Fuzzy Monte Carlo Simulation Research Articles

Integrated Approach to Construction Risk Management: Cost Implications

Managing risk in construction projects has proven to be a challenge for many project managers and stakeholders involved in projects. The lack of a systematic approach and standardized processes are key factors influencing improper risk management techniques. This research introduces a new model to evaluate and assess risk in terms of cost impact, utilizing a fuzzy Monte Carlo simulation approach for the first time. The method consists of ranking the top risks using a fuzzy logic system utilized in an objective manner by setting criteria for experts to rank the risk based on cost impact and probability to reduce human biases, then evaluating their cost impact through a Monte Carlo simulation both pre- and postmitigation. This work proposes a new strategy to elicit risk for construction projects based on risk cost impact, project type, project location, project contract type, and project delivery method. Based on the findings, implementation of a risk mitigation response plan can decrease the project cost remarkably. This model proved to be beneficial in forecasting risk impact when executed on a commercial construction project in California. This model can be applied as a general tool for risk mitigation processes for the construction industry.

Reliability analysis of corrosion initiation in reinforced concrete structures subjected to chlorides in presence of epistemic uncertainties

This paper presents a methodology for assessing the corrosion initiation in reinforced concrete (RC) structures subjected to chlorides, with a focus on the influence of epistemic uncertainties inherent to input parameters. Epistemic uncertain parameters were modeled using fuzzy probability theory. The chloride penetration was modeled using a finite element solution of the coupled heat transfer, moisture and chloride transport in concrete. The environmental conditions were modeled using a stochastic process. The reliability analysis was undertaken using a hybrid fuzzy Monte Carlo simulation. As an illustration, the durability of concrete basins of a newly constructed waste water treatment plant, with respect to reinforcement corrosion, was examined. The time to corrosion initiation was found to approximately follow a generalized extreme value distribution with fuzzy parameters. The stochastic modeling of exposure conditions accelerated the corrosion initiation. The time to corrosion initiation is highly sensitive to the epistemic uncertainty in the threshold chloride level in concrete. Reducing this uncertainty will result in an important improvement in accuracy. The proposed method is suitable for durability assessment of recent RC structures with little or no available performance data.

FUZZY MONTE CARLO SIMULATION OPTIMIZATION FOR SELECTING MATERIALS IN GREEN BUILDINGS

Global interest in sustainable and green building design has been increasing in the last few decades. This interest is strengthened by the fact that sustainable measures help in reducing negative social and environmental impacts of buildings. For that, this paper aims to develop a mixed integer optimization model that aids architects/designers and owner representatives during design stage in selecting building materials taking into consideration costs and risks that are involved in the selection process. The model is developed as a simulation optimization tool based on the Leadership in Energy and Environmental Design (LEED) rating system for new construction. The developed model allows deterministic and probabilistic cost analysis of various design alternatives. In addition, it identifies the least possible cost to gain the LEED credits and the risks associated with materials’ quantities and materials’ unit prices. To illustrate the use of the proposed tool, a case study of an office building project constructed in Egypt is presented. An integrated Fuzzy Monte Carlo Simulation (FMCS) analysis is performed to account for the associated risks of using new materials in the considered case study. The proposed model is capable to capture the cost uncertainty of building materials and to identify the cost and sustainability performance of various building materials by relating the LEED rating system for new construction.

Fault trees analysis using expert opinion based on fuzzy‐bathtub failure rates

AbstractThe main objective of fault tree analysis method is to estimate the “Top Event occurrence probability”. This requires determination of failure time distribution functions also known as “Bathtub Curves” for each of the system elements/events. This paper introduces a novel method to determine the failure time distribution functions using possibility theory. For this purpose, fuzzy‐bathtub distributions using expert opinions are generated for basic events and fuzzy formulas are derived for static and dynamic gates fault tree constructions. This process completed by proposed fuzzy Monte Carlo simulation throughout the preferred operational time and uses the actual time‐to‐failure data. Accordingly, the Top Event failure curve and the reliability profile of the system are depicted based on the defuzzificated basic‐events' bathtub‐failure‐rates. The results show that the proposed method not only is feasible and powerful but can also be accurate more than the other probabilistic and possibilistic techniques because of the component failure rates follow the real failure distributions.

Monte Carlo vs. Fuzzy Monte Carlo Simulation for Uncertainty and Global Sensitivity Analysis

Monte Carlo simulation (MCS) has been widely used for the uncertainty propagations of building simulation tools. In general, most unknown inputs for the MCS are regarded as single probability distributions based on experts’ subjective judgements and assumptions, when simulation information and measured data are inaccurate and insufficient. However, this can lead to meaningless and untrustworthy results, since the results are obtained using only single probability distributions without considering reducible possibilities of some unknown inputs. This paper introduces a fuzzy MCS for dealing with the aforementioned problems. In comparison with the MCS, the fuzzy MCS has the advantage of considering the aleatory and epistemic uncertainty, and can provide a family of probability distributions. This paper also discusses how fuzzy MCS could be effectively used for uncertainty and global sensitivity analysis.

A fuzzy approach to reliability based design of storm water drain network

This paper proposes an approach to estimate reliability of a storm water drain (SWD) network in fuzzy framework. It involves: (i) use of proposed fuzzy Monte-Carlo simulation (FMCS) methodology to estimate fuzzy reliability of conduits in the network, (ii) construction of a reliability block diagram (RBD) for the network (system) using suggested guidelines, and (iii) use of the RBD and reliability estimates of the conduits in the network to compute system reliability based on a proposed procedure. In addition, a system reliability based methodology is proposed for design/retrofitting of SWD network by optimization of its conduit dimensions. Conventionally used reliability analysis approaches assume that the cumulative distribution function (CDF) of performance function (marginal safety) of conduits follows Gaussian distribution, which cannot be ensured in the real world scenario. The proposed approach alleviates the need for making such assumptions and can account for linguistic ambiguity in variables defining the performance function. Effectiveness of the proposed approach is demonstrated on a hypothetical SWD network and a real network in Bangalore, India. Comparison of the results obtained from the proposed approach with those from conventional Monte-Carlo simulation (MCS) reliability assessment approach indicated that the estimate of system reliability and conduit reliability are higher with FMCS approach. Consequently, conduit dimensions required to attain required system (network) reliability could be expected to be lower when FMCS approach is used for designing or retrofitting a system.

A New Combined Assessment of Mixed Uncertainty in Spatial Models: Conceptualization and Implementation

AbstractUncertainty quantification is not often performed in spatial modeling applications, especially when there is a mixture of probabilistic and non‐probabilistic uncertainties. Furthermore, the effect of positional uncertainty is often not assessed, despite its relevance to geographical applications. Although there has been much work in investigating the aforementioned types of uncertainty in isolation, combined approaches have not been much researched. This has resulted in a lack of tools for conducting mixed uncertainty analyses that include positional uncertainty. This research addresses the issue by first presenting a new, flexible, simulation‐oriented conceptualization of positional uncertainty in geographic objects called F‐Objects. F‐Objects accommodates various representations of uncertainty, while remaining conceptually simple. Second, a new Python‐based framework is introduced, termed Wiggly and capable of conducting mixed uncertainty propagation using fuzzy Monte Carlo simulation (FMCS). FMCS combines both traditional Monte Carlo with fuzzy analysis in a so‐called hybrid approach. F‐Objects is implemented within the Wiggly framework, resulting in a tool capable of considering any combination of: (1) probabilistic variables; (2) fuzzy variables; and (3) positional uncertainty of objects (probabilistic/fuzzy). Finally, a realistic GIS‐based groundwater contamination problem demonstrates how F‐Objects and Wiggly can be used to assess the effect of positional uncertainty.

Fuzzy Monte Carlo Simulation using point-cloud-based probability–possibility transformation

Fuzzy Monte Carlo Simulation (FMCS) uses both the probability density function ( pdf) and possibility distributions (e.g., fuzzy numbers) to model the uncertainty/imprecision associated with the input parameters and, then, to simulate the uncertainty/imprecision associated with the output parameters. A probability–possibility transformation is needed to transfer the information of a fuzzy number into its equivalent pdf, while performing the simulation. This study deals with an approach of FMCS that uses a point-cloud-based probability–possibility transformation. Let x( t), t = 0,1,…, n, be a set of points that represents some random states of an uncertain/imprecise quantity. The collection of points ( x( t), x( t+ i)), t = 0,…, n– i, i∈ {1,2,…} is called point-cloud, providing a visual/computational representation of variability, modality, and ranges associated with the quantity. This study identifies the pdf and possibility distribution (fuzzy number) underlying a given point-cloud. Using these distributions, the relationships between the triangular fuzzy number and unimodal pdf (normal/uniform distributions) are identified. Two numerical examples are described elucidating the effectiveness of the proposed transformation. The first example deals with the issue of monitoring a FMCS process. The other example deals with the issue of making a decision by using FMCS.

Reliability analysis of a rubble mound breakwater using the theory of fuzzy random variables

This study investigates the possibility of applying the theory of fuzzy random variables through the fuzzy Monte Carlo simulation approach for the reliability-based risk analysis of a rubble-mound breakwater. The results are presented and compared with the traditional Monte Carlo calculation. This study indicates that the present theory may provide a useful tool for the joint handling of randomness and fuzziness in the computation of reliability and may have a good potential to be used for reliability assessment of coastal structures.

Failure probability evaluation of passive system using fuzzy Monte Carlo simulation

Passive systems have become an inherent feature of the advanced reactors. The main reason being the passive systems are, theoretically, more reliable than the active ones. Nevertheless the passive system may fail to fulfill its mission not only because of a consequence of classical mechanical failure of component (passive or active) of the passive system, but also due to the deviation from expected behavior due to physical phenomena mainly related to thermal hydraulic or due to different boundary or initial conditions. In this paper the methodology used for performing the passive system reliability analysis has been discussed. A case study on passive decay heat removal system (PDHRS) of large sized pressurized heavy water reactor (PHWR) has been discussed. Thermal hydraulic analysis have been carried out by using RELAP5 code to generate the response surface (from various ranges of identified key parameter values), keeping the criterion as clad surface temperature exceeding certain critical value. Some uncertainties, due to incomplete information, cannot be handled satisfactorily in the probability theory and the fuzzy set theory is more appropriate. In this study the random variables are considered as fuzzy numbers and the fuzzy set theory is employed. In addition, the Monte Carlo simulation technique is utilized to evaluate the probability of failure of system.

Fuzzy Monte Carlo Simulation and Risk Assessment in Construction

Abstract: Monte Carlo simulation has been used extensively for addressing probabilistic uncertainty in range estimating for construction projects. However, subjective and linguistically expressed information results in added non‐probabilistic uncertainty in construction management. Fuzzy logic has been used successfully for representing such uncertainties in construction projects. In practice, an approach that can handle both random and fuzzy uncertainties in a risk assessment model is necessary. This article discusses the deficiencies of the available methods and proposes a Fuzzy Monte Carlo Simulation (FMCS) framework for risk analysis of construction projects. In this framework, we construct a fuzzy cumulative distribution function as a novel way to represent uncertainty. To verify the feasibility of the FMCS framework and demonstrate its main features, the authors have developed a special purpose simulation template for cost range estimating. This template is employed to estimate the cost of a highway overpass project.