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Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map

Tianxu Zhu Orcid Logo, Genbei Zhang, Chaoping Zang, Michael Friswell

Journal of Sound and Vibration, Volume: 569, Start page: 117998

Swansea University Author: Michael Friswell

  • Accepted Manuscript under embargo until: 8th August 2024

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DOI (Published version): 10.1016/j.jsv.2023.117998

Abstract

Global correlation analysis is an important technique to quantify both the shape and amplitude differences between two response vectors. In linear dynamic systems, differences between two Frequency Response Functions (FRFs) are quantified as scalar number curves of the Global Shape Criterion (GSC) a...

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Published in: Journal of Sound and Vibration
ISSN: 0022-460X 1095-8568
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa64063
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Abstract: Global correlation analysis is an important technique to quantify both the shape and amplitude differences between two response vectors. In linear dynamic systems, differences between two Frequency Response Functions (FRFs) are quantified as scalar number curves of the Global Shape Criterion (GSC) and the Global Amplitude Criterion (GAC), to represent FRF similarities at different frequencies. From linear to nonlinear, responses are usually obtained at different frequencies to form the Frequency Response Curve (FRC), replacing the FRF for dynamic analysis. Extending the concept of global correlation analysis from linear FRFs to nonlinear FRCs could quantify shape and amplitude similarities between nonlinear models. However, global correlation analysis for multivalued FRCs with a strong nonlinearity is hard to conduct, as strongly nonlinear correlation functions have complex multivalued phenomena with real/fake characteristics. In this paper, the Global Shape Curve Criterion (GSCC) and Global Amplitude Curve Criterion (GACC) are proposed for the correlation analysis of strongly nonlinear FRCs, which can quantify the similarity between two FRCs with different and complex multivalued phenomena. Through the arclength-based separation, multivalued FRCs are separated to single-valued response branches, in order to compute single-valued correlation functions that form the multivalued correlation function. The computed correlations contain the GSCC and GACC, which separately represent shape and amplitude differences between two FRCs at each frequency. The multivalued correlation function is represented as a Correlation-Map (C-MAP) to extract real correlation characteristics, for accurate correlation analysis. The multivalued correlation analysis is first verified on a 3 DOF model with a strong nonlinearity. Differences between the reference and initial multivalued FRCs are successfully quantified as scalar curves and the GACC may be more sensitive than the GSCC on models with a local nonlinearity. Then, the proposed method is further validated on an experimental 3 DOF model. Very complex 15-valued correlation functions between FRCs with different multivalued phenomena are established. Even so, the real correlations are still successfully extracted by the C-MAP. These show the validity and superiority of the proposed method.
Keywords: Multivalued correlation function, Multivalued frequency response curve, Strongnonlinearity, Correlation-map, Arclength-based separation
College: Faculty of Science and Engineering
Funders: The authors gratefully appreciate the financial support for this work provided by the National Natural Science Foundation of China (12072146) and the National Major Foundational Projects of Aero-engines and Gas Turbines (J2019-I-0008-0008, J2019-IV-0004-0071, J2019-Ⅳ-0023-0091). The support of the Jiangsu Province Key Laboratory of Aerospace Power System, the Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology are also gratefully acknowledged.
Start Page: 117998

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