Stochastic analysis of a three phase composite using variational asymptotic based homogenization technique coupled with stochastic reduced order model

This work introduces a practical approach for accelerating probabilistic, high-fidelity prognostics using the stochastic reduced order model (SROM) method and its availability in the open-source Python package, SROMPy. SROMs are used as an efficient Monte Carlo simulation (MCS) method, providing low-dimensional representations of random model inputs enabling rapid and non-intrusive uncertainty propagation. This study represents the first application of the SROM approach in the field of prognostics and health management and serves as a tutorial demonstration of the SROMPy software package. The relative ease of applying SROMs with SROMPy for uncertainty propagation is demonstrated on an example of probabilistic, non-planar crack growth simulation. Results show that the SROM approach agrees well with results from MCS while providing orders of magnitude computational speedup. The complete source code and input data required to reproduce the results in this paper are available online to facilitate further evaluation and adoption of the SROM method by researchers in the field.

This paper presents a novel statistical approach, referred to as the stochastic reduced order model (SROM) method, to predict the statistics of crosstalk in the presence of multiple uncertainty sources. In this paper, the cable is modelled using a three-conductor transmission line, and the SROM method is applied to obtain the statistics of crosstalk subject to two independent uncertain sources. Compared with the conventional Monte Carlo (MC) method, it is found that the SROM method can produce accurate statistics of crosstalk using a small computational cost. The Stochastic Collocation (SC) method is also implemented to validate the efficacy of the SROM method. Since the implementation of the SROM method is non-intrusive, the application of this method to other uncertainty-embedded electromagnetic compatibility (EMC) problems is straightforward.

This paper introduces a novel statistical method, referred to as the stochastic reduced order model (SROM) method, to predict the variability of cable crosstalk subject to a range of parametric uncertainties. The SROM method is a new member of the family of stochastic approaches to quantify propagated uncertainty in the presence of multiple uncertainty sources. It is nonintrusive, accurate, efficient, and stable, thus could be a promising alternative to some well-established methods, such as the Stochastic Galerkin and stochastic collocation (SC) methods. In this paper, the SROM method is successfully applied to obtain the statistics of cable crosstalk subject to single and multiple uncertainty sources. The statistics of uncertain cable parameters is first accurately approximated by SROM, i.e., pairs of very few samples with known probabilities, such that the uncertain input space is well represented. Then, a deterministic solver is used to produce the samples of cable crosstalk with the corresponding probabilities, and finally the uncertainty propagated to the crosstalk is quantified with good accuracy. Compared to the conventional Monte-Carlo simulation, the statistics of crosstalk obtained by the SROM method converge much faster by orders of magnitude. Also, the computational cost of the SROM method is shown to be small and can be tuned flexibly depending on the accuracy requirement. The SC method based on tensor product sampling strategy is also implemented to validate the efficacy of the SROM method.

Model reduction in thin-walled open-section composite beams using Variational Asymptotic Method. Part II: Applications

The present paper deals with the stochastic natural frequency analysis of functionally graded material (FGM) plates by employing the multivariate adaptive regression splines surrogate (MARS) model. The gradation of material properties of constitute materials is carried out by power law distribution. The variation in material properties for different value of power law index or exponent is considered as input variables, while the first three natural frequencies are considered as output responses. The MARS model is coupled with the finite element model to reduce computational time. The results of the MARS model are validated with the results obtained from the traditional Monte Carlo simulation (MCS). The statistical analysis is portrayed to describe the probability density function of natural frequencies corresponding to power law index.KeywordsStochastic natural frequencyFunctionally graded materialsMonte Carlo simulationMultivariate adaptive regression splinesUncertainty quantification

Multi-scale stochastic dynamic response analysis of offshore risers with lognormal uncertainties

Due to the spatial variability of hydraulic properties, probabilistic slope seepage analysis becomes necessary. This study conducts a probabilistic analysis of slope seepage under rainfall, considering the spatial variability of saturated hydraulic conductivity. Through this, both the commonly used Monte Carlo simulation method and the proposed first-order stochastic moment approach are tested and compared. The results indicate that the first-order analysis approach is effective and applicable to the study of flow processes in a slope scenario. It is also capable of obtaining statistics such as mean and variance with a high enough accuracy. Using this approach, higher variabilities in the pressure head and the fluctuation of the phreatic surface in the slope are found with a higher value of the correlation length of the saturated hydraulic conductivity. The Monte Carlo simulation is found to be time-consuming: at least 10,000 realizations are required to reach convergence, and the number of realizations needed is sensitive to the grid density. A coarser grid case requires more realizations for convergence. If the number of realizations is not enough, the results are unreliable. Compared with Monte Carlo simulation, the accuracy of the first-order stochastic moment analysis is generally satisfied when the variance and the correlation length of the saturated hydraulic conductivity are not too large. This study highlights the applicability of the proposed first-order stochastic moment analysis approach in the slope scenario.

In this paper, Monte Carlo Simulation (MCS) method was used as an uncertainty assessment tool for air flow, net thrust measurement. Uuncertainty sources of the net thrust measurement were analyzed, and the probability distribution characteristics of each source were discussed. Detailed MCS methodology was described including the effect of the number of simulation. Compared to the conventional sensitivity coefficient method, the MCS method has advantage in the uncertainty assessment. The MCS is comparatively simple, convenient and accurate, especially for complex or nonlinear measurement modeling equations. The uncertainty assessment result by MCS was compared with that of the conventional sensitivity coefficient method, and each method gave different result. The uncertainties in the net thrust measurement by the MCS and the conventional sensitivity coefficient method were 0.906% and 1.209%, respectively. It was concluded that the first order Taylor expansion in the conventional sensitivity coefficient method and the nonlinearity of model equation caused the difference. It was noted that the uncertainty assessment method should be selected carefully according to the mathematical characteristics of the model equation of the measurement.

Determination of sensitivity gradient is a major prerequisite for structural optimization, reliability assessment, and parameter identification. As the conventional deterministic sensitivity analysis cannot provide complete information, stochastic analysis is needed to tackle the uncertainties in structural parameters. This study focuses on the utility of the stochastic finite-element method for random response sensitivity analysis. The stochastic modeling of a random parameter is based on a commonly used 2D local averaging method generalized for a 3D case. The Choleski decomposition technique is then employed for digital simulation. The Neumann expansion based finite-element simulation method is extended for stochastic sensitivity analysis. This technique leads to a considerable saving of computational time. Example problems are used to compare the accuracy of this method to the direct Monte Carlo simulation and perturbation method in terms of varying stochasticity and efficiency in CPU time.

This study presents a parallelized framework for the grid-and-radius-based Morgenstern–Price method to enable an efficient reliability analysis of unsaturated finite soil slopes under correlated and non-Gaussian conditions. To address the limitations of deterministic techniques and the significant computational demands associated with traditional Monte Carlo simulation, the framework incorporates surrogate modeling approaches, namely polynomial chaos expansion–enhanced Monte Carlo simulation (PCE-MCS) and Kriging-based Monte Carlo simulation (K-MCS). This research conducts a comprehensive evaluation of these surrogate-assisted methods with the gradient-based approaches for estimating the probability of failure (pf) under correlated and non-Gaussian distributions. The surrogate models exhibit exceptional accuracy (R2 > 99.7%, mean absolute error <0.6%) and drastically reduce computational cost compared with traditional methods. Parametric and variability studies show that increasing the mean stability number (0.005–0.065) and friction angle (20°–30°) reduces the pf from 19.19% to 0.005% and 14.9% to 0.01%, respectively, while higher variability increases pf. Similarly, increasing the air-entry value reduces pf from 29.8% to 0.01%, whereas pf rises to 15.1% and 21.8% with increases in soil–water characteristic curve parameters nf (0.1–3.25) and mf (0.25–1.65). A detailed comparison against gradient-based techniques such as the first-order reliability method (FORM) and the second-order reliability method (SORM) underscores the superiority of surrogate-based approaches. For instance, the FORM shows errors up to 92.59%, while SORM errors reach 62.75%, particularly in highly nonlinear or variable scenarios. In contrast, PCE-MCS and K-MCS errors remain generally below 10%. Furthermore, reliability-based design contour charts are developed using K-MCS. These charts align with the USACE reliability classification, enabling rapid and reliable assessment of unsaturated slope stability without the need for large-scale simulations. Therefore, by effectively bridging traditional geotechnical engineering and advanced surrogate techniques, the proposed approach enhances practical decision-making in unsaturated slope design and supports the advancement of reliability-based design optimization in geotechnical practice.

Comments on the paper: on repeated parameter sampling in Monte Carlo simulations

Thermal conductivity of Cu-matrix composites reinforced with coated SiC particles: Numerical modeling and experimental verification

Materials that simultaneously possess ultralow thermal conductivity, high stiffness, and damage tolerance are highly desirable for engineering applications. However, this combination of properties has never been demonstrated in a single material because thermal and mechanical properties are coupled in most fully dense and porous solids. A new class of lattice materials with nanoscale features, called nanolattices, can fill this void in the material property space by virtue of their architecture and nanoscale dimensions. Extensive work on nanolattice mechanical properties report their excellent stiffness-to-density ratio and recoverability from large compressive strains. In contrast, the framework for studying their thermal properties has not been established. Our work develops the computational and experimental tools necessary to study heat conduction in nanoarchitected materials and applies those tools to prove the viability of octet-truss nanolattices as multifunctional thermal insulators. We implement significant improvements to a phonon Monte Carlo method to solve the Boltzmann transport equation (BTE) in highly complex geometries like the octet-truss. No prior works solve the BTE in a domain as intricate as a nanolattice, so we create a geometry representation scheme that can model any arbitrary 3-D body. Our enhanced variance-reduced Monte Carlo code incorporates this scheme, allowing us to predict the thermal conductivity of nanolattices and analyze the phonon transport behavior in them. Results suggest that hollow-beam silicon nanolattices indeed reach ultralow thermal conductivities. Based on Monte Carlo and finite element simulations, we develop a predictive thermal conductivity model that accounts for both diffusive and radiative phonon transport in nanolattices. We also devise custom modifications to the 3ω method to experimentally measure the thermal conductivity of additively manufactured nanolattices. Since the serial fabrication process of nanolattices makes it costly to cover large areas, we design a specialized 3ω sample that minimizes the required structure size while maintaining good experimental sensitivity. We derive a new thermal model to account for conductive losses through the heater line in our novel sample geometry. 3ω measurements and compression tests of hollow-beam alumina nanolattices show that they combine ultralow thermal conductivity with excellent mechanical stiffness and resilience, which proves that nanolattices occupy a previously unreachable region in material property space. Our work provides motivation to further investigate and improve the thermal properties of architected materials.

Inevitable source-uncertainties in geometry configuration, boundary condition, and material properties may deviate the structural dynamics from its expected responses. This paper aims to examine the influence of these uncertainties on the vibration of functionally graded beams. Finite element procedures are presented for Timoshenko beams and utilized to generate reliable datasets. A prerequisite to the uncertainty quantification of the beam vibration using Monte Carlo simulation is generating large datasets, that require executing the numerical procedure many times leading to high computational cost. Utilizing artificial neural networks to model beam vibration can be a good approach. Initially, the optimal network for each beam configuration can be determined based on numerical performance and probabilistic criteria. Instead of executing thousands of times of the finite element procedure in stochastic analysis, these optimal networks serve as good alternatives to which the convergence of the Monte Carlo simulation, and the sensitivity and probabilistic vibration characteristics of each beam exposed to randomness are investigated. The simple procedure presented here is efficient to quantify the uncertainty of different stochastic behaviors of composite structures.

Two commercial-scale windrow composting methods were investigated for their relative costs of production and value for the horticulture industry, including: (i) aerobic (or thermophilic) composting; and (ii) fermentative (or static pile inoculated) composting. Economic costs, including opportunity costs, were estimated and analyzed using data from a case study on-site compost production for tree and shrub nursery production in British Columbia, Canada. Deterministic and stochastic budgeting models were used to determine breakeven prices and short-run shut-down prices (SRSDP), and testing for potential economies of scale. Monte Carlo simulations were used to assess the sensitivity of costs to uncertainty in key output variables. The composting methods used demonstrate that the composts produced are of satisfactory quality, with physical and chemical properties within typical recommended ranges for agricultural use. Total cost of producing a tonne of fermentative compost (CAD$23) was lower than for thermophilic compost (CAD$37). Short-term shutdown price was higher for thermophilic than for fermentative compost produced by CAD$11 tonne−1. Economies of scale were more apparent for thermophilic than the fermentative composting system. Conclusions from the stochastic analysis were consistent with results from the deterministic cost analysis. The empirical economic cost estimates are useful for a wide variety of audiences, including policy makers and decision makers interested in capital and operating costs of composting, and cost-based pricing strategy for compost produced. Breakeven prices fill an industry knowledge gap regarding profitability of compost production given prevailing market prices.