id_np.sq

Non-parametric identification

First contact

SQ file id_np.sq provides the identification methods to obtain a non-parametric model based on the measured input and output of an unknown system. Identification can be performed in the time domain or the frequency domain. The data can be retrieved from a file (typically created by an external real-time acquisition program) or generated by the SQ file.

For didactic purposes, synthetic data can be created for input U and output Y. The input is either white noise (each sample is a pseudo-random number chosen from a normal distribution), a pseudo-random binary sequence (each sample is 1 or -1 with a probability of 0.5), or a pseudo-random binary sequence where the probability to switch at each sample is 0.2 or 0.05 (colored noise). The output is Y = G * U + N, where G is the impulse response of a transfer function specified by the user (0.1/(z-0.9) by default) and N some white noise whose level can be adjusted.

Time-domain identification with correlation analysis

The covariance of the input Ruu and the cross covariance between the input and the output Ruy are calculated. If the input is white, Ruy is an approximation of the impulse response of the system, times a scalar factor. The input can be whitened with a finite-impulse response (FIR) filter.

Frequency-domain identification with spectral analysis

The spectrum of the system can be approximated either by dividing the output's discrete Fourier transform (FFT) by the input's, or (better if the output is disturbed by noise) by dividing Ruy's FFT (cross spectrum) by Ruu's (input's spectrum). The data can be split, so that the average of the FFT of each block of data is used. A time window is applied to each block to reduce the effect of the finite number of samples.

Remark: the splitting in n sequences is used only by the spectral analysis. The time window is used for all frequency-domain analysis methods, while the whitening filter is used only for correlation analysis.

Settings

System

The system used to create synthetic sampled data is given as the numerator and denominator of a discrete-time transfer function in positive powers of z.

Number of samples

Total number of samples which should be created.

White Noise or Pseudo-Random Binary Sequence

For synthetic data, the system input can be chosen among white noise, where each sample is the result of a normally distributed pseudo-random generator, or a pseudo-random binary sequence where the probability to switch the level at each sample is 50%, 20% or 5%. With 20% or 5%, the signal is significantly different from white noise.

Whitening Filter

For the correlation analysis, a whitening filter should be used if the system input is significantly different from white noise. The whitening filter is a finite-impulse response (FIR) filter whose inverse is the auto-regressive (AR) model which gives the non-white input. The whitening filter is not used for frequency-domain identification.

Rectangular/Triangular/Hann/Hamming Window

To reduce the effect of the finite number of samples (aliasing), a non-rectangular window can be applied to the input and output samples. The Hann and Hamming windows have a sinusoidal shape. The windows are not used for time-domain identification.

Multiple Sequences

For frequency-domain identification, it may be better to split the available data and use the different sequences to reduce the variance of the estimation. The price to pay is the lower resolution of the estimate. The number of sequences is set by moving the green vertical lines in the input or output figure.

Read Data File

The measurements are read from a text file, typically created by an acquisition program. This file should contain an array of two column (separated by spaces or tabulators) by n row (separated by carriage returns and/or line feeds). The first column corresponds to the system input, and the second column to the system output. Each row corresponds to a sample.