ESDU 93016:2010

This Data Item implements a Fortran computer program for the
parameter estimation of linear systems from frequency response
measurements. The method is primarily based on the procedure
described in ESDU 90006 but has been modified to account for the
effects of residual modes of response, i.e. gain and phase
variations of modes whose effects lie predominantly outside the
range of frequencies of the analysis data but which nevertheless
have an influence within the range of analysis.

The system is assumed modelled as a set of lightly-damped
coupled second-order differential equations with constant
coefficients and the response determined from solution of these
equations is equivalent to the sum of the responses of a related
set of single degree-of-freedom systems. It is also assumed that a
set of frequency response measurements is available from forced
harmonic excitations of the system and that these measurements
encompass the major response activity of the modes to be
identified. The method has been implemented as an automatic
computer-based procedure, but relies on a visual inspection of a
Nyquist plot of the measurement data to provide initial estimates
of the resonant frequency of each mode of response together with
the frequency bands of data associated with each mode. The computer
program has been written to deal with a single-input single-output
system where displacement measurements obtained at different
positions in the system are treated separately.

The program evaluates initial estimates of the natural frequency
and damping ratio of each mode together with the coefficients of
the complex forcing functions and residual terms. These values
provide a starting point for a nonlinear parameter estimation
procedure using a Newton-Gauss algorithm. Examples illustrate the
use of the computer program to estimate the parameters of systems
containing both two and four degrees-of-freedom.

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