An adaptive learning approach to the identification of structural and mechanical systems

AbstractThe identification of parameters in models of structural and mechanical systems is an important problem. The usual approaches are successive approximation schemes which require good initial guesses for rapid convergence. This paper shows how such initial approximations may be obtained. Notions from the field of artificial neural networks are used. In fact, new adaptive schemes for learning are presented and used in parameter estimation for both linear and nonlinear systems

INVERSE PROBLEM FOR LAGRANGIAN DYNAMICS FOR MULTI-DEGREE-OF- FREEDOM SYSTEMS WITH LINEAR DAMPING

ABSTRACT This paper deals with the inverse problem for Lagrangian dynamics for linear multi-degree-of-freedom systems. New results for linearly damped systems are obtained using extensions of results for single-degree-of-freedom systems. First, for a two-degree-of-freedom linear system with linear damping, the conditions for the existence of a Lagrangian are explicitly obtained by solving the Helmholtz conditions. Next, since the Helmholtz conditions are near-impossible to solve for general n-degree-of-freedom systems, a new simple procedure that does not require the use of the Helmholtz conditions and that is easily extended to n-degree-of-freedom linear systems, is developed. The emphasis is on obtaining the Lagrangians for these multi-degree-of-freedom systems in a simple manner, using insights obtained from our understanding of the inverse problem for single-and two-degree-of-freedom systems. Specifically we include systems that commonly arise in linear vibration theory with positive definite mass matrices, and symmetric stiffness and damping matrices. This method yields several new Lagrangians for linear multi-degree-of-freedom systems. Finally, conservation laws for these damped multidegree-of-freedom systems are found using the Lagrangians obtained

The identification of building structural systems. I. The linear case

This paper investigates the response of structural systems to strong earthquake ground shaking by utilizing some concepts of system identification. After setting up a suitable system model, the Weiner technique of nonparametric identification has been introduced and its experimental applicability studied. The sources of error have been looked into and several new results have been presented on accuracy calculations stemming from the various assumptions in the Wiener technique. The method has been applied in studying the response of a 9-story reinforced concrete structure to earthquake excitation as well as ambient vibration testing. The linear contribution to the total roof response during strong ground shaking has been identified, and it is shown that a marked nonlinear behavior is exhibited by the structure during the strong-motion portion of the excitation

When Does a Dual Matrix Have a Dual Generalized Inverse?

This paper deals with the existence of various types of dual generalized inverses of dual matrices. New and foundational results on the necessary and sufficient conditions for various types of dual generalized inverses to exist are obtained. It is shown that unlike real matrices, dual matrices may not have {1}-dual generalized inverses. A necessary and sufficient condition for a dual matrix to have a {1}-dual generalized inverse is obtained. It is shown that a dual matrix always has a {1}-, {1,3}-, {1,4}-, {1,2,3}-, {1,2,4}-dual generalized inverse if and only if it has a {1}-dual generalized inverse and that every dual matrix has a {2}- and a {2,4}-dual generalized inverse. Explicit expressions, which have not been reported to date in the literature, for all these dual inverses are provided. It is shown that the Moore–Penrose dual generalized inverse of a dual matrix exists if and only if the dual matrix has a {1}-dual generalized inverse; an explicit expression for this dual inverse, when it exists, is obtained irrespective of the rank of its real part. Explicit expressions for the Moore–Penrose dual inverse of a dual matrix, in terms of {1}-dual generalized inverses of products, are also obtained. Several new results related to the determination of dual Moore-Penrose inverses using less restrictive dual inverses are also provided