Structure discrimination in block-oriented models using linear approximations: A theoretic framework

In many engineering applications the level of nonlinear distortions in frequency response function (FRF) measurements is quantified using specially designed periodic excitation signals called random phase multisines and periodic noise. The technique is based on the concept of the best linear approximation (BLA) and it allows one to check the validity of the linear framework with a simple experiment. Although the classical BLA theory can handle measurement noise only, in most applications the noise generated by the system -called process noise -is the dominant noise source. Therefore, there is a need to extend the existing BLA theory to the process noise case. In this paper we study in detail the impact of the process noise on the BLA of nonlinear continuous-time systems operating in a closed loop. It is shown that the existing nonparametric estimation methods for detecting and quantifying the level of nonlinear distortions in FRF measurements are still applicable in the presence of process noise. All results are also valid for discrete-time systems and systems operating in open loop.

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“…Note that the observed process noise (14) might depend on the actual realization of the reference r(t). This is a major difference w.r.t.…”

Section: A Definition and Propertiesmentioning

confidence: 99%

Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback

Pintelon

Schoukens

Lataire

2020

IEEE Trans. Instrum. Meas.

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“…Approximating nonlinear systems for topology detection is not a new idea and various approaches exist [5,6] , but a common thread is the definition of an optimality criterion for the approximation that holds within a given class of systems and under a certain class of excitation signals. In the present work, the Best Linear Approximation (BLA) of Volterra nonlinear systems is exploited, assuming Gaussian excitation signals [7] .…”

Section: Introductionmentioning

confidence: 99%

Locating Nonlinearity in Mechanical Systems: A Dynamic Network Perspective

Noël

Schoukens

Hof

2018

Nonlinear Dynamics, Volume 1

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Though it is a crucial step for most identification methods in nonlinear structural dynamics, nonlinearity location is a sparsely addressed topic in the literature. In fact, locating nonlinearities in mechanical systems turns out to be a challenging problem when treated nonparametrically, that is, without fitting a model. The present contribution takes a new look at this problem by exploiting some recent developments in the identification of dynamic networks, originating from the systems and control community.

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“…As nonlinear mechanisms in structures are complex and various and as it is not intended here to build a model for each case, it is chosen to rely on black-box models. Among these black-box approaches, some assume a given form for the selected model (block-oriented models [2,10,5,28]) whereas some do not put constraints on the model structure. Because block-oriented models can be interpreted easily, this class of models has been retained.…”

Section: Introductionmentioning

confidence: 99%

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

Rébillat

Schoukens

2018

Mechanical Systems and Signal Processing

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Linearity is a common assumption for many real-life systems, but in many cases the non-linear behavior of systems cannot be ignored and must be modeled and estimated. Among the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are interesting as they are at the same time easy to interpret as well as to estimate. One way to estimate PHM relies on the fact that the estimation problem is linear in the parameters and thus that classical least squares (LS) estimation algorithms can be used. In that area, this article introduces a regularized LS estimation algorithm inspired on some of the recently developed regularized impulse response estimation techniques. Another mean to estimate PHM consists in using parametric or non-parametric exponential sine sweeps (ESS) based methods. These methods (LS and ESS) are founded on radically different mathematical backgrounds but are expected to tackle the same issue. A methodology is proposed here to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii) their robustness to noise. Tests are performed on simulated systems for several values of methods respective parameters and of signal to noise ratio. Results show that, for a given set of data points, the ESS method is less demanding in computational resources than the LS method but that it is also less accurate. Furthermore, the LS method needs parameters to be set in advance whereas the ESS method is not subject to conditioning issues and can be fully non-parametric. In summary, for a given set of data points, ESS method can provide a first, automatic, and quick overview of a nonlinear system than can guide more computa-tionally demanding and precise methods, such as the regularized LS one proposed here.

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Structure discrimination in block-oriented models using linear approximations: A theoretic framework

Cited by 30 publications

References 20 publications

Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback

Best Linear Approximation of Nonlinear Continuous-Time Systems Subject to Process Noise and Operating in Feedback

Locating Nonlinearity in Mechanical Systems: A Dynamic Network Perspective

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation

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