Inverse parameter estimation using compressed sensing and POD-RBF reduced order models

A novel algebraic method is described for the inverse estimation of model parameters such as material properties and boundary conditions in fluid flow and thermal systems, using sparse measurements or solution values at only a few locations. The method uses the principles of compressed sensing, and parametric reduced order models based on Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF). The inverse estimation is demonstrated for three applications. First, a mathematical problem to inversely calculate the coefficients of Fourier series of a generic function, with a few known values of the function. Second, estimating thermal conductivity in a two-dimensional heat transfer system, and third, a more practical problem of identifying the Mach number, Reynolds number and the angle of attack of the flow over an airfoil, given only a few values of pressure around the airfoil. The method could be useful in design synthesis and in estimation parameters for real-time computational model calibration.