On the Potential of a Multi-Fidelity G-POD Based Approach for Optimization and Uncertainty Quantification

2014 ◽  
Author(s):  
David J. J. Toal
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Uncertainty Quantification ◽  
Surrogate Models ◽  
Orthogonal Decomposition ◽  
High Fidelity ◽  
Computational Domain ◽  
Surrogate Modelling ◽  
Proper Orthogonal ◽  
Fidelity Model ◽  
Entire Computational Domain

Traditional multi-fidelity surrogate models require that the output of the low fidelity model be reasonably well correlated with the high fidelity model and will only predict scalar responses. The following paper explores the potential of a novel multi-fidelity surrogate modelling scheme employing Gappy Proper Orthogonal Decomposition (G-POD) which is demonstrated to accurately predict the response of the entire computational domain thus improving optimization and uncertainty quantification performance over both traditional single and multi-fidelity surrogate modelling schemes.

scholarly journals Proper Orthogonal Decomposition as Surrogate Model for Aerodynamic Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Valentina Dolci ◽  
Renzo Arina
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Parameter Space ◽  
Surrogate Model ◽  
Orthogonal Decomposition ◽  
High Fidelity ◽  
Aerodynamic Optimization ◽  
Model Based ◽  
Flow Past ◽  
First Case ◽  
Proper Orthogonal

A surrogate model based on the proper orthogonal decomposition is developed in order to enable fast and reliable evaluations of aerodynamic fields. The proposed method is applied to subsonic turbulent flows and the proper orthogonal decomposition is based on an ensemble of high-fidelity computations. For the construction of the ensemble, fractional and full factorial planes together with central composite design-of-experiment strategies are applied. For the continuous representation of the projection coefficients in the parameter space, response surface methods are employed. Three case studies are presented. In the first case, the boundary shape of the problem is deformed and the flow past a backward facing step with variable step slope is studied. In the second case, a two-dimensional flow past a NACA 0012 airfoil is considered and the surrogate model is constructed in the (Mach, angle of attack) parameter space. In the last case, the aerodynamic optimization of an automotive shape is considered. The results demonstrate how a reduced-order model based on the proper orthogonal decomposition applied to a small number of high-fidelity solutions can be used to generate aerodynamic data with good accuracy at a low cost.

scholarly journals Uncertainty Quantification of Stochastic Impact Dynamic Oscillator Using a Proper Orthogonal Decomposition-Polynomial Chaos Expansion Technique

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Biswarup Bhattacharyya ◽  
Eric Jacquelin ◽  
Denis Brizard
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Uncertainty Quantification ◽  
Contact Force ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Orthogonal Decomposition ◽  
Chaos Expansion ◽  
Time Step ◽  
Impact Oscillator ◽  
Proper Orthogonal

Abstract A proper orthogonal decomposition (POD)-based polynomial chaos expansion (PCE) is utilized in this article for the uncertainty quantification (UQ) of an impact dynamic oscillator. The time-dependent nonsmooth behavior and the uncertainties are decoupled using the POD approach. The uncertain response domain is reduced using the POD approach, and the dominant POD modes are utilized for the UQ of the response quantity. Furthermore, the PCE model is utilized for the propagation of the input uncertainties. Two different cases of impact oscillator are considered, namely, single impact and multiple impact. The contact between two bodies is modeled by Hertz’s law. For both the cases, UQ is performed on the projectile displacement, projectile velocity, and contact force. A highly nonsmooth behavior is noticed for the contact force. For that reason, most number of POD modes are required to assess the UQ of contact force. All the results are compared with the Monte Carlo simulation (MCS) and time domain PCE results. Very good accuracies are observed for the PCE and the POD-PCE predicted results using much less number of model evaluations compared to MCS. As the PCE coefficients are dependent on time, the PCE model is computed at each time step. On the contrary, for the POD-PCE model, the PCE coefficients are computed for the number of POD modes only: it is much less than the PCE model.

Proper orthogonal decomposition Pascal polynomial-based method for solving Sobolev equation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Dehghan ◽  
Baharak Hooshyarfarzin ◽  
Mostafa Abbaszadeh
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Meshfree Method ◽  
Orthogonal Decomposition ◽  
Sobolev Type ◽  
Computational Domain ◽  
Sobolev Equation ◽  
Content Type ◽  
Proper Orthogonal

Purpose This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover, this method does not require establishing grids in the computational domain. Design/methodology/approach In this study, the authors present a meshfree method based on Pascal polynomial expansion for the numerical solution of the Sobolev equation. In general, Sobolev-type equations have several applications in physics and mechanical engineering. Findings The authors use the Crank-Nicolson scheme to discrete the time variable and the Pascal polynomial-based (PPB) method for discretizing the spatial variables. But it is clear that increasing the value of the final time or number of time steps, will bear a lot of costs during numerical simulations. An important purpose of this paper is to reduce the execution time for applying the PPB method. To reach this aim, the proper orthogonal decomposition technique has been combined with the PPB method. Originality/value The developed procedure is tested on various examples of one-dimensional, two-dimensional and three-dimensional versions of the governed equation on the rectangular and irregular domains to check its accuracy and validity.

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