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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

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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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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.</abstract><type>Journal Article</type><journal>Journal of Sound and Vibration</journal><volume>569</volume><journalNumber/><paginationStart>117998</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0022-460X</issnPrint><issnElectronic>1095-8568</issnElectronic><keywords>Multivalued correlation function, Multivalued frequency response curve, Strongnonlinearity, Correlation-map, Arclength-based separation</keywords><publishedDay>20</publishedDay><publishedMonth>1</publishedMonth><publishedYear>2024</publishedYear><publishedDate>2024-01-20</publishedDate><doi>10.1016/j.jsv.2023.117998</doi><url>http://dx.doi.org/10.1016/j.jsv.2023.117998</url><notes/><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><apcterm/><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.</funders><projectreference/><lastEdited>2024-09-05T12:02:59.0544602</lastEdited><Created>2023-08-09T09:49:30.2648645</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering</level></path><authors><author><firstname>Tianxu</firstname><surname>Zhu</surname><orcid>0000-0003-2511-2677</orcid><order>1</order></author><author><firstname>Genbei</firstname><surname>Zhang</surname><order>2</order></author><author><firstname>Chaoping</firstname><surname>Zang</surname><order>3</order></author><author><firstname>Michael</firstname><surname>Friswell</surname><order>4</order></author></authors><documents><document><filename>64063__28276__ba9a6be147bd4f55ac1802812dc03a84.pdf</filename><originalFilename>64063.pdf</originalFilename><uploaded>2023-08-09T09:51:33.4269263</uploaded><type>Output</type><contentLength>6065207</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2024-08-08T00:00:00.0000000</embargoDate><documentNotes>Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by-nc-nd/4.0/</licence></document></documents><OutputDurs/></rfc1807>
spelling v2 64063 2023-08-09 Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2023-08-09 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. Journal Article Journal of Sound and Vibration 569 117998 Elsevier BV 0022-460X 1095-8568 Multivalued correlation function, Multivalued frequency response curve, Strongnonlinearity, Correlation-map, Arclength-based separation 20 1 2024 2024-01-20 10.1016/j.jsv.2023.117998 http://dx.doi.org/10.1016/j.jsv.2023.117998 COLLEGE NANME COLLEGE CODE Swansea University 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. 2024-09-05T12:02:59.0544602 2023-08-09T09:49:30.2648645 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Tianxu Zhu 0000-0003-2511-2677 1 Genbei Zhang 2 Chaoping Zang 3 Michael Friswell 4 64063__28276__ba9a6be147bd4f55ac1802812dc03a84.pdf 64063.pdf 2023-08-09T09:51:33.4269263 Output 6065207 application/pdf Accepted Manuscript true 2024-08-08T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
spellingShingle Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
Michael Friswell
title_short Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
title_full Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
title_fullStr Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
title_full_unstemmed Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
title_sort Global correlation analysis of strongly nonlinear frequency responses using the arclength-based separation and the Correlation-Map
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Michael Friswell
author2 Tianxu Zhu
Genbei Zhang
Chaoping Zang
Michael Friswell
format Journal article
container_title Journal of Sound and Vibration
container_volume 569
container_start_page 117998
publishDate 2024
institution Swansea University
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doi_str_mv 10.1016/j.jsv.2023.117998
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
url http://dx.doi.org/10.1016/j.jsv.2023.117998
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description 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.
published_date 2024-01-20T12:02:59Z
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score 11.035634

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