Monte Carlo Simulation Method Research Articles

A simulation-based DEA approach for multiple criterion decision-making problems with uncertain mixed-criteria values

In ex-ante decision scenarios, predicting criterion values accurately is difficult for decision makers (DMs). Inconsiderable work is normally required for measuring criteria by uncertain random values or ordinal values. However, in the classical data envelopment analysis (DEA) model, criterion values are the constants that limit the application of the classical DEA model in ex-ante decision scenarios. This paper presents a simulation-based DEA approach, which captures random and ordinal criterion values by a simple and direct simulation-based approach. The approach includes three steps. In the first step, Monte Carlo simulation methods are used to convert uncertain random values or ordinal values into cardinal data. In the second step, we use traditional DEA methods to compute the efficiency score of decision-making units (DMUs). In the third step, we ranked all DMUs by calculating the DEA-efficient acceptability of each DMU in multiple simulations and then selected the optimal DMU. The proposed approach is illustrated by experimental examples and a case study of a municipal wastewater treatment system.

Manufacturing sensitivity study of tensegrity structures using Monte Carlo simulations

The successful construction of a tensegrity structure requires not only design techniques but also a means to account for any manufacturing or assembly errors. As a tensegrity is prestressed and is often stabilised by its prestress, it requires a form-finding technique to determine the balanced configuration in the design phase; this property also makes it challenging for engineers to evaluate the effect of manufacturing imperfections on the self-equilibrated configuration. In this paper we investigate the sensitivity of tensegrity structures to manufacturing imperfections, using a stiffness-matrix-based form-finding technique in combination with the Monte Carlo simulation method to introduce manufacturing length errors. The effects at the structural level are captured, and two general relationships between the variance of the input manufacturing error and the output distribution of the member tensions, between the variance and the mean across all groups, are observed. By identifying the most sensitive member group, this work provides a design and analysis strategy when the natural length errors of members are considered for tensegrity structures.

Data-driven uncertainty quantification and sensitivity studies in free vibration behavior of bio-inspired helicoidal laminated composite cylindrical shells

The uncertainty in the ply orientation of bio-inspired helicoidal laminated composite cylindrical shells is quantified. The frequencies obtained from the higher-order shear deformation theory are trained to formulate a surrogate model in the multi-output Gaussian Process Regression algorithm framework, and the stochastic analysis is then carried out using the Monte Carlo simulation method. For simply supported and clamped shells, uncertainties in the top and bottom-most layers widely affect the free vibration behavior of the shells compared to the inner-most or central layers, whereas for cantilever shells, opposite trend is observed. The inclusion of noise widely affects the free vibration behavior.

Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimating the scale parameter of the Weibull distribution. To evaluate their performance, we generate simulated datasets with different sample sizes and varying parameter values. A technique for pre-estimation shrinkage is suggested to enhance the precision of estimation. Simulation experiments proved that the Bayesian shrinkage estimator and shrinkage pre-estimation under the squared loss function method are better than the other methods because they give the least mean square error. Overall, our findings highlight the advantages of shrinkage Bayesian estimation methods for the proposed distribution. Researchers and practitioners in fields reliant on extreme value analysis can benefit from these findings when selecting appropriate Bayesian estimation techniques for modeling extreme events accurately and efficiently.

Combined Shewhart–EWMA and Shewhart–CUSUM monitoring schemes for time between events

AbstractTo improve the detecting abilities of upward and downward parameter changes in high‐quality process, two combined schemes by integrating memory‐type, that is, exponentially weighted moving average (EWMA) or cumulative sum (CUSUM), and memoryless, that is, Shewhart, are proposed for monitoring the time between events (TBE), which is modeled as an exponential distributed variable. A Monte Carlo simulation method is employed to obtain the Run Length () properties, that is average run length (), of the proposed schemes for different parameter settings. The nearly optimal monitoring parameter combinations under different change size are obtained by minimizing the out‐of‐control with the satisfied in‐control . Using the designed parameters, the performance of the proposed monitoring schemes is compared with the existing EWMA and CUSUM TBE. The results show that the proposed combined Shewhart–EWMA or Shewhart–CUSUM TBE generally perform better than the corresponding EWMA or CUSUM TBE for large changes and they also show better performance than the Shewhart TBE for small changes. Finally, a real dataset of organic light‐emitting diode (OLED) failure time from Sumsung company is employed to indicate the usage and implementation of combined TBE schemes.

Optimal annuitisation, housing and reverse mortgage in retirement in the presence of a means-tested public pension

AbstractIn this paper we develop a model to find optimal decisions in retirement with respect to the consumption, risky asset allocation, access to annuities, reverse mortgage and the option to scale housing in the presence of a means-tested public pension. To solve the corresponding high-dimensional optimal stochastic control problem, we use the Least-Squares Monte Carlo simulation method. The model is applied in the context of the Australian retirement system. Few retirees in Australia utilise financial products in retirement, such as annuities or reverse mortgages. Since the government-provided means-tested Age Pension in Australia is an indirect annuity stream which is typically higher than the consumption floor, it can be argued that this could be the reason why many Australians do not annuitise. In addition, in Australia where assets allocated to the family home are not included in the means tests of Age Pension, the incentive to over-allocate wealth into housing assets is high. This raises the question whether a retiree is really better off over-allocating into the family home, while accessing home equity later on either via downsizing housing or by taking out a reverse mortgage. Our findings confirm that means-tested pension crowds out voluntary annuitisation in retirement, and that annuitisation is optimal sooner rather than later once retired. We find that it is never optimal to downscale housing when the means-tested pension and a reverse mortgage are available; only when there is no other way to access equity then downsizing is the only option.

Risk assessment of exposure to 12 kinds of mycotoxins through consumption of Pericarpium Citri Reticulatae collected from Three Gorges Reservoir area of China

A method for simultaneous determination of 12 mycotoxins in Pericarpium Citri Reticulataeby HPLC-MS/MS was established to analyze the residues of mycotoxins, inwhich from Three Gorges Reservoir area of China, including AFB1, AFB2, AFG1, AFG2, T-2, FB1, FB2, FB3, ZEN, OTA, OTB and DON.In addition, a probabilistic assessment model based on Monte Carlo simulation method was established in combination with pollution data, and the health risk assessment was carried out by the exposure limit method (MOE).The results showed that the method with strong specificity, good linearity and accurate recovery was established and could be used for the determination of 12 mycotoxins in Pericarpium Citri Reticulatae.In general, the total pollution rate of different degrees of pollution in the 36 batches of Pericarpium Citri Reticulatae sampleswas 75 %. It should be noted thatthe proportion of positive samplescontaminated by one toxin was the highest (59.26 %), and the detection rate of FB3 in Pericarpium Citri Reticulataewas the highest (66.67%), followed by AFG1 (44.44 %), indicating that the medicinal material polluted by AFG1 and AFB3 alone or simultaneously was more serious. Specifically, the detection rate of mycotoxins in Chongqing was the highest (92.31%) on account of the high temperature and humidity in Chongqing, followed by Southeast of Sichuan (83.33%) and West of Hubei (45.45%).On the other hand, the MOE of AFB1 and AFB2 calculated were both greater than 10000, indicating that the health risk of AFB1 and AFB2 exposure caused by taking Pericarpium Citri Reticulatae was low, but the risk of high intake population was higher than that of conventional intake population, which needed to be paid attention to. This study can provide a reference for the safety assessment of clinical medication of Pericarpium Citri Reticulatae inThree Gorges Reservoir area.

Study on the carbon footprint impact analysis method of integrated energy system operation in low-carbon park considering multi-domain dynamic characteristics

Low-carbon parks are an important battlefield for China to achieve the goal of peaking carbon neutrality. Accurate and efficient analysis and tracking of park carbon footprint is a necessary measure to reduce carbon and save energy in parks. Aiming at the problems of less research on the carbon footprint of low-carbon parks at home and abroad and the lack of tracking and analysis methods of dynamic influencing factors of carbon footprint, this paper focuses on the carbon footprint of typical low-carbon parks during operation and proposes a dynamic tracking method of the carbon footprint of low-carbon parks that considers the dynamic characteristics of carbon emissions in various fields. In this paper, the hierarchical impact structure of the carbon footprint of low-carbon parks was first constructed, including the impact of population, economy, construction, energy, transportation, and industry. LMDI (Logarithmic Mean Divisia Index) was used to decompose the macro-level impact of the carbon footprint of low-carbon parks. Secondly, this paper establishes a dynamic simulation model of carbon emissions of low-carbon parks in the fields of building, energy, transportation, and industry, which can realize 8760 hours of dynamic simulation calculation throughout the year. Based on dynamic simulation, this paper carries out single factor sensitivity analysis and combines the Monte Carlo simulation method to complete quantitative calculation of dynamic second-order influence weight of carbon footprint. Finally, a multi-domain impact analysis and tracking method for the carbon footprint of low-carbon parks is obtained.

Parametric and nonparametric versions of adaptive CUSUM charts for monitoring the location of individual measurements

Control charts are customarily developed under the assumption of normal quality characteristics to be monitored. However, in many real dataset applications, the normality assumption is not easy to hold. The in-control (IC) robustness of the charting schemes has significant importance for the valid out-of-control (OOC) performance. This article intends to investigate the IC robustness of the unbiased-function-based adaptive cumulative sum (ACUSUM) chart and nonparametric ACUSUM (NPACUSUM) chart against the non-normal process distributions including symmetrical, skewed, and contaminated normal distributions. The OOC run length profiles of the ACUSUM and the proposed NPACUSUM charts for the individual measurements against the non-normal distributions are also a part of this study. The run length profiles of the proposed charting schemes have been computed using the Monte Carlo simulation method. The artificial datasets have been taken from some symmetric and skewed distributions to implement the proposals. An electrical engineering dataset has also been taken for the implementation of the proposal on a real dataset.

Simulation Method for the Impact of Atmospheric Wind Speed on Optical Signals in Satellite–Ground Laser Communication Links

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems.

Quantitative study of random walk parameters in node2vec model

In this paper, the Monte Carlo simulation method is used to investigate a generalized random walk model based on node2vec which is a popular algorithm in network embedding and has been widely applied in various domains such as link prediction, node classification, recommendation systems, etc. The aim is to quantitatively study the impact of the random walk parameters(including the number of walks per initial node r, the length of each walk l, the return parameter α, the common neighbor parameter β, and the outgoing parameter γ) on the embedding results. Specifically, the cross entropy is utilized as an observation to compare the difference between the frequency of nodes after random walks and the normalized degree sequence of nodes. The results show that the clustering coefficient significantly impacts the cross entropy. For networks with high clustering coefficient, the value of β should closely approximate that of γ, whereas for networks with low clustering coefficient, the value of β should be significantly smaller than that of γ. The value of α should be less than or equal to the minimum values between β and γ. Finally, the embedding effects of different random walk parameters are tested using node classification and link prediction tasks in real-world networks, and the results indicate that cross entropy can provide guidance for obtaining high-quality node embedding.

Estimating Market Power Exertion in the U.S. Beef Packing Industry: An Illustration of Data Aggregation Bias Using Simulated Data

This study investigates data aggregation bias in estimating market power in the U.S. beef packing industry using New Empirical Industrial Organization (NEIO) models and shows empirical procedures that can alleviate the bias. Unlike many earlier studies in estimating market power exertion, our study examines the data aggregation bias when market-level data are used in place of firm-level data and show how the bias could be reduced. We first derive data aggregation bias analytically, then empirically investigate the aggregation bias by estimating both firm and aggregate industry models. Because the firm-level data are not available, we use simulated data generated from the Monte Carlo simulation method. Hybrid models, combining limited firm-level data with aggregate data, are also estimated to illustrate how the aggregation bias could be reduced. Our results show that aggregate models with industry-level data tend to underestimate market power exertion in the U.S. beef packing industry, and the aggregation bias is statistically significant at the 1% level. Comparing results from hybrid models with firm-level estimates, we find that hybrid models reduce the bias but do not remove the aggregation bias significantly. The sensitivity analysis shows that market power estimate and aggregation bias are sensitive to functional forms.

Effect of functionalization on the adsorption performance of carbon nanotube as a drug delivery system for imatinib: molecular simulation study

In this study, efficiency of functionalized carbon nanotube as a potential delivery system for imatinib anti-cancer drug was investigated. Accordingly, carboxyl and hydroxyl functionalized carbon nanotube were inspected as a notable candidate for the carriage of this drug in aqueous media. For this purpose, possible interactions of imatinib with pure and functionalized carbon nanotube were considered in aqueous media. The compounds were optimized in gas phase using density functional calculations. Solvation free energies and association free energies of the optimized structures were then studied by Monte Carlo simulation and perturbation method in water environment. Outcomes of quantum mechanical calculations presented that pure and functionalized carbon nanotubes can act as imatinib drug adsorbents in gas phase. However, results of association free energy calculations in aqueous solution indicated that only carboxyl and hydroxyl functionalized carbon nanotubes could interact with imatinib. Monte Carlo simulation results revealed that electrostatic interactions play a vital role in the intermolecular interaction energies after binding of drug and nanotube in aqueous solution. Computed solvation free energies in water showed that the interactions with functionalized carbon nanotubes significantly enhance the solubility of imatinib, which could improve its in vivo bioavailability.

Monte Carlo simulation studies of reliability in psychometrics

Monte Carlo simulation studies are widely used in reliability research. This study reviewed 85 published Monte Carlo simulation studies investigating reliability. The review focused on the prevalence of particular reliability estimation methods and estimators, as well as adherence to previous recommendations for the Monte Carlo simulation method. It appears researchers do not fully adhere to these recommendations. Most of the reviewed studies have limitations in at least one of the following: reporting on the data generation procedure, selection of the number of replications, selection of conditions, benchmark utilization, and performance evaluation. Findings also suggest internal consistency in general and coefficient α are the most prevalent. Conversely, some reliability estimation methods and estimators that can be useful under many empirical conditions appear to be mostly overlooked. In the case of internal consistency, these are relatively obscure forms of α, λ2, λ4, μ-series, Kristof's coefficient, Feldt-Gilmer coefficient, maximal reliability, greatest lower bound to reliability, ω family, structural equation modeling-based coefficients, and internal consistency confidence intervals. Overlooked reliability estimation methods are parallel forms, test-retest, multilevel reliability, latent class-based reliability, reliability of an individual, and Bayesian reliability. Suggestions for future research have been offered.

Time-dependent reliability assessment and optimal design of corroded reinforced concrete beams

It remains a significant challenge to quantitatively describe the corrosion of reinforced concrete (RC) structures under chloride penetration. Moreover, when considering uncertainties throughout the life cycle of corroded RC structures for assessing their safety, reliability, and optimal design, the complexity of the problem intensifies. To address these issues, this paper studies the time-dependent reliability analysis and optimal design of corroded RC beams. At first, the time-dependent reliability of beams is investigated by considering both the serviceability limit state (SLS), which corresponds to the corrosion initiation of the reinforced steel, and the ultimate limit state (ULS), associated with the bending failure of the beam. This analysis takes into account the time-dependent chloride diffusion coefficient and incorporates a stochastic process. The reliability is evaluated using the Monte Carlo Simulation (MCS) method and the cumulative distribution function (CDF) method. Subsequently, a time-dependent reliability-based design optimization (TRBDO) problem is formulated, and the PSO-MCS, a methodology incorporating a particle swarm optimization (PSO) algorithm and MCS is adopted to solve it. After optimization, the initial cost of the specific RC beam is reduced from 1351.879€ to 1247.075€, while the time-dependent reliability within [0, 100] years is improved from 0.6057 to 0.6508. The effectiveness of the CDF, MCS and PSO-MCS methods are demonstrated through reliability analysis and design examples of corroded RC beams.

Simulation Models in a Fluidity Test of the Al-Si Alloy

The goal of the fluidity test is to evaluate the ability of the melt to fill the cavity of the mold, which is one of the factors affecting the final quality of the castings. It is a technological test that is basically not standardized, therefore it is realized in different forms, for example using “horizontal” and “vertical” molds. The “horizontal” mold makes it easier to fulfill the condition of repeatability, therefore it was used to calculate the capability of the test by the Measurement Systems Analysis (MSA) method. The results of the tests in both molds were used to calculate regression equations that allow the fluidity to be determined with strong reliability based on variables such as melt temperature, casting speed, and mold temperature. In addition, the effects of input data variability (uncertainty) on the resulting fluidity value were analyzed using regression equations and the Monte Carlo simulation. The contribution of the article is the analysis of the capability of the measurement process of the fluidity and a prediction of the results of its tests using the Monte Carlo simulation method.

Probabilistic assessment of existing shield tunnel longitudinal responses to tunnelling

AbstractThis paper proposes a probabilistic‐based framework to assess the failure probability of the existing shield tunnel owing to undercrossing tunnelling. A novel deterministic model using the two‐phase analysis method is presented to evaluate the longitudinal behaviours of the in‐service shield tunnel. First, the tunnelling‐induced settlement is estimated using the Loganathan and Poulos’ method; second, the longitudinal beam‐spring model (LBSM), which can explicitly consider the circumferential joints, is applied to reflect the performances of the existing shield tunnel. Two well‐documented case histories are selected to validate the effectiveness of the deterministic analysis model. The predictions are also compared with previous analytical methods. Afterward, to improve the computational efficiency, a surrogate model is then established to replace deterministic model and perform the global sensitivity analysis (GSA). A probabilistic analysis is further performed to explore the tunnelling‐induced deformation characteristics of the shield tunnel by means of Monte Carlo simulation (MCS) method. Parametric analyses are further performed to explore the influences of key variables on the failure probabilities of the existing shield tunnel. The results show the proposed deterministic model gives a satisfactory prediction in tunnelling‐induced responses of the existing shield tunnel. The LBSM can reflect the segmental ring and joint deformations more realistically. The uncertainties in the ground elastic modulus, joint rotation stiffness and the joint shearing stiffness dominate the tunnel settlement, joint opening and dislocation, respectively. The failure probability of tunnel settlement is more sensitive to volume loss than that of the joint opening and dislocation. The whole system failure probability is identical to that of the tunnel settlement failure mode. By increasing the coefficient of variation (COV) of random variables, probability density function (PDF) curves for neutral and pessimistic conditions become lower and wider, and the maximum joint opening and dislocation positions corresponding to the peaks of PDF apparently deviate from that of the determinate results. Increasing the two tunnel clearances, the allowable volume loss for opening and dislocation increase linearly, but it has insignificant influence on the tunnel failure mode. However, enlarge the new tunnel diameter leads to rapid decrease in the allowable volume loss for all failure modes.

Linewidth characterization of a self-traceable grating by SEM

To achieve high-precision nanometrology, a self-traceable grating reference material has been reported and prepared using atom lithography and soft x-ray interference techniques (Liu et al 2021 Nanotechnology 32 175 301). In this work, we employ a Monte Carlo simulation method to investigate the scanning electron microscopy (SEM) image contrast and linewidth characterization of the grating linewidth. The 3D structure of mushroom-shaped grating lines made of multilayers (Pt, SiO2 and Si) is modeled according to transmission electron microscopy (TEM) images, enabling the SEM linescan profiles of secondary electron signals to be obtained for different values of structural linewidth parameters from Monte Carlo simulations. Using the principle of the model-based library method, a model database of Monte Carlo-simulated SEM linescan profiles is thus constructed by varying the incident electron beam conditions and the grating linewidths; then, the grating linewidth is successfully characterized using experimental SEM images. The comparison with the TEM measurement reveals that the measurement accuracy is verified to within 0.3% for the linewidth of ∼25 nm.

Time-varying reliability models for parallel systems consisting of beam structures with crack flaws

Abstract. Time-varying reliability assessment of parallel systems of beam structures with crack defects is of great importance for structural safety evaluation. In this paper, time-varying reliability models for parallel systems with cracked beams are proposed. In the modeling process, the statistical correlation between crack depth, random working load, random strength degradation, and random stress response as well as the complex failure correlation jointly caused by these factors are considered. Based on the finite element analysis of the cracked beams, the reliability models are constructed by combining the neural network and the response surface agent model. The validity of the model is verified by the Monte Carlo simulation method. The results show that crack depth and working load dispersion have important effects on reliability and failure correlation.

An improved analytical solution to outcrossing rate for scalar nonstationary and non-gaussian processes

For time-dependent reliability methods, there is a lack of analytical solutions to outcrossing rates of nonstationary and non-Gaussian processes. This paper aims to propose an analytical method to determine this type of outcrossing rate with improved accuracy and efficiency. The novelty of this proposed method is that it can consider the probabilistic properties of non-Gaussian processes by combining a two-component parallel system model with higher-order moments-based reliability indexes. The main contributions of this method are: (1) compared with PHI2+ method, it is more accurate for the calculation of the outcrossing rate of nonstationary and non-Gaussian processes with nonlinear limit state functions; (2) compared with MPHI2 method, it is analytical and not only applicable for the nonstationary stochastic processes but also insensitive to time increments; and (3) it is not only more accurate than the existing methods for nonstationary and non-Gaussian processes but also more computation efficient than the Monte Carlo simulation method. The proposed method has shown its advantages for practical structures with neither Gaussian processes nor linear limit state functions, which are beneficial for both researchers and asset managers to evaluate the time-dependent reliability of structures accurately and to develop risk-informed maintenance schemes with a view to prolonging their service life.