Three-dimensional Random Field Research Articles

Reliability Analysis Method of Rotating Machinery Based on Conditional Random Field.

Rotating machinery is indispensable mechanical equipment in modern industrial production. However, rotating machinery is usually under heavy load. Due to the complexity of its structure and the severity of its working conditions, it is urgent to find effective condition monitoring methods and fault maintenance strategies for its safe and reliable operation. The conditional random field is derived from the maximum entropy model, which solves the problem of label bias and improves the convergence speed of model training. Combining Kriging theory and random field theory, this study proposes a three-dimensional conditional random field generation method based on failure time, applies this method to the comparison of measured data and other nonconditional random fields, and then analyzes the failure probability of rotating machinery in the failure process by combining the numerical calculation results and reliability theory. It is found that the conditional random field generation method can effectively describe the spatial variability of rotating machinery parameters. Compared with the nonconditional random field, the reliability index of rotating machinery failure time is improved by 0.8823, so the conditional random field can better describe the reliability of rotating machinery.

Numerical investigation on pullout capacity of helical piles under combined loading in spatially random clay

Helical piles are one promising foundation option in offshore industries to support wind turbines and floating structures. During service, the helical piles are subjected to combined loading originating from the superstructure and environmental factors. For the inclined pullout capacity of helical piles, several studies focused on the influence of helical plate configurations and soil properties. In contrast, this paper aims to assess the effect of the random distribution of soil strength. This is undertaken through the use of a large deformation random finite element analysis combing the random field theory, coupled Eulerian-Lagrangian method and Monte Carlo approach. Spatial variability and linearly increasing with depth of soil strength are modeled as a three-dimensional random field and a mean trend term. The probabilistic failure envelope as well as the failure mechanism can be then determined from each random realization. It is found that soil randomness has an insignificant influence on the failure mechanism. For different spatial soil configurations, the probabilistic failure envelopes vary widely from one another. An equation is established to fit the envelopes with different occurrence probabilities and probabilistic analyses are conducted. The present findings might help to improve the helical pile design practices to achieve better reliability.

Three-Dimensional Probabilistic Analysis of the Surface Settlement Based on Spatial Variability of Soil Properties: Case Study Zarbalizadeh NATM Tunnel

The design and construction of a tunnel in urban areas need special considerations. Usually, the excessive settlement caused by tunnelling during the construction process damages the adjacent infrastructures and utilities, especially if the tunnel is excavated by the new Austrian tunnelling method (NATM). Thus, it is important to make accurate predictions and effective control on tunnelling-induced settlement. In this study, the soil’s Young’s modulus was modelled using a three-dimensional random field and coupled with a finite difference method (FDM) analysis to reveal the scale of fluctuations (SOF) effects on the maximum surface settlement (Smax). The Fourier series method is employed to generate the field of Young’s modulus for soil, and sensitivity studies are further performed via Monte-Carlo simulations (MCS). The results demonstrate that the mean value of Smax increased from 28 to 31 mm and its coefficient of variation (COV) increased from 0.02 to 0.35, with an increasing horizontal SOF but both stabilize at higher values of SOF. Furthermore, the probability of failure increases as the COV increases for each allowable limit greater than the verification FDM of Smax. It is observed that ignoring the spatial variability of the soil properties leads to an underestimate of excessive surface settlement risk.

Spin activity correlations in driven disordered systems

We study the spatio-temporal correlations in the spin flipping activities of the disordered systems realized within the frame of the field-driven three-dimensional zero-temperature nonequilibrium random field Ising model. Our results for the spatial activity correlations reveal that the rate-dependent scaling holds in the full range of rate regimes provided that the system parameters satisfy the finite-size and rate-dependent scaling conditions. Temporal activity correlations show high sensitivity to the driving, allowing the collapsing of waiting time distributions only in the limit of slow driving rates. These findings, based on extensive numerical simulations of large systems, reliably demonstrate the observed behavior and could be relevant for studies on various, particularly experimental, nonequilibrium systems driven at finite rates.

Random Characteristics of Hydraulic Gradient through Three-Dimensional Multilayer Embankment

The distribution characteristics of hydraulic gradient in embankment are closely related to seepage failure. Seepage failures such as flowing soil and piping will lead to serious damage and even the overall failure of embankment. The hydraulic conductivity has strong spatial variability, which changes the distribution of hydraulic gradient in embankment and increases the difficulty for predicting the embankment seepage instability. In this study, the distribution of soil hydraulic conductivity in a section of Shijiu Lake embankment was obtained by the permeability test. Based on Local Average Subdivision technique, a three-dimensional multilayer random field of embankment hydraulic conductivity was generated. Then, the mean and standard deviation of overflow point height and hydraulic gradient were calculated by the Monte Carlo method, which combined the generated three-dimensional random model and the deterministic analysis method of seepage field. Finally, the coefficient of variation (COV) of hydraulic conductivity (0.1, 0.3, 0.5, 0.7, 1.0, 2.0, and 3.0), the fluctuation scale in vertical direction (3 m) and the fluctuation scale in horizontal plane (3 m, 6 m, 12 m, 24 m, 36 m, and 48 m) were selected respectively for analyzing the random characteristics of embankment overflow point height and hydraulic gradient under the influence of different COV and fluctuation scale of embankment soil hydraulic conductivity.

Application of Artificial Neural Network Algorithm in Facial Biological Image Information Scanning and Recognition.

In order to solve the problem that the accuracy of face recognition is not good due to the influence of jitter and environmental factors in the mobile shooting environment, this paper proposes the application of an artificial neural network algorithm in the information scanning and recognition of face biological images. The spatial neighborhood information is integrated into the amplitude detection of multipose face images, and the dynamic corner features of multipose face images are extracted. The structural texture information of multipose face images is compared to a global moving RGB three-dimensional bit plane random field, and the multipose face images are detected and fused. At different scales, appropriate feature registration functions are selected to describe the feature points of multipose face images. The parallax analysis of target pixels and key feature detection of multipose face images are carried out. Image stabilization and automatic recognition are realized by combining artificial neural network learning and feature registration methods. The experimental results show that the experiment is designed with MATLAB, the frame frequency of dynamic face image acquisition is 1200 kHz, the number of collected samples of the multipose face image is 2000, the training sample set is 200, the noise coefficient = 0.24, the number of multipose face image blocks is 120, and the structural similarity is 0.12. It is found that the output signal-to-noise ratio of multipose face image recognition using the method in this paper is high. Conclusion. This method has good performance in feature point registration and high recognition accuracy for multipose face image recognition.

Site-scale liquefaction potential analysis using a sectional random field model

This paper presents a new random field modeling to assess the site-scale spatial variability of soil properties applied in liquefaction mapping. In this procedure, the initial random fields are primarily generated, based on in-situ measured data. These initial fields are considered as the virtual known values to construct interior random fields, section-by-section and around a central axis. Assembling these sections results in a three-dimensional random field model. Through this approach, more accurate vertical semivariogram models can be available, in addition to a higher number of measured data involved in the generation of random fields. Based on a verification procedure, computational cost reduction and a more appropriate prediction of the layering characteristics are the two most important beneficial points of changing the modeling strategy from planar to sectional. The proposed approach is implemented in a case study in Oceano, California and the spatial distribution of liquefaction probability is estimated. It is concluded that the sectional random field can efficiently locate the liquefiable zone through the soil volume, based on liquefaction evidence. In addition to performing the liquefaction severity assessment, it is also illustrated that the hazard assessments based on liquefaction severity alone cannot provide the comprehensive prediction of liquefaction potential and may lead to unconservative engineering judgments.

Random failure mechanism method for assessment of working platform bearing capacity with a linear trend in undrained shear strength

A bearing capacity evaluation for the surface strip foundation on a working platform modelled on a two-layered substrate is considered in the study. The upper layer is assumed as man-made and well-controlled and thus non-variable. The lower layer modelling natural cohesive soil is subjected to spatial variability of undrained shear strength. The random failure mechanism method (RFMM) is used to evaluate the bearing capacity. This approach employs a kinematic assessment of the critical load and incorporates the averaging of three-dimensional (3D) random field along dissipation surfaces that result from the failure mechanism geometry. A novel version of the approach considering an additional linear trend of undrained shear strength in the spatially variable layer is proposed. The high efficiency of the RFMM algorithm is preserved. The influences of foundation length, trend slope in the spatially variable layer, fluctuation scales, and thickness of the homogenous sand layer on the resulting bearing capacity evaluations are analysed. Moreover, for selected cases, verification of the RFMM based assessment obtained using random finite difference method (RFDM) based on 3D analysis is provided. Two types of analyses are performed using RFDM based on associated and non-associated flow rules. For associated flow rule which corresponds to RFMM, the RFMM is conservative and efficient and thus it seems preferable. However, if RFDM employs non-associated flow rule (much lower dilation angle for sand layer), the efficient RFMM is no longer conservative. For this situation, a combined approach that improves the efficiency of the numerical method is suggested.

Efficient simulation of multivariate three-dimensional cross-correlated random fields conditioning on non-lattice measurement data

It is challenging to simulate large-scale or fine-resolution multivariate three-dimensional (3D) cross-correlated conditional random fields because of computational issues such as inverting, storing or Cholesky decomposition of large correlation matrices. Recently, an efficient univariate 3D conditional random field simulation method was developed based on the separability assumption of the autocorrelation functions in the vertical and horizontal directions. The developed simulation method allows for Kronecker-product derivations of the large correlation matrices and thus does not need to invert and store large matrices. Moreover, it can handle univariate non-lattice data (e.g., all soundings measure the data of one soil property and there exists missing data at some depths at some soundings). It may be more common to see multivariate non-lattice data (e.g., all soundings measure the data of multiple soil properties and there exists missing data of some properties at some depths at some soundings) in practical site investigations. However, the proposed method is not applicable to multivariate non-lattice data because it cannot directly account for the cross-correlation among different variables The purpose of the current paper is to extend the previous method to accommodate the multivariate non-lattice data. The extended method still takes advantage of the Kronecker-product derivations to avoid the mathematical operation of the large correlation matrices. A simulated example is adopted to illustrate the effectiveness of the extended method.

The effect of finite driving rate on avalanche distributions

We study distributions of spin avalanches in the three-dimensional nonequilibrium zero temperature random field Ising model driven by external magnetic field that is increased at constant rate. Our results show that avalanche distributions are affected by the driving regime and although the avalanche properties (e.g. size) remain power-law distributed above critical disorder, the scaling exponents vary with the driving rate. For slow driving, the integral distributions of nonspanning avalanches are almost the same as in the adiabatic and quasi-static driving regime and therefore described by constant values of power-law exponents. Owing to temporal overlapping and merging of avalanches, these distributions become markedly different with the increased driving rate which causes an increase of exponent values in the range of moderate driving rates and their saturation for fast driving. The integral distributions of all avalanches behave similarly but without the saturation of exponents for fast driving. Our results, based on extensive numerical simulations, could be relevant for studies of variety of systems in finite driving regime, particularly those with experimental realizations that are not easily attainable.

Model Updating of Slope Stability Analysis Using 3D Conditional Random Fields

AbstractIn situ soil properties exhibit spatial variability, which is often described using a three-dimensional (3D) random field. With site investigations, soil properties at some specific locatio...

Simulation of three-dimensional random field conditioning on incomplete site data

This paper proposes a novel method for simulating a three-dimensional (3D) random field conditional on site data. It is based on the assumption of separable auto-correlation in the vertical and horizontal directions. This novel method adopts special simulation techniques so that it can handle incomplete site data (e.g., missing data at some depths). Moreover, it can simulate a 3D conditional random field in a computationally efficient way without the need to invert and store large matrices. The proposed method simulates a 3D conditional random field with two steps. The first step simulates the missing site data to make the site data complete. The second step simulates the conditional random field at locations not explored by the soundings/boreholes. A simulated example is adopted to illustrate the effectiveness of the proposed method.

Heterogeneous Multi-Rate mass transfer models in OpenFOAM®

We implement the Multi-Rate Mass Transfer (MRMT) model for mobile–immobile transport in porous media (Haggerty and Gorelick, 1995; Municchi and Icardi, 2019 [1]) within the open-source finite volume library OpenFOAM® (Foundation, 2014). Unlike other codes available in the literature (Geiger et al., 2011 [2]; Silva et al., 2009), we propose an implementation that can be applied to complex three-dimensional geometries and highly heterogeneous fields, where the parameters of the MRMT can arbitrarily vary in space. Furthermore, being built over the widely diffused OpenFOAM® library, it can be easily extended and included in other models, and run in parallel. We briefly describe the structure of the multiContinuumModels library that includes the formulation of the MRMT based on the works of Haggerty and Gorelick (1995) and Municchi and Icardi (2020a). The implementation is verified against benchmark solutions and tested on two- and three-dimensional random permeability fields. The role of various physical and numerical parameters, including the transfer rates, the heterogeneities, and the number of terms in the MRMT expansions, is investigated. Finally, we illustrate the significant role played by heterogeneity in the mass transfer when permeability and porosity are represented using Gaussian random fields. Program summaryProgram Title: mrmtFoamCPC Library link to program files:https://dx.doi.org/10.17632/fkywm44j3y.1Developer’s repository link:https://github.com/multiform-UoN/mrmtFOAMLicensing provisions: GPL 3.0Programming language: C++Nature of problem: Large scale dynamics of heat and mass transfer in heterogeneous media where one mobile region coexists with multiple immobile regions.Solution method: The multi-rate mass transfer model is employed to described pre-asymptotic (i.e., non equilibrium ) transfer between regions. This method is implemented using the opensource finite volume library OpenFOAM®

Tensor train-Karhunen-Loève expansion: New theoretical and algorithmic frameworks for representing general non-Gaussian random fields

The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional physical domain in the tensor train format; secondly, to develop a new algorithmic framework for accurately computing the modes and describing the correlation structure of the latent factors beyond second order within moderate time. Central to the algorithmic framework is the tensor train decomposition of cumulant functions. This decomposition is accurately computed with a novel rank-revealing algorithm. For computing the modes, compared with existing Galerkin-type and collocation-type methods, the proposed computational procedure totally removes the need of selecting the basis functions or collocation points and the quadrature points, which not only greatly enhances adaptivity, but also avoids solving large-scale eigenvalue problems. Moreover, by computing with higher-order cumulant functions, the new theoretical and algorithmic frameworks show great potential for representing general non-Gaussian non-homogeneous random fields. Three numerical examples, including a three-dimensional random field discretization problem, illustrate the efficiency and accuracy of the proposed algorithmic framework.

Determination of limiting cavity depths for offshore spudcan foundations in a spatially varying seabed

The importance of accurate prediction of limiting cavity depths during offshore spudcan foundations installation has been variously highlighted in the literature. Nonetheless, most of the previous research is deterministic in nature and confined to homogenous soils. Since offshore clayey soils can be highly spatially variable, there is a practical need to take proper account of the spatial variability in the prediction of limiting cavity depths. In a bid to remedy this situation, large deformation finite element calculations combined with three-dimensional random fields were repeatedly conducted in this study within a Monte-Carlo framework. The continuous penetration of a spudcan initiated from surface was explicitly modeled until a full-localized flow-around mechanism was observed. Spatial variability was found to clearly affect the soil back-flow and thereby the limiting cavity depth, the latter of which takes a range of values that can be approximately modeled as a log-normal distribution. Characteristic limiting cavity depths at various probability levels were ascertained. An algebraic expression was proposed to explicitly predict the characteristic limiting cavity depths in random soils from the fractile. Particular attention was paid to the lower and upper 5% characteristic values, which are likely to be useful for reliability-based design.

Simulation of a random field with given distribution of one-dimensional integral

Abstract The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a layer 0 < z < H with given one-dimensional distribution and correlation function of the integral over coordinate z is solved. The gamma distribution with shape parameter ν and scale parameter θ is used in the work. An aggregate of n independent elementary horizontal layers of thickness h = H/n vertically shifted by a random value uniformly distributed in the interval (0, h) is considered as a basic model. For each elementary random field, the normalized correlation function of the corresponding integral over z coincides with the given one, the gamma distribution with parameters depending on the number of horizontal layers is used as a one-dimensional distribution. It is proved that for the constructed model the normalized correlation function of the integral over z coincides with the given normalized ‘horizontal’ correlation function, and the parameters of the one-dimensional distribution asymptotically converge to given values for n → + ∞, but the corresponding mathematical expectation and variance coincide exactly with given values. To extend the class of possible models, an additional randomization of the basic model is considered. In the conclusion the results of computations for a realistic version of the problem are presented.

New Discretization Methodology for Three-Dimensional Mechanical Parameters Considering Spatial Variations

In this paper, the uncertain mechanical parameters are modeled as spatial random fields (RFs). A new tetrahedral discretization methodology of three-dimensional (3D) RF is proposed based on the local average (LA) theory. An analytical formula and a numerical formula of the covariance for any two tetrahedral RF elements are developed. Its main advantage, compared to similar studies employing hexahedral discretization method, is that tetrahedral LA method can perfectly combine with tetrahedral finite element (FE) method. Also, the corresponding relation between RF mesh and FE mesh is clearer and the computer codes are simpler. The accuracy of proposed LA method in this study was verified by comparing with other discretization techniques of RF. Finally, an illustrative example is presented to demonstrate the analysis process. The validity and the advantage of the proposed LA method are proven. Taking the spatial variations of uncertain mechanical parameters into account, the stochastic effects of scale of fluctuation on the RF are estimated. The proposed method can be widely applied to 3D stochastic FE analysis, and the sample results will improve our understanding of the stochastic influence of scale of fluctuation on the RF.

Constructing a numerically statistical model of a homogeneous random field with the given distribution of the integral over one of the phase coordinates

The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a horizontal layer 0 z H with given one-dimensional distribution and correlation function of the integral over vertical coordinate z is solved. An aggregate of n independent elementary horizontal layers of thickness h = H/n, vertically shifted by a random value uniformly distributed in the interval (0, h) is considered as a basic model.

Foot intrinsic muscle forces impact on internal stresses and strain on diabetic foot subjects

This paper presents the analysis of the statistical size effect in steel structural elements using the stochastic finite element (FE) method. The three-dimensional random field theory is applied to simulate the uncertainty of a nonlinear material. The proposed approach, which combines the discrete random field describing the randomness of the material properties via Monte Carlo simulations, is used for computing the bearing capacity variability of the steel structures. In addition, the mapping interpolation method makes it possible to separate the random field mesh and FE model mesh. The three-dimensional random field for the material properties is established according to the yield strength with a lognormal distribution based on reasonable assumptions, and the corresponding random field parameters are studied. Finally, the results of experimental investigation and simulations are compared based on the tensile and bending tests, and they indicate that the statistical size effect cannot be overlooked in S235JR steel structural elements and that the use of stochastic FE in the analysis of the statistical size effect has tremendous potential.

Seismic response of pile–raft system embedded in spatially random clay

This note examines the seismic response of a pile–raft system using the random field finite-element method. The numerical method is validated by recently published centrifuge test results. The randomness in the maximum shear modulus of soils in the system is considered by three-dimensional random fields in order to investigate the statistical characteristics of the maximum pile bending moment response. The computed pile bending moment results indicate that the deterministic results can be linked up with the random analysis results by an amplification factor. Therefore, a reliability-based geotechnical design can be applied.