Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation
This paper discusses a new identification method for a linear single-degree-of-freedom system that uses a Gaussian random response and is based on the maximum likelihood estimation (MLE) method. The likelihood function of the proposed method consists of the analytical solution of the Fokker–Planck e...
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| Format: | Article |
| Language: | English |
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The Japan Society of Mechanical Engineers
2023-01-01
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| Series: | Mechanical Engineering Journal |
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| Online Access: | https://www.jstage.jst.go.jp/article/mej/10/1/10_22-00002/_pdf/-char/en |
| _version_ | 1797902183915585536 |
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| author | Soichiro TAKATA |
| author_facet | Soichiro TAKATA |
| author_sort | Soichiro TAKATA |
| collection | DOAJ |
| description | This paper discusses a new identification method for a linear single-degree-of-freedom system that uses a Gaussian random response and is based on the maximum likelihood estimation (MLE) method. The likelihood function of the proposed method consists of the analytical solution of the Fokker–Planck equation. We have already published a paper on theoretical and numerical considerations. However, in that study, the experimental verification of the proposed identification method was not performed. Therefore, in this study, we conduct an experimental verification of the proposed identification method. First, the identification algorithm is formulated in a spring-mass-damper system subjected to white noise excitation by a moving foundation to correspond to the actual experimental setup. A preliminary experiment in terms of the excitation source is conducted using a vibration speaker. In addition, the experimental modal analysis is performed to confirm the validity of the vibratory system. The fundamental operation test of the identification method is performed using the actual experimental random response data, and a dependency survey of the number of samples is conducted. From the results, the convergence behaviors of the estimation value are observed with an increasing number of samples in the spring constant and the ratio between the diffusion coefficient and the damping constant. In addition, benchmark tests are conducted using the half–power method (HPM) based on spectral analysis and the auto-regressive method (ARM) based on time–series analysis. In the case of spring constant estimation, the behaviors of the estimation value that converge to the true value are observed in all identification methods. In the ratio between the diffusion coefficient and damping constant, the behavior of the estimation value that converges to the true value is observed only in the proposed identification method. |
| first_indexed | 2024-04-10T09:13:41Z |
| format | Article |
| id | doaj.art-dbb22f96788f40e39840a4089b9de257 |
| institution | Directory Open Access Journal |
| issn | 2187-9745 |
| language | English |
| last_indexed | 2024-04-10T09:13:41Z |
| publishDate | 2023-01-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Mechanical Engineering Journal |
| spelling | doaj.art-dbb22f96788f40e39840a4089b9de2572023-02-21T02:22:42ZengThe Japan Society of Mechanical EngineersMechanical Engineering Journal2187-97452023-01-0110122-0000222-0000210.1299/mej.22-00002mejExperimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equationSoichiro TAKATA0Department of Mechanical Engineering, National Institute of Technology, Tokyo CollegeThis paper discusses a new identification method for a linear single-degree-of-freedom system that uses a Gaussian random response and is based on the maximum likelihood estimation (MLE) method. The likelihood function of the proposed method consists of the analytical solution of the Fokker–Planck equation. We have already published a paper on theoretical and numerical considerations. However, in that study, the experimental verification of the proposed identification method was not performed. Therefore, in this study, we conduct an experimental verification of the proposed identification method. First, the identification algorithm is formulated in a spring-mass-damper system subjected to white noise excitation by a moving foundation to correspond to the actual experimental setup. A preliminary experiment in terms of the excitation source is conducted using a vibration speaker. In addition, the experimental modal analysis is performed to confirm the validity of the vibratory system. The fundamental operation test of the identification method is performed using the actual experimental random response data, and a dependency survey of the number of samples is conducted. From the results, the convergence behaviors of the estimation value are observed with an increasing number of samples in the spring constant and the ratio between the diffusion coefficient and the damping constant. In addition, benchmark tests are conducted using the half–power method (HPM) based on spectral analysis and the auto-regressive method (ARM) based on time–series analysis. In the case of spring constant estimation, the behaviors of the estimation value that converge to the true value are observed in all identification methods. In the ratio between the diffusion coefficient and damping constant, the behavior of the estimation value that converges to the true value is observed only in the proposed identification method.https://www.jstage.jst.go.jp/article/mej/10/1/10_22-00002/_pdf/-char/enrandom vibrationsystem identificationfokker-planck equationvibration experimentmaximum likelihood estimation |
| spellingShingle | Soichiro TAKATA Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation Mechanical Engineering Journal random vibration system identification fokker-planck equation vibration experiment maximum likelihood estimation |
| title | Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation |
| title_full | Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation |
| title_fullStr | Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation |
| title_full_unstemmed | Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation |
| title_short | Experimental identification of a lumped mass-spring system based on maximum likelihood estimation using steady response distribution of Fokker-Planck equation |
| title_sort | experimental identification of a lumped mass spring system based on maximum likelihood estimation using steady response distribution of fokker planck equation |
| topic | random vibration system identification fokker-planck equation vibration experiment maximum likelihood estimation |
| url | https://www.jstage.jst.go.jp/article/mej/10/1/10_22-00002/_pdf/-char/en |
| work_keys_str_mv | AT soichirotakata experimentalidentificationofalumpedmassspringsystembasedonmaximumlikelihoodestimationusingsteadyresponsedistributionoffokkerplanckequation |