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On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error

Javad Taghipour, Hamed Haddad Khodaparast Orcid Logo, Michael Friswell, Hassan Jalali, Hadi Madinei Orcid Logo, Nidhal Jamia Orcid Logo

Applied Mathematical Modelling, Volume: 89, Issue: 1, Pages: 225 - 248

Swansea University Authors: Javad Taghipour, Hamed Haddad Khodaparast Orcid Logo, Michael Friswell, Hadi Madinei Orcid Logo, Nidhal Jamia Orcid Logo

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DOI (Published version): 10.1016/j.apm.2020.07.062

Abstract

The objective of this study is to investigate the sensitivity of the Equivalent Dynamic Stiffness Mapping (EDSM) identification method to typical types of inaccuracy that are often present during the identification process. These sources of inaccuracy may include the presence of noise in the simulat...

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Published in: Applied Mathematical Modelling
ISSN: 0307-904X
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa54985
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These sources of inaccuracy may include the presence of noise in the simulated/measured data, expansion error in the estimation of unmeasured coordinates, modelling error in the updated underlying linear model, and the error due to neglecting the higher harmonics in the nonlinear response of the system. An analytical study is performed to identify the structural nonlinearities of two nonlinear systems, a discrete three-DOF Duffing system and a cantilever beam with a nonlinear restoring force applied to the tip of the beam, considering the presence of all the aforementioned sources of inaccuracy. First, the EDSM technique is utilized to identify the nonlinear elements of two example systems to verify the accuracy of the EDSM technique. Finite Element modelling, the Modified Complex Averaging Technique (MCXA), and arc-length continuation are exploited in this study to obtain the steady state dynamics of the nonlinear systems. Numerical models of the two systems are then simulated in MATLAB and the numerical results of the simulation are used to identify the unknown nonlinear elements using the EDSM technique and investigate the effect of different sources of error on the outcome of the identification process. The nonlinear response of the system has been regenerated using the identified parameters with the sources of error present and the generated response has been compared to the simulated response in the absence of any noise or error. The EDSM technique is capable of identifying accurately the nonlinear elements in the absence of any source of inaccuracy although, based on the results, this method is highly sensitive to the aforementioned sources of inaccuracy that results in significant error in the identified model of the nonlinear system. Finally, an optimization-based framework, developed by the authors, is utilized to identify the nonlinear cantilever beam and the results are compared with the results of the EDSM technique. It is shown that by using the optimization method, the inaccuracy due to different sources of noise and error is significantly reduced. 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spelling 2020-09-17T14:07:45.1994980 v2 54985 2020-08-14 On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error dc7cba835218dde37fe7f447962d4058 Javad Taghipour Javad Taghipour true false f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false d9a10856ae9e6a71793eab2365cff8b6 0000-0002-3401-1467 Hadi Madinei Hadi Madinei true false 846b2cd3a7717b296654010df30cb22a 0000-0003-0643-7812 Nidhal Jamia Nidhal Jamia true false 2020-08-14 FGSEN The objective of this study is to investigate the sensitivity of the Equivalent Dynamic Stiffness Mapping (EDSM) identification method to typical types of inaccuracy that are often present during the identification process. These sources of inaccuracy may include the presence of noise in the simulated/measured data, expansion error in the estimation of unmeasured coordinates, modelling error in the updated underlying linear model, and the error due to neglecting the higher harmonics in the nonlinear response of the system. An analytical study is performed to identify the structural nonlinearities of two nonlinear systems, a discrete three-DOF Duffing system and a cantilever beam with a nonlinear restoring force applied to the tip of the beam, considering the presence of all the aforementioned sources of inaccuracy. First, the EDSM technique is utilized to identify the nonlinear elements of two example systems to verify the accuracy of the EDSM technique. Finite Element modelling, the Modified Complex Averaging Technique (MCXA), and arc-length continuation are exploited in this study to obtain the steady state dynamics of the nonlinear systems. Numerical models of the two systems are then simulated in MATLAB and the numerical results of the simulation are used to identify the unknown nonlinear elements using the EDSM technique and investigate the effect of different sources of error on the outcome of the identification process. The nonlinear response of the system has been regenerated using the identified parameters with the sources of error present and the generated response has been compared to the simulated response in the absence of any noise or error. The EDSM technique is capable of identifying accurately the nonlinear elements in the absence of any source of inaccuracy although, based on the results, this method is highly sensitive to the aforementioned sources of inaccuracy that results in significant error in the identified model of the nonlinear system. Finally, an optimization-based framework, developed by the authors, is utilized to identify the nonlinear cantilever beam and the results are compared with the results of the EDSM technique. It is shown that by using the optimization method, the inaccuracy due to different sources of noise and error is significantly reduced. Indeed, by using the optimization method, the necessity to use an expansion method and consider the higher harmonics of the response is eliminated. Journal Article Applied Mathematical Modelling 89 1 225 248 Elsevier BV 0307-904X Nonlinear structural dynamics, Identification, Model updating, Equivalent Dynamic Stiffness Mapping, Sensitivity to noise and error 1 1 2021 2021-01-01 10.1016/j.apm.2020.07.062 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-09-17T14:07:45.1994980 2020-08-14T10:11:17.5806683 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Javad Taghipour 1 Hamed Haddad Khodaparast 0000-0002-3721-4980 2 Michael Friswell 3 Hassan Jalali 4 Hadi Madinei 0000-0002-3401-1467 5 Nidhal Jamia 0000-0003-0643-7812 6 54985__17917__5fa74349a9f4442a8746237d0fc6663b.pdf 54985.pdf 2020-08-14T10:13:17.4054694 Output 8167173 application/pdf Accepted Manuscript true 2021-08-06T00:00:00.0000000 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license true English
title On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
spellingShingle On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
Javad Taghipour
Hamed Haddad Khodaparast
Michael Friswell
Hadi Madinei
Nidhal Jamia
title_short On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
title_full On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
title_fullStr On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
title_full_unstemmed On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
title_sort On the sensitivity of the equivalent dynamic stiffness mapping technique to measurement noise and modelling error
author_id_str_mv dc7cba835218dde37fe7f447962d4058
f207b17edda9c4c3ea074cbb7555efc1
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d9a10856ae9e6a71793eab2365cff8b6
846b2cd3a7717b296654010df30cb22a
author_id_fullname_str_mv dc7cba835218dde37fe7f447962d4058_***_Javad Taghipour
f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
d9a10856ae9e6a71793eab2365cff8b6_***_Hadi Madinei
846b2cd3a7717b296654010df30cb22a_***_Nidhal Jamia
author Javad Taghipour
Hamed Haddad Khodaparast
Michael Friswell
Hadi Madinei
Nidhal Jamia
author2 Javad Taghipour
Hamed Haddad Khodaparast
Michael Friswell
Hassan Jalali
Hadi Madinei
Nidhal Jamia
format Journal article
container_title Applied Mathematical Modelling
container_volume 89
container_issue 1
container_start_page 225
publishDate 2021
institution Swansea University
issn 0307-904X
doi_str_mv 10.1016/j.apm.2020.07.062
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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
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description The objective of this study is to investigate the sensitivity of the Equivalent Dynamic Stiffness Mapping (EDSM) identification method to typical types of inaccuracy that are often present during the identification process. These sources of inaccuracy may include the presence of noise in the simulated/measured data, expansion error in the estimation of unmeasured coordinates, modelling error in the updated underlying linear model, and the error due to neglecting the higher harmonics in the nonlinear response of the system. An analytical study is performed to identify the structural nonlinearities of two nonlinear systems, a discrete three-DOF Duffing system and a cantilever beam with a nonlinear restoring force applied to the tip of the beam, considering the presence of all the aforementioned sources of inaccuracy. First, the EDSM technique is utilized to identify the nonlinear elements of two example systems to verify the accuracy of the EDSM technique. Finite Element modelling, the Modified Complex Averaging Technique (MCXA), and arc-length continuation are exploited in this study to obtain the steady state dynamics of the nonlinear systems. Numerical models of the two systems are then simulated in MATLAB and the numerical results of the simulation are used to identify the unknown nonlinear elements using the EDSM technique and investigate the effect of different sources of error on the outcome of the identification process. The nonlinear response of the system has been regenerated using the identified parameters with the sources of error present and the generated response has been compared to the simulated response in the absence of any noise or error. The EDSM technique is capable of identifying accurately the nonlinear elements in the absence of any source of inaccuracy although, based on the results, this method is highly sensitive to the aforementioned sources of inaccuracy that results in significant error in the identified model of the nonlinear system. Finally, an optimization-based framework, developed by the authors, is utilized to identify the nonlinear cantilever beam and the results are compared with the results of the EDSM technique. It is shown that by using the optimization method, the inaccuracy due to different sources of noise and error is significantly reduced. Indeed, by using the optimization method, the necessity to use an expansion method and consider the higher harmonics of the response is eliminated.
published_date 2021-01-01T04:08:53Z
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score 11.037581

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