New Regularization Method for Calibrated POD Reduced-Order Models

• Published in: Mathematical modelling and analysis Vol. 21; no. 1; pp. 47 - 62
• Main Authors: El Majd, Badr Abou, Cordier, Laurent
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.01.2016; Vilnius Gediminas Technical University; Taylor&Francis and VGTU
• Subjects: Calibration; Computational fluid dynamics; Cylinders; Decomposition (Mathematics); Galerkin methods; L-curve; Lcurve; Mathematical models; Mathematical research; Mathematics; Mechanics; Numerical Analysis; optimization; Optimization and Control; Orthogonal functions; Physics; POD reduced-order model; Reduced order models; Regularization; singular value decomposition; Wakes; Lcurve; optimization; POD reduced-order model; singular value decomposition; regularization; Singular Value Decomposition; 91A10; L-curve; 76F20; 78M50; Optimization AMS Subject Classification: 78M34; POD Reduced-Order Model; Regularization
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/13926292.2016.1132486

Reduced-order models based on Proper orthogonal decomposition are known to suffer from a lack of accuracy due to the truncation effect introduced by keeping only the most energetic modes. In this paper, we propose a new regularized calibration method aiming at minimizing a weighted average of normalized error, and a term measuring the change of the coefficients from their value obtained by Galerkin projection. We also determine the optimal value of the regularization parameter by analogy of the L-curve method. This paper is a sequel of [8] in which we compared various methods of calibration and introduced a Tikhonov-based regularization method. The proposed approach is assessed for a two dimensional wake flow around a cylinder, characteristic of the configurations of interest.