Traditional Monte Carlo Simulation Research Articles

The model and characteristics of polarized light transmission applicable to polydispersity particle underwater environment

The information about the polarization of underwater objects can be affected by the absorption and scattering of water particles, making it challenging to detect underwater targets accurately. Therefore, it is essential to analyze the characteristics of polarization transmission in water. Traditional Monte Carlo simulations have yet to effectively treat particle size in water, which is unsuitable for the underwater environment of polydispersity particles with significant particle size differences. In this paper, a new simulation model using a Monte Carlo method with random sampling fitting phase functions is proposed, which makes the transmission characteristics of water particles more in line with the actual probability model of complex water bodies. The experimental results demonstrate that the proposed Monte Carlo method produces polarization closer to experimental results. The larger the particle size of water suspensions, the greater change of the polarization degree of polarized light. The polarization-maintaining characteristics of circularly polarized light are better than those of linearly polarized light, providing data support for the transmission and detection of underwater light.

A Reliability Assessment Method for Natural Gas Pipelines with Corroded Defects That Considers Detection Cycles

With the development of natural gas pipelines, the proportion of aged pipelines in service has been increasing, and corrosion remains a primary cause of pipeline failure. Regular inspections and reliability assessments are crucial to ensure the safe operation of pipelines. This study investigated an efficient reliability assessment method for corroded pipelines that considers in-line inspection intervals. First, this study compared the commonly used limit state equations for corrosion defects to select one suitable for X80-grade steel pipelines. Additionally, a Tail-Fit Monte Carlo Simulation (TF-MCS) algorithm was proposed to improve the computational speed by 30 times compared to traditional Monte Carlo simulations. Then, this study explored the inspection intervals used for reliability assessments of corroded pipelines. Finally, the parameter sensitivity was analyzed considering the yield strength, maximum operating pressure, and pipe diameter. This study ensures the reliable operation of corroded gas pipelines.

A Reliability Assessment Method for Natural Gas Pipelines with Corroded Defects That Considers Detection Cycles

With the development of natural gas pipelines, the proportion of aged pipelines in service has been increasing, and corrosion remains a primary cause of pipeline failure. Regular inspections and reliability assessments are crucial to ensure the safe operation of pipelines. This study investigated an efficient reliability assessment method for corroded pipelines that considers in-line inspection intervals. First, this study compared the commonly used limit state equations for corrosion defects to select one suitable for X80-grade steel pipelines. Additionally, a Tail-Fit Monte Carlo Simulation (TF-MCS) algorithm was proposed to improve the computational speed by 30 times compared to traditional Monte Carlo simulations. Then, this study explored the inspection intervals used for reliability assessments of corroded pipelines. Finally, the parameter sensitivity was analyzed considering the yield strength, maximum operating pressure, and pipe diameter. This study ensures the reliable operation of corroded gas pipelines.

Infinite series solution of the time-dependent radiative transfer equation in anisotropically scattering media

We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering. Higher-order corrections are addressed through numerical calculations or approximations.The RTE solution corresponds to Monte Carlo sampling of photon trajectories with fixed start and end points. Validated against traditional Monte Carlo simulations, featuring random end points, our solution demonstrates enhanced efficiency for both anisotropic and isotropic scattering functions, significantly reducing computational time and resources. The advantage of our method over Monte Carlo simulations varies with the position of interest and the asymmetry of light scattering, but it is typically orders of magnitude faster while achieving the same level of accuracy. The exploitation of hidden symmetries further accelerates our numerical calculations, enhancing the method’s overall efficiency.In addition, we extend our analysis to the first and second moments of the photon’s flux, elucidating the transition between transport and diffusive regimes.

Failure Probability Prediction for Offshore Floating Structures Using Machine Learning

Summary Accurately estimating the failure probability is crucial in designing civil infrastructure systems, such as floating offshore platforms for oil and gas processing/production, to ensure their safe operation throughout their service periods. However, as a system becomes complex, the evaluation of a limit state function may involve the use of an external computer solver, resulting in a significant computational burden to perform Monte Carlo simulations (MCS). Moreover, the high-dimensionality of the limit state function may limit efficient sampling of input variables due to the “curse of dimensionality.” To address these issues, an efficient machine learning framework is proposed, combining polynomial chaos expansion (PCE) and active subspace. This will enable the accurate and efficient evaluation of the failure probability of an offshore structure, which typically involves a large number of uncertain parameters. Unlike conventional PCE schemes that use the original random variable space or the auxiliary variable space for building a surrogate model, the proposed method utilizes a reduced-dimension space to circumvent the “curse of dimensionality.” An appropriate coordinate transformation is first sought so that most of the variability of a limit state function can be accounted for. Next, a PCE surrogate limit state function is constructed on the derived low-dimensional “active subspace.” The Gram-Schmidt orthogonalization process is used for making basis polynomial functions, which is particularly effective when input random parameters do not follow the Askey scheme and/or when a dependence structure between the input parameters exists. Therefore, a nonlinear iso-probabilistic transformation, which makes the convergence of a surrogate to the true model difficult, is not required, unlike traditional PCE. Numerical examples, including limit state functions related to structural dynamics problems, are presented to illustrate the advantages of the proposed method in estimating failure probabilities for complex structural systems. Specifically, the method exhibits significantly improved efficiency in estimating the failure probability of an offshore floating structure without compromising accuracy as compared to traditional PCE and MCS.

A line loss reduction optimization for renewable energy‐based distribution networks using a probabilistic approach

SummaryThe large integration of distributed generation (DG) and electric vehicles (EVs) facilitates daily life and reduces carbon emissions. However, it brings problems such as increased uncertainty and power electronic permeability to the distribution network. In this context, it is important to solve the line loss optimization problem as closely as possible to the real situation. Therefore, this paper solves the line loss optimization problem based on a probabilistic model of three‐phase unbalanced modern power electrical distribution network. Firstly, the paper proposes a frequency domain model of the distribution network and the optimization problem model. Then, to deal with the uncertainty of the system, the point estimation method (PEM) and Monte Carlo Simulation (MCS) are used. Finally, this paper proposes two optimization schemes considering the power quality when single and multiple DGs are integrated. The simulation results demonstrate that the PEM using the Gram–Charlier series expansion of the fourth‐order statistical moments to estimate the probability density function (PDF) is significantly less time consuming than the traditional MCS method while maintaining accuracy. The comparative analysis reveals that under the optimization scheme with single DG integration, the expected value of system line loss and expected line loss rate are reduced from 283.95 kW to 218.96 kW (22.89% reduction) and from 13.44% to 10.68%, respectively. Under the dual DG integrated optimization scheme, the expected value of line losses and expected line loss rate are reduced from 283.95 kW to 208.88 kW (26.4% reduction) and from 13.44% to 10.25%, respectively. However, after taking the uncertainty into account, the operational reliability of the system has been enhanced under different scenarios. In addition, it is found that the optimization approach incorporating multiple DG units can effectively mitigate the system line loss under diverse operational scenarios while enhancing the system's DG integration capability.

Reliability evaluation of steel beam resting on elastic foundation subjected to moving load using monte carlo simulation and latin hypercube sampling

Steel beams resting on the elastic foundation are an applied technique to minimize the impact of thermal expansion and vibrations on civil engineering structures such as bridges and buildings, due to their flexibility and ability to withstand large loads. In practice, the performance of steel beams resting on elastic foundations is affected by random factors such as exceeding load-bearing capacity, undesirable deformations, loss of soil resilience, or environmental corrosion. This study proposes a technique to evaluate the reliability of steel beams resting on the elastic foundation subjected to moving loads using discrete random input parameters through the Latin hypercube sampling and Monte Carlo simulation method. The reliability of steel beams obtained from the proposed method is then compared to that of the traditional Monte Carlo simulation. The results reveal that the proposed technique provides a high accuracy and computational resource savings compared to the traditional Monte Carlo method. Finally, the influence of the random input parameters is also assessed based on the Sobol' sensitivity index.

Robustness analysis of shield tunnels in non-uniformly settled strata based on fuzzy set theory

This study presents a robustness analysis of shield tunnels in non-uniformly settled strata based on the fuzzy point estimate method (FPEM) and geotechnical structural robustness analysis methods. The uncertainties of key geotechnical parameters and loads were characterized using the fuzzy sets and the influence ofdifferentfuzzy membership functions andboundary values on the robustness index of shield tunnel was investigated. The structural design of the shield tunnel cross-section in non-uniformly settled strata were optimized by considering the reliability and robustness indices of the shield tunnel under the ultimate limit states, serviceability limit states, and economic costs. The results indicate that compared with the traditional Monte Carlo simulations, the FPEM is computationally efficient with favorable accuracy, and is suitable for the robustness analysis of shield tunnels. Increase of the segment thickness, reinforcement ratio and diameter of the joint bolts can efficiently improve the design robustness of the shield tunnel. Besides, the boundary values and distribution characteristics of the membership function of the random variables in the FPEM have significant effects on the errors of the calculation results.

PELECTRE-Tri: Probabilistic ELECTRE-Tri Method—Application for the Energy Renovation of Buildings

This paper proposes the method pELECTRE Tri, a novel probabilistic Multi-Criteria Decision Making (MCDM) method using the traditional ELECTRE Tri, probability distribution, and Monte Carlo simulation to support informed decision-making in complex and uncertain decision environments. The proposed method is illustrated through a case study involving the renovation of three social housing buildings. The paper provides new insights into the application of probabilistic sorting MCDM in the context of energy efficiency in buildings and highlights the benefits of using probabilities rather than crisp values to categorize alternatives enabling stakeholders to make better use of available resources, especially when dealing with a large dataset of energy measures with different features. The methodology implemented in Python (DOI: 10.5281/zenodo.7967655) is available as an open source.

Time-dependent reliability analysis of reinforced concrete beams considering marine environmental actions

Under marine atmospheric environments, reinforced concrete (RC) structures may suffer from structural deterioration induced by environmental actions, affecting structural performance and safety. Thus, it is essential to evaluate and predict the deterioration process of an RC structure subject to environmental actions. This paper proposes a novel and generic computational framework to assess the time-dependent reliability of an RC beam under environmental actions. This framework includes a comprehensive life-cycle performance assessment model that considers climate change, two-dimensional chloride transport, the coupling effects and corrosion non-uniformity of reinforcement, and the nonlinear behavior of RC beams, which is validated by experimental studies. Additionally, performance functions for an RC beam are established for different failure modes, and their time-dependent probabilistic information and reliability index are captured using the probability density function-informed method (PDFM). To demonstrate the computational processes of the developed framework under practical marine atmospheric conditions, illustrative cases are presented. The accuracy and efficiency of the proposed method are validated by traditional Monte Carlo Simulation (MCS). Results indicate that the proposed method is feasible and efficient, aiding the life-cycle design and maintenance of RC structures.

Reliability assessment of an offshore wind turbine jacket under one ultimate limit state considering stress concentration with active learning approaches

At present, offshore wind turbine jacket structures are generally modeled with beam elements. The local joint flexibility and stress concentration of the joints are hardly considered. In this work, one jacket model is developed to consider joint stress concentration by using super-elements. Another jacket model is also developed with pure beam elements. The stress concentration is investigated between the two jacket models. Moreover, a general framework is proposed to conduct the reliability analysis with active learning Kriging approaches and one typical ultimate limit state is studied. At first, the developed jacket models are validated with the numerical simulation results of National Renewable Energy Laboratory (NREL) technical reports. Secondly, global sensitivity analysis is carried out to reduce the random parameters for the reliability analysis. In the end, the reliability analysis is conducted with active learning Kriging approaches. The results show the probabilities of failure of the beam model are very sensitive to the assumed stress concentration factors. More importantly, it is noticed that active learning Kriging approaches can efficiently and accurately assess the probabilities of failure. Compared with the traditional Monte Carlo simulation approach, active learning Kriging approaches can reduce computational loads by hundreds of times and have the same accuracy.

Probabilistic approach to investigate the impact of distributed generation on voltage deviation in distribution system

The increasing penetration of renewable-based generation in the distribution network adds randomness to the bus voltage due to its stochastic characteristics. Consequently, the distribution network faces voltage limit violations at multiple buses. In this scenario, the traditional voltage control method fails to maintain the voltage profile of the network due to its slow response time. A fast and dynamic voltage control technique can be achieved by utilizing the voltage-controlling capability of available DGs in the network with the information about the impact of DG-integrated bus on change in voltage at any bus in the network. Evaluating this information using the traditional probabilistic load flow method is computationally inefficient for real-time applications. Therefore, in this paper, a principal component analysis (PCA)-based novel probabilistic voltage sensitivity index (PVSI) is proposed. It ranks the DG-integrated buses by evaluating the impact of power perturbation at DG-integrated buses on changes in voltage at any bus in the network. The PVSI is analytically derived to reduce the computation time for ranking. Further, the proposed PVSI is validated on the 69-bus and the 141-bus distribution systems by comparing it with the traditional Monte Carlo simulation (MCS) and joint differential entropy (JDE) in terms of accuracy and computation time. From the simulation, it is observed that PVSI gives a similar ranking as both methods in less computation time. Due to the advantage in computation time, the proposed method enables the distribution system operator (DSO) to use this information for fast and dynamic voltage control in a real-time scenario.

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

The current work describes a stochastic framework to investigate the static response characteristics of periodic and random fiber arrays of reinforced three-phase composites with aleatory mechanical and thermal constituent properties. These properties were randomly modeled via Gaussian distribution using the statistical quantities of first and second moments. The framework is based on Variational Asymptotic Method (VAM) based homogenization technique coupled with Stochastic Reduced Order Model (SROM). When compared against the framework of VAM coupled with the traditional Monte Carlo Simulation (MCS) method, the computational cost of the SROM model with VAM was significantly less. Good agreement with solutions from traditional MCS combined with VAM was also achieved. To demonstrate applicability of the framework, a multivariate stochastic analysis was performed to determine the effect of fiber arrangements on the randomness of mechanical and thermal properties in a three-phase composite. Additionally, univariate stochastic analysis was performed, and the sensitivity of each constituent parameter corresponding to the stochastic homogenized response variable was investigated using the bivariate correlation and linear regression analysis methods.

A method for time‐varying reliability calculation of RC bridges considering random deterioration process

AbstractThis paper proposes a new method based on dual neural networks to improve the efficiency of time‐varying reliability calculation of bridge structures. Based on the basic theory of structural time‐varying reliability analysis, this method uses the dyadic neural network integration method to convert the time‐varying reliability calculation of bridges from the traditional Monte Carlo simulation to the direct integration operation, which improves operation efficiency and retains high working accuracy. In addition, considering the randomness of the decay process of different bridge resistances, the variation law of time‐varying reliability of bridges in the process of uncertain resistance reduction is studied, and an explicit formula for time‐varying reliability of bridges is given and solved by using the proposed dual neural network method. Finally, the effectiveness of the proposed method is verified by an engineering arithmetic example. The result indicates that the bridge has a greater probability of failure under random conditions.

Evaluation of probabilistic model solving methods for modern power electronic distribution networks with wind power integration

The emergence of more and more power electronic loads and Distributed Generation (DG) presents many challenges to the reliable operation of Distribution Networks (DN). The uncertainties of power electronic loads and DGs have increasingly profound impacts on distribution networks. Currently, probabilistic model solving methods for distribution networks often ignore the power quality and the unbalanced operation of the distribution network. Besides, the traditional Monte Carlo method is accurate, but the heavy calculation burden limits its application in practice. Therefore, the fast and accurate solving of probabilistic models of modern power electronic distribution networks urgently needs to be studied. Therefore, in this paper, a probability solving model for a three-phase unbalanced modern power electronic distribution network with DG integration is developed, and the probability model is solved using Point Estimation Method (PEM) combined with Gram–Charlier expansion and Monte Carlo Simulation (MCS). Besides, this paper presents a detailed analysis comparing the results of PEM and MCS solutions from the perspective of voltage, THD, and line loss. The results prove that the Probability density functions (PDFs) of the parameters obtained by the two methods are almost identical, and the relative errors of the indicators are less than 1%. Moreover, the PEM uses only 1.9% of the time taken by the traditional MCS method in solving modern probabilistic models of distribution networks with power electronic devices integration (wind power, EVC, .. etc.). It is shown that the PEM used in this paper, combined with Gram–Charlier expansion, is an accurate and efficient solving method for modern distribution networks, providing a reference for subsequent research.

A Yield Prediction Method Based on Nonparametric Statistical and Comparison With a Networks Method

In this paper, we propose a circuit yield prediction method to improve the efficiency of circuit yield prediction. Both traditional Monte Carlo simulation and the current popular machine learning for yield prediction require a large number of circuit simulation results, which increases production costs. This method finds the data boundary points through high-dimensional kernel density estimation, and performs simulation calculations on these boundary values instead of the overall simulation. Experiments show that, compared with machine learning and Monte Carlo methods, the proposed algorithm can efficiently predict the yield of circuits.

A Quasi–Monte Carlo Method With Krylov Linear Solvers for Multigroup Neutron Transport Simulations

In this work we investigate replacing standard quadrature techniques used in deterministic linear solvers with a fixed-seed Quasi–Monte Carlo (QMC) calculation to obtain more accurate and efficient solutions to the neutron transport equation (NTE). QMC is the use of low-discrepancy sequences to sample the phase-space in place of pseudorandom number generators used by traditional Monte Carlo (MC). QMC techniques decrease the variance in the stochastic transport sweep and therefore increase the accuracy of the iterative method. Historically, QMC has largely been ignored by the particle transport community because it breaks the Markovian assumption needed to model scattering in analog MC particle simulations. However, by using iterative methods the NTE can be modeled as a pure-absorption problem. This removes the need to explicitly model particle scattering and provides an application well suited for QMC. To obtain solutions we experimented with three separate iterative solvers: the standard Source Iteration (SI) Solver and two linear Krylov Solvers, i.e., the Generalized Minimal RESidual method (GMRES) and the BiConjugate Gradient STABilized method (BiCGSTAB). The resulting hybrid iterative-QMC solver was assessed on three slab geometry problems of one dimension. In each sample problem the Krylov Solvers achieve convergence with far fewer iterations (up to eight times) than the SI Solver. Regardless of the linear solver used, the hybrid method achieved an approximate convergence rate of as compared to the expected of traditional MC simulation across all test problems.

Influence of material uncertainties on thermo-elastic vibration characteristics of graphene reinforced functionally graded porous beams

This paper aims to study the influence of material uncertainties on thermo-elastic vibration response of functionally graded porous (FGP) beams reinforced with graphene platelets (GPLs) using the perturbation-based stochastic finite element method. The influence of material uncertainty on the vibration behavior of FGP-GPL reinforced beams subjected to thermal loading conditions have been discussed for low variability (randomness) in material design parameters (porosity content, amount of nanofillers) and material properties (Young’s modulus, density of metal matrix, and nanofillers) respectively. A C0 continuous stochastic finite element formulation based on higher-order shear deformation theory has been formulated. The convergence and validation of the present formulation have been compared with a traditional Monte-Carlo simulation to establish the accuracy of the present methodology. The homogenized effective material properties are estimated using the Halpin-Tsai micromechanics model and Voigt’s rule of mixture and are typically assumed to be varying along the thickness direction. The results highlighting the effect of uncertainty in material properties on the thermo-elastic vibration response of FGP-GPL reinforced beams have been discussed thoroughly.

Publisher’s Note

The emergence of more and more power electronic loads and Distributed Generation (DG) presents many challenges to the reliable operation of Distribution Networks (DN). The uncertainties of power electronic loads and DGs have increasingly profound impacts on distribution networks. Currently, probabilistic model solving methods for distribution networks often ignore the power quality and the unbalanced operation of the distribution network. Besides, the traditional Monte Carlo method is accurate, but the heavy calculation burden limits its application in practice. Therefore, the fast and accurate solving of probabilistic models of modern power electronic distribution networks urgently needs to be studied. Therefore, in this paper, a probability solving model for a three-phase unbalanced modern power electronic distribution network with DG integration is developed, and the probability model is solved using Point Estimation Method (PEM) combined with Gram–Charlier expansion and Monte Carlo Simulation (MCS). Besides, this paper presents a detailed analysis comparing the results of PEM and MCS solutions from the perspective of voltage, THD, and line loss. The results prove that the Probability density functions (PDFs) of the parameters obtained by the two methods are almost identical, and the relative errors of the indicators are less than 1%. Moreover, the PEM uses only 1.9% of the time taken by the traditional MCS method in solving modern probabilistic models of distribution networks with power electronic devices integration (wind power, EVC, .. etc.). It is shown that the PEM used in this paper, combined with Gram–Charlier expansion, is an accurate and efficient solving method for modern distribution networks, providing a reference for subsequent research.

Evaluating grid strength under uncertain renewable generation

The increasing displacement of synchronous generators with renewable resources such as wind and solar via power electronic interfaces causes a reduction in short-circuit strength and weak grid issues. The variation and uncertainty of renewable energy increase challenges for identifying weak grid conditions. This paper proposes an efficient method to analyze the impact of uncertain renewable energy on grid strength. The proposed method uses the probabilistic collocation method (PCM) to approximate the results of grid strength assessment under uncertain renewable generation, in order to reduce computational burden without compromising result accuracy when compared with traditional Monte Carlo simulation (MCS). To improve the accuracy of the approximation results, the proposed method integrates the K-means clustering technique with PCM to select the approximation samples of input variables. The efficacy of the proposed method is demonstrated by comparison with MCS on the modified IEEE 9-bus system and modified IEEE 39-bus system with multiple renewable generators.