Applications of Polynomial Chaos-Based Cokriging to Simulation-Based Analysis and Design Under Uncertainty

Nagawkar, Jethro; Leifsson, Leifur

doi:10.1115/1.0002000v

Cited by 3 publications

(4 citation statements)

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“…This work further merges the advantages of the predictive confidence interval by kriging and analytical observation statistics by PCE, which makes PC-Kriging more competitive for uncertainty quantification applications. Nagawkar and Leifsson [335] showed an overall better aerodynamic coefficient prediction advantage of the PC-Cokriging algorithm developed by Du and Leifsson [164] over PCE, kriging, PC-Kring, and cokriging in airfoil robust design. The PC-Cokriging algorithm showed significantly better performance on a borehole case [348] and a nondestructive testing case, however, the accuracy difference on aerodynamic coefficient prediction is narrowed down especially when more high-fidelity data are available.…”

Section: Aerodynamic Coefficient Modelingmentioning

confidence: 99%

Machine Learning in Aerodynamic Shape Optimization

Li¹,

Martins²

2022

Preprint

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Large volumes of experimental and simulation aerodynamic data have been rapidly advancing aerodynamic shape optimization (ASO) via machine learning (ML), whose effectiveness has been growing thanks to continued developments in deep learning. In this review, we first introduce the state of the art and the unsolved challenges in ASO. Next, we present a description of ML fundamentals and detail the ML algorithms that have succeeded in ASO. Then we review ML applications contributing to ASO from three fundamental perspectives: compact geometric design space, fast aerodynamic analysis, and efficient optimization architecture. In addition to providing a comprehensive summary of the research, we comment on the practicality and effectiveness of the developed methods. We show how cutting-edge ML approaches can benefit ASO and address challenging demands like interactive design optimization. However, practical large-scale design optimizations remain a challenge due to the costly ML training expense. A deep coupling of ML model construction with ASO prior experience and knowledge, such as taking physics into account, is recommended to train ML models effectively.

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Section: Aerodynamic Coefficient Modelingmentioning

confidence: 99%

Machine Learning in Aerodynamic Shape Optimization

Li¹,

Martins²

2022

Preprint

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“…These surrogate models are then used in optimization algorithms to efficiently make predictions, explore design space, and find optimal solutions. Surrogate-based design optimization is advantageous over conventional simulation-based optimization for computational efficiency [17,18], the effective exploration of high-dimensional design spaces [19,20], multi-objective optimization capabilities [21,22], sensitivity analysis [23], and uncertainty analysis [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Optimal Tilt-Wing eVTOL Takeoff Trajectory Prediction Using Regression Generative Adversarial Networks

Yeh,

2023

Mathematics

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Electric vertical takeoff and landing (eVTOL) aircraft have attracted tremendous attention nowadays due to their flexible maneuverability, precise control, cost efficiency, and low noise. The optimal takeoff trajectory design is a key component of cost-effective and passenger-friendly eVTOL systems. However, conventional design optimization is typically computationally prohibitive due to the adoption of high-fidelity simulation models in an iterative manner. Machine learning (ML) allows rapid decision making; however, new ML surrogate modeling architectures and strategies are still desired to address large-scale problems. Therefore, we showcase a novel regression generative adversarial network (regGAN) surrogate for fast interactive optimal takeoff trajectory predictions of eVTOL aircraft. The regGAN leverages generative adversarial network architectures for regression tasks with a combined loss function of a mean squared error (MSE) loss and an adversarial binary cross-entropy (BC) loss. Moreover, we introduce a surrogate-based inverse mapping concept into eVTOL optimal trajectory designs for the first time. In particular, an inverse-mapping surrogate takes design requirements (including design constraints and flight condition parameters) as input and directly predicts optimal trajectory designs, with no need to run design optimizations once trained. We demonstrated the regGAN on optimal takeoff trajectory designs for the Airbus A3 Vahana. The results revealed that regGAN outperformed reference surrogate strategies, including multi-output Gaussian processes and conditional generative adversarial network surrogates, by matching simulation-based ground truth with 99.6% relative testing accuracy using 1000 training samples. A parametric study showed that a regGAN surrogate with an MSE weight of one and a BC weight of 0.01 consistently achieved over 99.5% accuracy (denoting negligible predictive errors) using 400 training samples, while other regGAN models require at least 800 samples.

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“…These methods are preferred in optimisation studies due to their success in capturing local properties and are also used in uncertainty analysis. In addition, there are methods such as Polynomial Chaos-coKriging [26] and Sparse Polynomial Chaos-Kriging [27], which combine the ability to capture global features of orthogonal-based methods with the ability to capture local features of kernel-based methods.…”

Section: Introductionmentioning

confidence: 99%

“…Skewness is a measure of the asymmetry of the probability density of response relative to the mean and is calculated as in Equation (26). Kurtosis, on the other hand, expresses a measure of whether the data contain an abundance of outliers or lack of outliers relative to a normal distribution and is calculated as in Equation (26).…”

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confidence: 99%

Multi-Fidelity Low-Rank Approximations for Uncertainty Quantification of a Supersonic Aircraft Design

2022

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Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study.

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Applications of Polynomial Chaos-Based Cokriging to Simulation-Based Analysis and Design Under Uncertainty

Cited by 3 publications

References 0 publications

Machine Learning in Aerodynamic Shape Optimization

Machine Learning in Aerodynamic Shape Optimization

Optimal Tilt-Wing eVTOL Takeoff Trajectory Prediction Using Regression Generative Adversarial Networks

Multi-Fidelity Low-Rank Approximations for Uncertainty Quantification of a Supersonic Aircraft Design

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