Inverse Boundary Element Solution for Locating Subsurface Cavities in Thermal and Elastostatic Problems

Kassab, Alain J.; Moslehy, F.A.; Ulrich, T.W.; Pollard, John E.

doi:10.1007/978-3-642-79654-8_499

Cited by 2 publications

(6 citation statements)

References 3 publications

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“…This is achieved by the minimization of an objective function, S1, that quantifies the difference between the deformations u i obtained by BEM (Eq. (5)) and measured deformations u i providing the additional information obtained through experimental measurements on the exposed boundaries (see Divo et al [1], Ulrich et al [2], Kassab et al [3,4]). Upon convergence, a second objective function is defined and minimized to locate the cavity(ies) location(s) indicated as traction-free surface(s).…”

Section: Inverse Problem and Objective Functionmentioning

confidence: 99%

“…The purpose of the inverse geometric problem, that concerns this study, is to determine the hidden portion of the system geometry by using over-specified boundary conditions on the exposed portion. This problem has gained importance in thermal and solid mechanics applications for nondestructive detection of subsurface cavities (Ulrich et al [2], Kassab et al [3,4], Divo et al [5]). In thermal applications, the method requires over-specified boundary conditions at the surface, i.e., both temperature and flux must be given, Divo et al [1].…”

Section: Introductionmentioning

confidence: 99%

“…This inverse problem has applications in the identification of surfaces flaws and cavities and in shape optimization problems (Divo et al [1,5,[7][8][9], Ulrich et al [2], Kassab et al [3,4], Bialecki et al [6]). The computational burden is intensive due to the inherent nature of the solution of inverse problem which requires numerous forward problems to be solved, regardless of whether a numerical or analytical approach is taken to solve the associated direct problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Singular superposition elastostatics BEM/GA algorithm for cavity detection

Ojeda¹,

́amez²,

Divo³

et al. 2007

WIT Transactions on Modelling and Simulation, Vol 44

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A method for the efficient solution of the inverse geometric problem for cavity detection using a point load superposition technique in the elastostatics boundary element method (BEM) is presented in this paper. The superposition of point load clusters to simulate the presence of cavities offers tremendous advantages in reducing the computational time for the elastostatics field solution as no boundary re-discretization is necessary throughout the inverse problem solution process. The inverse solution is achieved in two steps: (1) fixing the location and strengths of the point loads, (2) locating the cavity(ies) geometry(ies). For a current estimated point load distribution, a first objective function measures the difference between BEM-computed and measured deformations at the measuring points. A Genetic Algorithm (GA) is employed to automatically alter the locations and strengths of the point sources to minimize the objective function. The GA is parallelized and dynamically balanced. Upon convergence, a second objective function is defined and minimized to locate the cavity(ies) location(s) indicated as traction-free surface(s). Results of cavity detection simulations using numerical experiments and simulated random measurement errors validate the approach in regular and irregular geometrical configurations with single and multiple cavities.

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Section: Inverse Problem and Objective Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Singular superposition elastostatics BEM/GA algorithm for cavity detection

Ojeda¹,

́amez²,

Divo³

et al. 2007

WIT Transactions on Modelling and Simulation, Vol 44

View full text Add to dashboard Cite

show abstract

“…This problem has gained importance in thermal and solid mechanics applications for nondestructive detection of subsurface cavities Ulrich et al [8], Kassab et al. [9,10]. In thermal applications, the method requires over-specified boundary conditions at the surface, i.e.…”

Section: Introductionmentioning

confidence: 98%

“…This inverse problem has applications in the identification of surfaces flaws and cavities and in shape optimization problems, see [8,9,10,[13][14][15][16]18]. The computational burden is intensive due to the inherent nature of the solution to this inverse problem which requires numerous forward problems to be solved, regardless of whether a numerical or analytical approach is taken to solve the associated direct problem.…”

Section: Introductionmentioning

confidence: 99%

Cavity detection in biomechanics by an inverse evolutionary point load BEM technique

Ojeda

Divo

Kassab

et al. 2008

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

An efficient solution of the inverse geometric problem for cavity detection using a point load superposition technique in the elastostatics boundary element method (BEM) is presented in this article. A superposition of point load clusters technique is used to simulate the presence of cavities. This technique offers tremendous advantages in reducing the computational time for the elastostatics field solution as no boundary re-discretization is necessary throughout the inverse problem solution process. The inverse solution is achieved in two steps: (1) fixing the location and strengths of the point loads, (2) locating the cavity geometry. For a current estimated point load distribution, a first objective function measures the difference between BEM-computed and measured deformations at selected points. A genetic algorithm is employed to automatically alter the locations and strengths of the point loads to minimize the objective function. Upon convergence, a second objective function is defined to locate the cavity geometry modelled as traction-free surface. Results of cavity detection simulations using numerical experiments and simulated random measurement errors validate the approach in regular and irregular geometrical configurations.

show abstract

Inverse Boundary Element Solution for Locating Subsurface Cavities in Thermal and Elastostatic Problems

Cited by 2 publications

References 3 publications

Singular superposition elastostatics BEM/GA algorithm for cavity detection

Singular superposition elastostatics BEM/GA algorithm for cavity detection

Cavity detection in biomechanics by an inverse evolutionary point load BEM technique

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