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

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 approx...

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Bibliographic Details
Published inIEEE transactions on instrumentation and measurement Vol. 69; no. 10; pp. 8600 - 8612
Main Authors Pintelon, Rik, Schoukens, Maarten, Lataire, John
Format Journal Article
LanguageEnglish
Published New York IEEE 01.10.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Approximation
Best linear approximation (BLA)
Closed loops
Continuous time systems
continuous-time
Discrete Fourier transforms
Discrete time systems
Distortion measurement
feedback
frequency response function (FRF)
Frequency response functions
Kernel
Linear approximation
Mathematical analysis
Noise
Noise measurement
Nonlinear distortion
Nonlinear response
Nonlinear systems
nonparametric estimation
Nonparametric statistics
process noise
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Summary: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 article, 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 an open loop.
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ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2020.2987476