Improved (non-)parametric identification of dynamic systems excited by periodic signals

Recently [1] a method has been developed to suppress nonparametrically the noise (and system) transients (leakage errors) in frequency response function and noise (co-)variance estimates of single-input, single-output systems excited by periodic signals. This paper extends the results of [1] to multiple-input, multiple-output systems where all inputs and outputs are disturbed by noise (i.e. an errors-in-variables framework). Two methods are presented: the first starts from multiple experiments with uncorrelated sets of inputs, and makes no assumption about the frequency response matrix (FRM); while the second only requires one single experiment, but assumes that the FRM can locally be approximated by a polynomial. Both methods estimate simultaneously the FRM, the noise level, and the level of the nonlinear distortions. For lightly damped systems, the proposed methods either significantly reduce the experiment duration or, for a given measurement time, significantly increase the frequency resolution of the FRM estimate. If the noise (and/or system) transients are the dominant error sources, then the proposed methods also significantly reduce the covariance matrix of the FRM estimates. The use of the nonparametric noise covariance estimates for parametric transfer function modelling is also discussed in detail.

...After truncation of the model structure in practice to a certain order, we will see that it is possible to obtain high quality nonparametric estimates of the HTF’s and their corresponding uncertainties via a fast LTI multi-input single-output (MISO) technique [17]...
...Further we have the advantage that the identification algorithm works for discretetime systems as well [17], because many of the advantages associated with the MIMO technique described in [17] are inherited...
...Further we have the advantage that the identification algorithm works for discretetime systems as well [17], because many of the advantages associated with the MIMO technique described in [17] are inherited...
...One of the interesting benefits of using multisine excitation is that multisines are able to split the nonlinear distortion from the noise in MIMO sytems [17], while this is not possible for arbitrary inputs [20], [21]...
...It can be observed from Figure 1 that the model being used for LPTV systems can be represented by a MISO LTI-system with shifted versions of the input spectrum U (ω) as input signals, as such improved nonparametric estimation schemes that are recently developed [20], [21], [17] for MIMO systems could succesfully be utilized...
...The reader is referred to [17], [20], [21] for a detailed theoretical analysis of the method...
...where E(k) stands for a white noise source, HZ(ωk) for a stable noise filter and TZ(ωk) the remaining noise leakage error due to the finite length of the DFT of the noise [17]; we get as frequency domain input-output description:...
...the frequency response matrix (FRM) from R(k) to Z(k) [17]...
...The noise transient term TZ(ωk) appearing in (9), which is an O(N −1/2 ), can be eliminated nonparametrically [17]...
...can be caluculated from the residuals [17], [20], [21]...
...The theory in [17], [20], [21] predicts that the bias of the estimate behaves as an O((l/N) 3 ); which means that doubling the...

Keywords (13)

Improved (non-)parametric identification of dynamic systems excited by periodic signals—The multivariate case,10.1016/j.ymssp.2010.10.019,Mechanical S

Citation Context (2)

Maarten Schoukens, et al. Parametric Identification of Parallel Hammerstein Systems

E. Louarroudi, et al. Estimation of nonparametric harmonic transfer functions for linear per...

References (3)

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Citations (2)

Parametric Identification of Parallel Hammerstein Systems (Citations: 1)

Estimation of nonparametric harmonic transfer functions for linear periodically time-varying systems using periodic excitations


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