Subspace Identification Method Incorporating Prior Information

Subspace Identification Method Incorporating Prior Information
Pavel Trnka and Vladim´ ır Havlena
Abstract — Subspace identification methods proved to be a
powerful tool, which can further benefit from the incorporation
of prior information. In the industrial environment, there is
often strong prior information about the identified system, that
can be used to improve the model quality and its compliance
with physical reality. Such prior information can be the known
static gains, the dominant time constants, the impulse response
smoothness, etc. An idea comes from the possibility to consider
the subspace identification as an optimization problem of
finding a model with the optimal multi-step predictions on
the experimental data. Further, the problem is reformulated
to the Bayesian framework allowing to combine available prior
information with the information contained in the experimental
data by covariance matrix shaping. The paper is completed with
an application to experimental data from an oil firing steam
boiler with the rated effective power of 100 MW.
I. I
NTRODUCTION
The favorable properties of Subspace State Space System
IDentification (4SID) have shown their suitability for the
industrial applications [1]. Mainly their numerical robustness
and ability to identify MIMO (Multiple Inputs Multiple
Outputs) systems with the same complexity as for SISO
(Single Input Single Output) systems without the need for
an extensive structural parameterization.
However, it is quite usual, that the input/output data
acquired from the identification experiments do not have the
sufficient quality to give a good model. This may be caused
by the fact, that the identification experiments in the indus-
trial environment are limited by the economical and safety
reasons, which results into data without proper excitation and
with strong noise contamination. The black-box approach,
such as in 4SID, relying only on the experimental data, may
fail in such cases.
In the practical applications there is often strong prior
information about the system, which can be exploited by
the identification algorithm to improve the identified model
quality. Such information can be: an approximate knowledge
of time constants, the known static gains, an integrating
character, step response smoothness etc. Incorporation of
prior information into 4SID methods will be addressed in
this article.
The previous works on subspace identification and prior
information incorporation were directed to the specific cases
[2], [3]. A more general solution is still not available. In
This work was supported by financial support of the Grant Agency of
Czech Republic under grant No. 102/05/0271 and 102/05/2075.
P. Trnka is with Honeywell Prague Laboratory, Honeywell
Intl., V Parku 2326/18, 148 00 Prague, Czech Republic
[email protected]
V. Havlena is with Honeywell Prague Laboratory, Honeywell
Intl., V Parku 2326/18, 148 00 Prague, Czech Republic
[email protected]
order to obtain a solution, the projections in the subspace
methods have to be treated in a more general way. The pro-