Conventional Monte Carlo Simulation Research Articles

Practical reliability analysis for earthquake-induced 3D landslide using stochastic response surface method

This study investigates the effect of spatial variability on the stability of a real 3D slope subjected to earthquakes by conventional Monte Carlo simulation (MCS) and a stochastic response surface method. The stochastic response surface method used in this study (VRSRSM) was combined with a variance reduction method due to spatial averaging of soil parameters in slope failure to reduce a large computational load due to the realization of spatially correlated input parameters in three-dimensional space. In order to verify the applicability of the stochastic response surface method with a variance reduction method for 3D slope reliability, the safety factor for a simple 3D slope under non-seismic and seismic conditions was analyzed by MCS and VRSRSM. The VRSRSM was applied to risk evaluation of deep-seated landslides caused by the 2016 Kumamoto earthquake along with backcalculation of strength parameters based on the slope failure geometry and field investigation.

Fragility assessment approach of deepwater drilling risers subject to harsh environments using Bayesian regularization artificial neural network

The drilling risers are the most critical and vulnerable connection of floating drilling platform and subsea wellhead. In order to improve the operation efficiency, the operators have attempted to suspend the drilling operations and keep the drilling risers connected to the wellhead to survive in the storm, thus the fragility of the drilling risers under storm is of paramount importance to drilling operations. This paper is aimed at proposing an efficient and robust BRANN-based non-intrusive approach for the fragility assessment of the deepwater drilling riser subject to storms. The proposed approach, which could effectively reflect the non-linear relationship between the input and output data, can generate thousands of non-numerical data under limited Finite Element Analysis (FEA) of the drilling risers, while the Monte Carlo Simulation (MCS) could be further incorporated to calculate the fragility curve. A case study was conducted to demonstrate the characteristics with respect to significantly computational reduction of the proposed approach compared to the conventional MCS method, and the proposed approach was verified to be robust and efficient in assessing the fragility of the drilling risers under storms. The related conclusions could be used to provide reference for operations of drilling risers under harsh environment.

A search method for probabilistic critical slip surfaces with arbitrary shapes and its application in slope reliability analysis

The Monte Carlo simulation (MCS) is generally accepted as an accurate approximation method in slope reliability analysis. However, low efficiency hinders its use. Based on the online sequential extreme learning machine (OS-ELM), the OS-ELM-MCS method is proposed, which overcomes the requirement of calculating the safety factor, respectively, when using a conventional MCS for reliability analysis. Combined with the multi-initial points sequential quadratic programming (MSQP) algorithm, a search method for probabilistic critical slip surfaces with arbitrary shapes is introduced. It is possible to conduct both a reliability analysis and deterministic analysis under the same algorithm framework. Based on the proposed method, reliability and deterministic analyses of two cases are carried out. Compared with the results of other methods, the accuracy of the reliability and deterministic analysis method is verified. This verifies that the accuracy and time performance of the proposed method are better than those of conventional algorithms. The results of these case studies reveal the differences between the conclusions of the reliability and deterministic analyses. Therefore, it is necessary to combine reliability analysis and deterministic analysis to improve the credibility of stability analysis results.

Modeling complex particles phase space with GAN for Monte Carlo SPECT simulations: a proof of concept

A method is proposed to model by a generative adversarial network the distribution of particles exiting a patient during Monte Carlo simulation of emission tomography imaging devices. The resulting compact neural network is then able to generate particles exiting the patient, going towards the detectors, avoiding costly particle tracking within the patient. As a proof of concept, the method is evaluated for single photon emission computed tomography (SPECT) imaging and combined with another neural network modeling the detector response function (ARF-nn). A complete rotating SPECT acquisition can be simulated with reduced computation time compared to conventional Monte Carlo simulation. It also allows the user to perform simulations with several imaging systems or parameters, which is useful for imaging system design.

Monte Carlo Simulation With Incremental Damage for Reliability Assessment of Power Electronics

Monte Carlo simulations have been widely used in the reliability assessment of power electronics systems. However, the conventional Monte Carlo simulation method is not directly suitable to be applied to the system with fault-tolerant operation, where the accumulated damage during the prefault operation needs to be taken into account as an initial damage during the postfault operation. To address this issue, a Monte Carlo simulation method based on incremental damage concept is proposed in this letter. The proposed method recursively accumulates the damage over time, making it possible to monitor the damage level of the individual sample when the failure occurs, and then being used as the initial damage during the postfault operation. Therefore, it can be applied to the power converters with fault-tolerant operation, which has been demonstrated with a case study of three-phase inverter having a fault-tolerant topology.

Reliable Calculation of Thermoacoustic Instability Risk Using an Imperfect Surrogate Model

Abstract One of the fundamental tasks in performing robust thermoacoustic design of gas turbine combustors is calculating the modal instability risk, i.e., the probability that a thermoacoustic mode is unstable, given various sources of uncertainty (e.g., operation or boundary conditions). To alleviate the high computational cost associated with conventional Monte Carlo simulation, surrogate modeling techniques are usually employed. Unfortunately, in practice, it is not uncommon that only a small number of training samples can be afforded for surrogate model training. As a result, epistemic uncertainty may be introduced by such an “inaccurate” model, provoking a variation of modal instability risk calculation. In the current study, using Gaussian process (GP) as the surrogate model, we address the following two questions: First, how to quantify the variation of modal instability risk induced by the epistemic surrogate model uncertainty? Second, how to reduce the variation of risk calculation given a limited computational budget for the surrogate model training? For the first question, we leverage on the Bayesian characteristic of the GP model and perform correlated sampling of the GP predictions at different inputs to quantify the uncertainty of risk calculation. We show how this uncertainty shrinks when more training samples are available. For the second question, we adopt an active learning strategy to intelligently allocate training samples such that the trained GP model is highly accurate particularly in the vicinity of the zero growth rate contour. As a result, a more accurate and robust modal instability risk calculation is obtained without increasing the computational cost of surrogate model training.

Simplified algebraic estimation for the quality control of DIA estimator

Based on the unifying framework of the detection, identification and adaption (DIA) estimators, quality control indices are refined and formulated by taking the uncertainty of the combined estimation-testing procedure into account and performing the propagation of uncertainty. These indices are used to measure the confidence levels of the testing decisions, the reliability of the specified alternative hypothesis models, as well as the biasedness and dispersion of the estimated parameters. A simplified algebraic estimation (SAE) method is developed to calculate these quality control indices for the application of single outlier DIA. Compared to the conventional Monte Carlo simulation method, the proposed SAE method can achieve an adequate estimation accuracy and significantly higher computation efficiency. Using a GNSS single-point positioning example, the performance of the SAE method is evaluated and the quality control of the conventionally used DIA estimator is demonstrated for practical applications.

Thermodynamics, EOS, and heat capacity in molecular modeling of self-assembled molecular layers.

Self-assembled monolayers (SAMs) on solid surfaces represent a rapidly developed class of non-autonomous phases widely used in organic electronics, sensors, catalysis, and other applications. In many cases, the same organic molecules form various stable and metastable polymorphous structures that can transform to each other at certain parameters. A high rigidity of SAMs extremely complicates the evaluation of the chemical potential using standard methods based on thermodynamic integration. This study presents results of molecular modeling of two-dimensional structures of tripod-shaped molecules associated with the trimesic acid (TMA) molecules. A technique used here is based on a recently developed method of external fields imposed on an elongated simulation cell in the framework of a kinetic Monte Carlo algorithm. These fields are the external potential and a damping field that reduces the intermolecular potential and affects the system similar to the increase in temperature. Equations of state (EOS) for several TMA polymorphs have been obtained with the conventional Monte Carlo simulation. It was shown that, in each case, only one constant links the chemical potential obtained with the external field method and the EOS at any temperature and pressure. The heat capacities of SAMs at constant volume and pressure were also determined as functions of temperature and compressibility of the structure at given degrees of freedom. The approach can be used as a general tool for modeling and evaluation of thermodynamic properties of various rigid structures, including SAMs of functional organic molecules.

Fabrication of Si photonic waveguides by electron beam lithography using improved proximity effect correction

In this work, electron beam lithography proximity effect correction (PEC) was experimentally studied for patterning of Si photonic waveguides with a relatively thick resist mask. Beam’s energy density distribution (EDD) was experimentally extracted by the line exposure method; however, exposure lines in this work were developed after cleavage with a high-contrast process to reduce developer-related effects. The measured line spread function was fitted to a 4-Gaussian function to model mid-range energy densities accurately. The extracted EDD showed less proximity effects compared to conventional Monte-Carlo simulation performed by a commercial software. PEC processes with both techniques were experimentally compared for a Si photonic waveguide pattern with different side-cladding trench widths. Microscopic images confirmed that the presented calibration method could achieve better development conditions near the required clearance dosage. Single-mode propagation loss for a 500 × 220 nm Si wire waveguide was reduced from 3.2 to 2.4 dB cm−1 using the presented process.

Run-out distance exceedance probability evaluation and hazard zoning of an individual landslide

Due to large uncertainties embedded in their geotechnical parameters, dynamic numerical models of landslide run-out distance can only be reliably applied to conduct post-failure back analyses, rather than accurate physical-based forward predictions. Therefore, it is important to quantify these uncertainties, and their effects, to improve the reliability of predictions. This paper proposes a run-out distance prediction methodology within a probabilistic framework to assess the exceedance probability of run-out distance for an individual landslide using a depth-integrated continuum method (Massflow) and a polynomial response surface method coupled with the first-order reliability method (RSM-FORM). The input parameters (i.e., friction angle and pore pressure ratio) are considered as random variables with reasonable probability density functions. The limit state function (LSF) is established based on a given threshold value of the run-out distance. The RSM is then adopted to establish a mathematical function that approximates the real LSF; and then, based on the fitted response surface, the FORM is employed to calculate the probability of the run-out distance exceeding the given threshold value. The 2015 Shenzhen landslide is considered as an example to illustrate the proposed methodology. The results show that our proposed methodology can successfully assess the exceedance probability of the run-out distance at different locations with acceptable computational errors. In addition, the computational efficiency is significantly improved compared to conventional Monte Carlo simulations. Moreover, according to the run-out distance-exceedance probability curve, the area potentially affected by the Shenzhen landslide can be classified into five categories (i.e., extremely high, high, medium, low, and extremely low) based on the different threshold values of exceedance probability (i.e., 50%, 10%, 1%, and 0.1%). The observed deposition area of the Shenzhen landslide lies within the extremely high and high hazard zones, demonstrating the feasibility of conducting landslide hazard zoning using the exceedance probability of the run-out distance. This study thus presents a practical procedure for enhancing the probabilistic run-out distance prediction of individual landslides and provides new ideas for conducting hazard zoning.

Fragility analysis of drilled shafts in sand – an analytical correspondence between reliability index and factor of safety

This paper establishes an analytical correlation between factor of safety (FS) and reliability index β values commonly used in the design of drilled shafts in sand. This is achieved through fragility analysis of unit shaft and base resistances, calculated using finite element analysis-based capacity calculation equations, for drilled shafts. Analytical fragility curves are developed for allowable unit resistances along the pile shaft and at the pile base. Developed fragility curves are used to map FS values with corresponding values of β. Such analytical FS–β correspondence is not well established in literature. Comparison of results from fragility analysis with those obtained through conventional Monte Carlo simulations reveals excellent agreement. Developed FS-β correlation is employed in reliability analysis to estimate load and resistance factors corresponding to different FS values. Evaluated load and resistance factors compare very well with AASHTO specifications.

Recloser placement optimization using the cross-entropy method and reassessment of Monte Carlo sampled states

This paper proposes an approach to optimize the location of reclosers in distribution feeders aiming to improve system reliability, minimize costs and reduce the occurrence of voltage sags. The approach is based on the cross-entropy method and the reassessment of sampled states generated using sequential Monte Carlo simulations. Results indicate the effectiveness of the approach, the importance of integrating reliability and power quality aspects to the analysis, and the computational gains of deploying a reassessment process of Monte Carlo sampled states instead of the conventional Monte Carlo simulation algorithm.

Wind fragility analysis of RC chimney with temperature effects by dual response surface method

Wind fragility analysis (WFA) of concrete chimney is often executed disregarding temperature effects. But combined wind and temperature effect is the most critical limit state to define the safety of a chimney. Hence, in this study, WFA of a 70 m tall RC chimney for combined wind and temperature effects is explored. The wind force time-history is generated by spectral representation method. The safety of chimney is assessed considering limit states of stress failure in concrete and steel. A moving-least-squares method based dual response surface method (DRSM) procedure is proposed in WFA to alleviate huge computational time requirement by the conventional direct Monte Carlo simulation (MCS) approach. The DRSM captures the record-to-record variation of wind force time-histories and uncertainty in system parameters. The proposed DRSM approach yields fragility curves which are in close conformity with the most accurate direct MCS approach within substantially less computational time. In this regard, the error by the single-level RSM and least-squares method based DRSM can be easily noted. The WFA results indicate that over temperature difference of 150°C, the temperature stress is so pronounced that the probability of failure is very high even at 30 m/s wind speed. However, below 100°C, wind governs the design.

Funnel hopping Monte Carlo: An efficient method to overcome broken ergodicity.

Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice, however, sampling of the complete configuration space is often hindered by high energy barriers between different regions of configuration space, which can make ergodic sampling completely infeasible within accessible simulation times. Although several extensions to the conventional Monte Carlo scheme have been developed, which enable the treatment of such systems, these extensions often entail substantial computational cost or rely on the harmonic approximation. In this work, we propose an exact method called Funnel Hopping Monte Carlo (FHMC) that is inspired by the ideas of smart darting but is more efficient. Gaussian mixtures are used to approximate the Boltzmann distribution around local energy minima, which are then used to propose high quality Monte Carlo moves that enable the Monte Carlo simulation to directly jump between different funnels. We demonstrate the method's performance on the example of the 38 as well as the 75 atom Lennard-Jones clusters, which are well known for their double funnel energy landscapes that prevent ergodic sampling with conventional Monte Carlo simulations. By integrating FHMC into the parallel tempering scheme, we were able to reduce the number of steps required significantly until convergence of the simulation.

Aeroelastic stability analysis using stochastic structural modifications

An experimental-based approach to flutter speed uncertainty quantification in aeroelastic systems is developed. The proposed technique considers uncertainty from a post-manufacture perspective. Variability due to manufacturing tolerances, damage and degradation is formulated as a stochastic structural modification to a single set of measured receptance data. The Sherman-Morrison formula is exploited so that the probability of flutter is evaluated either from parameter bounds or by using a first-order reliability method. The advantage of the formulation is that there is no requirement to model either the structure or aerodynamics, thereby avoiding model-form and parameter uncertainties. Numerical examples are provided, which demonstrate the efficiency of the method when compared to conventional Monte-Carlo simulation (MCS). The method is also demonstrated in experimental examples and it is shown to be eminently practical since the data required for MCS is generally not available in industrial practice.

Parametric uncertainty quantification in natural frequency of sandwich plates using polynomial neural network

In this paper, uncertainty quantification in natural frequencies for laminated soft core sandwich plates is presented by employing finite element (FE) coupled polynomial neural network (PNN) approach. The computational efficiency and accuracy is achieved by using PNN as surrogate model. Latin hypercube sampling method is employed for training of data in PNN model. The stochastic first three natural frequencies of sandwich plates are studied for individual variation in input parameters. The stochasticity in individual input parameters are considered in order to assess their influence on global response of the structure. The algorithm discussed in this article is observed to be converging with the previously published literature (for deterministic case) and validated with full scale Monte Carlo simulation (MCS) i.e. original finite element approach (for stochastic case). The computational time and cost reduced significantly by employing the present surrogate based FE approach compared to that of conventional Monte Carlo simulation approach.

Estimation of optimized timely system matrix with improved image quality in iterative reconstruction algorithm: A simulation study

The system matrix (SM) being a main part of statistical image reconstruction algorithms establishes relationship between the object and projection space. The aim was to determine it in a short duration time, towards obtaining the best quality of contrast images. In this study, a new analytical method based on Cavalieri's principle as subdividing common regions has been proposed in which the precision of the amounts of estimated areas was improved by increasing the number of divisions (NOD), and consequently the total SM's time was increased. An important issue is the tradeoff between the NODs and computational time. For this purpose, a Monte Carlo simulated Jaszczak phantom study was performed by the Monte Carlo N-Particle transport code version 5 (MCNP5) in which the tomographic images of resolution and contrast phantoms were reconstructed by maximum likelihood expectation maximization (MLEM) algorithm, and the influence of NODs variations was investigated. The results show that the lowest and best quality have been obtained at the NODs of 0 and 8, respectively and in the optimum case, the SM's total time at NOD of 8 was 925 s, which was much lower than those of the conventional Monte Carlo simulations and experimental test.

Data‐driven efficient reliability evaluation of power systems with wind penetration: an integrated GANs and CE method

The conventional Monte Carlo simulation may not be efficient enough for reliability evaluation of composite power systems. The cross-entropy (CE) algorithm is a promising state-of-the-art fast sampling method, while it has not been well developed in this field due to the implicit probability distributions of penetrated renewable energies. Specifically, the CE sampling requires the distributions of interest to be explicit and parametric, while some preconceived probabilistic distribution functions (PDFs) such as the Weibull distribution of wind speed make the results to deviate from the reality sometimes. In this study, a data-driven efficient approach for reliability evaluation of power systems with wind penetration is proposed utilising generative adversarial networks (GANs) and CE sampling. The distributions of wind speeds in multiple wind farms are estimated by GANs considering their spatial correlation without any prior knowledge. With the trained generative network mapping from the explicit Gaussian noise to the raw wind speed data, the CE sampling is successfully enabled to efficiently sample the system states with implicit PDFs, which are associated with wind speeds and component failures. A real wind speed dataset and the RTS testing system are utilised to verify the proposed integrated method, including the accuracy of distribution estimation and reliability evaluation result, as well as the speed-up efficiency of sampling.

Fast Monte Carlo Simulation for Pricing Equity-Linked Securities

In this paper, we present a fast Monte Carlo simulation (MCS) algorithm for pricing equity-linked securities (ELS). The ELS is one of the most popular and complex financial derivatives in South Korea. We consider a step-down ELS with a knock-in barrier. This derivative has several intermediate and final automatic redemptions when the underlying asset satisfies certain conditions. If these conditions are not satisfied until the expiry date, then it will be checked whether the stock path hits the knock-in barrier. The payoff is given depending on whether the path hits the knock-in barrier. In the proposed algorithm, we first generate a stock path for redemption dates only. If the generated stock path does not satisfy the early redemption conditions and is not below the knock-in barrier at the redemption dates, then we regenerate a daily path using Brownian bridge. We present numerical algorithms for one-, two-, and three-asset step-down ELS. The computational results demonstrate the efficiency and accuracy of the proposed fast MCS algorithm. The proposed fast MCS approach is more than 20 times faster than the conventional standard MCS.

Stochastic chemo-physical-mechanical degradation analysis on hydrated cement under acidic environments

The accumulation of material degradation under contact with aggressive aqueous environments could lead to reduced structural reliability. In terms of hydrated cementitious materials, such interactions often result in the chemo-physical-mechanical (CPM) degradation, which represents a multiphysics process of high non-linearity and complexity. By further considering the inevitable uncertainties associated with both the materials and the serving conditions, solving such a process requires novel probabilistic approaches. This paper presents a stochastic chemo-physical-mechanical (SCPM) degradation analysis on the hydrated cement under acidic environment. The SCPM analysis consists of modelling the stochastic chemophysical degradation by finite element method, and assessing the mechanical deterioration through analytical micromechanics. The proposed modelling framework couples the conventional Monte Carlo Simulation with a novel support vector regression algorithm. The present method is able to not only address the detailed degradation mechanisms, but also ensure low computational costs for an accurate SCPM degradation assessment.