User`s guide

Modeling Multiple-Output Systems
After validating the single-output models, use vertical concatenation to
combine these partial models into a single multiple-output m odel. For more
information about concate na tion, see “Conc aten a tin g iddat a Objec ts” on page
1-65 or “Concatenating idfrd Objects” on page 1-71.
You can try refining the concatenated multiple-output model u sing the
origina l (mu lti pl e- output) data set.
Improving Multiple-Output Estimation Results by
Weighing Outputs During Estimation
When estimating linear and nonlinear black-box models f or multiple-output
systems, you can control the relative importance of output channels during
the estima t ion process. The ability to control how much each output is
weighed during estimation is useful when some of the measured outputs
have poor accuracy or should be treated as less important during estimation.
For exam p le , if you ha ve already modeled one output w ell, you might want
to focus the estimation on modeling the remaining outputs. Similarly, you
mightwanttorefine a model for a subset of outputs.
You can s pe c if y outpu t weights directly in the esti mation command using
the
Criterion and W eigh ting fields of the Algorithm property. You must
set the
Criterion field to Trace, and set the Weighti ng field to the matrix
that contains the output weights. The
Trace criterion minimizes the weighted
sum of the prediction errors using the weights speci fied by
Weighting.
The following code snippet shows how to specify the
Criterion and Weigh ting
Algorithm
fields as part of the pem command:
model=pem(z,2,'criterion','trace','we ighting',diag(Q,1))
where Q is a vector of positive values and the higher values for outputs to be
emphasized more during estimation.
You set
Weighting to a positive semi-definite symmetric matrix of size equal
to number of outputs. By default,
Weighting is an identity matrix, which
means that all outputs are weighed equally during estimation.
For more information about these Algorithm fieldsforlinearestimation,see
the
Algorithm Prope rtie s reference page. For more information about
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