Uncertainty laws of experimental modal analysis with known broadband input

‘Uncertainty law’ aims at closed-form asymptotic formulas for the relationship between the identification uncertainties of modal properties (e.g., natural frequency, damping ratio) and test configuration (e.g., noise level, number and location of sensors, data duration). Existing developments focuse...

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Main Authors: Ng, Ching-Tai, Wang, Peixiang, Au, Siu-Kui, Li, Binbin
Other Authors: School of Civil and Environmental Engineering
Format: Article
Language:English
Published: 2023
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Online Access:https://hdl.handle.net/10356/171047
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Institution: Nanyang Technological University
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spelling sg-ntu-dr.10356-1710472023-10-13T15:33:55Z Uncertainty laws of experimental modal analysis with known broadband input Ng, Ching-Tai Wang, Peixiang Au, Siu-Kui Li, Binbin School of Civil and Environmental Engineering Engineering::Civil engineering Forced Vibration Test Uncertainty Laws BAYOMA Signal-to-Noise Ratio Experimental Modal Analysis ‘Uncertainty law’ aims at closed-form asymptotic formulas for the relationship between the identification uncertainties of modal properties (e.g., natural frequency, damping ratio) and test configuration (e.g., noise level, number and location of sensors, data duration). Existing developments focused on the case of unknown-input (ambient), where it has been found that identification uncertainty does not vanish even for noiseless instruments, essentially because the input is unknown. A natural question is then on how the uncertainty depends on test configuration when the input is known, not to mention how the configuration should be quantified. Motivated by these and related questions, this paper develops the uncertainty laws of modal parameters for well-separated modes with known single broadband input, e.g., vibration test with a single shaker as in experimental modal analysis. Asymptotic expressions for the posterior coefficient of variation of modal parameters are derived via the Fisher Information Matrix for long data and small damping scenarios. Assumptions and theory are validated using synthetic and field test data. Governing factors motivated by the theory are investigated, including the equivalent modal signal-to-noise ratio (for known input), the number of measured degrees of freedom, shaker location, and data duration. By virtue of the Cramér-Rao bound in classical statistics, the developed uncertainty laws represent the lower bound of identification uncertainty with known broadband input that can be achieved by any unbiased estimator. They provide a scientific basis for planning and managing identification uncertainties in vibration tests with known input. Ministry of Education (MOE) Submitted/Accepted version This research is supported by the Natural Science Foundation of Zhejiang Province (LY21E080025; Wang & Li), Fundamental Research Funds for the Central Universities (2021XZZX040; Li) and Academic Research Fund Tier 1 (RG68/22; Au) from the Ministry of Education, Singapore. 2023-10-13T05:42:55Z 2023-10-13T05:42:55Z 2023 Journal Article Ng, C., Wang, P., Au, S. & Li, B. (2023). Uncertainty laws of experimental modal analysis with known broadband input. Mechanical Systems and Signal Processing, 204, 110624-. https://dx.doi.org/10.1016/j.ymssp.2023.110624 0888-3270 https://hdl.handle.net/10356/171047 10.1016/j.ymssp.2023.110624 204 110624 en RG68/22 Mechanical Systems and Signal Processing © 2023 Elsevier Ltd. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1016/j.ymssp.2023.110624. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Civil engineering
Forced Vibration Test
Uncertainty Laws
BAYOMA
Signal-to-Noise Ratio
Experimental Modal Analysis
spellingShingle Engineering::Civil engineering
Forced Vibration Test
Uncertainty Laws
BAYOMA
Signal-to-Noise Ratio
Experimental Modal Analysis
Ng, Ching-Tai
Wang, Peixiang
Au, Siu-Kui
Li, Binbin
Uncertainty laws of experimental modal analysis with known broadband input
description ‘Uncertainty law’ aims at closed-form asymptotic formulas for the relationship between the identification uncertainties of modal properties (e.g., natural frequency, damping ratio) and test configuration (e.g., noise level, number and location of sensors, data duration). Existing developments focused on the case of unknown-input (ambient), where it has been found that identification uncertainty does not vanish even for noiseless instruments, essentially because the input is unknown. A natural question is then on how the uncertainty depends on test configuration when the input is known, not to mention how the configuration should be quantified. Motivated by these and related questions, this paper develops the uncertainty laws of modal parameters for well-separated modes with known single broadband input, e.g., vibration test with a single shaker as in experimental modal analysis. Asymptotic expressions for the posterior coefficient of variation of modal parameters are derived via the Fisher Information Matrix for long data and small damping scenarios. Assumptions and theory are validated using synthetic and field test data. Governing factors motivated by the theory are investigated, including the equivalent modal signal-to-noise ratio (for known input), the number of measured degrees of freedom, shaker location, and data duration. By virtue of the Cramér-Rao bound in classical statistics, the developed uncertainty laws represent the lower bound of identification uncertainty with known broadband input that can be achieved by any unbiased estimator. They provide a scientific basis for planning and managing identification uncertainties in vibration tests with known input.
author2 School of Civil and Environmental Engineering
author_facet School of Civil and Environmental Engineering
Ng, Ching-Tai
Wang, Peixiang
Au, Siu-Kui
Li, Binbin
format Article
author Ng, Ching-Tai
Wang, Peixiang
Au, Siu-Kui
Li, Binbin
author_sort Ng, Ching-Tai
title Uncertainty laws of experimental modal analysis with known broadband input
title_short Uncertainty laws of experimental modal analysis with known broadband input
title_full Uncertainty laws of experimental modal analysis with known broadband input
title_fullStr Uncertainty laws of experimental modal analysis with known broadband input
title_full_unstemmed Uncertainty laws of experimental modal analysis with known broadband input
title_sort uncertainty laws of experimental modal analysis with known broadband input
publishDate 2023
url https://hdl.handle.net/10356/171047
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