Solution of coupled acoustic eigenvalue problems

Antti Ojalammi

Kytkettyjen akustisten ominaisarvotehtävien ratkaiseminen

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Tämä väitöskirja käsittelee elementtimenetelmällä diskretoitujen Laplace -operaattorin ominaisarvotehtävien ratkaisemista toisiinsa kytketyissä akustisissa systeemeissä. Tehtävä esiintyy erityisesti puheentutkimuksessa, jossa vokaaliäänteitä voidaan luokitella ääntöväylän alimpien resonanssitaajuuksien avulla. Näitä taajuuksia laskettaessa on huomioitava akustinen ympäristö. Tässä väitöskirjassa ääntöväylää käsitellään sisäsysteeminä, joka kytketään vakiorajapinnan yli ulkosysteemiin, eli ulkotilaan. Resonanssitaajuuksien laskentaan käytettävät laskennalliset mallit validoidaan MRI-datan keräämisen yhteydessä tallennettujen ääninäytteiden avulla. Tämä vaatii suuren määrän ääntöväylägeometrioita, joten työssä esitellään automatisoitu menetelmä pinta- ja laskentaverkkojen luomiseen MRI-datasta. Lisäksi työssä mallinnetaan laite jolla voidaan mitata 3D-tulostettujen ääntöväylägeometrioiden taajuusvasteita. MRI-laitteen pääkelan ahtaudesta johtuen äänitystilanteessa esiintyy seisovia aaltoja, jotka oskilloivat sekä pääkelan että ääntöväylän sisällä. Tästä syystä ulkotilan vaikutus täytyy mallintaa tarkasti. Jotta muuttumattomana pysyvän pääkelan vaikutus siihen kytkettyihin erilaisiin ääntöväylägeometrioihin voidaan mallintaa tehokkaasti, väitöskirjassa esitellään menetelmä laskennallisen vaativuuden vähentämiseksi tämänkaltaisissa tilanteissa. Edelläkuvatun menetelmän kehittämisessä tehdyt huomiot yleistettiin algebrallisesta asetelmasta jatkuvalle Laplace -operaattorin ominaisarvotehtävälle. Näin saatiin teoreettinen menetelmä, jolla ominaisfunktion käytös paikallisessa alialueessa saadaan ratkaistua paikallisen reunakäytöksen avulla. Menetelmän laskennallinen toteutus on aluehajotukseen perustuva ominaisarvotehtävien ratkaisumenetelmä, jossa alialueisiin liittyvät laskentatyöt ovat toisistaan riippumattomia. Menetelmää voidaan käyttää elementtimenetelmällä diskretoitujen ominaisarvotehtävien approksimatiiviseen ratkaisemiseen silloin kun vapausasteiden määrä on liian suuri yksittäiselle tietokoneelle. Tällöin ei välttämättä tarvita suurteholaskentaa. Lisäksi laskentatehtävät voidaan lähettää verkon yli eri tietokoneille laskettavaksi, jolloin menetelmä soveltuu myös pilvilaskentaympäristöihin.

Julkaisun otsikon käännös	Kytkettyjen akustisten ominaisarvotehtävien ratkaiseminen
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hannukainen, Antti, Vastuuprofessori Malinen, Jarmo, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-64-0066-2
Sähköinen ISBN	978-952-64-0067-9
Tila	Julkaistu - 2020
OKM-julkaisutyyppi	G5 Tohtorinväitöskirja (artikkeli)

Tutkimusalat

akustiikka
Helmholtz
ominaisarvo
puheentutkimus
aluehajotusmenetelmät

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-64-0067-9

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title = "Solution of coupled acoustic eigenvalue problems",

abstract = "This thesis concerns the solution of finite element discretised Laplacian eigenvalue problems of coupled systems. A relevant application is studying human speech, where vowels are classified according to the lowest resonant frequencies of the vocal tract during sustained pronunciation. When computing these frequencies, the acoustic environment has to be accounted for. In this thesis, the vocal tract is considered as an interior system that is coupled with its acoustic environment, the exterior system. The coupling occurs through a fixed interface. Models for computing the resonant frequencies are validated against data consisting of simultaneous MRI images and sound recordings. As the validation requires a large number of vocal tract geometries, an automatic extraction algorithm that generates vocal tract surface triangulations from MRI data is introduced. An instrument for performing frequency sweeps on physical models printed using these geometries was also modelled as a part of this thesis. The confined space inside the head coil of the MRI machine creates an acoustic environment where mixed modes appear. That is, standing waves that oscillate both inside the oral cavity and the head coil are formed. Hence, it is important that the acoustic environment consisting of the MRI coil is accurately modelled when validating computational models. To efficiently solve relevant resonances related to different vocal tract geometries coupled with the unchanging MRI head coil, a method for reducing the computational complexity related to the fixed exterior system is introduced. The mathematical observations related to the aforementioned method were generalised from an algebraic setting to a continuous Laplace eigenvalue problem. As a result, a theory for obtaining information on an eigenfunction in a local subdomain from localised boundary data was developed. The computational realisation of this theory is a domain decomposition type eigenvalue solver where tasks related to each subdomain are mutually independent. This method can be used to approximately solve finite element discretised eigenvalue problems where the number of degrees of freedom is prohibitively large for a single workstation to compute. Such an eigenvalue solver can be used to efficiently solve large eigenvalue problems without the need for a supercomputer. Due to the independence of computations related to subdomains, tasks can be sent over a network connection, making the method suitable for cloud computing environments.",

keywords = "acoustics, Helmholtz, eigenvalue, FEM, MRI, speech, domain decomposition, akustiikka, Helmholtz, ominaisarvo, puheentutkimus, aluehajotusmenetelm{\"a}t, acoustics, Helmholtz, eigenvalue, FEM, MRI, speech, domain decomposition",

author = "Antti Ojalammi",

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N2 - This thesis concerns the solution of finite element discretised Laplacian eigenvalue problems of coupled systems. A relevant application is studying human speech, where vowels are classified according to the lowest resonant frequencies of the vocal tract during sustained pronunciation. When computing these frequencies, the acoustic environment has to be accounted for. In this thesis, the vocal tract is considered as an interior system that is coupled with its acoustic environment, the exterior system. The coupling occurs through a fixed interface. Models for computing the resonant frequencies are validated against data consisting of simultaneous MRI images and sound recordings. As the validation requires a large number of vocal tract geometries, an automatic extraction algorithm that generates vocal tract surface triangulations from MRI data is introduced. An instrument for performing frequency sweeps on physical models printed using these geometries was also modelled as a part of this thesis. The confined space inside the head coil of the MRI machine creates an acoustic environment where mixed modes appear. That is, standing waves that oscillate both inside the oral cavity and the head coil are formed. Hence, it is important that the acoustic environment consisting of the MRI coil is accurately modelled when validating computational models. To efficiently solve relevant resonances related to different vocal tract geometries coupled with the unchanging MRI head coil, a method for reducing the computational complexity related to the fixed exterior system is introduced. The mathematical observations related to the aforementioned method were generalised from an algebraic setting to a continuous Laplace eigenvalue problem. As a result, a theory for obtaining information on an eigenfunction in a local subdomain from localised boundary data was developed. The computational realisation of this theory is a domain decomposition type eigenvalue solver where tasks related to each subdomain are mutually independent. This method can be used to approximately solve finite element discretised eigenvalue problems where the number of degrees of freedom is prohibitively large for a single workstation to compute. Such an eigenvalue solver can be used to efficiently solve large eigenvalue problems without the need for a supercomputer. Due to the independence of computations related to subdomains, tasks can be sent over a network connection, making the method suitable for cloud computing environments.

AB - This thesis concerns the solution of finite element discretised Laplacian eigenvalue problems of coupled systems. A relevant application is studying human speech, where vowels are classified according to the lowest resonant frequencies of the vocal tract during sustained pronunciation. When computing these frequencies, the acoustic environment has to be accounted for. In this thesis, the vocal tract is considered as an interior system that is coupled with its acoustic environment, the exterior system. The coupling occurs through a fixed interface. Models for computing the resonant frequencies are validated against data consisting of simultaneous MRI images and sound recordings. As the validation requires a large number of vocal tract geometries, an automatic extraction algorithm that generates vocal tract surface triangulations from MRI data is introduced. An instrument for performing frequency sweeps on physical models printed using these geometries was also modelled as a part of this thesis. The confined space inside the head coil of the MRI machine creates an acoustic environment where mixed modes appear. That is, standing waves that oscillate both inside the oral cavity and the head coil are formed. Hence, it is important that the acoustic environment consisting of the MRI coil is accurately modelled when validating computational models. To efficiently solve relevant resonances related to different vocal tract geometries coupled with the unchanging MRI head coil, a method for reducing the computational complexity related to the fixed exterior system is introduced. The mathematical observations related to the aforementioned method were generalised from an algebraic setting to a continuous Laplace eigenvalue problem. As a result, a theory for obtaining information on an eigenfunction in a local subdomain from localised boundary data was developed. The computational realisation of this theory is a domain decomposition type eigenvalue solver where tasks related to each subdomain are mutually independent. This method can be used to approximately solve finite element discretised eigenvalue problems where the number of degrees of freedom is prohibitively large for a single workstation to compute. Such an eigenvalue solver can be used to efficiently solve large eigenvalue problems without the need for a supercomputer. Due to the independence of computations related to subdomains, tasks can be sent over a network connection, making the method suitable for cloud computing environments.

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