The Aumann-Gould Integral

We introduce and study a multi-valued integral of Aumann-type where the selectors are Gould integrals of real functions with respect to finitely additive vector-valued measures. We also discuss the relationship between this kind of integral and the M-Gould set-valued integral with respect to a finitely additive multimeasure M. Received: November 17, 2006, Revised: September 17, 2007 and January, 8, 2008, Accepted: March 13, 2008.     

Damage identification in a concrete dam by fitting measured modal parameters

We propose a method, based on an inverse problem, to obtain numerically the material parameters that characterize the elasticity tensor of a body with linear elastic behavior, using accurate measurements of the first modal parameters, namely the natural frequencies and the modes of vibration (the eigenfrequencies and the eigenvectors). Appropriate functionals are defined, whose minimum points correspond to the unknown material parameters. To obtain these minimum points a highly nonlinear parametric optimization problem is solved. Its resolution involves specific mathematical tools like the derivative of the eigenvalues and eigenvectors with respect to the material parameters, the adjoint method, and gradient methods for the minimization of the functional. An application is presented, which considers a cracked dam in which is assumed the presence of transversely isotropic material in the cracked zone. The material parameters of the transversely isotropic material are obtained by minimizing the distance between the modal parameters (eigenfrequencies and eigenvectors) of a numerical model of the dam and the observed modal parameters physically measured in the dam. The algorithm is implemented in a C++ home made code with the aid of open-source libraries for scientific computation.