Traditional Monte Carlo Method Research Articles

Reliability analysis of a nonlinear rotor/stator contact system in the presence of aleatory and epistemic uncertainty

On the basis of an overview of the global responses of a nonlinear Jeffcott rotor/stator contact model, the system reliability was evaluated subject to mixed aleatory-epistemic uncertainty. We used a likelihood-based approach for reliability modeling and analysis. In the context of uncertainty quantification, some advanced Bayesian techniques were adopted to reduce the computation cost in traditional Monte Carlo method. The parameters’ effects on reliability were studied, incorporating both rotor physical background and inherent uncertain factors. This framework could be applied in the field of industrial manufacturing & mounting, risk assessment, product maintaining and benefit rotary machines from design phase to operation stage.

Quasi-Monte Carlo Methods Applied to Tau-Leaping in Stochastic Biological Systems

Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow {mathcal {O}}(N^{-1/2}) convergence rates as a function of the number of sample paths N. This paper investigates the combination of (randomised) quasi-Monte Carlo methods with an efficient sample path simulation procedure, namely tau -leaping. We show that this combination is often more effective than traditional Monte Carlo simulation in terms of the decay of statistical errors. The observed convergence rate behaviour is, however, non-trivial due to the discrete nature of the models of chemical reactions. We explain how this affects the performance of quasi-Monte Carlo methods by looking at a test problem in standard quadrature.

Reliability analysis for highly non-linear and complex model using ANN-MCM simulation

To predict reliability for highly non-linear and complex model efficiently and accurately, an artificial neural network (ANN) based Monte Carlo method (MCM) is proposed. In this method, ANN trained by backpropagation (BP) algorithm is developed to establish the relationship between inputs and outputs. The trained ANN model is then connected to MCM to predict reliability and reliability sensitivity of structure. To examine the accuracy and efficiency of the proposed method, results obtained by polynomial-FOSM (first-order second moment) method and ANN-AFOSM (advanced first-order second moment) method are provided. Compared with the traditional Monte Carlo method, the time consumed by ANN-MCM, polynomial-FOSM and ANN-AFOSM methods only accounts for 0.14% of the traditional MCM. The reliability analysis and reliability sensitivity analysis results of ANN-MCM method are very close to traditional MCM, polynomial-FOSM method yields large errors, ANN-AFOSM is in between. It shows that the proposed method is of high accuracy and efficiency.

Multiple agents and reinforcement learning for modelling charging loads of electric taxis

The charging load modelling of electric vehicles (EVs) is of great importance for safe and stable operation of power systems. However, it is difficult to use the traditional Monte Carlo method and mathematical optimization methods to establish a detailed and precise charging load model for EVs in both the temporal and spatial scales, especially for plug-in electric taxis (PETs) due to its strong random characteristics and complex operation behaviors. In order to solve this problem, multiple agents and the multi-step Q(λ) learning are utilized to model the charging loads of PETs in both the temporal and spatial scales. Firstly, a multi-agent framework is developed based on java agent development framework (JADE), and a variety of agents are built to simulate the operation related players, as well as the operational environment. Then, the multi-step Q(λ) learning is developed for PET Agents to make decisions under various situations and its performances are compared with the Q-learning. Simulation results illustrate that the proposed framework is able to dynamically simulate the PET daily operation and to obtain the charging loads of PETs in both the temporal and spatial scales. The multi-step Q(λ) learning outperforms Q-learning in terms of convergence rate and reward performance. Moreover, the PET shift strategies and electricity pricing mechanisms are investigated, and the results indicate that the appropriate operation rules of PETs significantly improve the safe and reliable operation of power systems.

A review of tools, models and techniques for long-term assessment of distribution systems using OpenDSS and parallel computing

Many distribution system studies require long-term evaluations (e.g. for one year or more): Energy loss minimization, reliability assessment, or optimal rating of distributed energy resources should be based on long-term simulations of the distribution system. This paper summarizes the work carried out by the authors to perform long-term studies of large distribution systems using an OpenDSS-MATLAB environment and parallel computing. The paper details the tools, models, and procedures used by the authors in optimal allocation of distributed resources, reliability assessment of distribution systems with and without distributed generation, optimal rating of energy storage systems, or impact analysis of the solid state transformer. Since in most cases, the developed procedures were implemented for application in a multicore installation, a summary of capabilities required for parallel computing applications is also included. The approaches chosen for carrying out those studies used the traditional Monte Carlo method, clustering techniques or genetic algorithms. Custom-made models for application with OpenDSS were required in some studies: A summary of the characteristics of those models and their implementation are also included.

A Fast Method for Reliability Evaluation of Ultra High Voltage AC/DC System Based on Hybrid Simulation

The construction and operation of the ultrahigh voltage power grid has solved the problem of optimal allocation of energy resources and played a key role in promoting social development. However, concerns about its safety have kept growing in recent years. In order to analyze the reliability of ultrahigh voltage AC/DC system combined with the quasi-Monte Carlo method and PSD-BPA simulation, the reliability model of various components and system is established, and the simulation speed is improved with accuracy ensured. In order to ensure the compatibility and efficiency of the software, we design the BPA-Matpower data interface, and the data translation from BPA to Matpower is realized by fourth conversion. Then, we propose an index system for reliability evaluation, concise and easy to compute, to reflect the reliability of the UHV grids and the characteristics of AC and DC systems. Based on actual regional powergrid, we compare the model in this paper with the traditional sequential Monte Carlo method, and carry out the analysis of the component sensitivity to study the multi-fault characteristics and the weakness of the system, and verify the scientific and effective result of this paper.

An efficient method for fractured shale reservoir history matching: The embedded discrete fracture multi-continuum approach

In this study, we established a more efficient approach for fractured shale reservoir modeling with an emphasis on simplifying and automating the workflow for assisted history matching and uncertainty quantification. The improvement is especially notable for the process of history matching since the fracture geometry and properties can be directly set as parameters to be history matched. The resultant approach not only shows a significant reduction in the computational time while maintaining model accuracy, but also provides an automatic method for modifying the fracture related parameters - a laborious process in the traditional workflow.In the forward reservoir model, we implemented and extended the Embedded Discrete Fracture Model (Embedded DFM) approach for fractures with arbitrary strike and dip angle to a multiple porosity/permeability setting. The fractures are naturally discretized by the boundary of parent matrix grid blocks. Control volumes of fracture segments are generated according to the specific geometry of each of the segments. Three types of non-neighbor connections are then generated, namely the connection between the fracture segment and its parent matrix grid blocks, the connection between two intersecting fracture segments from different fractures, and the connection between two neighbor fracture segments from the same fracture. For each of the non-neighbor connections, transmissibility can be calculated honoring the physics of the flow.In our approach with Embedded Discrete Fracture Multiple-Porosity Model, the matrix is sub-divided into three porosity types, namely organic matrix (kerogen), inorganic matrix and natural fractures, with the necessary physics included for each of the porosity types. The macro fractures are explicitly represented with Embedded DFM. The proposed model provides a coherent method for characterizing the organic matrix, inorganic matrix, micro fractures as well as the hydraulic fractures of shale reservoirs. It offers a computationally efficient approach for modeling the severe heterogeneity due to hydraulic and natural fractures. Compared with traditional discrete fracture models, fewer grid blocks and lower levels of refinement are required. Compared with multiple porosity method, the proposed model has desirable accuracy for the simulation of reservoirs with large scale fractures.In the history matching and uncertainty quantification stage, due to the low efficiency of traditional Markov Chain Monte Carlo (MCMC) method when applied to reservoir history matching, a more advanced algorithm of two-stage MCMC is employed to evaluate the uncertainty for all the parameters. Since no upscaling of the fracture related parameters is required, the reservoir model can be generated by a pre-processor based on the proposed parameter, which maintains the adequacy of a Gaussian distribution assumption. Therefore, the workflow can be completely automated. By incorporating Embedded DFM and multiple porosity/permeability approaches, the improved model facilitates the history matching of fractured shale reservoirs by cutting the total amount of grid blocks, reducing the complexity of the gridding process, as well as improving the accuracy of fluid transportation within and among different porosity types.

Uncertainty propagation for statistical impact prediction of space debris

Predictions of the impact time and location of space debris in a decaying trajectory are highly influenced by uncertainties. The traditional Monte Carlo (MC) method can be used to perform accurate statistical impact predictions, but requires a large computational effort. A method is investigated that directly propagates a Probability Density Function (PDF) in time, which has the potential to obtain more accurate results with less computational effort. The decaying trajectory of Delta-K rocket stages was used to test the methods using a six degrees-of-freedom state model. The PDF of the state of the body was propagated in time to obtain impact-time distributions. This Direct PDF Propagation (DPP) method results in a multi-dimensional scattered dataset of the PDF of the state, which is highly challenging to process. No accurate results could be obtained, because of the structure of the DPP data and the high dimensionality. Therefore, the DPP method is less suitable for practical uncontrolled entry problems and the traditional MC method remains superior. Additionally, the MC method was used with two improved uncertainty models to obtain impact-time distributions, which were validated using observations of true impacts. For one of the two uncertainty models, statistically more valid impact-time distributions were obtained than in previous research.

Optimization-based inverse analysis for membership function identification in fuzzy steady-state heat transfer problem

Based on the optimization design technology and fuzzy uncertainty theory, this paper proposes a novel inverse analysis method for membership function identification in steady-state heat transfer problem with fuzzy modeling parameters. The system subjective uncertainties associated with expert opinions are quantified as fuzzy parameters, which can be converted into interval variables by level-cut strategy. By means of the errors between measured and calculated temperature data, the parameter identification process is executed as a nested-loop optimization model. To avoid the considerable computational cost caused by nested-loop, an interval vertex method is presented to replace the inner-loop for predicting the temperature response bounds. The eventual membership functions of input fuzzy parameters are constructed by using the fuzzy decomposition theorem. Comparing results with traditional Monte Carlo method, a numerical example about 3D air cooling system is provided to verify the feasibility of proposed method for fuzzy parameter identification in engineering.

Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach

• Comprehensive analysis of impact of parametric uncertainties on simulation of CO 2 storage in porous media is performed. • A non-isothermal two-phase two-component flow system is considered. • Rigorous numerical study of the accuracy of the polynomial chaos surrogate model is performed. • A comprehensive global sensitivity analysis is conducted. This work focuses on the simulation of CO 2 storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on CO 2 leakage. To simulate the process, a non-isothermal two-phase two-component flow system with equilibrium phase exchange is used. Since model evaluations are computationally intensive, instead of traditional Monte Carlo methods, we rely on polynomial chaos (PC) expansions for representation of the stochastic model response. A non-intrusive approach is used to determine the PC coefficients. We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies. In addition to characterizing the distributions of model observables, we compute probabilities of excess CO 2 leakage. Moreover, we consider the injection rate as a design parameter and compute an optimum injection rate that ensures that the risk of excess pressure buildup at the leaky well remains below acceptable levels. We also provide a comprehensive analysis of sensitivities of CO 2 leakage, where we compute the contributions of the random parameters, and their interactions, to the variance by computing first, second, and total order Sobol’ indices.

Using the multi-objective optimization replica exchange Monte Carlo enhanced sampling method for protein\u2013small molecule docking

BackgroundIn this study, we extended the replica exchange Monte Carlo (REMC) sampling method to protein–small molecule docking conformational prediction using RosettaLigand. In contrast to the traditional Monte Carlo (MC) and REMC sampling methods, these methods use multi-objective optimization Pareto front information to facilitate the selection of replicas for exchange.ResultsThe Pareto front information generated to select lower energy conformations as representative conformation structure replicas can facilitate the convergence of the available conformational space, including available near-native structures. Furthermore, our approach directly provides min-min scenario Pareto optimal solutions, as well as a hybrid of the min-min and max-min scenario Pareto optimal solutions with lower energy conformations for use as structure templates in the REMC sampling method. These methods were validated based on a thorough analysis of a benchmark data set containing 16 benchmark test cases. An in-depth comparison between MC, REMC, multi-objective optimization-REMC (MO-REMC), and hybrid MO-REMC (HMO-REMC) sampling methods was performed to illustrate the differences between the four conformational search strategies.ConclusionsOur findings demonstrate that the MO-REMC and HMO-REMC conformational sampling methods are powerful approaches for obtaining protein–small molecule docking conformational predictions based on the binding energy of complexes in RosettaLigand.

Solving Method of Workspace for 6 DOF Robot Based on Vision

In order to get the solution of the robot workspace, a method that based on the SimMechanics model in Matlab and the Monte-Carlo method was adopted to solve the robot workspace．Matlab/Simulink software was used to realize movement simulation of robot arms and got a compact workspace. Compared to traditional Monte-Carlo method, this method had the advantages of better speed in solving workspace，strong visibility and avoiding complicated mathematical operations, which provided an important basis for robot's obstacle avoidance planning.

Effcient Sequential Monte-Carlo Samplers for Bayesian Inference

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such inference problems. However, in the presence of a high-dimensional and/or multi-modal posterior distribution, it is widely documented that standard Monte-Carlo techniques could lead to poor performance. In this paper, the study is focused on a Sequential Monte-Carlo (SMC) sampler framework, a more robust and efficient Monte Carlo algorithm. Although this approach presents many advantages over traditional Monte-Carlo methods, the potential of this emergent technique is however largely under-exploited in signal processing. In this work, we aim at proposing some novel strategies that will improve the efficiency and facilitate practical implementation of the SMC sampler specifically for signal processing applications. Firstly, we propose an automatic and adaptive strategy that selects the sequence of distributions within the SMC sampler that minimizes the asymptotic variance of the estimator of the posterior normalization constant. This is critical for performing model selection in modelling applications in Bayesian signal processing. The second original contribution we present improves the global efficiency of the SMC sampler by introducing a novel correction mechanism that allows the use of the particles generated through all the iterations of the algorithm (instead of only particles from the last iteration). This is a significant contribution as it removes the need to discard a large portion of the samples obtained, as is standard in standard SMC methods. This will improve estimation performance in practical settings where computational budget is important to consider.

Forecasting with Many Predictors Using Message Passing Algorithms

Machine learning methods are becoming increasingly popular in economics, due to the increased availability of large datasets. In this paper I evaluate a recently proposed algorithm called Generalized Approximate Message Passing (GAMP), which has been popular in signal processing and compressive sensing. I show how this algorithm can be combined with Bayesian hierarchical shrinkage priors typically used in economic forecasting, resulting in computationally efficient schemes for estimating high-dimensional regression models. Using Monte Carlo simulations I establish that in certain scenarios GAMP can achieve estimation accuracy comparable to traditional Markov chain Monte Carlo methods, at a tiny fraction of the computing time. In a forecasting exercise involving a large set of orthogonal macroeconomic predictors, I show that Bayesian shrinkage estimators based on GAMP perform very well compared to a large set of alternatives.

Computed torque control of fully-actuated nondeterministic multibody systems

Multibody dynamics plays a key role in the modeling, simulation, design, and control of many engineering problems. The dynamics of these complex systems can be highly sensitive to uncertainty. In this paper, the method of Polynomial Chaos Expansion (PCE) is extended and integrated with Computed Control Torque Law (CTCL) to model and control fully-actuated nondeterministic multibody systems. PCE provides an efficient mathematical formulation to introduce and propagate uncertainty through the system’s dynamics by compactly projecting each stochastic response output and random input onto a space of appropriate independent orthogonal polynomial base functions. In this paper, a new mathematical formulation is further generated to express CTCL in the PCE scheme. The PCE-based CTCL presented is able to overcome the system’s nonlinearities by using feedback linearization to evaluate generalized driving forces, thus making the nondeterministic multibody system follow the desired trajectory. Herein, this method is applied to control a fully-actuated four-degree-of-freedom Selective Compliance Assembly Robot Arm (SCARA) with multiple uncertainties in the system parameters. The comparison between the time efficiency and accuracy of the PCE-based CTCL and the traditional Monte Carlo method indicates that PCE can provide the desired accuracy in a more time effective manner for some engineering problems.

Analysis of voltage stability uncertainty using stochastic response surface method related to wind farm correlation

Wind speed follows the Weibull probability distribution and wind power can have a significant influence on power system voltage stability. In order to research the influence of wind plant correlation on power system voltage stability, in this paper, the stochastic response surface method (SRSM) is applied to voltage stability analysis to establish the polynomial relationship between the random input and the output response. The Kendall rank correlation coefficient is selected to measure the correlation between wind farms, and the joint probability distribution of wind farms is calculated by Copula function. A dynamic system that includes system node voltages is established. The composite matrix spectral radius of the dynamic system is used as the output of the SRSM, whereas the wind speed is used as the input based on wind farm correlation. The proposed method is compared with the traditional Monte Carlo (MC) method, and the effectiveness and accuracy of the proposed approach is verified using the IEEE 24-bus system and the EPRI 36-bus system. The simulation results also indicate that the consideration of wind farm correlation can more accurately reflect the system stability.

Bayesian Calibration and Uncertainty Quantification for a Physics-Based Precipitation Model of Nickel–Titanium Shape-Memory Alloys

Uncertainty quantification (UQ) is an emerging field that focuses on characterizing, quantifying, and potentially reducing, the uncertainties associated with computer simulation models used in a wide range of applications. Although it has been successfully applied to computer simulation models in areas such as structural engineering, climate forecasting, and medical sciences, this powerful research area is still lagging behind in materials simulation models. These are broadly defined as physics-based predictive models developed to predict material behavior, i.e., processing-microstructure-property relations and have recently received considerable interest with the advent of emerging concepts such as Integrated Computational Materials Engineering (ICME). The need of effective tools for quantifying the uncertainties associated with materials simulation models has been identified as a high priority research area in most recent roadmapping efforts in the field. In this paper, we present one of the first efforts in conducting systematic UQ of a physics-based materials simulation model used for predicting the evolution of precipitates in advanced nickel–titanium shape-memory alloys (SMAs) subject to heat treatment. Specifically, a Bayesian calibration approach is used to conduct calibration of the precipitation model using a synthesis of experimental and computer simulation data. We focus on constructing a Gaussian process-based surrogate modeling approach for achieving this task, and then benchmark the predictive accuracy of the calibrated model with that of the model calibrated using traditional Markov chain Monte Carlo (MCMC) methods.

Numerical Analysis of a Transmission Line Illuminated by a Random Plane-Wave Field Using Stochastic Reduced Order Models

A novel nonintrusive statistical approach, known as the stochastic reduced order model (SROM) method, is applied to efficiently estimate the statistical information of the terminal response (i.e., the induced current) in transmission lines excited by a random incident plane-wave field. The idea of the SROM method is conceptually simple, i.e., to represent the uncertain input space dimensioned by random variables using the SROM-based input model. This input model consists of a very small number of selected samples with assigned probabilities. Thus, only these input samples in the model need to be evaluated using the deterministic solver. The SROM-based output model can be constructed to approximate the propagated uncertainty to the real output response with elementary calculation. The efficiency and accuracy of the SROM method to obtain the statistics of the induced current are analyzed using two examples, where the complexity of the uncertain input space gradually increases. The performance of the SROM method is compared with that of the traditional Monte Carlo (MC) method. The stochastic collocation (SC) method based on sparse grid sampling strategy computed via the Smolyak algorithm is also implemented to fairly evaluate the SROM performance. The result shows that the SROM method is much more efficient than the MC method to obtain accurate statistics of the induced current, and even shows a faster convergence rate compared with that of the SC method in the examples considered. Therefore, the SROM method is a suitable approach to investigate the variability of radiated susceptibility in electromagnetic compatibility problems with a random incident wave.

Monte Carlo simulations of polycrystalline ferroelectrics: Effects of electric field and grain size on dynamic electric polarization

The present work incorporates a two dimensional Monte Carlo based polycrystalline simulation analysis for ferroelectric thin films. In the two stage process; first, grain growth is simulated via a traditional Q-State Monte Carlo method, taking into account isotropic grain boundary energies. Second, the grain growth results are incorporated within an electric polarization model, combining contributions from a three component Hamiltonian, including the electrostatic potential, nearest neighbor electrical interactions, and electrostatic energy. Among other findings, the results suggest a strong correlation between electric polarization and grain size, particularly at relatively large electric field frequencies.

On the parametric uncertainty quantification of the Rothermel's rate of spread model

Parametric uncertainty quantification of the Rothermel's fire spread model is presented using the Polynomial Chaos expansion method under a Non-Intrusive Spectral Projection (NISP) approach. Several Rothermel's model input parameters have been considered random with an associated prescribed probability density function. Two different vegetation fire scenarios are considered and NISP method results and performance are compared with four other stochastic methodologies: Sensitivity Derivative Enhance Sampling; two Monte Carlo techniques; and Global Sensitivity Analysis. The stochastic analysis includes a sensitivity analysis study to quantify the direct influence of each random parameter on the solution. The NISP approach achieved performance three orders of magnitude faster than the traditional Monte Carlo method. The NISP capability to perform uncertainty quantification associated with fast convergence makes it well suited to be applied for stochastic prediction of fire spread.