{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T21:29:45Z","timestamp":1778102985797,"version":"3.51.4"},"reference-count":51,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T00:00:00Z","timestamp":1659657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11672058"],"award-info":[{"award-number":["11672058"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Understanding the nonlinear dynamic characteristics of engineering structures is challenging, especially for the systems that exhibit asymmetric nonlinear behavior. This paper compared four parameter identification methods for asymmetric nonlinear systems incorporating quadratic and cubic stiffness nonlinearities. Hilbert transform, zero-crossing, direct quadrature, and wavelet transform were used to obtain the backbone, envelope, and restoring force curves from the free vibration time history. A nonlinear curve-fitting method was then applied to estimate the stiffness parameters of the asymmetric systems, and a linear least square fitting approach was utilized to estimate the damping parameters of the asymmetric systems. We used the Helmholtz\u2013Duffing oscillator as a numerical example and a nonlinear vibration absorber with geometric imperfections to verify the feasibility and accuracy of these methods. The advantages and disadvantages of these methods and the deviations in estimated results are discussed.<\/jats:p>","DOI":"10.3390\/s22155854","type":"journal-article","created":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T04:16:55Z","timestamp":1660018615000},"page":"5854","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3950-3150","authenticated-orcid":false,"given":"Shibo","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, China"},{"name":"Institute of Internal Combustion Engine, Dalian University of Technology, Dalian 116023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4882-6659","authenticated-orcid":false,"given":"Bin","family":"Tang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, China"},{"name":"Institute of Internal Combustion Engine, Dalian University of Technology, Dalian 116023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"44502","DOI":"10.1115\/1.4029689","article-title":"On the effects of mistuning a force excited system containing a quasi-zero-stiffness vibration isolator","volume":"13","author":"Abolfathi","year":"2015","journal-title":"J. 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