Bayesian operational modal analysis

Bayesian operational modal analysis (BAYOMA) adopts a Bayesian system identification approach for operational modal analysis (OMA). Operational modal analysis aims at identifying the modal properties (natural frequencies, damping ratios, mode shapes, etc.) of a constructed structure using only its (output) vibration response (e.g., velocity, acceleration) measured under operating conditions. The (input) excitations to the structure are not measured but are assumed to be 'ambient' ('broadband random'). In a Bayesian context, the set of modal parameters are viewed as uncertain parameters or random variables whose probability distribution is updated from the prior distribution (before data) to the posterior distribution (after data). The peak(s) of the posterior distribution represents the most probable value(s) (MPV) suggested by the data, while the spread of the distribution around the MPV reflects the remaining uncertainty of the parameters.

Pros and cons

In the absence of (input) loading information, the identified modal properties from OMA often have significantly larger uncertainty (or variability) than their counterparts identified using free vibration or forced vibration (known input) tests. Quantifying and calculating the identification uncertainty of the modal parameters become relevant.

The advantage of a Bayesian approach for OMA is that it provides a fundamental means via the Bayes' Theorem to process the information in the data for making statistical inference on the modal properties in a manner consistent with modeling assumptions and probability logic.

The potential disadvantage of Bayesian approach is that the theoretical formulation can be more involved and less intuitive than their non-Bayesian counterparts. Algorithms are needed for efficient computation of the statistics (e.g., mean and variance) of the modal parameters from the posterior distribution. Unlike non-Bayesian methods, the algorithms are often implicit and iterative. E.g., optimization algorithms may be involved in the determination of most probable value, which may not converge for poor quality data.

Methods

Bayesian formulations have been developed for OMA in the time domain[1] and in the frequency domain using the spectral density matrix[2] and fast Fourier transform (FFT)[3] of ambient vibration data. Based on the formulation for FFT data, fast algorithms have been developed for computing the posterior statistics of modal parameters.[4] Recent developments based on EM algorithm[5] show promise for simpler algorithms and reduced coding effort. The fundamental precision limit of OMA has been investigated and presented as a set of uncertainty laws which can be used for planning ambient vibration tests.[6]

Connection with maximum likelihood method

Bayesian method and maximum likelihood method (non-Bayesian) are based on different philosophical perspectives but they are mathematically connected; see, e.g.,[7] and Section 9.6 of.[4] For example,

  • Assuming a uniform prior, the most probable value (MPV) of parameters in a Bayesian method is equal to the location where the likelihood function is maximized, which is the estimate in Maximum Likelihood Method
  • Under a Gaussian approximation of the posterior distribution of parameters, their covariance matrix is equal to the inverse of Hessian of the negative log of likelihood function at the MPV. Generally, this covariance depends on data. However, if one assumes (hypothetically; non-Bayesian) that the data is indeed distributed as the likelihood function, then for large data size it can be shown that the covariance matrix is asymptotically equal to the inverse of the Fisher information matrix (FIM) of parameters (which has a non-Bayesian origin). This coincides with the Cramer–Rao bound in classical statistics, which gives the lower bound (in the sense of matrix inequality) of the ensemble variance of any unbiased estimator. Such lower bound can be reached by maximum-likelihood estimator for large data size.
  • In the above context, for large data size the asymptotic covariance matrix of modal parameters depends on the 'true' parameter values (a non-Bayesian concept), often in an implicit manner. It turns out that by applying further assumptions such as small damping and high signal-to-noise ratio, the covariance matrix has mathematically manageable asymptotic form, which provides insights on the achievable precision limit of OMA and can be used to guide ambient vibration test planning. This is collectively referred as 'uncertainty law'.[6]

See also

Notes

  • See monographs on non-Bayesian OMA [8][9][10] and Bayesian OMA [4]
  • See OMA datasets [11]
  • See Jaynes[12] and Cox[13] for Bayesian inference in general.
  • See Beck[14] for Bayesian inference in structural dynamics (relevant for OMA)
  • The uncertainty of the modal parameters in OMA can also be quantified and calculated in a non-Bayesian manner. See Pintelon et al.[15]

References

  1. ^ Yuen, K.V.; Katafygiotis, L.S. (2001). "Bayesian time-domain approach for modal updating using ambient data". Probabilistic Engineering Mechanics. 16 (3): 219–231. doi:10.1016/S0266-8920(01)00004-2.
  2. ^ Yuen, K.V.; Katafygiotis, L.S. (2001). "Bayesian spectral density approach for modal updating using ambient data". Earthquake Engineering & Structural Dynamics. 30 (8): 1103–1123. doi:10.1002/eqe.53. S2CID 110355068.
  3. ^ Yuen, K.V.; Katafygiotis, L.S. (2003). "Bayesian Fast Fourier Transform approach for modal updating using ambient data". Advances in Structural Engineering. 6 (2): 81–95. doi:10.1260/136943303769013183. S2CID 62564168.
  4. ^ a b c Au, S.K. (2017). Operational Modal Analysis: Modeling, Inference, Uncertainty Laws. Springer.
  5. ^ Li, B.; Au, S.K. (2019). "An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes". Mechanical Systems and Signal Processing. 132: 490–511. Bibcode:2019MSSP..132..490L. doi:10.1016/j.ymssp.2019.06.036. hdl:10356/149983. S2CID 199124928.
  6. ^ a b Au, S.K.; Brownjohn, J.M.W.; Mottershead, J. (2018). "Quantifying and managing uncertainty in operational modal analysis". Mechanical Systems and Signal Processing. 102: 139–157. Bibcode:2018MSSP..102..139A. doi:10.1016/j.ymssp.2017.09.017. hdl:10871/30384.
  7. ^ Au, S.K.; Li, B. (2017). "Posterior uncertainty, asymptotic law and Cramér‐Rao bound". Mechanical Systems and Signal Processing. 25 (3): e2113. doi:10.1002/stc.2113. S2CID 55868193.
  8. ^ Van Overschee, P.; De Moor, B. (1996). Subspace Identification for Linear Systems. Boston: Kluwer Academic Publisher.
  9. ^ Schipfors, M.; Fabbrocino, G. (2014). Operational Modal Analysis of Civil Engineering Structures. Springer.
  10. ^ Brincker, R.; Ventura, C. (2015). Introduction to Operational Modal Analysis. John Wiley & Sons. doi:10.1002/9781118535141. ISBN 9781118535141.
  11. ^ "Operational Modal Analysis Dataverse".
  12. ^ Jaynes, E.T. (2003). Probability Theory: The Logic of Science. United Kingdom: Cambridge University Press.
  13. ^ Cox, R.T. (1961). The Algebra of Probable Inference. Baltimore: Johns Hopkins University Press.
  14. ^ Beck, J.L. (2010). "Bayesian system identification based on probability logic". Structural Control and Health Monitoring. 17 (7): 825–847. doi:10.1002/stc.424. S2CID 122257401.
  15. ^ Pintelon, R.; Guillaume, P.; Schoukens, J. (2007). "Uncertainty calculation in (operational) modal analysis". Mechanical Systems and Signal Processing. 21 (6): 2359–2373. Bibcode:2007MSSP...21.2359P. doi:10.1016/j.ymssp.2006.11.007.

Read other articles:

Hati Seluas Samudera

Hati Seluas SamuderaGenre Roman Remaja Ditulis olehPietrajaya BurnamaSutradaraJopi BurnamaPemeran Paramitha Rusady Yati Octavia Elma Theana Jeremy Thomas Anjas Mara Penggubah lagu tema Ags. Arya Dipayana Dwiki Dharmawan Lagu pembukaHati Seluas Samudera oleh Uchy AmyrthaLagu penutupHati Seluas Samudera[a]Penata musikDwiki DharmawanNegara asalIndonesiaJmlh. musim1Jmlh. episode10ProduksiProduser eksekutif Dhamoo Punjabi Gobind Punjabi ProduserRaam PunjabiPengaturan kameraKamera tu...

 

Kota Sawahlunto

Kota SawahluntoKotaDari Atas, Searah Jarum jam: Pemandangan Kota Sawahlunto dari Puncak Cemara, Stasiun Kereta Api Sawahlunto, Museum Kereta Api, Wisata Alam Batu Runcing, Lapangan Segitiga, Gedung Pusat Kebudayaan Kota Sawahlunto, Balai Kota Sawahlunto LambangJulukan: Kota ArangPetaKota SawahluntoPetaTampilkan peta SumatraKota SawahluntoKota Sawahlunto (Indonesia)Tampilkan peta IndonesiaKoordinat: 0°40′58″S 100°46′42″E / 0.6828°S 100.7783°E / -0.6828;...

 

Daftar basilika di Kolombia

Basilika Katedral Primatial Maria Dikandung Tanpa Noda, Bogotá Ini adalah daftar lengkap Basilika di Kolombia. Basilika adalah gelar yang diberikan kepada beberapa gereja Katolik. Berdasarkan hukum kanonik tidak ada gereja Katolik yang dapat dihormati dengan gelar basilika kecuali mendapatkan hibah apostolik atau berdasarkan kebiasaan dahulu kala.[1] Gelar ini diberikan kepada gereja-gereja besar yang penting sebagai tempat ziarah atau untuk pengabdian tertentu seperti kepada orang s...

Teluk Alaska (seri web)

Artikel ini bukan mengenai Teluk Alaska. Teluk AlaskaGenre Drama Roman Remaja BerdasarkanTeluk Alaskaoleh Eka AryaniSkenarioFiona MahdalenaSutradaraAdhe DharmastriyaPemeran Syifa Hadju Devano Danendra Kaneishia Yusuf Taha Tolu Amara Sophie Lagu pembukaCerita Remaja oleh Devano DanendraLagu penutupPerih oleh MadukinaPenata musikGanden Bramanto S.Negara asalIndonesiaBahasa asliBahasa IndonesiaJmlh. musim1Jmlh. episode8ProduksiProduser eksekutif Dhamoo Punjabi Jeff Han Kaichen Li Lesley Si...

 

Ini Sahur

Ini SahurGenreGelar wicaraKomediPembuatWishnutama Roan Y. AnpriraPresenterSuleAndre TaulanyNegara asalIndonesiaBahasa asliBahasa IndonesiaProduksiLokasi produksiStudio PSI Pengadegan (2014) Sound Stage NET., Graha Mitra, Karet Semanggi, Setiabudi, Jakarta Selatan (2015-2019)Durasi150 menitRumah produksiNET. EntertainmentDistributorNet Visi MediaIndika GroupRilis asliJaringanNET.Format gambarHDTV (1080i 16:9)Format audioDolby Digital 5.1Rilis29 Juni 2014 (2014-06-29) –4 Juni 2019&...

 

Bell 212

1968 utility helicopter family by Bell This article is about the civil versions and operators of the Bell 212. For the military versions and operators, see UH-1N Twin Huey. For an overview of the whole Huey family of aircraft, see Bell Huey family. For the computer modem, see Bell 212A. Bell 212 Bell 212 operated by Kachina departs from the Mojave Spaceport Role Medium utility helicopterType of aircraft National origin United States/Canada Manufacturer Bell Helicopter First flight 1968 Introd...

Abel Muzorewa

Abel Muzorewa Primo ministro dello Zimbabwe RhodesiaDurata mandato1 giugno 1979 –11 dicembre 1979 PredecessoreIan Smith SuccessoreRobert Mugabe Dati generaliPartito politicoUnited African National Council Abel Tendekayi Muzorewa (Rhodesia Meridionale, 14 aprile 1925 – Harare, 8 aprile 2010) è stato un politico zimbabwese, per breve tempo Primo ministro dello Zimbabwe Rhodesia, all'epoca stato non riconosciuto dominato da una minoranza di bianchi nel paese. Indice 1 Bio...

 

Centerville, Iowa

For the unincorporated community, see Centerville, Boone County, Iowa. City in Iowa, United StatesCentervilleCityAppanoose County Courthouse and the Centerville Square SealLocation of Centerville, IowaCentervilleShow map of IowaCentervilleShow map of the United StatesCoordinates: 40°43′51″N 92°53′00″W / 40.73083°N 92.88333°W / 40.73083; -92.88333Country United StatesState IowaCountyAppanooseArea[1] • Total4.87 sq mi (...

 

Coppa CONMEBOL 1996

Coppa CONMEBOL 1996 Competizione Coppa CONMEBOL Sport Calcio Edizione 5ª Organizzatore CONMEBOL Date 10 settembre - 4 dicembre 1996 Partecipanti 16 Risultati Vincitore  Lanús(1º titolo) Secondo  Ind. Santa Fe Statistiche Miglior marcatore Óscar Mena(Lanús), 5 gol Incontri disputati 30 Gol segnati 94 (3,13 per incontro) Cronologia della competizione 1995 1997 Manuale La Coppa CONMEBOL 1996 è stata la quinta edizione del torneo. Alla manifestazione parteciparono 16 sq...

Erovnuli Liga 2022

Erovnuli Liga 2022Crystalbet National League 2022 Competizione Erovnuli Liga Sport Calcio Edizione 34ª Organizzatore GFF Date dal 25 febbraio 2022al 3 dicembre 2022 Luogo  Georgia Partecipanti 10 Formula Girone all'italiana Risultati Vincitore Dinamo Tbilisi(19º titolo) Retrocessioni Sioni BolnisiLok’omot’ivi Tbilisi Statistiche Miglior marcatore Flamarion (19) Incontri disputati 180 Gol segnati 492 (2,73 per incontro) Cronologia della competizione 2021 2023 Manu...

 

Endah Laras

Endah LarasLahirEndah Sri Murwani(1976-08-03)3 Agustus 1976Sukoharjo, Jawa Tengah, IndonesiaNama lainEndah LarasAlmamaterInstitut Seni Indonesia SurakartaPekerjaanPenyanyiaktrispenariKeluargaSruti Respati (adik)Karier musikGenreKeroncongInstrumenVokalukulelepianoTahun aktif1992—sekarang Endah Sri Murwani, lebih dikenal dengan nama Endah Laras (lahir 3 Agustus 1976) adalah penyanyi, aktris, dan penari berkebangsaan Indonesia. Endah mengawali kariernya pada 1992 dengan menjadi konduktor...

 

ソー (オー＝ド＝セーヌ県)

Sceaux 行政国 フランス地域圏 (Région) イル＝ド＝フランス地域圏県 (département) オー＝ド＝セーヌ県郡 (arrondissement) アントニー郡小郡 (canton) 小郡庁所在地INSEEコード 92071郵便番号 92330市長（任期） フィリップ・ローラン（2008年-2014年）自治体間連合 (fr) メトロポール・デュ・グラン・パリ人口動態人口 19,679人（2007年）人口密度 5466人/km2住民の呼称 Scéens地理座標 北緯48度4...

Sjair Abdoel Moeloek

Sjair Abdoel Moeloek SampulPengarangRaja Ali HajiNegaraHindia BelandaBahasaMelayuGenreSyairPenerbitTijdschrift voor Neerl. IndiëTanggal terbit1847 Sjair Abdoel Moeloek (EYD: Syair Abdul Muluk) adalah syair tahun 1847[a] yang menurut beberapa sumber dikarang oleh Raja Ali Haji atau putrinya, Saleha. Syair ini bercerita tentang seorang wanita yang menyamar sebagai pria untuk membebaskan suaminya dari Sultan Hindustan; Sultan menangkapnya dalam sebuah serangan ke kerajaan mereka. B...

 

西遊記大結局之仙履奇緣

本條目存在以下問題，請協助改善本條目或在討論頁針對議題發表看法。 此條目需要編修，以確保文法、用詞、语气、格式、標點等使用恰当。 (2013年8月6日)請按照校對指引，幫助编辑這個條目。（幫助、討論） 此條目剧情、虛構用語或人物介紹过长过细，需清理无关故事主轴的细节、用語和角色介紹。 (2020年10月6日)劇情、用語和人物介紹都只是用於了解故事主軸，輔助�...

 

André Diethelm

French politician and Resistance member This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: André Diethelm – news · newspapers · books · scholar · JSTOR (July 2020) (Learn how and when to remove this message) You can help expand this article with text translated from the corresponding article in French. (J...

Kang Eun-tak

Ini adalah nama Korea; marganya adalah Shin. Pada nama panggung/nama pena, nama belakangnya adalah Kang. Kang Eun-takBagian karpet merah upacara pembukaan Festival Film Fantastis Internasional Bucheon, 2015LahirShin Seul-gi16 Agustus 1982 (umur 41)Korea SelatanPendidikanInstitut Seni Seoul - TeaterPekerjaanAktorTahun aktif2006-sekarang Nama KoreaHangul강은탁 Alih AksaraGang Eun-takMcCune–ReischauerKang Ŭnt'akNama lahirHangul신슬기 Alih AksaraSin Seul-giMcCune–Reisch...

 

Blaye

For the wine, see Blaye (wine). Subprefecture and commune in Nouvelle-Aquitaine, FranceBlayeSubprefecture and communeA general view of Blaye FlagCoat of armsLocation of Blaye BlayeShow map of FranceBlayeShow map of Nouvelle-AquitaineCoordinates: 45°07′43″N 0°39′40″W / 45.1286°N 0.6611°W / 45.1286; -0.6611CountryFranceRegionNouvelle-AquitaineDepartmentGirondeArrondissementBlayeCantonL'EstuaireGovernment • Mayor (2020–2026) Denis Baldès ...

 

親俄

此條目没有列出任何参考或来源。 (2021年8月9日)維基百科所有的內容都應該可供查證。请协助補充可靠来源以改善这篇条目。无法查证的內容可能會因為異議提出而被移除。 親俄（英語：Russophilia），其英文的字面意思是對俄羅斯或俄羅斯人的喜好。其具体意涵是對俄羅斯（包括蘇聯和/或俄羅斯帝國時代）、俄羅斯歷史和俄羅斯文化的欽佩和喜愛。与亲俄相反的情感是反俄�...

Ikayaki

Cet article est une ébauche concernant la gastronomie et le Japon. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Ikayaki Ikayaki. Lieu d’origine Japon Température de service Chaud Ingrédients Calmar modifier  L’ikayaki (いか焼き／イカ焼き／烏賊焼?, calmar grillé ou cuisiné) est un plat populaire au Japon, où il est dégusté sur le pouce. Dans la majeure partie du Japon, le terme d�...

 

العلاقات الإيطالية الميانمارية

العلاقات الإيطالية الميانمارية إيطاليا ميانمار   إيطاليا   ميانمار تعديل مصدري - تعديل   العلاقات الإيطالية الميانمارية هي العلاقات الثنائية التي تجمع بين إيطاليا وميانمار.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة ومرجعية للدولتين: و�...