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A Robust Technique for Lumped Parameter Inverse Boundary Value Problems

[+] Author Affiliations
P. Venkataraman

Rochester Institute of Technology, Rochester, NY

Paper No. DETC2012-70343, pp. 861-872; 12 pages
doi:10.1115/DETC2012-70343
From:
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 32nd Computers and Information in Engineering Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4501-1
  • Copyright © 2012 by ASME

abstract

A natural approach to the inverse coupled nonlinear lumped parameter problem is to use a continuous approximation of the data and its derivatives using Bezier functions. The method is robust and does not need regularization or other transformation to convert the inverse problem to a well-posed one. The Bezier function technique first identifies continuous Bezier functions to represent the measured data using a recursive Bezier filter. These Bezier functions also provide information on the derivatives of the functions over the range of the independent variable. This is used in two ways. First, the residuals of the differential equations now depend on the distributed parameters alone. Second, the boundary conditions for a reduced range of the independent variable are easily generated. The lumped parameters are determined through two applications of standard unconstrained optimization. The first application identifies the parameters by minimizing the sum of the least squared error in the residuals over the range of the data. This also provides a robust initial guess for the second optimization. In the second optimization, the parameters are determined once again using a collocation technique to integrate the solution and reduce the sum of the absolute error with respect to the smooth representation of the data. Fluid flow in a long vertical channel with fluid injection is used to illustrate the procedure. The measured data is simulated using random perturbations about the smooth solution to the forward problem. The results show that the Bezier function technique can identify a solution even with severe perturbations in the data. It is also shown that using the information from a clipped region can lead to a well-posed problem.

Copyright © 2012 by ASME

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