A Nonparametric Regularization for Spectrum Estimation of Time-Varying Output-Only Measurements

In this work, an advanced 2D nonparametric correlogram method is presented to cope with output-only measurements of linear (slow) time-varying systems. The proposed method is a novel generalization of the kernel function-based regularization techniques that have been developed for estimating linear...

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Bibliographic Details
Published in:Vibration 2024-03, Vol.7 (1), p.161-176
Main Authors: Csurcsia, Péter Zoltán, Ajmal, Muhammad, De Troyer, Tim
Format: Article
Language:English
Subjects:
autocorrelation
Computer simulation
Computer-generated environments
Cost function
Cross correlation
Engineering models
Estimates
Estimation
Fourier transforms
Identification
Impulse response
industrial measurements
Kernel functions
Measurement
Methods
nonparametric methods
Nonparametric tests
Operational Modal Analysis
Regularization
Regularization methods
Response functions
Robustness (mathematics)
Smoothness
Spectral energy distribution
Statistics
System identification
Time measurement
time-varying structures
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Description
Summary:In this work, an advanced 2D nonparametric correlogram method is presented to cope with output-only measurements of linear (slow) time-varying systems. The proposed method is a novel generalization of the kernel function-based regularization techniques that have been developed for estimating linear time-invariant impulse response functions. In the proposed system identification technique, an estimation method is provided that can estimate the time-varying auto- and cross-correlation function and indirectly, the time-varying auto- and cross-correlation power spectrum estimates based on real-life measurements without measuring the perturbation signals. The (slow) time-varying behavior means that the dynamic of the system changes as a function of time. In this work, a tailored regularization cost function is considered to impose assumptions such as smoothness and stability on the 2D auto- and cross-correlation function resulting in robust and uniquely determined estimates. The proposed method is validated on two examples: a simulation to check the numerical correctness of the method, and a flutter test measurement of a scaled airplane model to illustrate the power of the method on a real-life challenging problem.
ISSN:2571-631X
2571-631X
DOI:10.3390/vibration7010009