Monte Carlo Simulation Procedure Research Articles

Validation of Monte Carlo simulation for discontinuity locations in space

Baecher disk model is the most commonly accepted and widely used 3-D discontinuity network model (3DDNM). Monte Carlo simulation (MCS) for discontinuity locations is an important step for constructing Baecher disk model. Uniform distributions are usually used to simulate the locations, based on the assumption that trace spacings along a sampling line (SL) obey an exponential distribution. However, no researchers have validated whether the trace spacings simulated using aforementioned method obey the observed exponential distribution in the field. The aim of this study is to perform the validation using a hypothetical 3DDNM. This study includes a brief review of the MCS procedure for discontinuity locations, construction of a hypothetical 3DDNM, and the goodness-of-fit test procedure for simulated trace spacings along SL. Seven sampling line groups (SLG) are used, and each SLG contains twenty SL having a same direction vector. The possible points of intersection between each SL and all simulated discontinuities are obtained, the spacings of those points are calculated, Kolmogorov–Smirnov tests are used to test the goodness-of-fit to the spacings along different SL, and the theoretical values and simulated values of parameter λ of exponential distributions for different SL are also calculated. The results show that: (a) for all SL the trace spacings obey exponential distributions at the 5% significance level; (b) for all SLG the simulated values of λ fluctuate around their theoretical values, and the mean simulated values are very close to its theoretical values; (c) therefore, it is valid to use uniform distributions to simulate locations in space for those discontinuities, whose observed trace spacings follow exponential distributions. The validation procedure developed in this study are also applicable to 3DDNM constructed for field cases.

Modelling and detection of failure in medical electrodes

In this paper we have studied the failures in medical electrodes such as electroencephalogram electrodes (EEG) being used for collecting brain signals. As those electrodes have to guarantee high level of reliability it is important to explore and predict the possible occurrence of failures in there structure. The electrode tip (needle) made of stainless steel is covered with thin oxide film acting as a dielectric and determing the total electrode resistance. In fact, studying the fluctuations of that resistance gives the insight into defects of the whole structure. The electrical properties of the oxide layer are characterized by charge hopping mechanism and the total resistance could be modeled by implementing random resistance network (RRN) methodology.The applied computational algorithm is based on Monte Carlo simulation procedure with direct and iteration methods. The obtained simulation results show non-gaussian Bramwell-Holdsworth-Pinton (BHP) distribution of the total resistance fluctuations, and they verified by the experiments.

Reliability Analysis of Load-SharingK-out-of-NSystem Considering Component Degradation

TheK-out-of-Nconfiguration is a typical form of redundancy techniques to improve system reliability, where at leastK-out-of-Ncomponents must work for successful operation of system. When the components are degraded, more components are needed to meet the system requirement, which means that the value ofKhas to increase. The current reliability analysis methods overestimate the reliability, because using constantKignores the degradation effect. In a load-sharing system with degrading components, the workload shared on each surviving component will increase after a random component failure, resulting in higher failure rate and increased performance degradation rate. This paper proposes a method combining a tampered failure rate model with a performance degradation model to analyze the reliability of load-sharingK-out-of-Nsystem with degrading components. The proposed method considers the value ofKas a variable which is derived by the performance degradation model. Also, the load-sharing effect is evaluated by the tampered failure rate model. Monte-Carlo simulation procedure is used to estimate the discrete probability distribution ofK. The case of a solar panel is studied in this paper, and the result shows that the reliability considering component degradation is less than that ignoring component degradation.

Spectral representation-based neural network assisted stochastic structural mechanics

This paper explores the applicability of artificial neural networks (ANN) for predicting the spread of structural response under the presence of uncertain parameters described as random fields. The use of ANN is carried out in combination with Monte Carlo simulation (MCS) for calculating response statistics in stochastic analysis of structural systems using finite elements. To this extent, the ANNs are trained with a few samples, following a conventional MCS procedure and used henceforth to predict the stochastic response for the rest of samples. The basic idea is to achieve a dimensionality reduction of the input ANN training space by using as input vector the random phase angles of the spectral representation method instead of the random variables describing the uncertain input parameters. A further improvement of the efficiency of the proposed approach is achieved by exploiting the uniform distribution of the random phase angles, in order to span efficiently the training space using a latin hypercube sampling (LHS) technique. The advantage of this approach over conventional computation of stochastic response via a standard stochastic finite element-based MCS is the fast and reliable prediction of the required response sample space which can be accomplished at a fraction of computing time and is independent of the size of the finite element model. Numerical results are presented, demonstrating the efficiency and the applicability of the proposed methodology as well as its distinct advantages over existing ANN-based stochastic finite element methodologies (SFEM).

Transient response of stochastic finite element systems using Dynamic Variability Response Functions

In this study a methodology is presented for effective analysis of dynamic systems with stochastic material properties. The concept of dynamic mean and variability response functions, recently established for linear stochastic single degree of freedom oscillators, is extended to general finite element systems such as statically indeterminate beam/frame structures and plane stress problems, leading to closed form integral expressions for their dynamic mean and variability response. The integrand of these integral expressions involves the spectral density function of the uncertain material properties and the so called dynamic mean and variability response functions respectively, which are assumed to be deterministic, i.e. independent of the power spectrum as well as the marginal pdf of the uncertain parameters. A finite element method-based fast Monte Carlo simulation procedure is used for the accurate and efficient numerical evaluation of these functions. In order to demonstrate the validity of the proposed procedure, the results obtained using the aforementioned integral expressions are compared to brute-force Monte Carlo simulation. As a further validation of the assumption of independence of the variability response function to the stochastic parameters of the problem, the concept of the generalized variability response function was applied and compared to the steady state dynamic variability response function. The methodology is applied in a dynamically loaded statically indeterminate beam/frame structure and a plane stress problem. The dynamic mean and variability response functions, once established, can be used to perform sensitivity/parametric analyses with respect to various probabilistic characteristics involved in the problem (i.e., correlation distance, standard deviation) and to establish realizable upper bounds on the dynamic mean and variance of the response, at practically no additional computational cost.

Estimation of long-term extreme response of operational and parked wind turbines: Validation and some new insights

In current wind turbine design standard, the long-term extreme responses of operational and parked wind turbines with various mean recurrence intervals (MRIs) are estimated from probability distribution of short-term 10-min extreme response under the assumption that the short-term extremes are statistically independent. This study examines the adequacy of this critical assumption through a Monte Carlo simulation procedure. The 10-min mean wind speed series are simulated based on translation process theory with prescribed Weibull distribution and power spectrum. The extreme response series are then generated using the distribution of extreme response under various mean wind speeds. The distribution of annual extreme response is determined from simulated samples and compared to that from distribution of short-term extreme. The results illustrate that the short-term extreme responses can be considered to be independent, while the mean wind speeds exhibit certain level of correlation. This study also presents improved methods for estimating long-term extreme response of parked turbines by using more accurate modeling of distribution tail of mean wind speed. A mixed distribution is suggested, which combines bulk distribution estimated from moderate wind speed data and tail distribution estimated by fitting the excesses above a given threshold with generalized Pareto and three parameters Weibull distributions. A new method of directly using annual maximum wind speed distribution is also proposed that takes into account the independent number of wind speed process in terms of extremal index. The results reveal the importance of better modeling of wind speed distribution tail in the estimation of extreme response of parked turbines.

A Generalized Sampling Approach for Multilinear Utility Functions Given Partial Preference Information

The assessment and characterization of multilinear utility functions (MLUFs) may require the elicitation of many attribute weights. In this case, the decision maker may find it difficult to provide precise assessments and may instead be more comfortable providing a range in which the scaling parameters fall or specifying that some parameters are larger than others. The question then becomes how the analyst should formulate a recommendation given this partial preference information. In this paper, we present a generalized Monte Carlo simulation procedure to test the sensitivity of MLUFs to changes in the scaling parameters. Specifically, we admit any preference information that can be expressed as a linear constraint. We then sample from the set of all possible MLUFs matching these constraints. We consider the additive MLUF, the multiplicative MLUF, the utility-independent MLUF, and the generalized utility-independent MLUF. In so doing, we also demonstrate how analysts can test the sensitivity of their analysis to the structure of the MLUF itself. We illustrate the flexibility of our method within the context of a coal-fired power plant siting decision used by previous authors.

Mechanism based assessment of damage-dependent fragility curves for RC building classes

Seismic fragility curves play a critical role in risk assessment because they represent the probability of attaining different damage states given the ground motion intensity. However, in case of repeated earthquakes, the seismic vulnerability of buildings varies due to damage and this shall be properly considered for the realistic estimate of evolving seismic risk during a seismic sequence. This paper presents a methodology for the assessment of damage-dependent fragility curves for existing reinforced concrete (RC) building classes. The derivation of fragility curves is based on a hybrid method that combines observational based “empirical” curves and mechanical based assessment of buildings’ residual capacity (REC), that is a measure of seismic capacity, which may be reduced due to seismic damage. A mechanism based procedure to assess building REC, and its variation for increasing ductility demand, is presented. Then, in order to be able to apply such procedure to RC building classes, a simulated design procedure is implemented that allows the automatic design of elements dimensions and reinforcement, as well as the characterization of the building nonlinear model needed for mechanism based analysis. Applying a Monte Carlo simulation procedure the geometric, structural and mechanical parameters, from which the design depends on, are varied according to representative distributions and populations of building models are generated and analyzed with mechanism based approach. The procedure is implemented for buildings that are prone to first storey mechanism and is applied for existing RC building classes in L’Aquila.

A Layered Fault Tree Model for Reliability Evaluation of Smart Grids

The smart grid concept has emerged as a result of the requirement for renewable energy resources and application of new techniques. It is proposed as a practical future form of power distribution system. Evaluating the reliability of smart grids is of great importance and significance. Focusing on the perspective of the consumers, this paper proposes a layered fault tree model to distinguish and separate two different smart grid power supply modes. Revised importance measures for the components in the fault tree are presented considering load priority, aiming to find the weak parts of the system and to improve the design and using. A corresponding hierarchical Monte Carlo simulation procedure for reliability evaluation is proposed based on the layered fault tree model. The method proposed in this paper is tested on a case of reliability assessment for the Future Renewable Electric Energy Delivery and Management (FREEDM) system. The proposed technique can be applicable to other forms of smart grids.

Safety examination of existing concrete structures using the global resistance safety factor concept

Current design procedures for structural concrete elements are based on member level (or local) safety checks, in the sense that the safety condition is evaluated at each cross-section individually. In the examination of existing structures, the exploitation of the redundancy of the structural system and its redistribution capacity may prove necessary to fulfil the safety requirements, demanding for a system level (or global) safety evaluation. This can be achieved using nonlinear finite element analysis (NLFEA) procedures and requires a safety format different than that based on partial safety factors.In this work, a simple safety format tailored for NLFEA of existing structures is described. It is shown how to define a global resistance safety factor based on a simple semi-probabilistic approach in line with the recommendations of the new Swiss standards for existing structures [1,2] that can capture the sensitiveness of the structural system resistance, R, to the random variation of the input variables. Besides enabling the use of updated information regarding the material properties, the proposed procedure allows performing reliability differentiation based on risk analysis, being therefore suitable for the safety examination of existing bridges.The definition of the semi-probabilistic global resistance safety factor is based on the assumption of a log-normal probability density function for the resistance R and on an estimate of its coefficient of variation, vR. The existing proposals for estimating vR are reviewed and compared. For statically determined structures with a single dominant failure mode (axial compression, bending or shear) the examination values of R computed with global resistance safety factors are shown to compare well with those obtained with partial safety factors. The reliability of the examination values of R is also evaluated through a comparison with the Monte Carlo simulation procedure and it is shown that the global resistance safety factor method is sufficiently accurate. Finally, a case-study is presented illustrating the application of the proposed procedure in the structural safety examination of an existing prestressed concrete bridge.

Monte Carlo Simulation Approach with Ordinal Optimization Based STATCOM Installation Strategy for Transmission System Loading Margin Enhancement

The power system loading margin enhancement problem to determine an optimal Static Synchronous Compensator (STATCOM) installation can be formulated as a mixed discrete-continuous nonlinear optimization problem (MDCP). In the paper, long-term efficiency of STATCOM installation to enhance transmission system loading margin (LM) is evaluated using a Monte Carlo Simulation (MCS) procedure with an Ordinal Optimization (OO) based STATCOM installation strategy to solve the MDCP. First under each N-1 contingency with bigger risk index (RI) value, the crude model is used to estimate the rough solution for each candidate, and then the exact method is used to a smaller set to determine the good enough solutions. Obtained from the union of the respective good enough solutions for all considered contingencies, the scheme with the smallest number of STATCOM units enabling the network to provide required average LM is recommended.

Benchmark Dose Calculation for Ordered Categorical Responses

The use of benchmark dose (BMD) calculations for dichotomous or continuous responses is well established in the risk assessment of cancer and noncancer endpoints. In some cases, responses to exposure are categorized in terms of ordinal severity effects such as none, mild, adverse, and severe. Such responses can be assessed using categorical regression (CATREG) analysis. However, while CATREG has been employed to compare the benchmark approach and the no-adverse-effect-level (NOAEL) approach in determining a reference dose, the utility of CATREG for risk assessment remains unclear. This study proposes a CATREG model to extend the BMD approach to ordered categorical responses by modeling severity levels as censored interval limits of a standard normal distribution. The BMD is calculated as a weighted average of the BMDs obtained at dichotomous cutoffs for each adverse severity level above the critical effect, with the weights being proportional to the reciprocal of the expected loss at the cutoff under the normal probability model. This approach provides a link between the current BMD procedures for dichotomous and continuous data. We estimate the CATREG parameters using a Markov chain Monte Carlo simulation procedure. The proposed method is demonstrated using examples of aldicarb and urethane, each with several categories of severity levels. Simulation studies comparing the BMD and BMDL (lower confidence bound on the BMD) using the proposed method to the correspondent estimates using the existing methods for dichotomous and continuous data are quite compatible; the difference is mainly dependent on the choice of cutoffs for the severity levels.

A Modified Empirical Martingale Simulation for Financial Derivative Pricing

This article extends the empirical martingale simulation (EMS) method from using a risk-neutral measure to using a dynamic measure for financial derivative pricing. Although the EMS is shown to be capable of obtaining consistent estimate of financial derivative prices in a more efficient way than the standard Monte Carlo simulation procedure, it can proceed only under a risk-neutral framework. In practice, however, it is cumbersome to obtain the explicit expression of a risk-neutral model when dealing with a complex model. To alleviate this difficulty, we compute the financial derivative prices under the dynamic model and impose the martingale property on the simulated sample paths of both the change of measure process and the underlying asset prices under the dynamic P measure. Hence, we call this modification the empirical P-martingale simulation (EPMS). The strong consistency of the EPMS is established and its efficiency is performed by simulation in the GARCH framework. Simulation results shows that EPMS has the similar variance reduction as the EMS method in option pricing if the risk-neutral model can be obtained, and is more efficient than the standard Monte Carlo simulation in most cases.

Multi-objective preventive maintenance and replacement scheduling in a manufacturing system using goal programming

This research presents a new multi-objective nonlinear mixed-integer optimization model to determine Pareto-optimal preventive maintenance and replacement schedules for a repairable multi-workstation manufacturing system with increasing rate of occurrence of failure. The operational planning horizon is segmented into discrete and equally-sized periods and in each period three possible maintenance actions (repair, replacement, or do nothing) have been considered for each workstation. The optimal maintenance decisions for each workstation in each period are investigated such that the objectives and the requirements of the system can be achieved. Total operational costs, overall reliability and the system availability are incorporated as the objective functions and the multi-objective model is solved using a hybrid Monte Carlo simulation and goal programming procedure to obtain set of non-dominated schedules. The effectiveness and feasibility of the proposed solution methodology are demonstrated in a manufacturing setting and the computational performance of method in obtaining Pareto-optimal solutions is evaluated. Such a modeling approach and the proposed solution algorithm could be useful for maintenance planners and engineers tasked with the problem of developing optimal maintenance plans for complex productions systems.

Monte Carlo Simulation을 이용한 도시하천의 고수위 Rating Curve 개발

본 연구에서는 도시하천을 대상으로 Monte Carlo Simulation (MCS)에 의한 모의발생 기법 적용으로 최적화된 강우-유출 모형과 홍수위 추적모형 연계를 통한 고수위 Rating Curve 작성법을 제안하였다. 대상유역의 관측 자료로부터 작성된 수위-유량곡선식은 유량측정의 오차와 더불어 고수위에 대한 불확실성을 내포하고 있음을 확인할 수 있었으며, 관측치와의 표준오차(<TEX>$S_e$</TEX>)는 0.056으로, 무작위 불확실성(<TEX>$2S_{mr}$</TEX>)은 평균 <TEX>${\pm}1.43%$</TEX>, 최대 <TEX>${\pm}4.27%$</TEX>로 분석되었다. 또한, 전대수지법과 Stevens방법에 의한 고수위 연장은 도시하천 유역 규모에 비하여 수위에 따른 홍수량이 과대 산정되는 문제점이 있는 것으로 분석되었다. 마지막으로, MCS에 의한 다량의 수문자료군 확보를 통한 수위-유량 관계곡선의 연장방법은 고수위에 대한 불확실성을 감소시켜며, 보다 신뢰성 있는 고수위 연장이 가능하였다. 향후 본 연구의 결과는 MCS에 의한 고수위 연장 시스템 구축을 통한 도시하천유역의 실시간 홍수 예 경보 활용에 적용이 가능할 것으로 사료된다. In this study, we proposed a methodology to develop Rating Curves for high water level using rainfall generation by the Monte Carlo Simulation (MCS) technique, optimized rainfall-runoff model, and flood routing model in an urban stream. The developed stage discharge Rating Curve based on observed data was contained flow measurement errors and uncertainties. The standard error (<TEX>$S_e$</TEX>) for observations was 0.056, and the random uncertainty (<TEX>$2S_{mr}$</TEX>) was analyzed by <TEX>${\pm}1.43%$</TEX> on average, and up to <TEX>${\pm}4.27%$</TEX>. Moreover, it was found that the Rating Curve extensions by way of logarithmic and Stevens methods were overestimated to compare with the urban basin scale. Finally, we confirmed that the high water level extension by random generation of hydrological data using MCS can be reduced uncertainty of the high water level, and it will consider as a more reliable approach for high water level extension. In the near future, this results can be applied to real-time flood alert system for urban streams through construction of the high water level extension system using MCS procedures.

A reverse Monte Carlo method for deriving optical constants of solids from reflection electron energy-loss spectroscopy spectra

A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO2 in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules. Our results show that the dielectric function can be obtained by the RMC method even with a wide range of initial trial parameters. The RMC method is thus a general and effective method for determining the optical properties of solids from REELS measurements.

Management Insights

Management Insights

Total Cost Control in Project Management via Satisficing

We consider projects with uncertain activity times and the possibility of expediting, or crashing, them. Activity times come from a partially specified distribution within a family of distributions. This family is described by one or more of the following details about the uncertainties: support, mean, and covariance. We allow correlation between past and future activity time performance across activities. Our objective considers total completion time penalty plus crashing and overhead costs. We develop a robust optimization model that uses a conditional value-at-risk satisficing measure. We develop linear and piecewise-linear decision rules for activity start time and crashing decisions. These rules are designed to perform robustly against all possible scenarios of activity time uncertainty, when implemented in either static or rolling horizon mode. We compare our procedures against the previously available Program Evaluation and Review Technique and Monte Carlo simulation procedures. Our computational studies show that, relative to previous approaches, our crashing policies provide both a higher level of performance, i.e., higher success rates and lower budget overruns, and substantial robustness to activity time distributions. The relative advantages and information requirements of the static and rolling horizon implementations are discussed. This paper was accepted by Dimitris Bertsimas, optimization.

Construction Engineering Bidding Risk Analysis

In the Bill of Quantities mode, the bidder must take risks of his tender offer. This paper researched on the uncertainty of construction projects costs, proposed Monte Carlo simulation method and procedure to simulate the construction projects costs on the basis of the construction projects costs conform to the characteristics of normal distribution, and also put forward a method to calculate risks of the tender offer in accordance with the established bidding strategy, which are helpful to the risk management and control of project contracting enterprises.

A Bayesian Method for Short-Term Probabilistic Forecasting of Photovoltaic Generation in Smart Grid Operation and Control

A new short-term probabilistic forecasting method is proposed to predict the probability density function of the hourly active power generated by a photovoltaic system. Firstly, the probability density function of the hourly clearness index is forecasted making use of a Bayesian auto regressive time series model; the model takes into account the dependence of the solar radiation on some meteorological variables, such as the cloud cover and humidity. Then, a Monte Carlo simulation procedure is used to evaluate the predictive probability density function of the hourly active power by applying the photovoltaic system model to the random sampling of the clearness index distribution. A numerical application demonstrates the effectiveness and advantages of the proposed forecasting method.