Structure and System Nonprobabilistic Reliability Solution Method Based on Enhanced Optimal Latin Hypercube Sampling

2015 ◽  
Vol 15 (01) ◽  
pp. 1450034 ◽  
Author(s):  
Xin-Dang He ◽  
Wen-Xuan Gou ◽  
Yong-Shou Liu ◽  
Zong-Zhan Gao
Keyword(s):  
Solution Method ◽  
Probability Distributions ◽  
Latin Hypercube Sampling ◽  
Computational Effort ◽  
Interval Uncertainty ◽  
Limited Information ◽  
Latin Hypercube ◽  
Convex Model ◽  
Reliability Method ◽  
Optimal Latin Hypercube Sampling

Using the convex model approach, the bounds of uncertain variables are only required rather than the precise probability distributions, based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information. This paper aims to develop a novel nonprobabilistic reliability solution method for structures with interval uncertainty variables. In order to explore the entire domain represented by interval variables, an enhanced optimal Latin hypercube sampling (EOLHS) is used to reduce the computational effort considerably. Through the proposed method, the safety degree of a structure with convex modal uncertainty can be quantitatively evaluated. More importantly, this method can be used to deal with any general problems with nonlinear and black-box performance functions. By introducing the suggested reliability method, a convex-model-based system reliability method is also formulated. Three numerical examples are investigated to demonstrate the efficiency and accuracy of the method.

scholarly journals Optimal Latin hypercube sampling-based surrogate model in NAPLs contaminated groundwater remediation optimization process

2017 ◽  
Vol 18 (1) ◽  
pp. 333-346 ◽  
Author(s):  
Jiannan Luo ◽  
Yefei Ji ◽  
Wenxi Lu ◽  
He Wang
Keyword(s):  
Surrogate Model ◽  
Groundwater Remediation ◽  
Model Performance ◽  
Latin Hypercube Sampling ◽  
Feasible Region ◽  
Contaminated Groundwater ◽  
Chance Constrained Programming ◽  
Latin Hypercube ◽  
Optimal Latin Hypercube Sampling ◽  
The Impact

Abstract A surrogate model based groundwater optimization model was developed to solve the non-aqueous phase liquids (NAPLs) contaminated groundwater remediation optimization problem. To illustrate the impact of sampling method improvement to the surrogate model performance improvement, aiming at a nitrobenzene contaminated groundwater remediation problem, optimal Latin hypercube sampling (OLHS) method was introduced to sample data in the input variables feasible region, and a radial basis function artificial neural network was used to construct a surrogate model. Considering the surrogate model's uncertainty, a chance-constrained programming (CCP) model was constructed, and it was solved by genetic algorithm. The results showed the following, for the problem considered in this study. (1) Compared with the Latin hypercube sampling (LHS) method, the OLHS method improves the space-filling degree of sample points considerably. (2) The effects of the two sampling methods on surrogate model performance were analyzed through comparison of goodness of fit, residual and uncertainty. The results indicated that the OLHS-based surrogate model performed better than the LHS-based surrogate model. (3) The optimal remediation strategies at 99%, 95%, 90%, 85%, 80% and 50% confidence levels were obtained, which showed that the remediation cost increased with the confidence level. This work would be helpful for increasing surrogate model performance and lowering the risk of a groundwater remediation strategy.

scholarly journals Comparison of Factorial and Latin Hypercube Sampling Designs for Meta-Models of Building Heating and Cooling Loads

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 512
Author(s):  
Younhee Choi ◽  
Doosam Song ◽  
Sungmin Yoon ◽  
Junemo Koo
Keyword(s):  
Latin Hypercube Sampling ◽  
Building Design ◽  
Gain Coefficient ◽  
Design Parameters ◽  
Latin Hypercube ◽  
Heating And Cooling ◽  
Factor Design ◽  
Heating Loads ◽  
Cooling Loads ◽  
Interest In Research

Interest in research analyzing and predicting energy loads and consumption in the early stages of building design using meta-models has constantly increased in recent years. Generally, it requires many simulated or measured results to build meta-models, which significantly affects their accuracy. In this study, Latin Hypercube Sampling (LHS) is proposed as an alternative to Fractional Factor Design (FFD), since it can improve the accuracy while including the nonlinear effect of design parameters with a smaller size of data. Building energy loads of an office floor with ten design parameters were selected as the meta-models’ objectives, and were developed using the two sampling methods. The accuracy of predicting the heating/cooling loads of the meta-models for alternative floor designs was compared. For the considered ranges of design parameters, window insulation (WDI) and Solar Heat Gain Coefficient (SHGC) were found to have nonlinear characteristics on cooling and heating loads. LHS showed better prediction accuracy compared to FFD, since LHS considers the nonlinear impacts for a given number of treatments. It is always a good idea to use LHS over FFD for a given number of treatments, since the existence of nonlinearity in the relation is not pre-existing information.

Some Important Issues on First-Order Reliability Analysis With Nonprobabilistic Convex Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
C. Jiang ◽  
G. Y. Lu ◽  
X. Han ◽  
R. G. Bi
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Probability Model ◽  
Mean Value ◽  
Convex Model ◽  
First Order ◽  
Reliability Method ◽  
Complex Engineering ◽  
Mean Value Method ◽  
Form Type

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the well-established techniques in probability-based reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used first-order reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convex-model-based reliability analysis. Two FORM-type approximations, namely, the mean-value method and the design-point method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.

Aerodynamic Efficiency Optimization of the 1st Stage of Transonic High Pressure Turbine through Lean and Sweep Angles

2019 ◽  
Vol 36 (3) ◽  
pp. 245-256
Author(s):  
Yoonki Kim ◽  
Sanga Lee ◽  
Kwanjung Yee ◽  
Young-Seok Kang
Keyword(s):  
High Pressure ◽  
Surrogate Model ◽  
Design Space ◽  
Latin Hypercube Sampling ◽  
Expected Improvement ◽  
Total Efficiency ◽  
High Pressure Turbine ◽  
Sweep Angle ◽  
Design Variables ◽  
Optimal Latin Hypercube Sampling

Abstract The purpose of this study is to optimize the 1st stage of the transonic high pressure turbine (HPT) for enhancement of aerodynamic performance. Isentropic total-to-total efficiency is designated as the objective function. Since the isentropic efficiency can be improved through modifying the geometry of vane and rotor blade, lean angle and sweep angle are chosen as design variables, which can effectively alter the blade geometry. The sensitivities of each design variable are investigated by applying lean and sweep angles to the base nozzle and rotor, respectively. The design space is also determined based on the results of the parametric study. For the design of experiment (DoE), Optimal Latin Hypercube sampling is adopted, so that 25 evenly distributed samples are selected on the design space. Sequentially, based on the values from the CFD calculation, Kriging surrogate model is constructed and refined using Expected Improvement (EI). With the converged surrogate model, optimum solution is sought by using the Genetic Algorithm. As a result, the efficiency of optimum turbine 1st stage is increased by 1.07 % point compared to that of the base turbine 1st stage. Also, the blade loading, pressure distribution, static entropy, shock structure, and secondary flow are thoroughly discussed.

On the Probability Distribution of Mooring Line Tensions in a Directional Environment

2011 ◽  
Author(s):  
Jan Mathisen ◽  
Siril Okkenhaug ◽  
Kjell Larsen
Keyword(s):  
Time Series ◽  
Probability Distributions ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Extreme Value ◽  
Mooring Line ◽  
Large Set ◽  
Short Term ◽  
Reliability Method ◽  
Line Design

A joint probabilistic model of the metocean environment is assembled, taking account of wind, wave and current and their respective heading angles. Mooring line tensions are computed in the time domain, for a large set of short-term stationary conditions, intended to span the domain of metocean conditions that contribute significantly to the probabilities of high tensions. Weibull probability distributions are fitted to local tension maxima extracted from each time series. Long time series of 30 hours duration are used to reduce statistical uncertainty. Short-term, Gumbel extreme value distributions of line tension are derived from the maxima distributions. A response surface is fitted to the distribution parameters for line tension, to allow interpolation between the metocean conditions that have been explicitly analysed. A second order reliability method is applied to integrate the short-term tension distributions over the probability of the metocean conditions and obtain the annual extreme value distribution of line tension. Results are given for the most heavily loaded mooring line in two mooring systems: a mobile drilling unit and a production platform. The effects of different assumptions concerning the distribution of wave heading angles in simplified analysis for mooring line design are quantified by comparison with the detailed calculations.

Latin Hypercube Sampling

2019 ◽  
pp. 29-44
Author(s):  
Guojun Gan ◽  
Emiliano A. Valdez
Keyword(s):  
Latin Hypercube Sampling ◽  
Latin Hypercube

Uncertainty Quantification of Turbulence Model Coefficients via Latin Hypercube Sampling Method

2010 ◽  
Author(s):  
Matthew C. Dunn ◽  
Babak Shotorban ◽  
Abdelkader Frendi
Keyword(s):  
Uncertainty Quantification ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Sampling Method ◽  
Latin Hypercube Sampling ◽  
Recirculation Region ◽  
Free Shear Layer ◽  
Latin Hypercube ◽  
Reattachment Point ◽  
Turbulent Dissipation

This paper is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are determined from experiments performed on elementary flows and they are subject to uncertainty. The widely used k–ε turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for the flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte-Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise velocity component in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly affected.

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