A matrix projection method for on line stable estimation of 1D and 3D shear building models

An estimation method is presented that combines the use of recursive least squares, a matrix parameterized model, Gershgorin circles and tridiagonal matrices properties to allow the identification of stable shear building models in the presence of low excitation or low damping. The resultant scheme yields a significant reduction on the number of calculations involved, when compared with the standard vector parameterization based schemes. As real buildings are always open loop stable, the use of an stable shear building model for vibration control purposes allows the design of more robust control laws. Extensive simulation results are presented for cases of low excitation comparing the results of using or not this matrix projection method with different sets of initial conditions. Results indicate that the use of this projection method does not have an influence in the recovery of natural frequencies, however, it significantly improves the recovery of mode shapes.