The proper orthogonal decomposition (POD) based reduced-order model (ROM) has been an effective tool for flow field prediction in the engineering industry. The sample selection in the design space for POD basis constr...
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ISBN:
(数字)9781624106101
ISBN:
(纸本)9781624106101
The proper orthogonal decomposition (POD) based reduced-order model (ROM) has been an effective tool for flow field prediction in the engineering industry. The sample selection in the design space for POD basis construction affects the ROM performance sensitively. adaptivesampling can significantly reduce the number of samples to achieve the required model accuracy. In this work, we propose a novel adaptivesampling algorithm, called conjunction sampling strategy, which is based on proven strategies. The conjunction sampling strategy is demonstrated on airfoil flow field prediction within the transonic regime. We demonstrate the performance of the proposed strategy by running 10 trials for each strategy for the robustness tests. Results show that the conjunction sampling strategy consistently achieves higher predictive accuracy compared with Latin hypercube sampling (LHS) and existing strategies. Specifically, under the same computational budget (40 training samples in total), the conjunction strategy reduced the L-2 error by 56.7% compared with LHS. In addition, the conjunction strategy reduced the standard deviation of L-2 errors by 62.1% with a 2.6% increase on the mean error compared with the best existing strategy.
Some popular functions used to test global optimization algorithms, such as the Branin-Hoo and Himmelblau functions, have multiple local optima, all with the same value of the objective function. That is all local opt...
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ISBN:
(数字)9781624105982
ISBN:
(纸本)9781624105982
Some popular functions used to test global optimization algorithms, such as the Branin-Hoo and Himmelblau functions, have multiple local optima, all with the same value of the objective function. That is all local optima are also global optima. This renders them easy to optimize, because it is impossible for the algorithm to get stuck in a local optimum that is not the global one. Such functions actually present an opportunity to create challenging problems for optimization algorithms, because, as illustrated here, it is easy to convert them to functions with competitive local optima by adding a localized bump at the location of one of the optima. This process is illustrated here for the Branin-Hoo function, which has three global optima. We use the popular Python SciPy differential evolution (DE) optimizer for the illustration, because its wide use is likely to imply a well written code. DE also allows the use of the gradient-based BFGS local optimizer for final convergence. By making a large number of replicate runs we establish the probability of reaching a global optimum with the original and weaponized Branin-Hoo. With the original function we find 100% probability of success with a moderate number of function evaluations. With the weaponized version, we found that the probability of getting trapped in a non-global optimum can be made small only with a much larger number of function evaluations.
This paper develops a multifidelity method to reuse information from optimization history for adaptively refining surrogates in reliability-based design optimization (RBDO). RBDO can be computationally prohibitive due...
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ISBN:
(数字)9781624105784
ISBN:
(纸本)9781624105784
This paper develops a multifidelity method to reuse information from optimization history for adaptively refining surrogates in reliability-based design optimization (RBDO). RBDO can be computationally prohibitive due to numerous evaluations of the expensive high-fidelity models to estimate the probability of failure of the system in each optimization iteration. In this work, the high-fidelity model evaluations are replaced by cheaper-to-evaluate adaptively refined surrogate evaluations in the probability of failure estimation. The method reuses the past optimization iterations as an information source for devising an efficient multifidelity active learning (adaptivesampling) algorithm to refine the surrogates that best locate the failure boundary. We implement the information-reuse method using a multifidelity extension of efficient global reliability analysis that combines the expected feasibility function with a weighted lookahead information gain criterion to pick both the next sample location and information source used to evaluate the sample.
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