Using SDM to Train Neural Networks for Solving Modal Sensitivity Problems

The Structural Dynamics Modi$cation (SDM) algorithm is very useful for solving the so-called forward variahnal problem for structures. That is, given changes in a structure’s mass, stijj%ess, or damping properties, SDM efficiently yields the corresponding changes in its modal properties. There are several important classes of problems, however, that require solutions to the inverse variutional problem, or modal sensitivity problem That is, given changes in a structure’s modal properties, what corresponding changes in its mass, stiffness, and damping propem’es have taken place. Applications such as structural damage detection, finite element model updating using test data, and vibration suppression or control through structural modification all require solutions to the modal sensitivity problem Unlike the forward variational problem, the modal sensitivity problem cannot be solved in a straightforward manner. For most practical cases, its solution requires the inversion of a rank deficient matrix, which creates numerical dificulties. Neural networks offer promise for solving the moaial sensitivity problem, because of their pattern recognition and interpolation capabilities. In or&r to solve an inverse variational problem, however, a neural network must be “trained” using a set of so1uu~on.s to its corresponding forward variational problem Training a neural network typically requires hundreds, even thousands of solution sets. In this paper we show how SDM can be used to train a neural network for solving the modal sensitivity problem Because SDM only requires the modal parameters of the structure, which can be obtained from a modal test or a finite element mo&k this method can be applied in a wide variety of experimental and analytical cases.