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You can use the following approaches to validate models:
Comparing simulated or predicted model output to measured output.
To simulate identified models in the Simulink® environment, see Simulating Identified Model Output in Simulink.
Analyzing autocorrelation and cross-correlation of the residuals with input.
See Residual Analysis.
Analyzing model response. For more information, see the following:
For information about the response of the noise model, see Noise Spectrum Plots.
Plotting the poles and zeros of the linear parametric model.
For more information, see Pole and Zero Plots.
Comparing the response of nonparametric models, such as impulse-, step-, and frequency-response models, to parametric models, such as linear polynomial models, state-space model, and nonlinear parametric models.
Note: Do not use this comparison when feedback is present in the system because feedback makes nonparametric models unreliable. To test if feedback is present in the system, use the advice command on the data.
Compare models using Akaike Information Criterion or Akaike Final Prediction Error.
Plotting linear and nonlinear blocks of Hammerstein-Wiener and nonlinear ARX models.
Displaying confidence intervals on supported plots helps you assess the uncertainty of model parameters. For more information, see Computing Model Uncertainty.
For plots that compare model response to measured response and perform residual analysis, you designate two types of data sets: one for estimating the models (estimation data), and the other for validating the models (validation data). Although you can designate the same data set to be used for estimating and validating the model, you risk over-fitting your data. When you validate a model using an independent data set, this process is called cross-validation.
Note: Validation data should be the same in frequency content as the estimation data. If you detrended the estimation data, you must remove the same trend from the validation data. For more information about detrending, see Handling Offsets and Trends in Data.
The following table summarizes the types of supported model plots.
|Plot Type||Supported Models||Learn More|
|Model Output||All linear and nonlinear models||Simulating and Predicting Model Output|
|Residual Analysis||All linear and nonlinear models||Residual Analysis|
|Transient Response||Impulse and Step Response Plots|
All linear models
|Frequency Response Plots|
|Noise Spectrum||Noise Spectrum Plots|
|Poles and Zeros||All linear parametric models||Pole and Zero Plots|
|Nonlinear ARX||Nonlinear ARX models only||Nonlinear ARX Plots|
|Hammerstein-Wiener||Hammerstein-Wiener models only||Hammerstein-Wiener Plots|
You can display the confidence interval on the following plot types:
|Plot Type||Confidence Interval Corresponds to the Range of ...||More Information on Displaying Confidence Interval|
|Simulated and Predicted Output||Output values with a specific probability of being the actual output of the system.||Model Output Plots|
|Residuals||Residual values with a specific probability of being statistically insignificant for the system.||Residuals Plots|
|Impulse and Step||Response values with a specific probability of being the actual response of the system.||Impulse and Step Plots|
|Frequency Response||Response values with a specific probability of being the actual response of the system.||Frequency Response Plots|
|Noise Spectrum||Power-spectrum values with a specific probability of being the actual noise spectrum of the system.||Noise Spectrum Plots|
|Poles and Zeros||Pole or zero values with a specific probability of being the actual pole or zero of the system.||Pole-Zero Plots|