Title
Cubic Spline Anchored Grid Pattern Algorithm For High-Resolution Detection Of Subsurface Cavities By The Ir-Cat Method
Abstract
An algorithm is presented for the high-resolution detection of irregular-shaped subsurface cavities within irregular-shaped bodies by the IR-CAT method. The theoretical basis of the algorithm is rooted in the solution of an inverse geometric steady-state heat conduction problem. A Cauchy boundary condition is prescribed at the exposed surface, and the inverse geometric heat conduction problem is formulated by specifying the thermal condition at the inner cavities walls, whose unknown geometries are to be detected. The location of the inner cavities is initially estimated, and the domain boundaries are discretized. Linear boundary elements are used in conjunction with cubic splines for high resolution of the cavity walls. An anchored grid pattern (AGP) is established to constrain the cubic spline knots that control the inner cavity geometry to evolve along the AGP at each iterative step. A residual is defined measuring the difference between imposed and computed boundary conditions. A Newton-Raphson method with a Broyden update is used to automate the detection of inner cavity walls. During the iterative procedure, the movement of the inner cavity walls is restricted to physically realistic intermediate solutions. The proposed cubic spline algorithm is general and can be extended to detect multiple cavities. Numerical simulation demonstrates the superior resolution of the cubic spline AGP algorithm over the linear spline-based AGP in the detection of an irregular-shaped cavity. Numerical simulation is also used to test the sensitivity of the linear and cubic spline AGP algorithms by simulating bias and random error in measured surface temperatures. The proposed AGP algorithm is shown to satisfactorily detect cavities with these simulated data. © 1994 Taylor & Francis Group, LLC.
Publication Date
1-1-1994
Publication Title
Numerical Heat Transfer, Part B: Fundamentals
Volume
26
Issue
1
Number of Pages
63-77
Document Type
Article
Identifier
scopus
Personal Identifier
scopus
DOI Link
https://doi.org/10.1080/10407799408914917
Copyright Status
Unknown
Socpus ID
0028467199 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/0028467199
STARS Citation
Kassab, Alain J. and Pollard, John E., "Cubic Spline Anchored Grid Pattern Algorithm For High-Resolution Detection Of Subsurface Cavities By The Ir-Cat Method" (1994). Scopus Export 1990s. 337.
https://stars.library.ucf.edu/scopus1990/337