Lagrangian Multi-Class Traffic State Estimation

Lagrangian Multi-Class Traffic State Estimation Yufei Yuan This thesis is a result from a project funded by Delft University of Technology (TUDelft) and the Netherlands Research School for Transport, Infrastructure and Logistics (TRAIL). Cover illustration: Yufei Yuan and Jing Wei Lagrangian Multi-Class Traffic State Estimation Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op dinsdag 19 maart 2013 om 10:00 uur door Yufei YUAN Master of Science in Transport and Planning geboren te Guilin, China Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. S.P. Hoogendoorn Copromotor: Dr. ir. J.W.C. van Lint Samenstelling promotiecommissie : Rector Magnificus, voorzitter Prof. dr. ir. S.P. Hoogendoorn, Technische Universiteit Delft, promotor Dr. ir. J.W.C. van Lint, Technische Universiteit Delft, copromotor Prof. dr. ir. C. Vuik, Technische Universiteit Delft Prof. ir. L.H. Immers, Technische Universiteit Delft Prof. dr. R.E. Wilson, University of Bristol Prof. dr. L. Leclercq, Ecole´ Nationale des Travaux Publics de l’Etat´ Prof. dr. P.B. Mirchandani, Arizona State University Prof. dr. ir. B. van Arem, Technische Universiteit Delft, reservelid TRAIL Thesis Series no. T2013/5, the Netherlands Research School TRAIL TRAIL P.O. Box 5017 2600 GA Delft The Netherlands Phone: +31 (0) 15 278 6046 E-mail: [email protected] ISBN: 978-90-5584-162-2 Copyright c 2013 by Yufei Yuan All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, in- cluding photocopying, recording or by any information storage and retrieval system, without written permission from the author. Printed in the Netherlands 路漫漫其修远兮,吾将上下而求索. The road ahead will be long and the climb will be steep, but I will never terminate pursuit. Preface Traffic and transport research is truly attractive to me. To explore the problem that relates closely to our life also motivates me. This is the reason why I dive into the field of traffic science. After my bachelor graduation in engineering mechanics in Shanghai China, I came to the Netherlands to start my master study at the department of Transport and Planning, Delft University of Technology in 2006. I succeeded in obtaining my degree within two years. With my ongoing curiosity in traffic, I decided to pursuit a PhD degree in the same department. The four year PhD life is really an unforgettable and precious experience to me. It expands my view and horizon not only in the field of traffic science but also in the society and the world. Upon the completion of my PhD thesis, I would like to take the opportunity to thank all the people who helped me during my PhD study. First of all, I would like to express my heartfelt thanks to my promotor, Serge Hoogen- doorn, for giving me sufficient guidance and confidence. I feel very grateful and proud of being one of your master and PhD students. Your research attitude has strongly in- fluenced me and your ideas always inspire me. Thank you! I am also deeply indebted to my excellent daily supervisor and copromotor, Hans van Lint, for giving me kind and patient monitoring. Your critical comments and suggestions enabled me to make this research and my thesis better than I could have done by myself. When there were moments that I doubted about my research, you always supported me and gave me confidence. Thanks a lot! I would like to express my thanks to my supervisor Jos Vrancken from the TBM fac- ulty, for leting me join the C4C project and for all the useful advice and support. I feel rather gratitude to my supervisor Eddie Wilson in England, for hosting me, for his kind supervision and collaboration when I exchanged at the University of Southampton as a guest researcher, and also for the final checking of my thesis. I also want to thank other committee members for their useful comments. During my PhD research, I have the pleasure to work with my wonderful colleagues at the department. I would like to address my special thanks to Thomas, Femke and Olga. Thomas, thank you very much for all the inspiring discussion during the past four years and for the collaboration on projects, papers and Ping-Pong tournaments. Femke, thank you for the discussion and collaboration on papers. I learned a lot from you. Olga, thank you for always patiently answering lots of basic questions about the Dutch ii Lagrangian Multi-Class Traffic State Estimation language, and helping me with the translation of my summary and propositions. I also want to thank my other colleagues: Winnie, Victor, Adam and Chris, for their help and the chance to exchange ideas; Kees, Edwin, Peter, Nicole, Piet, Priscilla, Dehlaila, Charelle and Conchita, for all the technical and administrative support; Meng, Yaqing, Mo, Yubin, Gijs, Eric-sander, Tamara, Giselle, Kakpo, Bernat, Pavle, Daniel, Mario, Wouter, Mahtab, Mignon, Guus, Ramon and Raymond, for all the wonderful moments. Furthermore, my gratitude also goes to my (former) office mates: Tamara, Thomas, Olga, Fangfang, Lucas, Clarie, Feifei and Gerdien. I feel comfortable to work with you. I had a great time and enjoyed the multi-culture environment in our department. My special thanks goes to Zhiwei for the friendship since the first year of undergrad- uate, Xiaoxiao for all the sharing and discussion, Xuying for all her help and support, Kai and Feng for the proof reading and all the valuable comments on my thesis, Yong and Jing for helping me visualise my research concept. Finally, I would like to thank my family, who have always been supporting me. Special gratitude to my mother, who is consistently supporting, caring and listening to me. I dedicate this thesis to my mom, with love and thanks for her endless and unconditional love throughout my life. Yufei Yuan, February 2013 Dedicated to my mother for her endless and unconditional love Contents Prefacei List of Figuresx List of Tables xii Notation xiii 1 Introduction1 1.1 Background...............................2 1.2 Traffic state estimation.........................2 1.3 Dynamic traffic flow models......................4 1.4 Data assimilation............................5 1.5 Observation models and empirical data.................6 1.6 Research contributions and relevance..................7 1.6.1 Scientific contributions.....................7 1.6.2 Practical contributions.....................9 1.7 Outline of this thesis.......................... 10 2 The state-of-the-art in traffic state estimation 13 2.1 Introduction............................... 14 2.2 A new classification framework for model-based traffic state estimation research............................... 16 2.3 Choices in traffic process models.................... 17 2.3.1 Eulerian formulated traffic process models.......... 17 2.3.2 Lagrangian formulated traffic process models......... 19 iv Lagrangian Multi-Class Traffic State Estimation 2.4 Choices for incorporating observation models............. 20 2.5 Data-assimilation techniques...................... 23 2.5.1 Overview of recursive assimilation techniques......... 23 2.5.2 Motivation for applying the EKF................ 24 2.6 Research direction and main challenges................ 26 2.7 Summary................................ 26 3 Model-based mixed-class state estimation in Lagrangian coordinates 29 3.1 Introduction............................... 30 3.2 Process models: Eulerian and Lagrangian formulations of mixed-class first-order traffic model......................... 30 3.2.1 Mixed-class Eulerian formulated process model........ 30 3.2.2 Mixed-class Lagrangian formulated process model...... 31 3.3 Modelling network discontinuities in the Lagrangian formulation... 34 3.3.1 Eulerian formulated node models............... 35 3.3.2 Lagrangian formulated node models.............. 36 3.4 Observation models for mixed-class Lagrangian formulation..... 39 3.5 Mixed-class Lagrangian traffic state estimation based on the Extended Kalman Filter.............................. 43 3.6 Advantages of Lagrangian formulation for traffic state estimation... 46 3.7 Summary and discussion........................ 47 4 Model-based multi-class state estimation in Lagrangian coordinates 49 4.1 Introduction............................... 50 4.2 Multi-class Lagrangian traffic flow models: continuum forms and dif- ferent discretisation approaches..................... 50 4.2.1 Eulerian formulated multi-class models............ 50 4.2.2 Lagrangian formulated multi-class models........... 51 “Piggy-back” formulation................... 51 “Multi-pipe” formulation.................... 52 4.2.3 Discussion and choice..................... 55 4.3 Multi-class node model for network discontinuities.......... 57 Contents v 4.4 Observation models for multi-class Lagrangian formulation...... 59 4.5 Multi-class Lagrangian traffic state estimation based on the Extended Kalman Filter.............................. 60 4.6 Summary and discussion........................ 64 5 Case studies for Lagrangian traffic state estimation 65 5.1 Introduction............................... 66 5.1.1 Experimental setup....................... 66 5.1.2 Experimental objectives.................... 66 5.2 Link-level validation of Lagrangian traffic state estimation...... 67 5.2.1 Data and test network...................... 67 5.2.2 Experimental scenarios..................... 68 5.2.3 Performance criteria...................... 69 5.2.4

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