Three-dimensional Random Field Research Articles

Evaluating the load-bearing capacity of corroded cables in long-span cable-stayed bridges: A stochastic corrosion field simulation approach

In cable-stayed bridges, cables are the primary load-bearing components. The corrosion of high-strength steel wires within these cables can degrade their bearing capacity, which in turn impacts the safety and durability of long-span cable-stayed bridges. To address this concern, a three-dimensional random field model was proposed in this study to evaluate the residual bearing capacity of corroded cables. This model considers the random distribution of the strength of high-strength wires along both axial and cross-sectional directions caused by corrosion. Subsequently, a three-dimensional spatial correlation model was developed based on field test results from two stay cables in service on an actual bridge. This model represents the strength distribution of corroded high-strength steel wires within the cable. Finally, the evaluation model developed in this study was employed to assess the bearing performance of two corroded cables with different degrees of corrosion. The results were then compared with test outcomes. The results show that the proposed evaluation model can accurately estimate the bearing performance of corroded cables.

Lateral holding behaviour of torpedo piles in spatially variable soil: Development of a probabilistic design approach

Offshore torpedo piles are increasingly being utilised in deepwater oil and gas development as part of a taut-leg mooring system. As these piles commonly experience inclined loading in service, accurately determining their lateral holding capacity is crucial. Despite the fact that natural soil characteristics exhibit significant spatial variability, existing studies are mostly deterministic in nature. This paper presents probabilistic analyses of the lateral holding capacity of torpedo piles, explicitly considering the spatial variability of soil shear strength. Large deformation finite element calculations are combined with three-dimensional random field generation in a Monte Carlo framework. The results show that while spatial variability does not apparently alter the failure mechanism of laterally loaded torpedo piles, it significantly influences their holding capacity. The routine deterministic calculation, neglecting spatial variability, would probably yield unconservative estimates. To address this challenge, a probabilistic Broms method is developed, which enables engineers to produce lateral holding capacity estimates with varying confidence levels, using local strength data rather than central tendency. Furthermore, endeavours are also made to calibrate the safety factor, extensively employed in deterministic design practices, from a probabilistic perspective, providing practicing engineers with a viable alternative in scenarios where a local strength profile is unavailable.

Probabilistic analysis of homogenized elastic property for resin products fabricated by additive manufacturing based on three-dimensional random field modeling of microstructure

Additive manufacturing (AM) techniques have been used in several fields of science and industry, and fabrication techniques are being updated. For this fact, especially, for industrial use, mechanical property evaluation methodologies for AM products and standards for product quality assessment should also be well established. In this paper, a probabilistic evaluation of the homogenized elastic properties of a resin product fabricated by a material extrusion-based AM technique is attempted by considering the randomness of both material and microscopic geometrical quantities. This AM method fabricates a resin structure by piling up melted resin, and to decrease consumed material and influence of thermal deformation, the inner structure of the fabricated products will include many pores and its geometry is difficult to be well controlled. From this fact, the products will be regarded as a heterogeneous material with complex random microstructure. This will cause difficulty in the evaluation of its apparent material properties and therefore a probabilistic homogenization analysis is attempted for quantitative estimation of the apparent material property in this study. In particular, to investigate probabilistic properties of microscopic geometry, a random field modeling technique is employed for the evaluation of autocorrelation of the microscopic geometrical parameter, and the results of the autocorrelation identified by experimental observation are introduced to the probabilistic homogenization analysis. The two-dimensional or three-dimensional random field modeling is attempted, and the effectiveness of this approach is investigated by comparing it with the experimental result.

Reliability-based evaluation of ultimate embedment depths of torpedo anchors in spatially variable clay

In this study, a large deformation random finite element (LDRFE) method was used to investigate the dynamic penetration of anchor piles in spatially variable clay. Validation of the rationality of the proposed methodology using data from published studies. The randomness of the undrained shear strength of the soil in the system is considered by three-dimensional random fields to investigate the anchor penetration mechanism and quantitatively assess the ultimate embedment depths (Hran ) of the anchor in spatially variable clay. The strain softening and strain rate effects of the soft clayey soil were considered. The findings indicate that the variability in soil strength significantly affects the flow pattern and failure mechanism of the soil, consequently influencing the Hran of the anchor. Furthermore, according to the computed Hran results, a coefficient of variation of soil shear strength φ can be used to connect the deterministic (Hdet ) and random analysis results. This correlation may facilitate further development of reliability-based designs.

Optical momentum distributions in monochromatic, isotropic random vector fields

Abstract We investigate the decomposition of the electromagnetic Poynting momentum density in three-dimensional random monochromatic fields into orbital and spin parts, using analytical and numerical methods. In sharp contrast with the paraxial case, the orbital and spin momenta in isotropic random fields are found to be identically distributed in magnitude, increasing the discrepancy between the Poynting and orbital pictures of energy flow. Spatial correlation functions reveal differences in the generic organization of the optical momenta in complex natural light fields, with the orbital current typically forming broad channels of unidirectional flow, and the spin current manifesting larger vorticity and changing direction over subwavelength distances. These results are extended to random fields with pure helicity, in relation to the inclusion of electric-magnetic democracy in the definition of optical momenta.

Higher-order spectral representation method: New algorithmic framework for simulating multi-dimensional non-Gaussian random physical fields

This study derives a novel higher-order spectral representation method (HOSRM) to represent and simulate multi-dimensional fourth-order non-Gaussian random physical fields. The method primarily extends the traditional second-order spectral representation method (SRM) for simulating non-Gaussian random physical fields by introducing higher-order cumulant function tensors and trispectrum tensors, thereby accomplishing the modeling of fourth-order non-Gaussian random physical fields (symmetric nonlinear physical fields) from a frequency domain perspective. In an endeavor to enhance the simulation efficiency of this theoretical framework, the Fast Fourier Transform (FFT) algorithm is astutely amalgamated into the simulation. This integration contributes significantly to the augmentation of computational efficiency. Furthermore, exhaustive derivations and proofs are presented for the first-order, second-order, and fourth-order ensemble properties of simulated fourth-order non-Gaussian random physical fields. Subsequently, the reliability and accuracy of the proposed algorithm framework are validated through numerical simulations of two two-dimensional and two three-dimensional non-Gaussian random physical fields. The findings demonstrate that the simulated sample function effectively captures the probability characteristics of the random field, including mean, variance, and kurtosis. Finally, an in-depth analysis of numerical simulation results highlights the difference between the proposed method and the traditional second-order spectral representation method, which further underscores the distinctive attributes and potential superiority of the proposed method.

Gaussian random field-based characterization and reconstruction of cancellous bone microstructure considering the constraint of correlation structure

The macro scale physical properties of cancellous bone materials are governed by the microstructural features, which is of great significance for the multi-scale research of cancellous bone and the inverse design of bone-mimicking materials. Therefore, it is essential to characterize the natural cancellous bone samples, and reconstruct the microstructures with the biomimetic osteointegration and mechanical properties. In this research, a novel approach for the characterization and reconstruction of cancellous bone was proposed, based on the medical image analysis and anisotropic three-dimensional Gaussian random field (GRF). The geometric similarity, i.e. the interface curvature distribution (ISD), was meticulously studied, which is important to the osteointegration ability. And the mechanical properties were validated by the stress-strain curves under the large compressive strain simulated by the smoothed particle hydrodynamic (SPH) method. In addition, the effects of the generation parameters of GRF-based biomimetic microstructures on the apparent properties were analyzed. The ISD results demonstrated that both GRF and micro-CT groups had the similar columnar morphological properties, while the latter had more hyperbolic features. And it was found that the GRF-based biomimetic microstructures and the natural bone samples based on micro-CT (MCT) had the similar failure mode. The concordance correlation coefficient between MCT and GRF pairs was 0.8685, with a Pearson ρ value of 0.8804, and significance level p<0.0001. The Bland-Altman LoA was 0.1647 MPa with 95 % (1.96SD) lower and upper bound value between −0.2892 and 0.6185 MPa. The two groups had almost the same elastic modulus with the mean absolute percentage error (MAPE) of 7.84 %. While the yield stress and total conversion energy of the GRF-based samples were lower than those of the natural bone samples, and the MAPE were 16.99 % and 16.27 %, respectively. Although it meant the lower structural efficiency, the huge design space of this approach and advanced 3D printing technology can provide great potential for the design of orthopedic implants.

Heterogeneous nucleation in the random field Ising model.

We investigate the nucleation dynamics of the three-dimensional random field Ising model under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus and use forward flux sampling for the direct estimation of nucleation rates. For moderate to strong disorder, our results indicate that the size of the nucleating cluster is not a good reaction coordinate, contrary to the pure Ising model. We rectify this problem by introducing a coordinate that also accounts for the location of the nucleus. Using the free energy barrier to predict the nucleation rate, we find reasonable agreement, although deviations become stronger as disorder increases. We attribute this effect to cluster shape fluctuations. We also discuss finite-size effects on the nucleation rate.

Three-dimensional reliability stability analysis of earth-rock dam slopes reinforced with permeable polymer

Polymer is a new repair and reinforcement material for earth-rock dams developed in recent years. Models are developed where spatial variability is incorporated into the analytical framework to evaluate the stability and reliability of reinforced three-dimensional dam slopes. The Karhunen-Loeve (K-L) expansion method is employed to generate three-dimensional random fields. The simplified Bishop method and Monte Carlo method are used to calculate the safety factors and failure probabilities of the dam slopes. With the implementation of polymer grouting reinforcement, the safety factors are improved and the failure probabilities are reduced. The reinforcement effect will be affected by the amount of polymer dosing, dam slope characteristics, and polymer grouting parameters. The impact of various longitudinal autocorrelation distances on reliability is influenced by the length of the dam slope itself. An increase of the safety factor by approximately 37% can be achieved through a polymer dosing of around 3%. Nevertheless, with the elevation of dam slope height and slope ratio, the effectiveness of polymer reinforcement is diminished.

Probabilistic analysis on the lateral capacity of suction caissons in spatially variable soils

This paper aims to investigate the ultimate lateral capacity of suction caissons embedded in clay with spatially varying undrained shear strength in the framework of probabilistic analysis for the first time. A non-stationary three-dimensional random field is used to represent the undrained shear strength with a linearly increasing trend with depths below the mudline. The stochastic finite difference method is employed to determine the probabilistic ultimate lateral capacity of suction caissons. The influences of the clay undrained strength heterogeneity κ, the coefficient of variation of undrained strength COVsu, and the autocorrelation distances on the probability density function (PDF) curves and cumulative distribution function (CDF) curves of the normalized ultimate lateral capacity N h are investigated . It is found that both the mean and standard deviation of normalized ultimate lateral capacity N h increase with the undrained strength heterogeneity κ, but the coefficient of variation of N h does not. Besides, the small autocorrelation distance of clay results in the low variability of normalized ultimate lateral capacity. This indicates the significance of probabilistic site characterization of the undrained strength of clay.

An iterative multi-fidelity scheme for simulating multi-dimensional non-Gaussian random fields

This paper presents an efficient multi-fidelity scheme to simulate multi-dimensional non-Gaussian random fields that are specified by covariance functions and marginal probability distribution functions. To develop the multi-fidelity scheme, two numerical algorithms are proposed in turn. The first algorithm is used to simulate random samples of the random field. In this algorithm, initial random samples are first generated to meet the marginal distribution and an iterative procedure is adopted to change the ranking of the random samples to match the target covariance function. By using the above algorithm, random samples satisfying the target covariance function and the target marginal distribution are obtained, but it is computationally intensive and is not suitable to simulate large-scale random fields. By taking advantage of Karhunen–Loève expansion, a multi-fidelity algorithm is then proposed to reduce the computational effort. The random variables in Karhunen–Loève expansion are calculated via performing the first algorithm on the low-fidelity model and the deterministic functions in Karhunen–Loève expansion are solved on the high-fidelity model. In this way, the proposed method has low computational effort and a high fidelity simultaneously. Three numerical examples, including two- and three-dimensional non-Gaussian random fields, are used to verify the good performance of the proposed algorithms.

Numerical modelling of the keying process for a suction embedded plate anchor in spatially varying clays

ABSTRACT As the exploration of oil and gas moves into deeper water, suction embedded plate anchors (SEPLAs) are developed to answer the growing demand for anchor-mooring systems. The keying process of SEPLAs has been extensively reported assuming a spatially homogeneous soil which is a departure from reality. This study conducts a comprehensive investigation of the keying process of SEPLA in spatially varying clay through a large deformation random finite element method coupled with the Monte Carlo simulations. The numerical model is validated with the results from the existing centrifuge test and numerical analysis. The spatial randomness of soil strength is assumed to be a three-dimensional (3D) random field to explore the failure mechanism and statistical characteristics of rotational response and pullout behaviour. The normalised factor of the upper 5% fractile of embedment loss is presented as an algebraic expression of the coefficient of variation of soil strength. The relationship between safety factor and failure probability is determined based on the requirement of pullout capacity. Finally, the applicability of the present results to different soil properties is verified.

Investigation of the peak punch-through capacity of spudcan on sand overlying spatially variable clay

Accurately estimating peak penetration resistance in punch-through sensitive deposits is crucial for managing risks during jack-up rig installations. While offshore clays exhibit significant spatial variability, necessitating consideration of spatial variability in predicting peak penetration resistance. This study investigates the effects of spatial variability of underlying clay on the failure mechanism and magnitude of peak penetration resistance during punch-through incidents. The Modified Linear Estimation Method was used to generate three-dimensional random fields, incorporated into coupled Eulerian Lagrangian finite element analyses to simulate spudcan penetration from the ground surface. Results show that while spatial variability has an insignificant effect on the failure mechanism in the upper sand layer, it significantly alters soil flow in the underlying clay, leading to variations in peak penetration resistance. The peak penetration resistance follows a log-normal distribution, and a relationship was established between the probability of failure and the factor of safety. This study highlights the importance of considering soil spatial variability and demonstrates the significant impact of underlying clay on the failure mechanism and magnitude of peak penetration resistance during punch-through incidents, which might be helpful for the safety management of industry.

Structured Hybrid Message Passing Based Channel Estimation for Massive MIMO-OFDM Systems

This paper investigates uplink channel estimation for massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with uniform planar array (UPA) antennas at the base station (BS). We first establish a triple beam-based channel model using sampled steering vectors. Based on the presented channel model, we further develop a three-dimensional (3D) Markov random field (MRF) probability model to capture the structured channel sparsity. Then constrained Bethe free energy (BFE) minimization is introduced to provide a systematic theoretical framework for message passing. Under this framework, we derive a structured hybrid message passing (SHMP) algorithm to address the channel estimation problem. The proposed algorithm can significantly improve the estimation accuracy by exploiting the clustered sparse structure of channels with low complexity. Moreover, aiming at the fine factors of the triple beam-based channel model and the coupling parameter of the 3D-MRF sparsity model, we analyze the effect of their different settings in the numerical simulation. Finally, extensive simulation results verify the superiority of the proposed SHMP algorithm.

Modified Matrix Decomposition Method for Generating Multivariate Three-Dimensional Cross-Correlated Random Fields

Modified Matrix Decomposition Method for Generating Multivariate Three-Dimensional Cross-Correlated Random Fields

Large-deformation modelling of earthquake-triggered landslides considering non-uniform soils with a stratigraphic dip

Natural soil slopes often exhibit both spatial variability and stratigraphic dips due to complex depositional processes of soil, exerting a remarkable influence on landslide behaviors. Existing research mostly focused on the influence of soil spatial variability on slope stability or landslide runout behaviors, and the investigation of the effect of stratigraphic dip on large-deformation landslide consequences are relatively limited and have not been fully understood. This study therefore proposed a random large-deformation finite-element (LDFE) computation framework, combining the coupled Eulerian-Lagrangian technique and a three-dimensional (3D) rotational random field to insight the earthquake-triggered landslide consequences considering non-uniform soils with a stratigraphic dip. The whole runout process of earthquake-triggered landslides from activation to termination is realistically reproduced. By implementing both two-dimension (2D) and 3D random LDFE analyses coupled with Monte-Carlo simulations, both effects of spatial non-uniformity and stratigraphic dip of soil on the evolution process and consequences of landslides are analyzed in detail. The results reveal that the stratigraphic dip greatly influences landslide behaviors. In addition, the 2D analyses probably underestimate the landslide consequences when contrasting with 3D analyses. These findings highlight the importance of considering stratigraphic dip of soil slope and the advantage of 3D random LDFE analysis on landslide behaviors.

Random finite element analysis of a clay-core-wall rockfill dam considering three-dimensional conditional random fields of soil parameters

Structural reliability and safety have been investigated using the random finite element method (RFEM) based on conditional random field (RF) by many researchers. However, the constraint RFEM has not been studied sufficiently to assess its influences on dam structural behaviours, especially in clay-core-wall rockfill dams. In this study, based on Kriging theory and in-situ measurements, a method is applied for constructing conditional RFs of dam material parameters. The results demonstrate that conditional RF has little effect on the mean values of maximum settlement, maximum deformation gradient and hydraulic fracture area ratio; relative to the unconditional simulations, the relative differences are 1%, 3%, and 7%, respectively. By establishing an effective Kriging estimation, the standard deviations of conditional maximum settlement, maximum deformation gradient and hydraulic fracture area ratio are relatively reduced by 16%, 4%, and 24%, respectively. Thus, the conditional simulation can provide more accurate security estimations for the cumulative probabilities of the structural responses. Measurement layout has a great effect on variation accuracy of random structural responses. The measurements should be taken near the locations of the structural behaviours of interest so that the conditional RFs can more accurately represent the spatial variability of soil properties and reduce simulation variation.

3D large-deformation modelling on face instability and sinkhole formation during tunnelling through non-uniform soils

Natural soils exhibit spatially non-uniform properties, bringing some uncertainties on the evaluation of tunnel stability. This study therefore investigates the face instability and in particular to the sinkhole formation in spatially non-uniform soils by conducting large-deformation finite-element (LDFE) analyses combined with a three-dimensional random field. The results from LDFE analyses indicate that soil spatial non-uniformity greatly affects the failure mechanism as well as the face stability. The stability factor in non-uniform soils is averagely smaller than the deterministic solution in a uniform soil, implying the assumption of uniform soil conditions likely underestimates probability of failure of a tunnel face. With regard to the sinkhole behaviour, the average ground settlement obtained from random analysis is greater than that from deterministic analysis. This underscores the necessity of considering the soil spatial non-uniformity in the analysis of the sinkhole behaviour. This study provides an improved understanding on the face stability and sinkhole formation during tunnelling through non-uniform soils.

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.

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.