Estimation of Structural Parameters Using Transfer Matrices and State Vectors

A new system identification (SI) method based on Transfer Matrix (TM) concept is proposed here to identify structural stiffness. Transfer matrices based on lumped mass and the more accurate consistent mass models are used here, based on displacement measurements in the time domain. The consistent mass based TM is derived from the dynamic stiffness matrix of a beam element. The state vector at a location is the sum of the internal and external contributions of displacements, forces and moments at that point - when multiplied with the (TM), we obtain the adjacent state vectors. The method of identification proposed here involves predicting the displacements at certain locations using the TM, and comparing them with the measured displacements at those locations. The mean square deviations between the measured and predicted responses at all locations are minimized using an optimization algorithm, and the optimization variables are the unknown stiffness parameters in the TM. A non-classical heuristic Particle Swarm Optimization algorithm (PSO) is used, since it is especially suited for global search. Different strategies for calculating the initial state vector, as well as two identification processes viz., simultaneous and successive methods, are discussed. Numerical simulations are carried out on four examples ranging from a simple spring mass system to a nine member framed structure. The speed and accuracy of identification using this method are good. One main advantage of this method is that it can be applied at any portion of the structure to identify the local parameters in that zone without the need to model the entire global structure.