Links to Exploration step
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">EEMD-MUSIC-Based Analysis for Natural Frequencies Identification of Structures Using Artificial and Natural Excitations</title><author><name sortKey="Camarena Martinez, David" sort="Camarena Martinez, David" uniqKey="Camarena Martinez D" first="David" last="Camarena-Martinez">David Camarena-Martinez</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Amezquita Sanchez, Juan P" sort="Amezquita Sanchez, Juan P" uniqKey="Amezquita Sanchez J" first="Juan P." last="Amezquita-Sanchez">Juan P. Amezquita-Sanchez</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Valtierra Rodriguez, Martin" sort="Valtierra Rodriguez, Martin" uniqKey="Valtierra Rodriguez M" first="Martin" last="Valtierra-Rodriguez">Martin Valtierra-Rodriguez</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Romero Troncoso, Rene J" sort="Romero Troncoso, Rene J" uniqKey="Romero Troncoso R" first="Rene J." last="Romero-Troncoso">Rene J. Romero-Troncoso</name><affiliation><nlm:aff id="I2">HSPdigital-CA Telematica, Procesamiento Digital de Señales, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle km 3.5+1.8, Palo Blanco, 36700 Salamanca, GTO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Osornio Rios, Roque A" sort="Osornio Rios, Roque A" uniqKey="Osornio Rios R" first="Roque A." last="Osornio-Rios">Roque A. Osornio-Rios</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Garcia Perez, Arturo" sort="Garcia Perez, Arturo" uniqKey="Garcia Perez A" first="Arturo" last="Garcia-Perez">Arturo Garcia-Perez</name><affiliation><nlm:aff id="I2">HSPdigital-CA Telematica, Procesamiento Digital de Señales, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle km 3.5+1.8, Palo Blanco, 36700 Salamanca, GTO, Mexico</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">24683346</idno><idno type="pmc">3934768</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3934768</idno><idno type="RBID">PMC:3934768</idno><idno type="doi">10.1155/2014/587671</idno><date when="2014">2014</date><idno type="wicri:Area/Pmc/Corpus">000539</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000539</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">EEMD-MUSIC-Based Analysis for Natural Frequencies Identification of Structures Using Artificial and Natural Excitations</title><author><name sortKey="Camarena Martinez, David" sort="Camarena Martinez, David" uniqKey="Camarena Martinez D" first="David" last="Camarena-Martinez">David Camarena-Martinez</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Amezquita Sanchez, Juan P" sort="Amezquita Sanchez, Juan P" uniqKey="Amezquita Sanchez J" first="Juan P." last="Amezquita-Sanchez">Juan P. Amezquita-Sanchez</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Valtierra Rodriguez, Martin" sort="Valtierra Rodriguez, Martin" uniqKey="Valtierra Rodriguez M" first="Martin" last="Valtierra-Rodriguez">Martin Valtierra-Rodriguez</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Romero Troncoso, Rene J" sort="Romero Troncoso, Rene J" uniqKey="Romero Troncoso R" first="Rene J." last="Romero-Troncoso">Rene J. Romero-Troncoso</name><affiliation><nlm:aff id="I2">HSPdigital-CA Telematica, Procesamiento Digital de Señales, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle km 3.5+1.8, Palo Blanco, 36700 Salamanca, GTO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Osornio Rios, Roque A" sort="Osornio Rios, Roque A" uniqKey="Osornio Rios R" first="Roque A." last="Osornio-Rios">Roque A. Osornio-Rios</name><affiliation><nlm:aff id="I1">HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</nlm:aff></affiliation></author><author><name sortKey="Garcia Perez, Arturo" sort="Garcia Perez, Arturo" uniqKey="Garcia Perez A" first="Arturo" last="Garcia-Perez">Arturo Garcia-Perez</name><affiliation><nlm:aff id="I2">HSPdigital-CA Telematica, Procesamiento Digital de Señales, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle km 3.5+1.8, Palo Blanco, 36700 Salamanca, GTO, Mexico</nlm:aff></affiliation></author></analytic><series><title level="j">The Scientific World Journal</title><idno type="eISSN">1537-744X</idno><imprint><date when="2014">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>This paper presents a new EEMD-MUSIC- (ensemble empirical mode decomposition-multiple signal classification-) based methodology to identify modal frequencies in structures ranging from free and ambient vibration signals produced by artificial and natural excitations and also considering several factors as nonstationary effects, close modal frequencies, and noisy environments, which are common situations where several techniques reported in literature fail. The EEMD and MUSIC methods are used to decompose the vibration signal into a set of IMFs (intrinsic mode functions) and to identify the natural frequencies of a structure, respectively. The effectiveness of the proposed methodology has been validated and tested with synthetic signals and under real operating conditions. The experiments are focused on extracting the natural frequencies of a truss-type scaled structure and of a bridge used for both highway traffic and pedestrians. Results show the proposed methodology as a suitable solution for natural frequencies identification of structures from free and ambient vibration signals.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Doebling, S" uniqKey="Doebling S">S Doebling</name></author><author><name sortKey="Farrar, C" uniqKey="Farrar C">C Farrar</name></author><author><name sortKey="Prime, M" uniqKey="Prime M">M Prime</name></author><author><name sortKey="Shevitz, D" uniqKey="Shevitz D">D Shevitz</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Bai, X" uniqKey="Bai X">X Bai</name></author><author><name sortKey="Zhang, X" uniqKey="Zhang X">X Zhang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Amezquita Sanchez, Jp" uniqKey="Amezquita Sanchez J">JP Amezquita-Sanchez</name></author><author><name sortKey="Osornio Rios, R" uniqKey="Osornio Rios R">R Osornio-Rios</name></author><author><name sortKey="Romero Troncoso, R" uniqKey="Romero Troncoso R">R Romero-Troncoso</name></author><author><name sortKey="Dominguez Gonzalez, A" uniqKey="Dominguez Gonzalez A">A Dominguez-Gonzalez</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="He, Xh" uniqKey="He X">XH He</name></author><author><name sortKey="Hua, X" uniqKey="Hua X">X Hua</name></author><author><name sortKey="Chen, Z" uniqKey="Chen Z">Z Chen</name></author><author><name sortKey="Huang, F" uniqKey="Huang F">F Huang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Shi, W" uniqKey="Shi W">W Shi</name></author><author><name sortKey="Shan, J" uniqKey="Shan J">J Shan</name></author><author><name sortKey="Lu, X" uniqKey="Lu X">X Lu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pieraccini, M" uniqKey="Pieraccini M">M Pieraccini</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hu, W" uniqKey="Hu W">W Hu</name></author><author><name sortKey="Cunha, A" uniqKey="Cunha A">Á Cunha</name></author><author><name sortKey="Caetano, E" uniqKey="Caetano E">E Caetano</name></author><author><name sortKey="Magalhaes, F" uniqKey="Magalhaes F">F Magalhães</name></author><author><name sortKey="Moutinho, C" uniqKey="Moutinho C">C Moutinho</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ibrahim, Z" uniqKey="Ibrahim Z">Z Ibrahim</name></author><author><name sortKey="Reynolds, P" uniqKey="Reynolds P">P Reynolds</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Siringoringo, D" uniqKey="Siringoringo D">D Siringoringo</name></author><author><name sortKey="Fujino, Y" uniqKey="Fujino Y">Y Fujino</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Peeters, B" uniqKey="Peeters B">B Peeters</name></author><author><name sortKey="De Roeck, G" uniqKey="De Roeck G">G de Roeck</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Brownjohn, J" uniqKey="Brownjohn J">J Brownjohn</name></author><author><name sortKey="Magalhaes, F" uniqKey="Magalhaes F">F Magalhaes</name></author><author><name sortKey="Caetano, E" uniqKey="Caetano E">E Caetano</name></author><author><name sortKey="Cunha, A" uniqKey="Cunha A">A Cunha</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kim, C" uniqKey="Kim C">C Kim</name></author><author><name sortKey="Kawatani, M" uniqKey="Kawatani M">M Kawatani</name></author><author><name sortKey="Hao, J" uniqKey="Hao J">J Hao</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Andersen, P" uniqKey="Andersen P">P Andersen</name></author><author><name sortKey="Brincker, R" uniqKey="Brincker R">R Brincker</name></author><author><name sortKey="Kirkegaard, P" uniqKey="Kirkegaard P">P Kirkegaard</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Urgessa, Gs" uniqKey="Urgessa G">GS Urgessa</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Brincker, R" uniqKey="Brincker R">R Brincker</name></author><author><name sortKey="Zhang, L" uniqKey="Zhang L">L Zhang</name></author><author><name sortKey="Andersen, P" uniqKey="Andersen P">P Andersen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Yan, B" uniqKey="Yan B">B Yan</name></author><author><name sortKey="Miyamoto, A" uniqKey="Miyamoto A">A Miyamoto</name></author><author><name sortKey="Bruhwiler, E" uniqKey="Bruhwiler E">E Brühwiler</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Amezquita Sanchez, J" uniqKey="Amezquita Sanchez J">J Amezquita-Sanchez</name></author><author><name sortKey="Garcia Perez, A" uniqKey="Garcia Perez A">A Garcia-Perez</name></author><author><name sortKey="Romero Troncoso, R" uniqKey="Romero Troncoso R">R Romero-Troncoso</name></author><author><name sortKey="Osornio Rios, R" uniqKey="Osornio Rios R">R Osornio-Rios</name></author><author><name sortKey="Herrera Ruiz, G" uniqKey="Herrera Ruiz G">G Herrera-Ruiz</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Yan, B" uniqKey="Yan B">B Yan</name></author><author><name sortKey="Miyamoto, A" uniqKey="Miyamoto A">A Miyamoto</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chen, S" uniqKey="Chen S">S Chen</name></author><author><name sortKey="Liu, J" uniqKey="Liu J">J Liu</name></author><author><name sortKey="Lai, H" uniqKey="Lai H">H Lai</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Tang, J" uniqKey="Tang J">J Tang</name></author><author><name sortKey="Chiou, D" uniqKey="Chiou D">D Chiou</name></author><author><name sortKey="Chen, C" uniqKey="Chen C">C Chen</name></author><author><name sortKey="Chiang, W" uniqKey="Chiang W">W Chiang</name></author><author><name sortKey="Hsu, W" uniqKey="Hsu W">W Hsu</name></author><author><name sortKey="Liu, T" uniqKey="Liu T">T Liu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Liu, T" uniqKey="Liu T">T Liu</name></author><author><name sortKey="Chiang, W" uniqKey="Chiang W">W Chiang</name></author><author><name sortKey="Chen, C" uniqKey="Chen C">C Chen</name></author><author><name sortKey="Hsu, W" uniqKey="Hsu W">W Hsu</name></author><author><name sortKey="Lu, L" uniqKey="Lu L">L Lu</name></author><author><name sortKey="Chu, T" uniqKey="Chu T">T Chu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Liu, T" uniqKey="Liu T">T Liu</name></author><author><name sortKey="Chiang, W" uniqKey="Chiang W">W Chiang</name></author><author><name sortKey="Chen, C" uniqKey="Chen C">C Chen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Hsu, W" uniqKey="Hsu W">W Hsu</name></author><author><name sortKey="Chiou, D" uniqKey="Chiou D">D Chiou</name></author><author><name sortKey="Chen, C" uniqKey="Chen C">C Chen</name></author><author><name sortKey="Liu, M" uniqKey="Liu M">M Liu</name></author><author><name sortKey="Chiang, W" uniqKey="Chiang W">W Chiang</name></author><author><name sortKey="Huang, P" uniqKey="Huang P">P Huang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chang, K M" uniqKey="Chang K">K-M Chang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wu, Z" uniqKey="Wu Z">Z Wu</name></author><author><name sortKey="Huang, N" uniqKey="Huang N">N Huang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Jiang, X" uniqKey="Jiang X">X Jiang</name></author><author><name sortKey="Adeli, H" uniqKey="Adeli H">H Adeli</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Osornio Rios, R" uniqKey="Osornio Rios R">R Osornio-Rios</name></author><author><name sortKey="Amezquita Sanchez, J" uniqKey="Amezquita Sanchez J">J Amezquita-Sanchez</name></author><author><name sortKey="Romero Troncoso, R" uniqKey="Romero Troncoso R">R Romero-Troncoso</name></author><author><name sortKey="Garcia Perez, A" uniqKey="Garcia Perez A">A Garcia-Perez</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Huang, N" uniqKey="Huang N">N Huang</name></author><author><name sortKey="Shen, Z" uniqKey="Shen Z">Z Shen</name></author><author><name sortKey="Long, S" uniqKey="Long S">S Long</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wu, Z" uniqKey="Wu Z">Z Wu</name></author><author><name sortKey="Huang, Ne" uniqKey="Huang N">NE Huang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Garcia Perez, A" uniqKey="Garcia Perez A">A Garcia-Perez</name></author><author><name sortKey="Romero Troncoso, Rdj" uniqKey="Romero Troncoso R">RDJ Romero-Troncoso</name></author><author><name sortKey="Cabal Yepez, E" uniqKey="Cabal Yepez E">E Cabal-Yepez</name></author><author><name sortKey="Osornio Rios, Ra" uniqKey="Osornio Rios R">RA Osornio-Rios</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Young, K" uniqKey="Young K">K Young</name></author><author><name sortKey="Adeli, H" uniqKey="Adeli H">H Adeli</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">ScientificWorldJournal</journal-id><journal-id journal-id-type="iso-abbrev">ScientificWorldJournal</journal-id><journal-id journal-id-type="publisher-id">TSWJ</journal-id><journal-title-group><journal-title>The Scientific World Journal</journal-title></journal-title-group><issn pub-type="epub">1537-744X</issn><publisher><publisher-name>Hindawi Publishing Corporation</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">24683346</article-id><article-id pub-id-type="pmc">3934768</article-id><article-id pub-id-type="doi">10.1155/2014/587671</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title>EEMD-MUSIC-Based Analysis for Natural Frequencies Identification of Structures Using Artificial and Natural Excitations</article-title></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">http://orcid.org/0000-0003-0862-0821</contrib-id><name><surname>Camarena-Martinez</surname><given-names>David</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Amezquita-Sanchez</surname><given-names>Juan P.</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">http://orcid.org/0000-0003-3839-1396</contrib-id><name><surname>Valtierra-Rodriguez</surname><given-names>Martin</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Romero-Troncoso</surname><given-names>Rene J.</given-names></name><xref ref-type="aff" rid="I2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Osornio-Rios</surname><given-names>Roque A.</given-names></name><xref ref-type="aff" rid="I1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Garcia-Perez</surname><given-names>Arturo</given-names></name><xref ref-type="aff" rid="I2"><sup>2</sup></xref><xref ref-type="corresp" rid="cor1">*</xref></contrib></contrib-group><aff id="I1"><sup>1</sup>HSPdigital-CA Mecatronica, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Campus San Juan del Rio, Rio Moctezuma 249, 76807 San Juan del Rio, QRO, Mexico</aff><aff id="I2"><sup>2</sup>HSPdigital-CA Telematica, Procesamiento Digital de Señales, DICIS, Universidad de Guanajuato, Carr. Salamanca-Valle km 3.5+1.8, Palo Blanco, 36700 Salamanca, GTO, Mexico</aff><author-notes><corresp id="cor1">*Arturo Garcia-Perez: <email>agarcia@hspdigital.org</email></corresp><fn fn-type="other"><p>Academic Editors: S. Berretti and V. Ponomaryov</p></fn></author-notes><pub-date pub-type="collection"><year>2014</year></pub-date><pub-date pub-type="epub"><day>10</day><month>2</month><year>2014</year></pub-date><volume>2014</volume><elocation-id>587671</elocation-id><history><date date-type="received"><day>12</day><month>10</month><year>2013</year></date><date date-type="accepted"><day>22</day><month>12</month><year>2013</year></date></history><permissions><copyright-statement>Copyright © 2014 David Camarena-Martinez et al.</copyright-statement><copyright-year>2014</copyright-year><license license-type="open-access"><license-p>This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p></license></permissions><abstract><p>This paper presents a new EEMD-MUSIC- (ensemble empirical mode decomposition-multiple signal classification-) based methodology to identify modal frequencies in structures ranging from free and ambient vibration signals produced by artificial and natural excitations and also considering several factors as nonstationary effects, close modal frequencies, and noisy environments, which are common situations where several techniques reported in literature fail. The EEMD and MUSIC methods are used to decompose the vibration signal into a set of IMFs (intrinsic mode functions) and to identify the natural frequencies of a structure, respectively. The effectiveness of the proposed methodology has been validated and tested with synthetic signals and under real operating conditions. The experiments are focused on extracting the natural frequencies of a truss-type scaled structure and of a bridge used for both highway traffic and pedestrians. Results show the proposed methodology as a suitable solution for natural frequencies identification of structures from free and ambient vibration signals.</p></abstract></article-meta></front><body><sec id="sec1"><title>1. Introduction</title><p>Nowadays, the vibration-based structural health monitoring (SHM) is a major and fast growing research discipline for several fields such as mechanical engineering, aeronautics, and civil engineering, among others, because it allows the examination of the dynamic characteristics of a specific structure. The basic idea in vibration-based SHM is that physical variations in the structure change its modal parameters and, consequently, its vibration response also experiments disturbances. Therefore, accurate identification and measurement of modal parameters such as natural frequencies are fundamental in vibration-based SHM in order to estimate different structural conditions [<xref rid="B1" ref-type="bibr">1</xref>, <xref rid="B2" ref-type="bibr">2</xref>]. Moreover, a correct identification of modal parameters allows building a proper analytical model, as well as determining the existence and location of structural damage, and in some cases calculating the lifetime of the structure [<xref rid="B3" ref-type="bibr">3</xref>]. Several vibration excitation sources have been used to excite civil structures in order to measure their modal properties, which can be classified into two groups. The first one named artificial excitation uses mechanical shakers, drop weights, shoot rockets, control devices, and so on. The second group, named natural excitation, uses ambient vibrations such as wind and earthquakes. The ambient vibration testing has the advantage of being inexpensive and not interrupting the normal operation since no excitation equipment and traffic interruption are needed and also has potentials for implementing real-time condition assessment [<xref rid="B4" ref-type="bibr">4</xref>–<xref rid="B6" ref-type="bibr">6</xref>]. However, the modal parameter identification of civil engineering structures using the field ambient vibration measurement is a complicated procedure, since ambient vibration data is nonstationary and it is embedded in high-level noise. Therefore, it is desirable to have a reliable data analysis or signal processing method capable of analyzing ambient vibrations.</p><p>In the past few years, a number of different techniques have been proposed to estimate the modal parameters of a structure such as the peak-picking method (PP) [<xref rid="B7" ref-type="bibr">7</xref>], the frequency response function (FRF) [<xref rid="B8" ref-type="bibr">8</xref>], the natural excitation technique (NexT) [<xref rid="B9" ref-type="bibr">9</xref>], the stochastic subspace identification method (SSI) [<xref rid="B10" ref-type="bibr">10</xref>, <xref rid="B11" ref-type="bibr">11</xref>], the multivariate AR model [<xref rid="B12" ref-type="bibr">12</xref>], the autoregressive-moving average model (ARMA) [<xref rid="B13" ref-type="bibr">13</xref>], the eigensystem realization algorithm (ERA) [<xref rid="B14" ref-type="bibr">14</xref>], the enhanced frequency domain decomposition (EFDD) [<xref rid="B15" ref-type="bibr">15</xref>], and the McKelvey frequency domain subspace algorithm [<xref rid="B14" ref-type="bibr">14</xref>]. However, these methods assume the structural response is stationary in order to simplify the signal processing, which is not true in many cases, and therefore the modal parameters cannot be adequately analyzed by these methods [<xref rid="B4" ref-type="bibr">4</xref>]. Besides, some methods need a large set of data to identify accurately the modal parameters and, moreover, the results may be affected in noisy conditions [<xref rid="B16" ref-type="bibr">16</xref>, <xref rid="B17" ref-type="bibr">17</xref>]. To overcome these drawbacks, new tools, such as the wavelet transform (WT) [<xref rid="B18" ref-type="bibr">18</xref>, <xref rid="B19" ref-type="bibr">19</xref>], the Hilbert-Huang transform (HHT) [<xref rid="B20" ref-type="bibr">20</xref>–<xref rid="B22" ref-type="bibr">22</xref>], and the empirical mode decomposition (EMD) with random decrement (RD) [<xref rid="B4" ref-type="bibr">4</xref>], have been used to estimate the modal parameters of a structure as well as for damage detection. The WT method provides the time-scale analysis of a transient and nonstationary signal since it decomposes the signal into time-scale representation rather than time-frequency representation. Unfortunately, the WT capabilities are significantly degraded in noisy environments, as the case of real applications; besides, it requires many decomposition levels to be able to measure the modal parameters [<xref rid="B19" ref-type="bibr">19</xref>]. The HHT provides a time-frequency representation of nonstationary and transient signals. Its characteristics have been demonstrated to be more precise for decomposing a signal in the time-frequency domain than WT [<xref rid="B23" ref-type="bibr">23</xref>]. The HHT is based on two-steps, which are the EMD and the Hilbert transform (HT) methodologies. The EMD method decomposes any data into a set of band-limited quasistationary functions, called intrinsic mode functions (IMFs); later, the Hilbert transform is applied to each IMF, which allows obtaining the amplitude and phase angle of each IMF. Regrettably, the major drawback of EMD method is the so-called mode mixing effect, where the mode mixing indicates that oscillations with the same time scale have been assigned to different IMFs [<xref rid="B24" ref-type="bibr">24</xref>]. For this reason, [<xref rid="B25" ref-type="bibr">25</xref>] proposed the ensemble EMD (EEMD) method in order to solve the problems of mode mixing caused by an intermittent frequency in the EMD method. Despite this, the EEMD-HT, EMD-HT, and EMD-RD methods have some difficulties to detect or extract close space modes, which are present in many civil structures due to the symmetrical geometry and similar physical properties in different directions. In addition, these methods are also very susceptible to noise. Therefore, it would be desirable to have a technique that helps the EEMD to extract the natural frequencies of a structure with great efficiency and accuracy, especially those modes that are very close. Regarding close frequency components, a high-resolution spectral estimation through the multiple signal classification (MUSIC) algorithm has been successfully presented for very close frequency components, even for data with low signal-to-noise ratio [<xref rid="B26" ref-type="bibr">26</xref>, <xref rid="B27" ref-type="bibr">27</xref>]; therefore, the MUSIC algorithm is a promising technique to detect the close space modes of the structures.</p><p>The contribution of this paper is to present a new EEMD-MUSIC-based methodology to identify modal frequencies in structures ranging from free and ambient vibration signals produced by artificial and natural excitations. The EEMD is used to decompose the vibration signal into a set of IMFs and then MUSIC identifies the natural frequencies of the structure. The usefulness and effectiveness of the proposed methodology are assessed through three experimental cases. In the first experiment, a numerical simulation is carried out to validate the accuracy and noise immunity of the proposed methodology for extracting the natural frequencies, especially when the modal frequencies are close. The second experiment is focused on extracting the modes of a truss-type scaled structure by using an artificial excitation, where the results are compared with the obtained values through finite element analysis (FEA). Finally, the third experiment concentrates on identifying the natural frequencies of a bridge with natural excitation by using a set of field ambient vibration measurements. Analytical and experimental results show an excellent identification of the natural modes even when the signal is embedded in high-level noise, and, more importantly, the results demonstrate that the methodology provides a suitable alternative approach to natural frequencies identification from free and ambient data by using artificial and natural excitations.</p></sec><sec id="sec2"><title>2. Mathematical Background</title><p>This section presents the mathematical background of the proposed techniques for vibration analysis of structures.</p><sec id="sec2.1"><title>2.1. Empirical Mode Decomposition</title><p>The EMD method is a data-processing technique for analyzing nonstationary and nonlinear signals. The EMD method decomposes the vibration signal into a set of band-limited quasistationary functions called IMFs. Each IMF has to satisfy the following two conditions: (i) the number of zero crossings and the number of extrema must either equal or differ by at most one and (ii) the mean value of the envelope defined by the local maxima and the envelope defined by the local minima must be zero [<xref rid="B28" ref-type="bibr">28</xref>].</p><p>The process for obtaining each IMF is called the sifting process, which is described as follows.<list list-type="simple"><list-item><label>(1)</label><p>Identify the maxima and minima of the signal <italic>x</italic>(<italic>t</italic>).</p></list-item><list-item><label>(2)</label><p>Generate an upper and lower envelop by using cubic spline interpolation. The average of the two envelops is <italic>m</italic><sub>1</sub>(<italic>t</italic>). Subtract <italic>m</italic><sub>1</sub>(<italic>t</italic>) from the original signal <italic>x</italic>(<italic>t</italic>) to obtain
<disp-formula id="EEq1"><label>(1)</label><mml:math id="M1"><mml:mtable><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>Determine if (<xref ref-type="disp-formula" rid="EEq1">1</xref>) satisfies the conditions (i) and (ii). If not, repeat the first two steps until <italic>h</italic><sub><italic>k</italic></sub>(<italic>t</italic>) satisfies the conditions (i) and (ii); then, <italic>h</italic><sub><italic>k</italic></sub>(<italic>t</italic>) is the first IMF defined as
<disp-formula id="EEq2"><label>(2)</label><mml:math id="M2"><mml:mtable><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mtext>IMF</mml:mtext><mml:mn>1</mml:mn><mml:mo>.</mml:mo><mml:mo> </mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p></list-item><list-item><label>(3)</label><p>After IMF1 is obtained, subtract <italic>c</italic><sub>1</sub> from the original signal <italic>x</italic>(<italic>t</italic>)and calculate the residue signal as follows:
<disp-formula id="EEq3"><label>(3)</label><mml:math id="M3"><mml:mtable><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p></list-item><list-item><label>(4)</label><p>Treat <italic>r</italic><sub>1</sub> as the original signal and repeat the procedure from step (1) to step (3) to obtain the other IMF (<italic>c</italic><sub>2</sub>, <italic>c</italic><sub>3</sub>,…, <italic>c</italic><sub><italic>n</italic></sub>). The process is stopped when the final residual signal <italic>r</italic><sub><italic>n</italic></sub>(<italic>t</italic>) is a monotonic function.</p></list-item><list-item><label>(5)</label><p>At the end of the procedure, the signal <italic>x</italic>(<italic>t</italic>) is decomposed into <italic>n</italic> intrinsic modes <italic>c</italic><sub><italic>i</italic></sub>(<italic>t</italic>) and a residue <italic>r</italic><sub><italic>n</italic></sub>(<italic>t</italic>). Now, the original signal can be represented by
<disp-formula id="EEq4"><label>(4)</label><mml:math id="M4"><mml:mtable><mml:mtr><mml:mtd><mml:mi>x</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p></list-item></list></p></sec><sec id="sec2.2"><title>2.2. Ensemble Empirical Mode Decomposition</title><p>The EEMD is an adaptive and noise-assisted method proposed by [<xref rid="B25" ref-type="bibr">25</xref>, <xref rid="B29" ref-type="bibr">29</xref>] in order to improve the shortcomings of the EMD algorithm and provide a feasible solution of mode mixing caused by an intermittent frequency. The EEMD method defines the IMF set for an ensemble of trials, each one obtained by applying the EMD to the signal of interest with added independent identically distributed white noise of the same standard deviation.</p><p>According to [<xref rid="B25" ref-type="bibr">25</xref>], EEMD contains the following steps.<list list-type="order"><list-item><p>Add a white noise series to the targeted data.</p></list-item><list-item><p>Decompose the data with added white noise by EMD algorithm, described in <xref ref-type="sec" rid="sec2.1">Section 2.1</xref>.</p></list-item><list-item><p>Repeat steps (1) and (2) until the trial number is met, but with different white noise series each time.</p></list-item><list-item><p>Estimate the (ensemble) means of corresponding IMF of the decompositions as the desired output.</p></list-item></list></p></sec><sec id="sec2.3"><title>2.3. MUSIC Algorithm</title><p>MUSIC algorithm is known as a high-resolution method which can detect frequencies with low signal-to-noise ratio. MUSIC assumes that the discrete time signal <italic>x</italic>[<italic>n</italic>] can be represented as a sum of <italic>m</italic> complex sinusoid in noise <italic>e</italic>[<italic>n</italic>] [<xref rid="B30" ref-type="bibr">30</xref>]. Consider
<disp-formula id="EEq5"><label>(5)</label><mml:math id="M5"><mml:mtable><mml:mtr><mml:mtd><mml:mi>x</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>−</mml:mo></mml:mover><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mi>π</mml:mi><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi>e</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0,1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>with
<disp-formula id="EEq6"><label>(6)</label><mml:math id="M6"><mml:mtable><mml:mtr><mml:mtd><mml:mover accent="true"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>−</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>where <italic>N</italic>, <italic>B</italic><sub><italic>i</italic></sub>, and<italic>f</italic><sub><italic>i</italic></sub> are the number of sample data, the complex amplitude, and its frequency, respectively, and <italic>e</italic>[<italic>n</italic>] is a sequence of white noise with zero mean and a variance <italic>σ</italic><sup>2</sup>. This method uses the eigenvector decomposition of <italic>x</italic>[<italic>n</italic>] to obtain two orthogonal subspaces. The autocorrelation matrix <italic>R</italic> of the noisy signal <italic>x</italic>[<italic>n</italic>] is the sum of the autocorrelation matrices of the pure signal <italic>R</italic><sub><italic>s</italic></sub> and the noisy <italic>R</italic><sub><italic>n</italic></sub> as follows:
<disp-formula id="EEq7"><label>(7)</label><mml:math id="M7"><mml:mtable><mml:mtr><mml:mtd><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:munderover><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow><mml:mi>e</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msubsup><mml:mi>I</mml:mi><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>where <italic>P</italic> is the number of frequencies, the exponent <italic>H</italic> denotes Hermitian transpose, <italic>I</italic> is the identity matrix, and <italic>e</italic><sup><italic>H</italic></sup>(<italic>f</italic><sub><italic>i</italic></sub>) is the signal vector given by
<disp-formula id="EEq8"><label>(8)</label><mml:math id="M8"><mml:mtable><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>⌊</mml:mo><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mn mathvariant="normal">1</mml:mn></mml:mtd><mml:mtd><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mi>j</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mi>π</mml:mi><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msup></mml:mtd><mml:mtd><mml:mo>⋯</mml:mo></mml:mtd><mml:mtd><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mi>j</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mi>π</mml:mi><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo minsize="0.75em" maxsize="0.75em">(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mo minsize="0.75em" maxsize="0.75em">)</mml:mo></mml:mrow></mml:msup></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo>⌋</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p><p>From the orthogonality condition of both subspaces, the MUSIC pseudospectrum <italic>Q</italic> of the current space vector is given by
<disp-formula id="EEq9"><label>(9)</label><mml:math id="M9"><mml:mtable><mml:mtr><mml:mtd><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mtext>MUSIC</mml:mtext></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>e</mml:mi><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>where <italic>V</italic><sub><italic>m</italic>+1</sub> is the noise eigenvector. This expression exhibits the peaks that are exactly at frequency of principal sinusoidal component, where <italic>e</italic>(<italic>f</italic>)<sup><italic>H</italic></sup><italic>V</italic><sub><italic>m</italic>+1</sub> = 0.</p></sec></sec><sec id="sec3"><title>3. Proposed Methodology</title><p><xref ref-type="fig" rid="fig1">Figure 1</xref> shows the flowchart of the proposed EEMD-MUSIC-based methodology for identifying modal frequencies from free and ambient vibration signals produced by an artificial or a natural excitation. The first step is to acquire the vibration signal of the structure. Second, the sampled vibration signal is passed through a band-pass filter, in order to extract the bandwidth of interest related to the modal frequencies as well as to help solve the mode mixing. Third, the filtered vibration signal is decomposed into its IMF utilizing the EEMD. Finally, the MUSIC algorithm is applied to each IMF to compute the modal frequencies of the structure.</p><p>The usefulness of the proposed methodology is tested in three experiments. The first experiment focuses on the use of a synthetic signal to validate the accuracy and noise immunity of the proposed methodology (<xref ref-type="fig" rid="fig1">Figure 1(a)</xref>). In the second experiment, the proposed methodology is tested on a truss-type scaled structure located in a laboratory, where the excitation conditions are controlled (<xref ref-type="fig" rid="fig1">Figure 1(b)</xref>). Finally, the third experiment is carried out to show the effectiveness of the proposed methodology under real operating conditions. In this experiment, a real structure (a bridge) is analyzed, in which the natural excitation is used (<xref ref-type="fig" rid="fig1">Figure 1(c)</xref>).</p></sec><sec id="sec4"><title>4. Experimentation and Results</title><p>In order to show the effectiveness of the proposed methodology, three experiments are performed. The first experiment consists of a numerical simulation implemented to validate the accuracy and noise immunity of the proposed methodology for extracting the natural frequencies, especially when the natural frequencies are close. Further, the proposed methodology and different approaches are compared in order to validate their efficiency by estimating the natural frequencies. The second experiment concentrates on an artificial excitation of the free decay under forced vibration that is applied on a truss-type scaled structure for extracting the natural frequencies. The experimental results are compared with those obtained by FEA. Finally, the third experiment concentrates on identifying the natural frequencies of a bridge with natural excitation by using a set of field ambient vibration measurements. This experimentation takes into account that ambient vibration data is nonstationary and it is embedded in high-level noise.</p><sec id="sec4.1"><title>4.1. Synthetic Signal</title><p>In order to validate the proposed methodology performance, a comparison between different approaches, EEMD-FFT and -HT, and the discrete wavelet transform (DWT)-FFT, -HT, and -MUSIC methods is presented. For this, a synthetic signal with <italic>a priori</italic> known values is used, which appears in <xref ref-type="fig" rid="fig2">Figure 2</xref> and corresponds to a damped free vibration response of 4-degree of freedom system as follows:
<disp-formula id="EEq10"><label>(10)</label><mml:math id="M10"><mml:mtable><mml:mtr><mml:mtd><mml:mi>i</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:munderover><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:munderover><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>π</mml:mi><mml:msub><mml:mrow><mml:mi>ζ</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mrow><mml:mrow><mml:mi>sin</mml:mi></mml:mrow><mml:mo></mml:mo><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>π</mml:mi><mml:mi>f</mml:mi><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi>ω</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>where <italic>Aj</italic>, <italic>θj</italic>, <italic>fj</italic>, <inline-formula><mml:math id="M11"><mml:mi>f</mml:mi><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:msqrt><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msubsup><mml:mrow><mml:mi>ζ</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:msqrt></mml:math></inline-formula>, and <italic>ζj</italic>are the amplitude, phase, undamped natural frequency, damped natural frequency, and damping ratio of the <italic>j</italic>th mode, respectively, whereas <italic>ω</italic>(<italic>t</italic>) is a sequence of white noise. The used numerical values are <italic>f</italic><sub>1</sub> = 0.61 Hz, <italic>f</italic><sub>2</sub> = 0.73 Hz, <italic>f</italic><sub>3</sub> = 1.56 Hz, <italic>f</italic><sub>4</sub> = 4.35 Hz, <italic>ζ</italic><sub><italic>j</italic></sub> = 0.01, <italic>A</italic><sub><italic>j</italic></sub> = 1.0, and <italic>θ</italic><sub><italic>j</italic></sub> = 0, for <italic>j</italic> = 1, 2, 3, and 4, with a sampling frequency and sampling time of 50 Hz and 11 s, respectively. Besides, a 30% level noise for an SNR = 7.4 dB is used to test the efficiency and immunity of the techniques to noisy environments.</p><p>Firstly, the synthetic signal is decomposed, as shown in <xref ref-type="fig" rid="fig3">Figure 3</xref>, by the EEMD and DWT which is also a technique to decompose a signal into frequency bands named decompositions (DCs) [<xref rid="B3" ref-type="bibr">3</xref>]. Then, some IMFs and DCs are chosen for being analyzed. Regarding the IMFs (<xref ref-type="fig" rid="fig3">Figure 3(a)</xref>), the first two IMF levels are discarded since they contain the noise and high-frequency components; therefore, only the IMF3, IMF4, and IMF5 are considered to identify the natural modes. On the other hand and according to the DCs (<xref ref-type="fig" rid="fig3">Figure 3(b)</xref>), the first two decompositions, DC<sub>1</sub> and DC<sub>2</sub>, are discarded since they contain the high-frequency bands; consequently, the DC<sub>3 </sub>(3.125–6.25 Hz), DC<sub>5</sub> (0.781–1.5625 Hz), and DC<sub>6</sub> (0.390–0.781 Hz) are analyzed to identify the natural frequencies since they contain the frequencies of interest.</p><p>Later, the selected IMFs and DCs are processed by the HT, the FFT, and the proposed MUSIC method as shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>. From these figures, it is possible to observe that the EEMD-HT method (<xref ref-type="fig" rid="fig4">Figure 4(a)</xref>) and the DWT-HT method (<xref ref-type="fig" rid="fig4">Figure 4(b)</xref>) only detect three modes due to the fact that (i) the EEMD and DWT cannot separate close frequencies and (ii) that the HT can only identify one frequency by each IMF and DC, respectively. Similarly, the EEMD-FFT (<xref ref-type="fig" rid="fig4">Figure 4(c)</xref>) and the DWT-FFT (<xref ref-type="fig" rid="fig4">Figure 4(d)</xref>) cannot identify close modes due to overlapping frequency components and to the FFT resolution. On the other hand, the EEMD-MUSIC (<xref ref-type="fig" rid="fig4">Figure 4(e)</xref>) and the DWT-MUSIC (<xref ref-type="fig" rid="fig4">Figure 4(f)</xref>) identify clearly the four natural modes; however, the results for the natural frequencies obtained by DWT-MUSIC are degraded in noisy environments unlike the EEMD-MUSIC method. All the aforementioned results are presented in a normalized way for a better presentation and understanding.</p><p>Finally, <xref ref-type="table" rid="tab1">Table 1</xref> shows the numerical comparison between the reference values of the synthetic signal and the obtained values through the EEMD-HT, the EEMD-FFT, the DWT-HT, the DWT-FFT, the DWT-MUSIC, and the proposed EEMD-MUSIC methods. As a result of the capabilities of the EEMD-HT, the DWT-HT, the EEMD-FFT, and the DWT-FFT methods, the closest natural modes of the synthetic signal, <italic>f</italic><sub>1</sub> and <italic>f</italic><sub>2</sub>, are mixed and, therefore, only one value of them is obtained. On the other hand, the proposed EEMD-MUSIC method proved to be able to extract the four natural modes with higher accuracy than DWT-MUSIC since the results are affected by the noise level.</p><p>The overall proposed methodology for this and the two next study cases is implemented in the MATLAB Digital Signal Processing Toolbox. The MUSIC algorithm has an order of 4 and overlaps of 25%. Regarding the EEMD, the number of ensemble members is set to 100 and the standard deviation of white-noise series is set to 0.1. On the other hand, the Daubechies (db10) window is used as the mother wavelet in the DWT.</p></sec><sec id="sec4.2"><title>4.2. Artificial Excitation</title><p>In the second experiment, a tridimensional truss-type scaled structure, shown in <xref ref-type="fig" rid="fig5">Figure 5(a)</xref>, is used for extracting the natural frequencies by means of an artificial excitation. The modal testing is performed using a hanging mass of 14 kg as excitation source. The mass is tied in the first-bay in order to have the maximum displacement of the structure; then, the wire that subjects the mass is cut to induce a free vibration in the structure. The vibration signal is acquired using a MEMS-based triaxial accelerometer model LIS3L02AS4 from STMicroelectronics placed on top of the third bay as shown in <xref ref-type="fig" rid="fig5">Figure 5(a)</xref>. The accelerometer has a user-selectable full scale of ± 19.6 m/s<sup>2</sup>/± 58.8 m/s<sup>2</sup> with a 50 × 10<sup>−4</sup> m/s<sup>2</sup> resolution over 100 Hz. The accelerometer information is digitalized using a 12-bit 4-channel ADS7841 analog-to-digital converter (ADC) shown in <xref ref-type="fig" rid="fig5">Figure 5(b)</xref> from Texas Instruments, with a maximum sampling rate of 200 kHz in each channel. The obtained signals from the accelerometer are stored in a proprietary data acquisition system (DAS) and sent to a personal computer (PC) by universal serial bus (USB) protocol as shown in <xref ref-type="fig" rid="fig5">Figure 5(b)</xref>. The DAS uses a sampling frequency of 3.2 kHz for obtaining 22,400 samples during a time window of 7 s. The vertical free vibration signal, shown in <xref ref-type="fig" rid="fig6">Figure 6</xref>, is used to identify the vertical natural frequencies of the structure.</p><p><xref ref-type="fig" rid="fig7">Figure 7</xref> shows the first seven IMFs obtained from the free vibration response signals. The IMF1 and IMF2 contain noise and high-frequency components out of the frequency range of interest. On the other hand, from IMF3 to IMF6 are used for analysis with the MUSIC method because they contain the natural frequencies for the truss-type structure. The rest of the IMFs are discarded since they do not contain relevant information. <xref ref-type="fig" rid="fig8"> Figure 8</xref> displays the normalized pseudospectrum obtained from selected IMF, where each one of the natural frequencies is observed. The identification results by the proposed methodology are compared to those from FEA as well as from the experimental result identified with the DWT-MUSIC method. The obtained results are presented in <xref ref-type="table" rid="tab2">Table 2</xref>. It is worth noticing that only the DWT-MUSIC is used as an experimental comparative technique since it has the second best performance after EEMD-MUSIC, as shown in the previous study case. The proposed methodology identifies the natural frequencies reasonably closed when it is compared with the analytical estimation from the FEA. Evidently the small differences may be due to a number of real conditions that are not considered or completely represented in the FEA. On the contrary, the DWT-MUSIC method has a higher error in the identification of the natural frequencies due to the real noisy environment.</p></sec><sec id="sec4.3"><title>4.3. Natural Excitation</title><p>The bridge considered in this study is located in “San Juan del Rio, Queretaro, Mexico.” The bridge is used for both highway traffic and pedestrians as shown in <xref ref-type="fig" rid="fig9">Figure 9</xref>. The ambient vibration caused by traffic is on-line monitored through a triaxial accelerometer mounted in the middle of the bridge. The obtained signals from the accelerometer are stored in the DAS and sent to PC by USB protocol. The DAS uses a sampling frequency of 160 Hz for obtaining 32,000 samples during a time window of 200 s, where the vertical vibration response is plotted in <xref ref-type="fig" rid="fig10">Figure 10</xref>, and the filtered signal is analyzed through the EEMD method, and its results are shown in <xref ref-type="fig" rid="fig11">Figure 11</xref>. The IMF3 to IMF6 are selected to obtain the natural frequencies since it contains the interested frequency range of the bridge. <xref ref-type="fig" rid="fig12"> Figure 12</xref> displays the normalized pseudospectra obtained from selected IMF, where each one of the natural frequencies is observed (2.539 Hz, 5.313 Hz, 9.814 Hz, and 14.55 Hz).</p><p><xref ref-type="table" rid="tab3">Table 3</xref> shows a comparison between the values obtained from the proposed methodology and the results obtained by the DWT-MUSIC method. This method can detect the four natural frequencies; however, their accuracy is expected to be lower due to the noise, since ambient vibration data is embedded in high-level noise.</p></sec></sec><sec id="sec5"><title>5. Conclusions</title><p>In this paper, a new methodology based on the fusion of the EEMD and the MUSIC methods for identifying the natural frequencies of civil structures from free and ambient vibration response signals produced by artificial and natural excitations is presented. The effectiveness of the proposal is demonstrated through three experiments. (i) The numerical simulation shows that the proposal can identify closely spaced frequencies even in noisy environments unlike the EEMD-HT, DWT-HT, EEMD-FFT, and DWT-FFT methods; although the DWT-MUSIC method is able to detect close modes, it is sensitive to noisy environments, as the case of free and ambient vibration signals, which does not make it suitable for identifying accurately the natural modes, which is essential in the design of civil structures [<xref rid="B31" ref-type="bibr">31</xref>]. Besides, the decomposition level of the DWT has to be known or at least supposed <italic>a priori </italic>in order to have an adequate result, which is very difficult in real applications since all the signals may have different modes; consequently, the frequency band that contains the natural mode is also different. On the other hand, the EEMD does not have this drawback since it is an intuitive, unsupervised, and self-adaptive method that gives an automatic result. (ii) The very similar obtained natural frequencies through the proposal and FEM of a real truss-type structure make the proposal a suitable tool for the analysis of free vibration signals produced by artificial excitations. (iii) EEMD-MUSIC is a powerful approach for identifying natural frequencies in real and non-controlled civil structures (i.e. a bridge) from ambient vibration data, produced by natural excitations. which is a complicated task since they are nonstationary and embedded in high-level noise.</p><p>The immunity to noisy environments and the capability to identify closely spaced frequencies with high accuracy make the proposal a suitable and powerful tool for different research disciplines such as SHM, structural damage detection, and design structure, helping in the development of appropriate and accurate analytical models for improving the performance, resistance, and life service of the structures, among others.</p></sec></body><back><ack><title>Acknowledgments</title><p>This work was partially supported by CONACyT scholarship 229795 and SEP PIFI-2013 Universidad de Guanajuato projects.</p></ack><sec sec-type="conflict"><title>Conflict of Interests</title><p>The authors declare that there is no conflict of interests regarding the publication of this paper.</p></sec><ref-list><ref id="B1"><label>1</label><element-citation publication-type="gov"><person-group person-group-type="author"><name><surname>Doebling</surname><given-names>S</given-names></name><name><surname>Farrar</surname><given-names>C</given-names></name><name><surname>Prime</surname><given-names>M</given-names></name><name><surname>Shevitz</surname><given-names>D</given-names></name></person-group><article-title>Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review</article-title><source><italic>Los Alamos National Laboratory Report</italic></source><year>1996</year><issue>LA 13070-MS</issue></element-citation></ref><ref id="B2"><label>2</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bai</surname><given-names>X</given-names></name><name><surname>Zhang</surname><given-names>X</given-names></name></person-group><article-title>A novel evaluation method for building construction project based on integrated information entropy with reliability theory</article-title><source><italic>The Scientific World Journal</italic></source><year>2013</year><volume>2013</volume><fpage>8 pages</fpage><pub-id pub-id-type="publisher-id">573014</pub-id></element-citation></ref><ref id="B3"><label>3</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Amezquita-Sanchez</surname><given-names>JP</given-names></name><name><surname>Osornio-Rios</surname><given-names>R</given-names></name><name><surname>Romero-Troncoso</surname><given-names>R</given-names></name><name><surname>Dominguez-Gonzalez</surname><given-names>A</given-names></name></person-group><article-title>Hardware-software system for simulating and analyzing earthquakes applied to civil structures</article-title><source><italic>Natural Hazards and Earth System Science</italic></source><year>2012</year><volume>12</volume><issue>1</issue><fpage>61</fpage><lpage>73</lpage><pub-id pub-id-type="other">2-s2.0-84855800319</pub-id></element-citation></ref><ref id="B4"><label>4</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>He</surname><given-names>XH</given-names></name><name><surname>Hua</surname><given-names>X</given-names></name><name><surname>Chen</surname><given-names>Z</given-names></name><name><surname>Huang</surname><given-names>F</given-names></name></person-group><article-title>EMD-based random decrement technique for modal parameter identification of an existing railway bridge</article-title><source><italic>Engineering Structures</italic></source><year>2011</year><volume>33</volume><issue>4</issue><fpage>1348</fpage><lpage>1356</lpage><pub-id pub-id-type="other">2-s2.0-79951952917</pub-id></element-citation></ref><ref id="B5"><label>5</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shi</surname><given-names>W</given-names></name><name><surname>Shan</surname><given-names>J</given-names></name><name><surname>Lu</surname><given-names>X</given-names></name></person-group><article-title>Modal identification of Shanghai World Financial Center both from free and ambient vibration response</article-title><source><italic>Engineering Structures</italic></source><year>2012</year><volume>36</volume><fpage>14</fpage><lpage>26</lpage><pub-id pub-id-type="other">2-s2.0-84255201097</pub-id></element-citation></ref><ref id="B6"><label>6</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pieraccini</surname><given-names>M</given-names></name></person-group><article-title>Monitoring of civil infrastructures by interferometric radar: a review</article-title><source><italic>The Scientific World Journal</italic></source><year>2013</year><volume>2013</volume><fpage>8 pages</fpage><pub-id pub-id-type="publisher-id">786961</pub-id></element-citation></ref><ref id="B7"><label>7</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hu</surname><given-names>W</given-names></name><name><surname>Cunha</surname><given-names>Á</given-names></name><name><surname>Caetano</surname><given-names>E</given-names></name><name><surname>Magalhães</surname><given-names>F</given-names></name><name><surname>Moutinho</surname><given-names>C</given-names></name></person-group><article-title>LabVIEW toolkits for output-only modal identification and long-term dynamic structural monitoring</article-title><source><italic>Structure and Infrastructure Engineering</italic></source><year>2010</year><volume>6</volume><issue>5</issue><fpage>557</fpage><lpage>574</lpage><pub-id pub-id-type="other">2-s2.0-77953656440</pub-id></element-citation></ref><ref id="B8"><label>8</label><element-citation publication-type="confproc"><person-group person-group-type="author"><name><surname>Ibrahim</surname><given-names>Z</given-names></name><name><surname>Reynolds</surname><given-names>P</given-names></name></person-group><article-title>Modal testing of a cantilever grandstand</article-title><conf-name>Proceedings of the International Conference on Construction and Building Technology (ICCBT '08)</conf-name><conf-date>June 2008</conf-date><conf-loc>Kuala Lumpur, Malaysia</conf-loc><fpage>271</fpage><lpage>284</lpage></element-citation></ref><ref id="B9"><label>9</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Siringoringo</surname><given-names>D</given-names></name><name><surname>Fujino</surname><given-names>Y</given-names></name></person-group><article-title>System identification of suspension bridge from ambient vibration response</article-title><source><italic>Engineering Structures</italic></source><year>2008</year><volume>30</volume><issue>2</issue><fpage>462</fpage><lpage>477</lpage><pub-id pub-id-type="other">2-s2.0-37349075164</pub-id></element-citation></ref><ref id="B10"><label>10</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Peeters</surname><given-names>B</given-names></name><name><surname>de Roeck</surname><given-names>G</given-names></name></person-group><article-title>Reference based stochastic subspace identification in civil engineering</article-title><source><italic>Inverse Problems in Engineering</italic></source><year>2000</year><volume>8</volume><issue>1</issue><fpage>47</fpage><lpage>74</lpage><pub-id pub-id-type="other">2-s2.0-0038547884</pub-id></element-citation></ref><ref id="B11"><label>11</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Brownjohn</surname><given-names>J</given-names></name><name><surname>Magalhaes</surname><given-names>F</given-names></name><name><surname>Caetano</surname><given-names>E</given-names></name><name><surname>Cunha</surname><given-names>A</given-names></name></person-group><article-title>Ambient vibration re-testing and operational modal analysis of the Humber Bridge</article-title><source><italic>Engineering Structures</italic></source><year>2010</year><volume>32</volume><issue>8</issue><fpage>2003</fpage><lpage>2018</lpage><pub-id pub-id-type="other">2-s2.0-77953611453</pub-id></element-citation></ref><ref id="B12"><label>12</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kim</surname><given-names>C</given-names></name><name><surname>Kawatani</surname><given-names>M</given-names></name><name><surname>Hao</surname><given-names>J</given-names></name></person-group><article-title>Modal parameter identification of short span bridges under a moving vehicle by means of multivariate AR model</article-title><source><italic>Structure and Infrastructure Engineering</italic></source><year>2012</year><volume>8</volume><issue>5</issue><fpage>459</fpage><lpage>472</lpage><pub-id pub-id-type="other">2-s2.0-84856106664</pub-id></element-citation></ref><ref id="B13"><label>13</label><element-citation publication-type="confproc"><person-group person-group-type="author"><name><surname>Andersen</surname><given-names>P</given-names></name><name><surname>Brincker</surname><given-names>R</given-names></name><name><surname>Kirkegaard</surname><given-names>P</given-names></name></person-group><article-title>Theory of covariance equivalent ARMAV models of civil engineering structures</article-title><conf-name>Proceedings of 14th International Modal Analysis Conference</conf-name><conf-date>1996</conf-date><conf-loc>Dearborn, Mich, USA</conf-loc><fpage>518</fpage><lpage>524</lpage><pub-id pub-id-type="other">2-s2.0-0031675796</pub-id></element-citation></ref><ref id="B14"><label>14</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Urgessa</surname><given-names>GS</given-names></name></person-group><article-title>Vibration properties of beams using frequency-domain system identification methods</article-title><source><italic>Journal of Vibration and Control</italic></source><year>2011</year><volume>17</volume><issue>9</issue><fpage>1287</fpage><lpage>1294</lpage><pub-id pub-id-type="other">2-s2.0-79960683328</pub-id></element-citation></ref><ref id="B15"><label>15</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Brincker</surname><given-names>R</given-names></name><name><surname>Zhang</surname><given-names>L</given-names></name><name><surname>Andersen</surname><given-names>P</given-names></name></person-group><article-title>Modal identification of output-only systems using frequency domain decomposition</article-title><source><italic>Smart Materials and Structures</italic></source><year>2001</year><volume>10</volume><issue>3</issue><fpage>441</fpage><lpage>445</lpage><pub-id pub-id-type="other">2-s2.0-0035361632</pub-id></element-citation></ref><ref id="B16"><label>16</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yan</surname><given-names>B</given-names></name><name><surname>Miyamoto</surname><given-names>A</given-names></name><name><surname>Brühwiler</surname><given-names>E</given-names></name></person-group><article-title>Wavelet transform-based modal parameter identification considering uncertainty</article-title><source><italic>Journal of Sound and Vibration</italic></source><year>2006</year><volume>291</volume><issue>1-2</issue><fpage>285</fpage><lpage>301</lpage><pub-id pub-id-type="other">2-s2.0-30344488761</pub-id></element-citation></ref><ref id="B17"><label>17</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Amezquita-Sanchez</surname><given-names>J</given-names></name><name><surname>Garcia-Perez</surname><given-names>A</given-names></name><name><surname>Romero-Troncoso</surname><given-names>R</given-names></name><name><surname>Osornio-Rios</surname><given-names>R</given-names></name><name><surname>Herrera-Ruiz</surname><given-names>G</given-names></name></person-group><article-title>High-resolution spectral-analysis for identifying the natural modes of a truss-type structure by means of vibrations</article-title><source><italic>Journal of Vibration and Control</italic></source><year>2012</year><volume>19</volume><issue>16</issue><fpage>2347</fpage><lpage>2356</lpage></element-citation></ref><ref id="B18"><label>18</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yan</surname><given-names>B</given-names></name><name><surname>Miyamoto</surname><given-names>A</given-names></name></person-group><article-title>A comparative study of modal parameter identification based on wavelet and Hilbert-Huang transforms</article-title><source><italic>Computer-Aided Civil and Infrastructure Engineering</italic></source><year>2006</year><volume>21</volume><issue>1</issue><fpage>9</fpage><lpage>23</lpage><pub-id pub-id-type="other">2-s2.0-33646007341</pub-id></element-citation></ref><ref id="B19"><label>19</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chen</surname><given-names>S</given-names></name><name><surname>Liu</surname><given-names>J</given-names></name><name><surname>Lai</surname><given-names>H</given-names></name></person-group><article-title>Wavelet analysis for identification of damping ratios and natural frequencies</article-title><source><italic>Journal of Sound and Vibration</italic></source><year>2009</year><volume>323</volume><issue>1-2</issue><fpage>130</fpage><lpage>147</lpage><pub-id pub-id-type="other">2-s2.0-64449085356</pub-id></element-citation></ref><ref id="B20"><label>20</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tang</surname><given-names>J</given-names></name><name><surname>Chiou</surname><given-names>D</given-names></name><name><surname>Chen</surname><given-names>C</given-names></name><name><surname>Chiang</surname><given-names>W</given-names></name><name><surname>Hsu</surname><given-names>W</given-names></name><name><surname>Liu</surname><given-names>T</given-names></name></person-group><article-title>A case study of damage detection in benchmark buildings using a Hilbert-Huang Transform-based method</article-title><source><italic>Journal of Vibration and Control</italic></source><year>2010</year><volume>17</volume><issue>4</issue><fpage>623</fpage><lpage>636</lpage></element-citation></ref><ref id="B21"><label>21</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Liu</surname><given-names>T</given-names></name><name><surname>Chiang</surname><given-names>W</given-names></name><name><surname>Chen</surname><given-names>C</given-names></name><name><surname>Hsu</surname><given-names>W</given-names></name><name><surname>Lu</surname><given-names>L</given-names></name><name><surname>Chu</surname><given-names>T</given-names></name></person-group><article-title>Identification and monitoring of bridge health from ambient vibration data</article-title><source><italic>Journal of Vibration and Control</italic></source><year>2011</year><volume>17</volume><issue>4</issue><fpage>589</fpage><lpage>603</lpage><pub-id pub-id-type="other">2-s2.0-79954537802</pub-id></element-citation></ref><ref id="B22"><label>22</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Liu</surname><given-names>T</given-names></name><name><surname>Chiang</surname><given-names>W</given-names></name><name><surname>Chen</surname><given-names>C</given-names></name><etal></etal></person-group><article-title>Structural system identification for vibration bridges using the Hilbert-Huang transform</article-title><source><italic>Journal of Vibration and Control</italic></source><year>2012</year><volume>18</volume><issue>13</issue><fpage>1939</fpage><lpage>1956</lpage></element-citation></ref><ref id="B23"><label>23</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hsu</surname><given-names>W</given-names></name><name><surname>Chiou</surname><given-names>D</given-names></name><name><surname>Chen</surname><given-names>C</given-names></name><name><surname>Liu</surname><given-names>M</given-names></name><name><surname>Chiang</surname><given-names>W</given-names></name><name><surname>Huang</surname><given-names>P</given-names></name></person-group><article-title>Sensitivity of initial damage detection for steel structures using the Hilbert-Huang transform method</article-title><source><italic>Journal of Vibration and Control</italic></source><year>2013</year><volume>19</volume><issue>6</issue><fpage>857</fpage><lpage>878</lpage></element-citation></ref><ref id="B24"><label>24</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Chang</surname><given-names>K-M</given-names></name></person-group><article-title>Arrhythmia ECG noise reduction by ensemble empirical mode decomposition</article-title><source><italic>Sensors</italic></source><year>2010</year><volume>10</volume><issue>6</issue><fpage>6063</fpage><lpage>6080</lpage><pub-id pub-id-type="other">2-s2.0-77954786824</pub-id><pub-id pub-id-type="pmid">22219702</pub-id></element-citation></ref><ref id="B25"><label>25</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Wu</surname><given-names>Z</given-names></name><name><surname>Huang</surname><given-names>N</given-names></name></person-group><article-title>Ensemble empirical mode decomposition: a noise-assisted data analysis method</article-title><year>2005</year><issue>Series 193</issue><publisher-name>Center for Ocean-Land-Atmosphere Studies</publisher-name></element-citation></ref><ref id="B26"><label>26</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jiang</surname><given-names>X</given-names></name><name><surname>Adeli</surname><given-names>H</given-names></name></person-group><article-title>Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings</article-title><source><italic>International Journal for Numerical Methods in Engineering</italic></source><year>2007</year><volume>71</volume><issue>5</issue><fpage>606</fpage><lpage>629</lpage><pub-id pub-id-type="other">2-s2.0-34547595423</pub-id></element-citation></ref><ref id="B27"><label>27</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Osornio-Rios</surname><given-names>R</given-names></name><name><surname>Amezquita-Sanchez</surname><given-names>J</given-names></name><name><surname>Romero-Troncoso</surname><given-names>R</given-names></name><name><surname>Garcia-Perez</surname><given-names>A</given-names></name></person-group><article-title>MUSIC-ANN analysis for locating structural damages in a truss-type structure by means of vibrations</article-title><source><italic>Computer-Aided Civil and Infrastructure Engineering</italic></source><year>2012</year><volume>27</volume><issue>9</issue><fpage>687</fpage><lpage>698</lpage></element-citation></ref><ref id="B28"><label>28</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Huang</surname><given-names>N</given-names></name><name><surname>Shen</surname><given-names>Z</given-names></name><name><surname>Long</surname><given-names>S</given-names></name><etal></etal></person-group><article-title>The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis</article-title><source><italic>Proceedings of The Royal Society of London A</italic></source><year>1998</year><volume>454</volume><fpage>903</fpage><lpage>995</lpage><pub-id pub-id-type="other">2-s2.0-5444236478</pub-id></element-citation></ref><ref id="B29"><label>29</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wu</surname><given-names>Z</given-names></name><name><surname>Huang</surname><given-names>NE</given-names></name></person-group><article-title>Ensemble empirical mode decomposition: a noise-assisted data analysis method</article-title><source><italic>Advances in Adaptive Data Analysis</italic></source><year>2009</year><volume>1</volume><issue>1</issue><fpage>1</fpage><lpage>41</lpage><pub-id pub-id-type="other">2-s2.0-80052078099</pub-id></element-citation></ref><ref id="B30"><label>30</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Garcia-Perez</surname><given-names>A</given-names></name><name><surname>Romero-Troncoso</surname><given-names>RDJ</given-names></name><name><surname>Cabal-Yepez</surname><given-names>E</given-names></name><name><surname>Osornio-Rios</surname><given-names>RA</given-names></name></person-group><article-title>The application of high-resolution spectral analysis for identifying multiple combined faults in induction motors</article-title><source><italic>IEEE Transactions on Industrial Electronics</italic></source><year>2011</year><volume>58</volume><issue>5</issue><fpage>2002</fpage><lpage>2010</lpage><pub-id pub-id-type="other">2-s2.0-79954497420</pub-id></element-citation></ref><ref id="B31"><label>31</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Young</surname><given-names>K</given-names></name><name><surname>Adeli</surname><given-names>H</given-names></name></person-group><article-title>Fundamental period of irregular moment-resisting steel frame structures</article-title><source><italic>The Structural Design of Tall and Special Buildings</italic></source><year>2013</year></element-citation></ref></ref-list></back><floats-group><fig id="fig1" orientation="portrait" position="float"><label>Figure 1</label><caption><p>Proposed methodology. (a) Synthetic signal, (b) artificial excitation, and (c) natural excitation.</p></caption><graphic xlink:href="TSWJ2014-587671.001"></graphic></fig><fig id="fig2" orientation="portrait" position="float"><label>Figure 2</label><caption><p>Synthetic signal.</p></caption><graphic xlink:href="TSWJ2014-587671.002"></graphic></fig><fig id="fig3" orientation="portrait" position="float"><label>Figure 3</label><caption><p>IMFs and DCs obtained of the synthetic signal through EEMD and DWT, respectively.</p></caption><graphic xlink:href="TSWJ2014-587671.003"></graphic></fig><fig id="fig4" orientation="portrait" position="float"><label>Figure 4</label><caption><p>Results obtained by (a) EEMD-HT method, (b) DWT-HT, (c) EEMD-FFT, (d) DWT-FFT, (e) EEMD-MUSIC, and (f) DWT-MUSIC.</p></caption><graphic xlink:href="TSWJ2014-587671.004"></graphic></fig><fig id="fig5" orientation="portrait" position="float"><label>Figure 5</label><caption><p>Experimental setup: (a) overall system and (b) triaxial accelerometer and data acquisition system.</p></caption><graphic xlink:href="TSWJ2014-587671.005"></graphic></fig><fig id="fig6" orientation="portrait" position="float"><label>Figure 6</label><caption><p>Measured vertical acceleration.</p></caption><graphic xlink:href="TSWJ2014-587671.006"></graphic></fig><fig id="fig7" orientation="portrait" position="float"><label>Figure 7</label><caption><p>IMF obtained through EEMD for free vibration acceleration.</p></caption><graphic xlink:href="TSWJ2014-587671.007"></graphic></fig><fig id="fig8" orientation="portrait" position="float"><label>Figure 8</label><caption><p>Pseudospectra of different analyzed IMF.</p></caption><graphic xlink:href="TSWJ2014-587671.008"></graphic></fig><fig id="fig9" orientation="portrait" position="float"><label>Figure 9</label><caption><p>Analyzed bridge.</p></caption><graphic xlink:href="TSWJ2014-587671.009"></graphic></fig><fig id="fig10" orientation="portrait" position="float"><label>Figure 10</label><caption><p>Measured acceleration response.</p></caption><graphic xlink:href="TSWJ2014-587671.010"></graphic></fig><fig id="fig11" orientation="portrait" position="float"><label>Figure 11</label><caption><p>IMFs obtained through EEMD for ambient vibration acceleration.</p></caption><graphic xlink:href="TSWJ2014-587671.011"></graphic></fig><fig id="fig12" orientation="portrait" position="float"><label>Figure 12</label><caption><p>Pseudospectra of different analyzed IMFs.</p></caption><graphic xlink:href="TSWJ2014-587671.012"></graphic></fig><table-wrap id="tab1" orientation="portrait" position="float"><label>Table 1</label><caption><p>Results of identified natural frequencies with different methodologies.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="2" colspan="1">Reference values</th><th align="center" colspan="3" rowspan="1">EEMD</th><th align="center" colspan="3" rowspan="1">DWT</th></tr><tr><th align="center" rowspan="1" colspan="1">HT</th><th align="center" rowspan="1" colspan="1">FFT</th><th align="center" rowspan="1" colspan="1">MUSIC</th><th align="center" rowspan="1" colspan="1">HT</th><th align="center" rowspan="1" colspan="1">FFT</th><th align="center" rowspan="1" colspan="1">MUSIC</th></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1"><italic>f</italic><sub>1</sub> = 0.61</td><td align="center" rowspan="2" colspan="1">0.72*</td><td align="center" rowspan="2" colspan="1">0.68*</td><td align="center" rowspan="1" colspan="1"><bold>0.61</bold></td><td align="center" rowspan="2" colspan="1">0.70*</td><td align="center" rowspan="2" colspan="1">0.72*</td><td align="center" rowspan="1" colspan="1">0.61</td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>f</italic><sub>2</sub> = 0.73</td><td align="center" rowspan="1" colspan="1"><bold>0.73</bold></td><td align="center" rowspan="1" colspan="1">0.78</td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>f</italic><sub>3</sub> = 1.56</td><td align="center" rowspan="1" colspan="1">1.54</td><td align="center" rowspan="1" colspan="1">1.52</td><td align="center" rowspan="1" colspan="1"><bold>1.56</bold></td><td align="center" rowspan="1" colspan="1">1.31</td><td align="center" rowspan="1" colspan="1">1.55</td><td align="center" rowspan="1" colspan="1">1.56</td></tr><tr><td align="left" rowspan="1" colspan="1"><italic>f</italic><sub>4</sub> = 4.35</td><td align="center" rowspan="1" colspan="1">4.38</td><td align="center" rowspan="1" colspan="1">4.30</td><td align="center" rowspan="1" colspan="1"><bold>4.34</bold></td><td align="center" rowspan="1" colspan="1">4.41</td><td align="center" rowspan="1" colspan="1">4.38</td><td align="center" rowspan="1" colspan="1">4.37</td></tr></tbody></table><table-wrap-foot><fn><p>*Mixed modes.</p></fn></table-wrap-foot></table-wrap><table-wrap id="tab2" orientation="portrait" position="float"><label>Table 2</label><caption><p>Comparison of natural frequencies.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="1" colspan="1">Modes</th><th align="center" rowspan="1" colspan="1">Finite element analysis</th><th align="center" rowspan="1" colspan="1">Proposed methodology <break></break>(EEMD-MUSIC)</th><th align="center" rowspan="1" colspan="1">DWT-MUSIC</th></tr></thead><tbody><tr><td colspan="4" align="center" rowspan="1">Natural frequency (Hz)</td></tr><tr><td align="left" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">24.48</td><td align="center" rowspan="1" colspan="1">23.44</td><td align="center" rowspan="1" colspan="1">21.88</td></tr><tr><td align="left" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">25.50</td><td align="center" rowspan="1" colspan="1">25.00</td><td align="center" rowspan="1" colspan="1">26.56</td></tr><tr><td align="left" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">52.57</td><td align="center" rowspan="1" colspan="1">51.56</td><td align="center" rowspan="1" colspan="1">50.00</td></tr><tr><td align="left" rowspan="1" colspan="1">4</td><td align="center" rowspan="1" colspan="1">54.65</td><td align="center" rowspan="1" colspan="1">54.69</td><td align="center" rowspan="1" colspan="1">53.13</td></tr></tbody></table></table-wrap><table-wrap id="tab3" orientation="portrait" position="float"><label>Table 3</label><caption><p>Identified natural frequencies.</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="1" colspan="1">Modes</th><th align="center" rowspan="1" colspan="1">Proposed methodology</th><th align="center" rowspan="1" colspan="1">DWT-MUSIC</th></tr></thead><tbody><tr><td colspan="3" align="center" rowspan="1">Natural frequencies (Hz)</td></tr><tr><td align="left" rowspan="1" colspan="1">1</td><td align="center" rowspan="1" colspan="1">2.539</td><td align="center" rowspan="1" colspan="1">2.50</td></tr><tr><td align="left" rowspan="1" colspan="1">2</td><td align="center" rowspan="1" colspan="1">5.313</td><td align="center" rowspan="1" colspan="1">5.15</td></tr><tr><td align="left" rowspan="1" colspan="1">3</td><td align="center" rowspan="1" colspan="1">9.814</td><td align="center" rowspan="1" colspan="1">10.00</td></tr><tr><td align="left" rowspan="1" colspan="1">4</td><td align="center" rowspan="1" colspan="1">14.55</td><td align="center" rowspan="1" colspan="1">14.69</td></tr></tbody></table></table-wrap></floats-group></pmc></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Ticri/CIDE/explor/TelematiV1/Data/Pmc/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000539 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Pmc/Corpus/biblio.hfd -nk 000539 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Ticri/CIDE
|area= TelematiV1
|flux= Pmc
|étape= Corpus
|type= RBID
|clé=
|texte=
}}
| This area was generated with Dilib version V0.6.31. |  |