Monte Carlo Simulation Method Research Articles

Optimal Mission Abort Decisions for Multi-Component Systems Considering Multiple Abort Criteria

This paper studies the optimal mission abort decisions for safety-critical mission-based systems with multiple components. The considered system operates in a random shock environment and is required to accomplish a mission during a fixed mission period. If the failure risk of the system is very high, the main mission can be aborted to avoid higher failure cost. The main contribution of this study lies in the design and optimization of mission abort policies for multi-component systems with multiple abort criteria. Moreover, multi-level transitions are considered in this study to characterize the different shock-resistance abilities for components in different states. Mission abort decisions are determined based on the number of components in either defective or failed state. The problem is formulated in the framework of the finite Markov chain imbedding method. We use the Monte-Carlo simulation method to derive the mission reliability and system survivability. Numerical studies and sensitivity analysis are presented to validate the obtained result.

Time-Varying Reliability Analysis of Multi-Cracked Beams Considering Maintenance Dependence

Time-varying reliability models of multi-cracked beam structures are established in this paper, which provide a theoretical method for the safety evaluation of multi-cracked beam structures. The reliability models proposed in this paper consider the interaction between the complex statistical correlations between system parameters during system operation and maintenance correlations, which is a difficult problem in the time-varying reliability modeling that takes into account work mechanisms and maintenance behavior. In the proposed models, multiple cracked elements are regarded as a dependent series system. The stresses, crack extensions, and multiple failure modes between each element constitute the complex failure dependence of the system. The time-varying reliability models of a multi-cracked beam structure are established via the neural network method and failure dependence analysis. Moreover, the failure dependence coefficient is proposed to quantify the time-varying failure dependence. Based on the working principle of the beam structures and the maintenance mechanism for the cracked state of the beams, a time-varying system reliability mode considering the maintenance dependence is proposed. Furthermore, the maintenance dependence coefficient index is proposed to quantitatively measure the interaction between the maintenance dependence and the failure dependence. Finally, the validity of the model is verified through the Monte Carlo simulation method. In the numerical examples, the relationship between maintenance dependence and failure dependence is illustrated and the influences of the statistical characteristics of the maintenance characteristic parameters on the maintainability and failure dependence are analyzed.

Uncertainty Evaluation of Soil Heavy Metal(loid) Pollution and Health Risk in Hunan Province: A Geographic Detector with Monte Carlo Simulation.

Research on soil heavy metal(loid) pollution and health risk assessment is extensive, but a notable gap exists in systematically examining uncertainty in this process. We employ the Nemerow index, the health risk assessment model, and the geographic detector model (GDM) to analyze soil heavy metal(loid) pollution, assess health risks, and identify driving factors in Hunan Province, China. Furthermore, the Monte Carlo simulation (MCS) method is utilized to quantitatively evaluate the uncertainties associated with the sampling point positions, model parameters, and classification boundaries of the driving factors in these processes. The experimental findings reveal the following key insights: (1) Regions with high levels of heavy metal(loid) pollution, accompanied by low uncertainty, are identified in Chenzhou and Hengyang Cities in Hunan Province. (2) Arsenic (As) and chromium (Cr) are identified as the primary contributors to health risks. (3) The GDM results highlight strong nonlinear enhanced interactions among lithology and other factors. (4) The input GDM factors, such as temperature, river distance, and gross domestic product (GDP), show high uncertainty on the influencing degree of soil heavy metal(loid) pollution. This study thoroughly assesses high heavy metal(loid) pollution in Hunan Province, China, emphasizing uncertainty and offering a scientific foundation for land management and pollution remediation.

Molecular Simulation of Thermodynamic Properties of CH4/CO2 Adsorption by Coal Molecules at Different Temperatures and Moisture Contents under Variable Pressure Conditions.

In order to further elucidate the thermodynamic mechanism of CH4/CO2 adsorption by coal molecules, the adsorption behavior of a molecular model of coal (C206H128O36N2) at Wucaiwan, Zhundong was investigated by applying Materials Studio 2020 and Monte Carlo (GCMC) simulation methods, and the adsorption behavior of CH4 and CO2 was studied from the thermodynamic point of view under the conditions of different temperatures, pressures, and moisture contents. The results showed that at different temperatures or moisture contents, CH4 molecules had a low-density scattering distribution and CO2 molecules had a high-density polymerization distribution. Temperature and moisture content and adsorption constants a and b were negatively correlated. Under the same conditions, the relationship between single- and binary-component adsorption amounts was CO2 > CH4 and the relationship between heat of adsorption was CO2 > CH4. When adsorption potential energy or entropy of adsorption was the same, the adsorption capacity was CO2 > CH4. Temperatures and moisture contents were negatively correlated with the total adsorption capacity of CH4/CO2; pressure was positively correlated with the total adsorption capacity of CH4/CO2. The effect of temperature on the equivalent heat of adsorption was greater than that of pressure at different temperatures, and the entropy of adsorption was positively correlated between temperature and CH4/CO2, while the amount of adsorption was negatively correlated with the entropy of adsorption. The effect of moisture content on the equivalent heat of adsorption was greater than that of pressure at different moisture contents, and the entropy of adsorption was negatively correlated between moisture content and amount of adsorption. The adsorption entropy of CH4/CO2 was negatively correlated, and the adsorption amount was positively correlated to the adsorption entropy. At a temperature above 318 K or moisture content above 10%, the total CH4/CO2 adsorption decreased significantly and the CO2 adsorption decreased significantly. From a thermodynamic point of view, the presence of a large amount of H2O had a much greater effect on CO2 than on CH4, and an increase in temperature or moisture content was unfavorable for CO2 sequestration, CO2 stripping of CH4, and control of CH4 diffusion and desorption, whereas at low temperature, high pressure, and moisture content <1%, the effect of stripping, sequestration, and control was good.

Probabilistic code-based shear capacity model for I-shaped steel reinforced concrete (SRC) beams

A code-based probabilistic prediction model is developed for structural design and reliability analysis of the shear capacity of shear-critical steel reinforced concrete (SRC) beams. First, an experimental database of 83 shear tests was compiled from the literature, including steel-reinforced normal-strength concrete, steel-reinforced high-strength concrete, and steel reinforced lightweight aggregate concrete. Then, three deterministic formulations from the most commonly-used specifications JGJ, AIJ, and ACI-AISC were presented and compared against the database. Based on the different shear mechanism and formula considerations in the code-based deterministic models, this study developed 12 probabilistic models that account for both epistemic and aleatory uncertainty to examine the impact of concrete strength, shear span ratio, number of parameters, and their interactions. The Bayesian theory and Markov Chain Monte Carlo (MCMC) simulation method were utilized to calibrate the models by generating posterior distributions of the model parameters and the standard deviation (SD) of the model error. Optimal model selection hinges upon balancing precision and intricacy. An analysis was then conducted to evaluate the accuracy of the selected model, and the probabilistic model was applied to estimate the shear reliability of a SRC beam. Results demonstrate that the model objectively represents the probabilistic properties of the shear capacity of SRC beams and has the capability to conduct reliability analysis.

Value at Risk Calculation of Digital Bank Stocks Portfolio in Indonesia

&lt;p&gt;Nowadays, stock investment has been increasingly growing in society. In investing activities, there are risks that may be experienced by investors. However, sometimes many investors do not realize how much risk that they might suffer in the future. One way that can be done to measure this risk is to calculate the Value at Risk (VaR). This study aims to calculate the VaR value of digital bank stock portfolio in Indonesia. The calculation of VaR will be done using two methods, include the Historical Simulation and Monte Carlo Simulation method. From the calculation, VaR with Historical Simulation and Monte Carlo sequentially generate results of IDR 6,006,718 and IDR 10,797,904 for 99% confidence level, IDR 4,135,857 and IDR 5,376,949 for 95% confidence level, and IDR 3,219,885 and IDR 3,417,553 for 90% confidence level. Based on the results, it is found that VaR result is directly proportional to the confidence level used. Through the calculation results, it also found that VaR value with the Monte Carlo Simulation method are greater than those with the Historical Simulation method.&lt;/p&gt;

Bus routing fine-tuning for integrated network-based demand and bus bridging for a disrupted railway system

Unanticipated commuter railway disruptions inevitably tend to result in passenger bunching and frustration with considerable delays. Bus bridging strategy is a timely response approach to operationally handle and ease these scheduling disturbance issues. Conventional strategies, in this case, are apt to adding new/temporary bus routes, or, alternatively, sharply amending existing routes. Nonetheless, previous approaches have mainly been dedicated to reducing the delay of stranded passengers. This was done without integrating and considering the ordinary demand with the stranded demand through optimally handling time-dependent total passenger demand based on available service capacity. Consequently, this study creates a method on how to fine-tune bus-routing changes to handle these railway disruptions. This method allows for adjusting partial bus routes to optimally solve the combined problem of the railway passengers with bus bridging and to service all the network-based bus stops. We propose a mixed integer nonlinear programming model with multitype vehicles using a rolling horizon method to minimize total passenger delay from integrated bus bridging and existing bus services. Considering the extensive problem of the bus network with variable headways, we use a customized branch-and-bound algorithm incorporating an elitist genetic algorithm and the Monte Carlo simulation method to solve the model. A case study of the Shanghai Jinshan Railway shows that the result of total passenger delay of the proposed bus bridging modeling with rolling horizon is less by 37.23% than without rolling horizon for representing the advance of knowledge, and less by 60.7% than the do-nothing situation for representing the advance over practice.

Variability of sub-regional fibre strength in 3D orthogonal SiC fabrics and its effect on the constitutive response of composites

Various fibre damage may occur during 3D orthogonal SiC woven weaving, leading to the variability of sub-regional fibre strength. In this study, different types of yarns were divided into several subregions along the cross-section according to the possible damage modes. The fibres in different subregions were extracted, and the monofilament strength test was carried out. The results showed that the fibre strengths of yarns and yarn subregions followed normal distributions. The correlation between the fibre strength distribution of the in-situ yarns and the subregion fibre strength difference was verified by using the Monte Carlo simulation method. Finally, the sub-regional fibre strength difference was considered in the tensile simulation of 3D orthogonal woven SiC/SiC composites. The simulation results agree with the experimental results and showed that the variability of sub-regional fibre strength significantly affects the composite's constitutive behaviour.

Verification of structural reliability of a highway bridge in the state of Rio Grande do Sul

This study deals with the evaluation of the reliability index of prestressed girders members of road bridges in relation to the ultimate limit state (ULS) of bending failure. In a wide bibliographic review of scientific works that deal with structural reliability, prestressed structural elements and road bridges, it is observed that few of these deals specifically with the reliability of girders considering the codes NBR 7188 of 2013 and NBR 7187 of 2021. A mechanical model was developed for the calculation of the beam resistant moment and the Monte Carlo Method was used to obtain a data set that represents the statistics of the structure in the ULS. To obtain the reliability index B, the first order reliability method (FORM) was used. The values obtained by the analytical method are validated using the Monte Carlo simulation method. For all evaluated cases, the value of the reliability index was higher than 4.0, which is higher than the minimum required value of 3.5, showing that the national normative recommendations for the design of beam members guarantee a very conservative level of safety.

A novel Bayesian Max-EWMA control chart for jointly monitoring the process mean and variance: an application to hard bake process

In this article, we introduce a novel Bayesian Max-EWMA control chart under various loss functions to concurrently monitor the mean and variance of a normally distributed process. The Bayesian Max-EWMA control chart exhibit strong overall performance in detecting shifts in both mean and dispersion across various magnitudes. To evaluate the performance of the proposed control chart, we employ Monte Carlo simulation methods to compute their run length characteristics. We conduct an extensive comparative analysis, contrasting the run length performance of our proposed charts with that of existing ones. Our findings highlight the heightened sensitivity of Bayesian Max-EWMA control chart to shifts of diverse magnitudes. Finally, to illustrate the efficacy of our Bayesian Max-EWMA control chart using various loss functions, we present a practical case study involving the hard-bake process in semiconductor manufacturing. Our results underscore the superior performance of the Bayesian Max-EWMA control chart in detecting out-of-control signals.

Robust compromise multicriteria decision model to evaluate the level of achievement of graduation profile

We propose an approach of a robust compromise multi-criteria decision-making model that evaluates the level of competency achievement in graduation profiles. Quantitative information on qualifications of specific and generic competencies of a graduation profile was collected from professors, graduates, employers, community partners, and students' self-perception of achievement. This information was categorized using ordinal Likert scales generated through Monte Carlo simulation methods and copula modeling. The proposed model is validated using optimization methods. It provides a single score for the level of competency achievement, and the analysis is conducted using descriptive statistics and multivariate analysis of clusters. Simulated scenarios revealed that higher weights given by stakeholders in the construction of the robust compromise score were associated with higher evaluation scores of competencies from the same stakeholders. Scenarios with negative correlations between stakeholder qualifications about level of achievement of graduation profile yielded lower scores in the robust compromise multi-criteria decision-making model. Our proposal for Robust Compromise Multi-Criteria Decision Making Model offers more precise single scores, reducing the epistemological uncertainty associated with the input information.

Interaction of sulfasalazine with outer surface of boron-nitride nanotube as a drug carrier in aqueous solution: insights from quantum mechanics and Monte Carlo simulation

The improvement of the solubility of sulfasalazine in physiological media was the major aim of this study. Accordingly, BNNT inspected as a notable candidate for the carriage of this drug in aqueous media. For this purpose, four possible interactions of two tautomer of sulfasalazine with (9,0) boron-nitride 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 interaction of keto form of sulfasalazine produce the most stable complexes with boron-nitride nanotube in gas phase. Simulation results revealed that electrostatic interactions play a vital role in the intermolecular interaction energies after binding of drug and nanotube in aqueous solution. Results of association free energy calculations indicated that complexes of both two sulfasalazine tautomers (keto and enol) and nanotube were stable in solution. Computed solvation free energies in water showed that the interaction with boron-nitride nanotube significantly improved the solubility of sulfasalazine, which could improve its in vivo bioavailability.

Spatial distribution, ecological risk and health risk assessment of heavy metals in agricultural soil from Ankang basin, Shaanxi Province

In order to assess the heavy metal pollution features, ecological dangers, and health risk status posed to human beings by soils in the Ankang Basin, a study was conducted. This involved the collection of 38 surface soil samples, followed by the determination of elemental levels of arsenic, mercury, copper, cadmium, lead, chromium, nickel, and zinc. The concentrations of arsenic, mercury, copper, cadmium, lead, chromium, nickel, and zinc were quantified through the collection of 38 surface soil samples. The data obtained from the study was subjected to analysis and evaluation utilizing various academic methodologies, including the geo-accumulation index method, potential ecological risk assessment method, human health risk assessment model, and Monte Carlo simulation method. The findings indicated that the concentrations of the eight heavy metals in the soil above the background levels, with only Cadmium (Cd) marginally surpassing the threshold set for controlling soil pollution risks. The ground accumulation index revealed a higher degree of soil pollution with mercury, cadmium, copper, and zinc components. According to the possible ecological risk index, the presence of mercury and cadmium elements poses significant ecological hazards. The geographical distribution analysis suggests that these risks mostly stem from the combined impacts of human activities and the topographical and geomorphological characteristics of the river valley. The findings of the human health risk assessment indicated that the non-carcinogenic risk fell within acceptable limits. Additionally, it was observed that the carcinogenic risk associated with arsenic, mercury, cadmium, and nickel was comparatively greater for children as compared to adults. The results of the Monte Carlo simulations indicate that the non-carcinogenic hazards have a negligible effect on human health. However, it was seen that arsenic and nickel have a greater likelihood of presenting a substantial carcinogenic risk to humans, particularly in relation to the pediatric population, hence exerting a more pronounced impact on their health. In general, it is observed that conventional deterministic risk assessments tend to overstate the potential health risks associated with a given situation. Conversely, the utilization of Monte Carlo simulations has been found to effectively mitigate uncertainties in health risk assessments. It has been observed that children exhibit a higher vulnerability to both carcinogenic and non-carcinogenic health impacts resulting from exposure to heavy metals present in soil, in comparison to adults. It is recommended that residents prioritize the surveillance of soil heavy metals in relation to potential impacts on human health.

Coverage Enhancement of Light-Emitting Diode Array in Underwater Internet of Things over Optical Channels

The construction of the underwater Internet of Things (UIoT) is crucial to marine resource development, environmental observation, and tactical surveillance. The underwater optical wireless communication (UOWC) system with its large bandwidth and wide coverage facilitates the high-capacity information interconnection within the UIoT networks over short and medium ranges. To enhance the coverage characteristics of the UOWC system, an optimized lemniscate-compensated layout of light-emitting diode (LED) array is proposed in this paper, which can ameliorate the received optical power and reliability at the receiving terminal. Compared with traditional circular and rectangular layouts, the received optical power and bit error rate (BER) performance of the proposed system are analyzed based on the Monte Carlo simulation method. The analysis results show that the proposed LED array achieves a smaller peak power deviation and mean square error of the received optical power under three typical seawater environments. Furthermore, the proposed LED-array scheme supports a better BER performance of the UOWC system. For example, in turbid seawater with a transmission depth of 9.5 m, the BER of the proposed LED array layout is 1 × 10−7, which is better than the BER of 3.5 × 10−6 and 1 × 10−4 under the other two traditional light source layouts.

Strongly non-additive symmetric mixtures in slit-like pores

Using Monte Carlo simulation methods in the grand canonical ensemble, we have studied the behavior of symmetric binary mixtures confined between attractive planes. We have elucidated the effects of high negative geometric and energetic non-additivity on the phase behavior of mixtures in nanoscopic slit-like pores. In such systems, the geometric non-additivity favors mixing, while the energetic non-additivity favors the formation demixed dense phases. It has been shown that the confinement considerably influences the phase behavior. In particular, phase separation has been found to be suppressed in narrow pores, while in wide pores the phase behavior becomes qualitatively the same as in bulk systems. It has also been demonstrated that the demixed solid is stable over a certain temperature range in pores, while the bulk mixtures characterized by the same non-additivity exhibit only the presence of mixed solid.

Reliability evaluation of flexural capacity design provision for UHPC beams reinforced with steel rebars/prestressing tendons

This study investigated the reliability of the flexural capacity prediction models for ultra-high performance concrete (UHPC) beams in various standards, including the Chinese UHPC Code (draft), Chinese standards JGJ/T 465–2019 and JTG 3362–2018, Swiss standard SIA 2052–2016, and French standard NF P18–710–2016. The research was based on two comprehensive databases of 110 reinforced and 47 prestressed UHPC beams. Correlation analysis of the model errors of the flexural capacity formulae was conducted at first. Then, the reliability of the prediction models was analyzed through Monte Carlo simulation (MCS) and first-order second-moment (FOSM) method, considering the design parameters such as material strength, live-to-dead load ratio, longitudinal reinforcement ratio, and prestressing tendon ratio. The results indicated that the prediction model in Chinese UHPC Code (draft) could accurately predict the flexural capacity of reinforced and prestressed UHPC beams among the five specifications, with the mean model errors of 1.06 and 1.02, respectively. The reliability indexes of Chinese UHPC Code (draft), Swiss standard SIA 2052–2016, and French standard NF P18–710–2016 for both the reinforced and prestressed UHPC beams were significantly higher than the specified value of 4.2 in the Chinese standard. The sensitivity analysis showed that the reliability index increased with the increase of live-to-dead load ratio, but it was not significantly influenced by UHPC compressive strength. In addition, the reliability index decreased as the longitudinal reinforcement ratio and prestressing tendon ratio increased. Material partial factor of flexural resistance of the formula in Chinese UHPC Code (draft) was calibrated, and γc= 1.30 was recommended for UHPC beams for safety.

Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current

In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions L = 55, 101 and 151. The number of samples for each matrix was 5 × 106. The spatial distributions of the coordinates of the nodes creating the percolation channel were determined, and maps of the density distribution of these nodes were created. It has been established that in matrices with finite dimensions, an edge phenomenon occurs, consisting of a decrease in the concentration of nodes creating a percolation channel as one approaches the edge of the matrix. As the matrix dimensions increase, the intensity of this phenomenon decreases. This expands the area in which values close to the maximum occur. The length distributions of the left and right clusters of non-conducting nodes were determined for the situation when the next randomly selected node connects them and thus reaches the percolation threshold. It was found that clusters whose dimensions are close to half of the matrix dimensions are most likely to occur. The research shows that both the values of the standard deviation of the percolation threshold and the intensity of the edge phenomenon are clearly related to the dimensions of the matrices and decrease as they increase.

Bayesian cost-effectiveness analysis of Whole genome sequencing versus Whole exome sequencing in a pediatric population with suspected genetic disorders

Genetic diseases are medical conditions caused by sequence or structural changes in an individual’s genome. Whole exome sequencing (WES) and whole genome sequencing (WGS) are increasingly used for diagnosing suspected genetic conditions in children to reduce the diagnostic delay and accelerating the implementation of appropriate treatments. While more information is becoming available on clinical efficacy and economic sustainability of WES, the broad implementation of WGS is still hindered by higher complexity and economic issues. The aim of this study is to estimate the cost-effectiveness of WGS versus WES and standard testing for pediatric patients with suspected genetic disorders. A Bayesian decision tree model was set up. Model parameters were retrieved both from hospital administrative datasets and scientific literature. The analysis considered a lifetime time frame and adopted the perspective of the Italian National Health Service (NHS). Bayesian inference was performed using the Markov Chain Monte Carlo simulation method. Uncertainty was explored through a probabilistic sensitivity analysis (PSA) and a value of information analysis (VOI). The present analysis showed that implementing first-line WGS would be a cost-effective strategy, against the majority of the other tested alternatives at a threshold of €30,000–50,000, for diagnosing outpatient pediatric patients with suspected genetic disorders. According to the sensitivity analyses, the findings were robust to most assumption and parameter uncertainty. Lessons learnt from this modeling study reinforces the adoption of first-line WGS, as a cost-effective strategy, depending on actual difficulties for the NHS to properly allocate limited resources.

Foreign exchange option pricing under the 4/2 stochastic volatility model with CIR interest rates.

. Foreign exchange (FX) options are studied in a new stochastic volatility model (the 4/2 stochastic volatility model), which includes, as special instances, the Heston model and the 3/2 model, for the exchange rate in combination with the Cox-Ingersoll-Ross (CIR) dynamics for the domestic and foreign stochastic interest rates. We allow the correlation between the instantaneous volatility and the dynamics of the exchange rate, whereas the interest rates in both domestic and foreign markets are assumed to be independent of the dynamics of the exchange rate. We provide a semi-analytical formula for the price of the European FX call option via Fourier inversion. Through the change of measure technique, we derived explicit expressions for conditional characteristic functions. Our model is computationally tractable, thereby the pricing procedure is accurate and illustrates more efficiency in comparison to the Monte Carlo simulation method. Finally, we perform calibrations on market data, demonstrating that our model fits the implied volatilities well and outperforms the Heston model with CIR interest rates.

Radioactivity in a bucket

In radiation physics classes, point sources are typically used, for which it is relatively easy to describe the signal obtained by a radiation detector, such as the NaI(Tl) scintillation detector. The use of large extended radiation sources is generally avoided due to the mathematical complexity that their description may involve. However, the use of Monte Carlo simulation methods allows this limitation to be overcome. Potassium chloride, containing the 40K isotope, is an ideal candidate for carrying out this type of experiment. The source activity is obtained through the detection of the 1460.8 keV gamma-photon emitted in the 40K decay. In the first experiment, a cylindrical container is used, placing the NaI(Tl) detector in its center and filling the remaining space with potassium chloride. In a second, more complex case, a large radioactive source consisting of a container filled with a mixture of sand and potassium chloride, with the NaI(Tl) detector placed in the center of the mixture, is used. In this case, the mass of potassium chloride is approximately 1/5 of the sand mass. In both experiments, the detection efficiency is obtained by Monte Carlo simulation. A careful analysis of the experimental data allows to obtain a good agreement between the measured and calculated value of the activity.