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Major Benefits of using SSI in General
There are some technical benefits of the time domain
Stochastic Subspace Identification SSI algorithms compared to other commercially
available parametric model estimators working in the frequency domain and
relying on the estimation of half-power spectral densities. These benefits are
the same no matter if the traditional SSI algorithm or the revolutionary new
Crystal Clear SSI algorithm are used, and
with or without the use of
Automatic Mode Estimation for SSI.
Unbiased estimation – No systematic
estimation errors
No leakage – The SSI algorithms work in
time domain and are data-driven methods. Since the model estimation
is not relying on any Fourier transformations to frequency domain no
leakage is introduced. Leakage is always introduced when applying
the Fourier transformation and assuming periodicity. Leakage always
results in an unpredictable overestimation of the damping. No
problems with deterministic signals (harmonics) – Since the modal
parameters are extracted directly by fitting parameters to the raw
measured time histories, the presence of deterministic signals, such
as harmonics introduced by rotating machinery, does not create
problems. Harmonics are just estimated as very lightly damped modes.
Methods relying on the estimation of half power spectral densities
all assume that the excitation is broad-banded (white noise), and
the presence of deterministic signals introduce bias in the modal
parameter estimation.
Less random errors
Low-order model estimator - SSI algorithms
are born linear least-squares fitting techniques fitting state space
systems with correct noise modeling. This leads to the use of much
smaller model orders than other commercially available high order
model estimators. These estimators are often used to approximate a
non-linear least squares problem with a linear least-squares fitting
problem. This is an often seen approximation when fitting e.g.
polynomial matrix fractions. In order for this approximation to
work, a high-order polynomial order is needed. Since this leads to
the use of many parameters compared to a low-order technique, the
uncertainties of the high-order parameter estimates becomes larger.
More parameters are fitted with the same amount of data available,
meaning less independent information per estimated parameter. All
modal parameters are fitted in one operation. All parameters fitted
are taking advantage of the noise cancellation techniques of the
orthogonal projection of SSI. Other commercially available methods
often fit the poles (frequency and damping) first, and then use the
noisy spectral data and the estimated poles to fit the mode shapes
resulting in poor mode shape estimates.
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