Using Deterministic Chaos for Superefficient Monte Carlo Simulations

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.

This paper deals with the reliability assessment of electrical power supply systems under redundancy. For doing so, three probabilistic safety analysis (PSA) methods are proposed and developed namely fault tree analysis (FTA), reliability block diagram (RBD), and Monte Carlo Simulation (MC) method. The FTA method is performed using RiskSpectrumPSA® software and the RBD and MC methods are coded using Matlab software. The electrical power supply system reliability is analyzed and enhanced considering various cases of redundancy. The FTA method is based on qualitative and quantitative reliability assessment. The quantitative assessment calculates the failure probability of the top event, and the qualitative approach determines the minimal cut sets (MCS). However, the RBD and MC methods are proposed to compute the system failure probability. The considered methods are applied on three case studies and the obtained results are compared to each other. The obtained results show that the three methods provide almost the same results. Furthermore, the reliability of the electrical power supply is clearly enhanced with the number of redundant components.

In recent years, cone-beam computed tomography (CBCT) has played an important role in medical imaging. However, the applications of CBCT are limited due to the severe scatter contamination. Conventional Monte Carlo (MC) simulation can provide accurate scatter estimation for scatter correction, but the expensive computational cost has always been the bottleneck of MC method in clinical application. In this work, an MC simulation method combined with a variance reduction technique called correlated sampling is proposed for fast iterative scatter correction. Correlated sampling exploits correlation between similar simulation systems to reduce the variance of interest quantities. Specifically, conventional MC simulation is first performed on the scatter-contaminated CBCT to generate the initial scatter signal. In the subsequent correction iterations, scatter estimation is then updated by applying correlated MC sampling to the latest corrected CBCT images by reusing the random number sequences of the task-related photons in conventional MC. Afterward, the corrected projections obtained by subtracting the scatter estimation from raw projections are utilized for FDK reconstruction. These steps are repeated until an adequate scatter correction is obtained. The performance of the proposed framework is evaluated by the accuracy of the scatter estimation, the quality of corrected CBCT images and efficiency. Overall, the difference in mean absolute percentage error between scatter estimation with and without correlated sampling is 0.25% for full-fan case and 0.34% for half-fan case, respectively. In simulation studies, scatter artifacts are substantially eliminated, where the mean absolute error value is reduced from 15 to 2HU in full-fan case and from 53 to 13HU in half-fan case. Scatter-to-primary ratio is reduced to 0.02 for full-fan and 0.04 for half-fan, respectively. In phantom study, the contrast-to-noise ratio (CNR) is increased by a factor of 1.63, and the contrast is increased by a factor of 1.77. As for clinical studies, the CNR is improved by 11% and 14% for half-fan and full-fan, respectively. The contrast after correction is increased by 19% for half-fan and 44% for full-fan. Furthermore, root mean square error is also effectively reduced, especially from 78 to 4HU for full-fan. Experimental results demonstrate that the figure of merit is improved between 23 and 43 folds when using correlated sampling. The proposed method takes less than 25s for the whole iterative scatter correction process. The proposed correlated sampling-based MC simulation method can achieve fast and accurate scatter correction for CBCT, making it suitable for real-time clinical use.

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state (SLS) of single piles. This contributes to conducting the SLS reliability-based design (RBD) of piles. Based on a two-parameter, hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index (βsls) is obtained using the mean value first order second moment (MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation (MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement (slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety (FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

Evaluation of concepts of fin efficiency using Monte Carlo Simulation method

This article aims to investigate the means to obtain optimal hot stamping process parameters and the influence of the stochastic variability of these parameters on forming quality. A multi-objective stochastic approach, integrating response surface methodology (RSM), multi-objective genetic algorithm optimization non-dominated sorting genetic algorithm II (NSGA-II) and the Monte Carlo simulation (MCS) method is proposed in this article to achieve this goal. RSM was used to establish the relationship between the process parameters and forming quality indices. NSGA-II was utilized to obtain a Pareto frontier, which consists of a series of optimal process parameters. The MCS method was employed to study and reduce the influence of a stochastic property of these process parameters on forming quality. The results confirmed the efficiency of the proposed multi-objective stochastic approach during optimization of the hot stamping process. Robust optimal process parameters guaranteeing good forming quality were also obtained using this approach.

Objective: In situations where computed tomography (CT) scans are necessary for pregnant patients, such as in cases of trauma or other conditions that provide clinical benefit, accurately estimating the radiation dose to which the fetus is exposed is crucial. However, current methods are not sufficiently practical or feasible for routine clinical use. This study aims to assess and calculate the fetal dose and associated organ doses resulting from CT scans in pregnant patients using the Monte Carlo Simulation Method. Methods: Monte Carlo (MC) simulations and related calculations were conducted on pregnant patient phantoms for different gestational periods (8-15 weeks) using a 64-slice CT scanner (Discovery CT750 HD GE Healthcare) to estimate fetal doses. Organ dose calculations were also carried out. The MC code simulating dose distributions was validated with measurements from the CT Dose Index (CTDI) following AAPM protocols. Volumetric CTDI values from the MC simulations were normalized, enabling the development of a calculation algorithm for fetal dose assessments across different body regions and exposure settings. The algorithm, approved by the institutional review board, was validated through patient-specific MC simulations on CT data from pregnant patients (with gestational ages of 8-15 weeks) who had undergone CT scans. Results: Based on the data, it can be concluded that the fetus was exposed to low radiation doses, which do not present significant risk to fetal development. The doses observed in the study fell within acceptable clinical limits, indicating that fetal radiation exposure during CT scans can be managed safely with appropriate protocols. However, minimizing radiation exposure during pregnancy is essential. The use of low-dose protocols, as demonstrated in this study, is especially important for these patients. Moreover, the study’s findings highlight the importance of optimizing CT scan parameters and adopting radiation reduction strategies in routine clinical practice. Alternative imaging methods that utilize non-ionizing radiation, such as ultrasound or MRI, should also be considered when clinically appropriate. Conclusions: This study provides a clinically applicable approach to calculating fetal radiation doses during CT scans. The developed algorithm can help reduce fetal exposure and ensure patient safety. Future studies could expand on this research by validating the algorithm in larger patient cohorts and different gestational stages. The findings emphasize the need for radiology technologists to use the lowest possible dose protocols and explore non-ionizing imaging alternatives whenever feasible. .

Harmonics originated by non‐linear elements connected to power systems cause unwanted harmful technical problems. In this study a novel probabilistic harmonic load flow based on a point estimate method has been proposed. The proposed method surpasses the previous point estimate methods (PEMs) when generalising the approach to multiple random variables with various probabilistic distributions. Addressing the results of the Monte Carlo simulation (MCS) method as reference, the fast PEM has been applied to a modified version of the IEEE 14 bus test system and the advantages of this new method are highlighted. The results reveal less computational burden and time compared with the MCS method while the accuracy remains at a high level.

With the development of science and technology, reliability of power grids in rural areas in the algorithm have made new progress, in a variety of simulation methods, Monte Carlo simulation method because the sampling frequency has nothing to do with the grid size and the required accuracy only the features, so network security risk management in rural areas has been widely used. This article describes the sequential simulation, non-sequential Monte Carlo simulation of the basic principles of probabilistic simulation methods and characteristics.KeywordsMonte Carlo simulationPower systemRisk assessment

A Monte Carlo (MC) simulation is performed on peroxide induced branching reactions in a linear low density polyethylene (LLDPE) melt processed with different dicumyl peroxide (DCP) concentrations at various processing times and temperatures. The MC simulation can successfully monitor the microstructural changes due to the induced long chain branching (LCB), decreased terminal double bonds, and increased trans vinyl bonds in LLDPE during peroxide modification. The induced structural changes are in good agreement with the experimental results obtained by rheometery and SEC analysis. The changes in the gel content, , and MWD as a result of the peroxide modification are also determined. The simulation results also reveal that the chemical mechanism by which the modification proceeded is closely related to the changes in concentrations of reactive vinyl species of the PE molecules. Moreover, the results indicate that the degree of induced LCB increases almost linearly with the DCP concentrations. The findings of this paper indicate that the MC simulation method is able to predict the suitable processing conditions needed for inducing desirable structural changes in a LLDPE.

Information gap decision theory with risk aversion strategy for robust planning of hybrid photovoltaic/wind/battery storage system in distribution networks considering uncertainty

Market risk assessment is crucial for financial practitioners and helps manage potential losses from market volatility. This article compares three common VaR (value at risk) calculation methods - historical simulation, variance-covariance method and Monte Carlo simulation, and applies them to the past ten years of data of the Nasdaq Index. The results show that at a 95% confidence level, the VaR estimates given by these three methods are relatively close; however, at a 99% confidence level, the VaR values of Monte Carlo simulation and variance-covariance method are usually slightly higher than historical simulation. This shows that compared with historical simulation, these two methods are more sensitive to extreme market events and can more effectively capture tail risks when the market is volatile. In the future, machine learning technology is expected to improve the accuracy of VaR calculation, especially in dealing with high-dimensional data and complex nonlinear relationships.

In the present study, the overall stability of typical Korean composite caisson breakwaters that were initially designed following the conventional deterministic approach is investigated using reliability approaches. Therefore, the sensitivity of critical uncertainties regarding breakwater safety is analyzed. Uncertainty sources related to the structure, ocean conditions, and properties of the subsoil and rubble mound are considered in the reliability analysis. Sliding and overturning failures are presented as explicit equations, and three reliability methods, i.e., the mean value first-order second-moment, first-order reliability method, and Monte Carlo simulation, are applied in the evaluation process. Furthermore, the bearing capacity of the rubble mound and subsoil are analyzed using the discrete slice method conjugated with the Monte Carlo simulation. The results of this study establish that the sliding failure generally is the most frequent failure occurring among the above-mentioned overall stability failures (around 15 times more common than failures observed in the foundation). Additionally, it is found that the horizontal wave force primarily contributes to the sliding of the caisson body, whereas the friction coefficient is the main factor producing the resistance force. Furthermore, a much small probability of overturning failure implies that the overturning of a caisson around its heels uncommonly occurs during their lifetime, unlike other overall failure modes. Moreover, the failure in foundations may commonly encounter in the breakwater that has a high rubble mound structure compared with sliding mode. Particularly, the performance function of the all foundation bearing capacities presents a nonlinear behavior and positively skewed distribution when using the Monte Carlo simulation method. This phenomenon proves that simulation methods might be an appropriate approach to evaluate the bearing capacity of a breakwater foundation that can overcome several drawbacks of the conventional design approach.

When studying concrete impairment, the carbonation depth of concrete is regarded to be variable. Therefore, a time-varying reliability evaluation is important to perform a structural safety assessment. By analyzing 13,198 data on the carbonation depth of concrete, we propose a time-varying reliability evaluation based on the third-moment (TM) method to predict the service life of concrete. Validated by Monte Carlo (MC) simulation, the errors of the calculated results using time-varying reliability evaluation were within 4%. It is shown that the TM method proposed in this paper is more practical than traditional approaches such as MC simulation and second-moment (SM) methods in probability analysis. In this paper, exponential distribution was used to characterize the distribution of carbonation depths. Since paint was present on the concrete surface, numerous uncarbonized concrete components were found in the experiments; to develop a time-varying model considering the uncarbonized components, a function for evaluating the ratio of carbonized concretes is proposed. Overall, the time-varying TM method provided in this paper can act as a foundation for other investigations on probabilistic analysis, e.g., of compressive strength, deflection, and crack of concrete, which can be used to evaluate the reliability of concrete.

A combined Monte Carlo (MC) simulation and Genetic Algorithm (GA) method was proposed by other researchers for the optimisation of spare parts allocation. From case studies, it was found that the number of simulation trials of the existing method tended to be either excessive or inadequate. Thus, a simulation replication number control method making full use of the advance simulation effort is proposed and implemented into the existing method. A numerical example shows significant improvement on overall simulation efficiency and that at the same time the required accuracy is guaranteed. Furthermore, it is argued that application-specific knowledge should be embedded into the general GA procedure so that the evolution process can be more efficient. Heuristic methods for initial population preparation for GA with and without considering component cost difference are proposed and illustrated for spare parts allocation. A computing experiment was designed and performed to examine the influence of parameters for replication number control and initial population preparation. The generation of availability–cost curve further indicates the necessity to adopt heuristic methods to improve searching efficiency in GA.