Large Sample Properties of Simulations Using Latin Hypercube Sampling

Stein, Michael L.

doi:10.2307/1269769

Cited by 666 publications

(499 citation statements)

References 7 publications

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“…Lin et al ) studied the RBFs with three different kinds of sampling setsuniformly distributed 9-point, 13-point, and 25-point designs. In this case study, uniformly distributed sampling is considered but another famous sampling method is the Latin Hypercube Sampling (Stein, 1987). A 437-point response was considered as a benchmark of the true responses.…”

Section: Model Validationmentioning

confidence: 99%

Systematic Strategy for Modeling and Optimization of Thermal Systems With Design Uncertainties

Jaluria¹,

Gea²,

Lin³

2010

Frontiers in Heat and Mass Transfer

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Thermal systems play significant roles in the engineering practice and our lives. To improve those thermal systems, it is necessary to model and optimize the design and the operating conditions. More importantly, the design uncertainties should be considered because the failures of the thermal systems may be very dangerous and produce large loss. This review paper focuses on a systematic strategy of modeling and optimizing of the thermal systems with the considerations of the design uncertainties. To demonstrate the proposed strategy, one of the complicated thermal systems, Chemical Vapor Deposition (CVD), is simulated, parametrically modeled, and optimized. The operating conditions, inlet velocities and susceptor temperatures, are the most significant factors in the CVD and are chosen as the design variables. Several responses -including the percentage of the working area, the mean of the deposition rate, the root mean square of the deposition, and the surface kurtosis -are chosen based on the physical needs and statistical foundations, and are utilized to represent the productivity and the quality of the thin-film deposition. One of the Response Surface Method (RSM), the Radial Basis Function (RBF), is employed to formulate the objective and constraint functions for the optimization. However, it is not until the design uncertainties are considered that the thermal system designs have high risk of the violations of the performance constraints. The Reliability-Based Design Optimization (RBDO) algorithms are used to solve the optimization problems with the design uncertainties. The most famous RBDO methods are the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). In RBDO, probabilistic constraints are established with respect to either normally or non-normally distributed random variables. The optimal solutions are found subjected to the allowable level of the failure probabilities. The Monte Carlo Simulation (MCS) results can be used to evaluate the failure probabilities. As a result, the proposed systematic strategy of parametrically modeling and optimizing with design uncertainties can be applied to either experiments or simulations of other thermal systems to quantitatively represent the performances, improve their productivity, maintain the quality control, and reduce the probability of the system failure.

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Section: Model Validationmentioning

confidence: 99%

Systematic Strategy for Modeling and Optimization of Thermal Systems With Design Uncertainties

Jaluria¹,

Gea²,

Lin³

2010

Frontiers in Heat and Mass Transfer

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“…However, a number of numerical techniques are available for their evaluation, with the most prominent ones based on Monte Carlo simulation. 23,26 In this section, we present a Monte Carlo method for estimating the variance-based sensitivity indices that uses a Latin hypercube sampling scheme 38,[44][45][46] to efficiently sample the random factors and reduce estimation variance. We will be referring to this technique as Monte Carlo Latin hypercube sampling ͑MC-LHS͒.…”

Section: Monte Carlo Estimationmentioning

confidence: 99%

Probabilistic sensitivity analysis of biochemical reaction systems

Zhang¹,

Dempsey²,

Goutsias³

2009

The Journal of Chemical Physics

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Sensitivity analysis is an indispensable tool for studying the robustness and fragility properties of biochemical reaction systems as well as for designing optimal approaches for selective perturbation and intervention. Deterministic sensitivity analysis techniques, using derivatives of the system response, have been extensively used in the literature. However, these techniques suffer from several drawbacks, which must be carefully considered before using them in problems of systems biology. We develop here a probabilistic approach to sensitivity analysis of biochemical reaction systems. The proposed technique employs a biophysically derived model for parameter fluctuations and, by using a recently suggested variance-based approach to sensitivity analysis ͓Saltelli et al., Chem. Rev. ͑Washington, D.C.͒ 105, 2811 ͑2005͔͒, it leads to a powerful sensitivity analysis methodology for biochemical reaction systems. The approach presented in this paper addresses many problems associated with derivative-based sensitivity analysis techniques. Most importantly, it produces thermodynamically consistent sensitivity analysis results, can easily accommodate appreciable parameter variations, and allows for systematic investigation of high-order interaction effects. By employing a computational model of the mitogen-activated protein kinase signaling cascade, we demonstrate that our approach is well suited for sensitivity analysis of biochemical reaction systems and can produce a wealth of information about the sensitivity properties of such systems. The price to be paid, however, is a substantial increase in computational complexity over derivative-based techniques, which must be effectively addressed in order to make the proposed approach to sensitivity analysis more practical.

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“…Therefore, LHS is mainly used for simulating large-scale computation. Stein (1987) investigated that LHS decreases dispersion compared with SRS, and Owen (1992) proposed a central limit theorem for LHS.…”

Section: Latin Hypercube Samplingmentioning

confidence: 99%

Improvement of overtopping risk evaluations using probabilistic concepts for existing dams

Kwon

Moon

2005

Stoch Environ Res Ris Assess

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Hydrologic risk analysis for dam safety relies on a series of probabilistic analyses of rainfall-runoff and flow routing models, and their associated inputs. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated in order to evaluate the probability of dam overtopping. Typically, parametric density estimation methods have been applied in this setting, and the exhaustive Monte Carlo simulation (MCS) of models is used to derive some of the distributions. Often, the distributions used to model some of the random variables are inappropriate relative to the expected behaviour of these variables, and as a result, simulations of the system can lead to unrealistic values of extreme rainfall or water surface levels and hence of the probability of dam overtopping. In this paper, three major innovations are introduced to address this situation. The first is the use of nonparametric probability density estimation methods for selected variables, the second is the use of Latin Hypercube sampling to improve the efficiency of MCS driven by the multiple random variables, and the third is the use of Bootstrap resampling to determine initial water surface level. An application to the Soyang Dam in South Korea illustrates how the traditional parametric approach can lead to potentially unrealistic estimates of dam safety, while the proposed approach provides rather reasonable estimates and an assessment of their sensitivity to key parameters.

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Large Sample Properties of Simulations Using Latin Hypercube Sampling

Cited by 666 publications

References 7 publications

Systematic Strategy for Modeling and Optimization of Thermal Systems With Design Uncertainties

Systematic Strategy for Modeling and Optimization of Thermal Systems With Design Uncertainties

Probabilistic sensitivity analysis of biochemical reaction systems

Improvement of overtopping risk evaluations using probabilistic concepts for existing dams

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