using multi-experiment data using 'merge'

Hi there, I have a set of experimental data sets and I want to train a single model using all of these experiments. I am using 'merge' to create a 'multi-experiment' iddata object but would really like to know exactly how the identification routines (for example armax/pem/arx) treat this multi-experiment data to obtain a single model.

[Johannes Lips]

Although @Rajiv Singh already provided part of the answer by stating that a single cost function is used in multi-experiment iddatasets, I would be interested in seeing the underlying formula explicitly, on the help pages I only found this as relevant info: https://de.mathworks.com/help/ident/ug/dealing-with-multi-experiment-data-and-merging-models.html

Could someone provide a link to a page with the cost function written out for system identification of multi-experiment iddata objects?

Answer 1

[Violeta]

bump

Answer 2

[Rajiv Singh]

Multi-experiment data give you an opportunity to use multi data sets together for estimation. All data sets should have identical sample time, inter-sample behavior for inputs and start-time (do not use "merge" to combined data slices from different time ranges).

Estimation routines work by minimizing the prediction or simulation error. The minimization objective function is a weighted norm of this error. If you have multi-experiment data, the error vector is formed over the entire collection of experiments, assigning equal weight to observations in each experiment (in general; some experiment-specific modification may apply in some cases, such as when using LimitError>0).

Did you want to know something more specific?

Rajiv

[Yujiang Wu]

Hi, thanks for the reply. Then in terms of mimizing the cost function (min square error of the simulation error for example), what's the difference between merging multiexperiement and a (concatenated) super long data regord. If I have two experiemnts in a single iddata object that are used for estimation, does it estimate the model using the exp1 first, then use the estimated result as a starting point and estimate (refine) the parameters again using exp2. Then use the final obtained parameters to compute fitting error for ep1 and ep2.

What confused me a little bit is that we obtain a single estimated model based on multiple expriments, but we will also get different fitting results or different min square error for each single experiments. Ideally, I would expect a single fitting error describe the performance over all these experments. If we truly estimate the model using a super long data record, we will end up a single fitting error or a single minimized cost.

But it seems we don't have a sinlge cost when using a multiexperiments iddata. Can you explain more on this? Thanks.