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The basic general extension algorithm is proposed to reserve the most original points, but it costs too much time. The relationship of original sampling points in the new LHS structure is shown by a simple undirected acyclic graph. In order to get a strict LHS of larger size, some original points might be deleted. The extension algorithms start with an original LHS of size and construct a new LHS of size that contains the original points as many as possible. Grammatico (Supervisor 1) & M.M.For reserving original sampling points to reduce the simulation runs, two general extension algorithms of Latin Hypercube Sampling (LHS) are proposed.
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Fonseca (Supervisor 1), Olwijn Leeuwenburgh (Supervisor 1), S. Of convergence when compared to any of the other sampling techniques for both deterministic and robust UE(s2) - optimal design sampling strategies achieve better objective function values with an improved rate Results obtained with multivariate Gaussian sampling applied to the Rosenbrock function with high dimensionĪs well as a reservoir model for both deterministic and robust cases. Experiments are performed with all sampling strategies and compared to Gradient quality, objective function value, rate of convergence and robustness of the gradient for cases withĪnd without model uncertainty. The effectiveness of the sampling method is analyzed based on the approximate Variants for UE(s2) - optimal design are considered as an alternative to the often used multivariate Gaussian Sampling strategies (Sobol sampling, Latin Hypercube Sampling and UE(s2) - optimal design) and 3 This thesis aims to evaluate a number of different sampling strategies under theĬonstraint that ensemble size is smaller than number of control variables being optimized. This thesis deals with investigating alternativeĮffective sampling strategies for creating the ensemble for EnOpt to improve gradient quality and thereby Important and has received little attention in the literature.
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Size, the sampling strategy (distribution or type) used to generate the ensemble of controls is extremely Quality gradients which have been shown to affect the optimization performance. Smaller ensemble sizes leads to fewer functionĮvaluations and thus decreases the computational efficiency and time, however this results in inferior number of perturbed controls used to evaluate the gradient, becomesĪn important constraint for the applicability of the method. EnOpt being an ensemble based optimization Simulations are computationally expensive and time consuming. Geological model is considered uncertain (many equi-probable geological models are used). where the geological model is considered certain (single model) or for robust cases i.e. Model based life-cycle production optimization can be performed either deterministically One such method is calledĮnsemble Optimization (EnOpt) which has been shown as an effective stochastic gradient based optimization
#LATIN HYPERCUBE SAMPLING EQUIPROBABLE CODE#
Method like minimal code development, treatment of simulator as black-box. RecentlyĮnsemble based optimization techniques have gained popularity due to its advantages over adjoint Performed either by solving a system of adjoint equations or through ensemble based optimization. Optimization can be gradient based or gradient-free technique. Dynamic model-based optimization is an efficient concept of systemsĪnd control to determine these optimal controls (design variables) which maximizes an economic objectiveįunction like Net Present Value or sometimes a volumetric function like cumulative oil production. On finding efficient and optimal controls like bottom hole pressure or production and injection rates in wellsĭuring the production phase of oil. This effective hydrocarbon recovery strategy depends
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Natural gas from the reservoirs deep inside the earth. Sources of energy demands economical and efficient recovery of hydrocarbons like petroleum and AbstractIncreasing demand for energy, scarcity of conventional energy resources and lack of infrastructure for alternative