THE LINEAR OUTPUT RESIDUAL METHOD WITH COMPUTATIONALLY ADAPTIVE EXCITATION IN THE FREQUENCY DOMAIN—I. THEORY

Abstract

In this paper a linear parameter estimation procedure based on input and output measurements in the frequency domain is described. The method can also be used if the output measurements are not available for all the components of the mathematical model. The following problems of the method are discussed: ill-posedness (input residual method), non-linearity and the small region of attraction for the global minimum (output residual method) and unrealisable excitations (selective sensitivity). The method is based on an approximation of frequency response matrices by existing input and output measurements. These approximations are used to approximate the system responses for adaptive calculated excitations. The aim functional derived from these considerations consists of theL2-difference of the constant mathematical model response and the approximated system response for the computationally adaptive excitations. The adaptivity of the calculated excitation is chosen such that a possible bias is reduced. In the case of complete output measurements or of the sufficient excitation of the essential modes in the frequency interval under consideration, the method performs an unbiased estimate of the parameters sought.