistical description of turbulent velocity fields that consists of a superposition of multivariate Gaussian statistics with fluctuating covariances. We propose a new and efficient sampling algorithm for this Gaussian scale mixture and demonstrate how such “superstatistical” wind fields can be constrained on a certain number of real-world measurement data points from a meteorological mast array.Received 12 April 2022Revised 26 July 2022Accepted 22 August 2022DOI:https://doi.org/10.1103/PRXEnergy.1.023006Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtmospheric scienceBoundary layersShear flowsStochastic processesStructure & turbulence of boundary layersSustainabilityTurbulenceWind energyEnergy Science & TechnologyNonlinear DynamicsFluid DynamicsStatistical Physics

Computational generation of multiphase asphalt nanostructures using random fields

AbstractThis study presents a novel methodology to generate computational replicates of nanostructures of multiphase materials, such as asphalt binders, by integrating image analysis techniques with stochastic random field (RF) modeling. Image analysis techniques are used to identify and segment nanostructure images obtained by atomic force microscopy, while RF is used to model the spatial distribution of their material properties. The results of this process are images showing probable arrangements of nanostructures with stochastic material properties that replicate the experimentally obtained images. The computationally generated nanostructures are then used as inputs in a finite element model to evaluate the effect of heterogeneity on their mechanical response. The efficacy of the developed approach is demonstrated through simulations of asphalt binders’ nanostructures, which reveal novel insights regarding their nanoscale mechanical behavior and response. The FE simulations provided the link between the distribution of nanoscale properties of asphalt binders and variations in their mechanical response. The application of this methodology expands the body of knowledge beyond the deterministic analysis of asphalt binders toward probabilistic analysis and uncertainty quantification that considers their heterogeneous, multiphase structures. Consequently, the methodology can be used to design multiphase materials, such as asphaltic blends, with tailored properties and enhanced performance.

Stochastic field model for the residual radius along the length of naturally and artificially corroded rebars

This paper examines the random variation of the residual radius along the length of both naturally corroded and artificially corroded rebars. The rebars are washed to remove rust, and their residual area is measured by the water volume method for every 20-mm long segment of each rebar. Tests are carried out to determine the stationarity or non-stationarity of the stochastic field used to model the residual radius of the specimens. Then, the autocorrelation function, power spectrum and marginal probability distribution function of each specimen are estimated. It is found that the residual radius field of both naturally and artificially corroded rebars with mean corrosion levels below 20% is stationary, while the situation can change as the mean corrosion level increases and concrete cover spalling occurs. The residual radius field along the rebar length of stationary specimens is found to be white noise for both naturally and artificially corroded rebars. The marginal probability distribution function of the residual radius is determined to be skewed and can be fitted with a Beta distribution for naturally corroded rebars and with a Weibull distribution for artificially corroded rebars. This is the first paper studying and comparing both naturally and artificially corroded rebars.

Stability evaluation of earth-rock dam reinforcement with new permeable polymer based on reliability method

The stability of earth-rock dam slope has always been the focus of engineers. The existing dam slope reinforcement measures mainly include anchor rods, anchor cables, soil nails, frame lattice beams, micro-piles and so on. However, the construction technology of these reinforcement measures is relatively complex and will cause disturbances to varying degrees in the construction process. In this paper, a new type of permeable polymer material is proposed for grouting anti-seepage reinforcement of dam slopes, and a stochastic field model of slope parameters after reinforcement is established. By analyzing the safety factor and failure probability of different types slope before and after reinforcement, it can be found that the safety factor of the slope can be greatly improved after the slope is reinforced with permeable polymer grouting; as the gradient increases, although the reinforcement effect decreases slightly, it can still have a good reinforcement effect; as the slope height increases, the reinforcement effect decreases gradually; in general, for medium and low slopes, the improvement effect of safety factor can reach about 50%; in the aspect of slope reinforcement of earth-rock dam, permeable high polymer is more suitable for middle and low earth-rock dam reinforcement.

A metamodeling-based robust optimisation approach for structures subjected to random underground blast excitation

The blast hazards are associated with extreme randomness. Thus, structures under blast should be properly designed for such highly uncertain phenomena. However, codal stipulations and existing literature do not consider important uncertainty-related design issues, such as record-to-record variation of blast load, high uncertainty levels associated with blast parameters, and robustness of structural behaviour under extreme blast events. In the present study, a computationally efficient robust optimisation (RO) approach is proposed for blast-excited structures by addressing these issues. In doing so, a new CDF-based constraint formulation is developed in the dual response surface-based metamodeling framework to avoid the use of direct Monte Carlo simulation (MCS) during RO iterations. Thereby, the proposed approach becomes computationally much efficient than the conventional direct MCS-based RO. Since the proposed approach resorts to matching the CDF of the actual response, instead of the conventional RO formulations based on the first two statistical moments only, the approach is more realistic. The present approach adopts the moving least-squares method instead of the usual least-squares method to retain accuracy in response approximation. The blast load time-history is generated by a stochastic field model with proper validation through real blast data. Three example problems have been investigated to establish the effectiveness of the proposed RO procedure. The RO results depict that the present method yields economic design solutions, which are also insensitive to high uncertainty levels associated with the extreme blast load. The COV of performance function is substantially low even when input parameter uncertainty is high.

Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model.

We investigate oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model by simulating Mexican-hat-coupled stochastic processes. We find, for several choices of parameters, that spatial pattern formation in the temporal phases of the coupled processes occurs if and only if their amplitudes are allowed to grow unrealistically large. Stimulated by recent work on homeostatic inhibitory plasticity, we introduce static and plastic (adaptive) systemic inhibitory mechanisms to keep the amplitudes stochastically bounded. We find that systems with static inhibition exhibited bounded amplitudes but no sustained phase patterns. With plastic systemic inhibition, on the other hand, the resulting systems exhibit both bounded amplitudes and sustained phase patterns. These results demonstrate that plastic inhibitory mechanisms in neural field models can dynamically control amplitudes while allowing patterns of phase synchronization to develop. Similar mechanisms of plastic systemic inhibition could play a role in regulating oscillatory functioning in the brain.

Tropical cyclone damage assessment of distributed infrastructure systems under spatially correlated wind speeds

Probabilistic damage evaluation and loss estimation of spatially distributed infrastructure systems (e.g. an electric power system or a building portfolio) under a scenario tropical cyclone must consider the spatial correlation of cyclone wind speeds to estimate their impact on the built environment statistically. Previous studies have seldom considered the impact of this spatial correlation on damage assessments of distributed civil infrastructure. In this paper, a stochastic field model is developed to capture the uncertainty of cyclone wind speeds and their spatial correlation for the North Atlantic region. A series of recorded wind speed fields of historical cyclone events are examined. The bias values between the recorded wind speeds and computed wind speeds based on a widely used cyclonic wind field model are obtained. The statistics of the wind field bias are estimated using geostatistical tools. The effect of wind speed uncertainty and spatial correlation on performance assessment of distributed infrastructure systems is illustrated using an electric power system, where the metrics of performance are damage ratio, outage ratio and outage cost.

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome.

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

Study on surface characteristics and stochastic model of corroded steel in neutral salt spray environment

To study the surface morphology characteristic of corroded steel in a neutral salt spray environment, an artificial accelerated corrosion tests were carried out and eight batches of specimens with different corrosion ages were obtained. The corroded steel surface morphologies were collected by a non-contact 3D profiler, and the characteristic parameters were extracted by a special analysis program. The results showed that the corrosion depth of steel surfaces generally follows a normal distribution, while the pit depth and aspect ratio follow a lognormal distribution. As the degree of corrosion increases, the average value and standard deviation of corrosion depth, and logarithm mean value of the pit depth increase, while the logarithm mean value of the pit aspect ratio decreases. In addition, the pit density fluctuates in the range of 20–30 and the conical pits on the steel surface account for the largest proportion in the neutral salt spray corrosion environment. Based on the statistical results and parameter change laws, the stochastic field model of corrosion depth and the random distribution model of corrosion pit were established, and the corroded surfaces were reconstructed in the neutral salt spray corrosion environment.

A Map-Aided Navigation Algorithm without Preprocessing of Field Measurements

A new algorithm for geophysical map-aided navigation is proposed. It does not require any preliminary estimation of the field measured along the vehicle trajectory and, as consequence, does not need any stochastic field model. The algorithm uses a whole set of the available geophysical field measurements. The accuracy analysis procedure applied to estimate the effectiveness of the proposed algorithm is described. The features and advantages of this algorithm are illustrated by an example of marine gravity-aided navigation.

Interval K-L expansion of interval process model for dynamic uncertainty analysis

The interval process model describes a time-variant or dynamic uncertain parameter by the upper and lower bounds rather than the precise probability distribution at each time point, providing an effective structural dynamic uncertainty quantification model with insufficient sample information. By reference to the Karhunen-Loève (K-L) expansion for stochastic process and random field models, a novel expansion method for the interval process model, namely, the interval K-L expansion is proposed in this work. The interval K-L expansion describes the continuous uncertainty of the interval process in time domain by superposition of infinite deterministic time-related functions with uncorrelated interval coefficients, which makes the interval process model much more convenient to use. By introducing a splicing technique, the interval K-L expansion method for multiple correlated interval processes is also presented. Based on the interval K-L expansion, the vibration of structures subject to interval process excitations is analyzed, where the analytic formulation of dynamic response bounds for linear elastic systems and continuum structures are derived. Finally, several numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Wandering bumps in a stochastic neural field: A variational approach

We develop a generalized variational method for analyzing wandering bumps in a stochastic neural field model defined on some domain U. For concreteness, we take U=S1 and consider a stochastic ring model. First, we decompose the stochastic neural field into a phase-shifted deterministic bump solution and a small error term, which is assumed to be valid up to some exponentially large stopping time. An exact, implicit stochastic differential equation (SDE) for the phase of the bump is derived by minimizing the error term with respect to a weighted L2(U,ρ) norm. The positive weight ρ is chosen so that the error term consists of fast transverse fluctuations of the bump profile. We then carry out a perturbation series expansion of the exact variational phase equation in powers of the noise strength ϵ to obtain an explicit nonlinear SDE for the phase that decouples from the error term. Solving the corresponding steady-state Fokker–Planck equation up to O(ϵ), we determine a leading-order expression for the long-time distribution of the position of the bump. Finally, we use the variational formulation to obtain rigorous exponential bounds on the error term, demonstrating that with very high probability the system stays in a small neighborhood of the bump for times of order exp(Cϵ−1).

Artificial Neural Networks for Chemistry Representation in Numerical Simulation of the Flamelet-Based Models for Turbulent Combustion

Turbulent combustion is one of the key processes in many energy conversion systems in modern life. In order to improve combustion efficiency and suppress emission of pollutants, many efforts have been made by scholars to investigate turbulent flames. In the present study, Artificial neural network (ANN) was first employed for the storage and interpolation of the flamelet library in flamelet generated manifolds (FGM) model, in which Eulerian stochastic field (ESF) model was used to directly consider the probability density function of the control variables. This new model had been implemented in OpenFOAM and was validated by simulation of the Sandia Flame D under consideration of the detailed chemical reaction mechanism. By comparing the results of numerical simulations and experimental measurements of the temperature and the mass fraction of main components, the accuracy of the proposed ANN-ESFFGM model was verified. Through the use of ANNs to characterize the chemical reactions, the flame simulation accuracy of the new model is higher than that of the original ESFFGM model, especially in the prediction of the ignition position. With the increase in the number of stochastic fields, the simulation accuracy of the new turbulent combustion model is continuously improved until a certain value of stochastic fields was reached. Moreover, excessively high FGM table resolution has limited improvement in numerical simulation accuracy.

Deep Markov models of multidimensional random fields

Abstract The paper discusses the use of a doubly stochastic random field model based on autoregressions with multiple roots of characteristic equations for solving the problem of image generation and segmentation. It was proposed to form an image taking into account hidden Markov parameter fields. In particular, the correlation coefficients of the model, as well as the average values and brightness variances, are realizations of random fields, the assessment of which in explicit form is not possible. In addition, a modification of a variational autoencoder for a doubly stochastic model is considered. Finally, based on the use of a modified variational auto encoder, classification and segmentation of satellite images is performed. The combined use of the developed segmentation algorithm with the Unet neural network provides an increase in segmentation accuracy of 3%.