System Identification Toolbox

Compare Measured and Model Output

A very good way of obtaining insight into the quality of a model is to simulate it with the input from a fresh data set, and compare the simulated output with the measured one. This gives a good feel for which properties of the system have been picked up by the model, and which haven't.

This test is obtained by checking the Model View Model Output. Then the data set currently in the Validation Data box will be used for the comparison. The fit will also be displayed. This is computed as the percentage of the output variation that is reproduced by the model. So, a model that has a fit of 0% gives the same mean square error as just setting the model output to be the mean of the measured output.

If the model is unstable, or has integration or very slow time constants, the levels of the simulated and the measured output may drift apart, even for a model that is quite good (at least for control purposes). It is then a good idea to evaluate the model's predicted output rather than the simulated one. With a prediction horizon of k, the k-step ahead predicted output is then obtained as follows:

The predicted value y(t) is computed from all available inputs (used according to the model) and all available outputs up to time t-k,. The simulation case, where no past outputs at all are used, thus formally corresponds to k=. To check if the model has picked up interesting dynamic properties, it is wise to let the predicted time horizon (kT, T being the sampling interval) be larger than the important time constants.

Note here that different models use the information in past output data in their predictors in different ways. This depends on the disturbance model. For example, so called Output-Error models (obtained by fixing K to zero for state-space models and setting na=nc=nd=0 for input output models, see the previous section) do not use past outputs at all. The simulated and the predicted outputs, for any value of k, thus coincide.

Poles and Zeros

Residual Analysis