STATISTICAL AND ACOUSTICAL ROOM ANALYSIS THROUGH FACTOR MIXTURE MODELS A Degree Thesis Submitted to the Faculty of the Escola Tècnica d'Enginyeria de Telecomunicació de Barcelona Universitat Politècnica de Catalunya by Joan Pallarès Sadó In partial fulfilment of the requirements for the degree in Audiovisual Systems ENGINEERING Advisor: Stefan Weinzierl Berlin, February 2016 Abstract The acoustics of music rooms, theatre halls and venues in general depend greatly on the materials with which they have been built and designed. Yet the size, dimensions and morphology are factors that play a fundamental roll in the acoustical properties of the rooms. 300 concert venues from all over the world have been analysed and documented in dependence on these factors in order to respond the following aspects. On the one hand, the aim of the research is to prove if there is a correspondence between the morphological shape of rooms and their acoustical properties. In other words it is intended, by statistical analysis, to carry out a classification in classes in order to verify if such assumption is true or not. Moreover, a set of new acoustical variables is exposed as a result of the combination of original (primitive) acoustical parameters. For such achievements a statistical mixture model combining Latent Profile Analysis (LPA), Exploratory Factor Analysis (EFA) and Common Factor Analysis (CFA) has been developed. 1 Resum L’acústica de les sales de concerts, teatres i espais escènics en general depèn en gran mesura dels materials a partir dels quals s’han dissenyat i construït. No obstant això, les dimensions i la morfologia són factors que condicionen també les propietats acústiques de les sales. En aquest sentit, un total de 300 sales d’arreu del món han estat documentades i analitzades, d’acord amb els seus paràmetres acústics, per tal de donar resposta als següents aspectes. En primer terme, l’objectiu de la recerca és estudiar si existeix una correspondència entre la morfologia de les diferents sales i l’acústica d’aquestes. En altres paraules es pretén, mitjançant l’anàlisi estadística, dur a terme una classificació per classes amb la finalitat de comprovar si, efectivament, es verifica o no el plantejament. En segon lloc, es presenta un seguit de noves variables acústiques les quals són fruit de la combinació de paràmetres acústics originals (primitius). Per tal d’assolir ambdós objectius s'ha emprat un model que combina eines d'anàlisi estadística com són LPA (Latent Profile Analysis), EFA (Exploratory Factor Analysis) i CFA (Common Factor Analysis). 2 Resumen La acústica de las salas de conciertos, teatros y espacios escénicos en general depende en gran medida de los materiales a partir de los cuales se han diseñado y construido. Sin embargo, las dimensiones y la morfología son factores que condicionan también las propiedades acústicas de las salas. En este sentido, un total de 300 salas de todo el mundo han sido documentadas y analizadas, de acuerdo con sus parámetros acústicos, para dar respuesta a los siguientes aspectos. En primer término, el objetivo de la investigación es estudiar si existe una correspondencia entre la morfología de las diferentes salas y la acústica de éstas. En otras palabras se pretende, mediante el análisis estadístico, llevar a cabo una clasificación con el fin de comprobar si, efectivamente, se verifica o no dicho planteamiento. En segundo lugar, se presenta una serie de nuevas variables acústicas las cuales son fruto de la combinación de parámetros acústicos originales (primitivos). Para alcanzar ambos objetivos se ha empleado un modelo que combina herramientas de análisis estadístico como son LPA (Latent Profile Analysis), EFA (Exploratory Factor Analysis) y CFA (Common Factor Analysis). 3 To my parents Toni and Mª Antònia, my sister Anna and my brother Jordi. 4 Acknowledgements I’d like to express my gratitude and gratefulness to Dr.Stefan Weinzierl, head of TU-Berlin Audiokommunikation Department and advisor of the project, for giving me the opportunity of carrying out my thesis alongside with the team he leads. Secondly, to Dr. Steffen Lepa, member of the Audiokommunikation Department and advisor of the research, for providing me with the appropriate statistical background that enabled the mathematical analysis and the consequent achievement of the final results. Moreover, to the staff members and fellow students of the Audiokommunikation Research Group in the collection of data, hints and endorsement. Likewise, my thankfulness to Professor Antoni Carrión Isbert for his support as co-tutor of the project at home university, Telecom Barcelona-UPC. Finally, to Technische Universität of Berlin for hosting me during this period and for providing me with the necessary tools and infrastructures in order to develop the research. 5 Revision history and approval record Revision Date Purpose 0 02/01/2016 Document creation 1 02/02/2016 Document revision DOCUMENT DISTRIBUTION LIST Name e-mail Joan Pallarès Sadó [email protected] Stefan Weinzierl [email protected] Steffen Lepa [email protected] Written by: Reviewed and approved by: Date 02/01/2016 Date 02/02/2016 Name Joan Pallarès Sadó Name Stefan Weinzierl Position Project Author Position Project Supervisor 6 Table of contents Abstract ............................................................................................................................................................................ 1 Resum ............................................................................................................................................................................... 2 Resumen .......................................................................................................................................................................... 3 Acknowledgements ..................................................................................................................................................... 5 Revision history and approval record ................................................................................................................ 6 Table of contents .......................................................................................................................................................... 7 List of Figures ................................................................................................................................................................ 8 List of Tables .................................................................................................................................................................. 9 1. Introduction ...................................................................................................................................................... 10 1.1. Requirements and Specifications ................................................................................................... 10 1.2. Work Plan ................................................................................................................................................. 11 2. State of the art .................................................................................................................................................. 16 3. Methodology / project development: .................................................................................................... 17 4. Results .................................................................................................................................................................. 25 5. Budget .................................................................................................................................................................. 36 6. Conclusions and future development: ................................................................................................... 37 Bibliography: .............................................................................................................................................................. 38 Appendices (optional): ........................................................................................................................................... 40 Glossary ......................................................................................................................................................................... 50 7 List of Figures Figure 1 page 19 Figure 2 page 19 Figure 3 page 20 Figure 4 page 20 Figure 5 page 20 Figure 6 page 20 Figure 7 page 20 Figure 8 page 20 Figure 9 page 21 Figure 10 page 21 Figure 11 page 21 Figure 12 page 21 Figure 13 page 22 Figure 14 page 22 Figure 15 page 22 Figure 16 page 23 Figure 17 page 24 Figure 18 page 24 Figure 19 page 26 Figure 20 page 29 Figure 21 page 30 Figure 22 page 30 Figure 23 page 32 Figure 24 page 32 Figure 25 page 33 Figure 26 page 33 Figure 27 page 34 Figure 28 page 34 Figure 29 page 34 Figure 30 page 35 8 List of Tables Table 1 page 22 Table2 page 26 Table 3 page 27 Table 4 page 27 Table 5 page 27 Table 6 page 29 Table 7 page 31 Table 8 page 31 Table 9 page 31 9 1. Introduction Music rooms, theatre halls, opera houses and venues in general are daily frequented by thousands of people around the world looking forward to a vibrant artistic experience. The acoustics play an essential roll in it and engineers are conscious that an appropriate acoustical design can bring the spectator’s sensorial enjoyment to another level. This