I am trying to identify the transfer matrix of a TRMS and I have a set of estimation and validation data. However, I have two types of validation data, one set has been derived by applying the same type of input (as that of estimation data) to the system but at a different time and another one which includes an entirely different form of input. Which one would be a better choice as a validation data ?
The identification consists in applying or observing disturbance signals at the input of a system (for example for an electronic system, these can be of random or pseudo-random binary type, galois, sinus at multiple frequencies. .) and analyze the output in order to obtain a purely mathematical model. The different parameters of the model do not correspond to any physical reality in this case. The identification can be done either in time (time space) or in frequency (Laplace space). Avoiding purely theoretical models based on physical equations (usually differential equations), which are slow to obtain and often too complex for the given development time, is therefore possible with this technique.
** you can also consult MATLAB help; and also this link: http://www.gipsa-lab.grenoble-inp.fr/~ioandore.landau/identificationandcontrol/french/Transparents/Livre/Chapitre%20V.pdf
good luck
The answer is yes. Typically ID data and verification data should be different sequences. For instance you may take 2000 samples, use the first 1500 for ID and the rest for validation. Otherwise, validating the computed model with the same data is meaningless since you have already found the best fit to your data.
I'm inclined to say a direct 'yes'. But in reality one should be look at the intent of the identification itself. Some questions should be asked:
- Is the 'different' input affecting the system in question in the same region of interest as estimation input (e.g frequency range)? If so, it should have been included in the first place (through doing collinearity between dependent and independant variables).
- Is the 'different' input have a different signal-to-noise ratio as the validation input. If so, it would be prudent to analyze the estimated system from a robustness to external disturbances point of view.
If ultimately, it's not a question of which one is a 'better choice', but rather how much confidence do I have in my estimated model irrespective of the dataset used (besides the one used for estimation of course).
System Identification is an experimental approach for building dynamic model of a physical system. It is based on four main steps which are structure selection of the model tothe system to be identified, choice of the excitation signal, parametric estimation and validation.
1. The structure of the models can be classified into several categories depending on the system to be identified : monovariable or multivariable, deterministic or stochastic, continuous or discrete time, linear or nonlinear, stationary or non-stationary, parametric or non-parametric.
2. The choice of an excitation signal represents a fundamental problem for the identification of both linear and non-linear systems. Most of the existing methods for identifying these models assume that the input signal is of the white noise type. This type of signal is very interesting from the theoretical point of view because of its statistical properties. But, its practical use is not recommended. To overcome this problem, new sequences have been developed. Among them, we distinguish the pseudo-random binary sequence (PRBS) which is widely used for the identification of linear systems. The parameters are set taking into account only the dynamics of the system to be identified. Therefore, it can not be applied in the case of non-linear systems because they also require a judicious choice of excitation amplitudes to cover the entire operating range of the system to identify. An obvious solution to this problem is to extend the PRBS sequence at different amplitudes. This leads to an amplitude modulated PRBS sequence. The number of amplitudes contained in the excitation signal depends on the structure of the model. For example, this number must be equal to (N + 1) for a Volterra model of order N. Other types of signals such as sum of sinusoids, multi-pulses are also used.
3. The estimation of the parameters is generally performed by the application of linear or non-linear optimization techniques. Indeed, it consists in looking for a vector of the parameters θ minimizing a criterion J (θ) which is also known by the cost function. Many criteria based on the output error or on the prediction error are possible, the most widespread is the criterion of the minimum of the quadratic error which depends on the output error. This is the most commonly used, given its simplicity of implementation. Several methods of linear optimization or not ensure the minimization of the chosen criterion.
4. Validation is a necessary step since it makes it possible to check whether all the previous steps have been successfully completed or not. If the application of the data used in the previous steps to the model does not give satisfactory results, then the obtained model can not be accepted. In this case, we must review either the choice of excitation signals or the choice of the model. A direct method of validating a model is to test its generalization capabilities by validating the model on data different from those used in the previous steps. Generally, we divide the identification data in two sets. The first one is used to identify the parameters and the second is used to validate the models based on some criteria such errors, mean square error, etc.
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