Gappy proper orthogonal decomposition for flow reconstruction and flow sensing

The gappy POD is a is a modification of the basic POD method that handles incomplete or “ gappy ” data sets. An incomplete data vector can be reconstructed by representing it as a linear combination of known POD basis vectors. The modal content is determined by solving a small linear system. Further, if the snapshots themselves are damaged or incomplete, an iterative method can be used to derive the POD basis vectors. This method was developed by Everson and Sirovich in the context of reconstruction of images, such as human faces, from partial data.

The gappy POD is relevant for flow problems where incomplete data is available. For example, in experiments, data may only be available on the airfoil surface. Our research has shown that the gappy POD can be used to reconstruct both steady and unsteady flowfield data from limited surface pressure measurements.

Publications
Bui-Thanh, T., Damodaran, M. and Willcox, K., “Aerodynamic Data Reconstruction and Inverse Design using Proper Orthogonal Decomposition,” AIAA Journal, Vol. 42, No. 8, August 2004, pp. 1505-16.

Bui- Thanh , T., Damodaran , M. and Willcox , K., “Proper Orthogonal Decomposition Extensions for Parametric Applications in Transonic Aerodynamics”, AIAA Paper 2003-4213, presented at 15th Computational Fluid Dynamics Conference, Orlando, FL, June 2003.

Willcox , K., “Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition,” in Proceedings of the 5th SMA Symposium, January 2004, also AIAA Paper 2004-2415, submitted Computers and Fluids.

Bui- Thanh , T., “Proper Orthogonal Decomposition Extensions and their Applications in Steady Aerodynamics,” Masters Thesis ,Singapore -MIT Alliance , June 2003.