State Estimation for the discretized LWR PDE using explicit polyhedral representations of the Godunov scheme

Thai, Jérôme; Prodhomme, Boris; Bayen, Alexandre M.

doi:10.1109/acc.2013.6580198

Cited by 12 publications

(9 citation statements)

References 22 publications

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“…This section briefly summarizes results derived earlier on hybrid formulations of the Godunov scheme [27]. We use the first order Godunov scheme for the discretization of the Lighthill-Whitham-Richards equation with a triangular flux function, and proves that the resulting nonlinear dynamical system can be decomposed in a piecewise affine manner.…”

Section: A Hybrid Model For the Godunov Schemementioning

confidence: 99%

“…We consider the Lighthill-Whitham-Richards hydrodynamic model used earlier in [27] as the distributed parameter system model of interest:…”

Section: Discretization Of the Lwr Equationmentioning

confidence: 99%

“…State of the art traffic estimation techniques for this model include the application of the extended Kalman filter (EKF) to the LWR PDE by Schreiter et al [24], and to non-scalar traffic model by Papageorgiou [22]. The application of the EKF to the LWR PDE model is problematic due to the non-differentiability of its discretization, a problem which has been partially adressed in [3] and [27]. The ensemble Kalman filter (EnKF) has also been applied to a velocitybased model in [29], in order to circumvent the difficulties of non-differentiability of numerical solutions to these PDEs such as the one presented in this article.…”

Section: Introductionmentioning

confidence: 99%

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State estimation for polyhedral hybrid systems and applications to the Godunov scheme

Thai

Bayen

2013

Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control

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In this article, the problem of estimating the state of a discretized hyperbolic scalar partial differential equation is studied. The discretization of the Lighthill-Whitham-Richards equation with a triangular flux function using the Godunov scheme is shown to lead to a hybrid linear system or Switched Linear Systems (SLS) with a number of modes exponential in the size of the discretized model. Some geometric properties of the partition of the space into polyhedra (in which a mode is active) are exploited to find heuristics to reduce the number of modes to a representative set. This motivates a new approach inspired from a well established technique for hybrid system estimation, namely the interactive multiple model (IMM). qThe performance of this new variant of the IMM is compared to the extended Kalman filter and the ensemble Kalman filter using the Mobile Millennium data set.

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Section: A Hybrid Model For the Godunov Schemementioning

confidence: 99%

“…We consider the Lighthill-Whitham-Richards hydrodynamic model used earlier in [27] as the distributed parameter system model of interest:…”

Section: Discretization Of the Lwr Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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State estimation for polyhedral hybrid systems and applications to the Godunov scheme

Thai

Bayen

2013

Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control

Self Cite

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show abstract

“…Pendekatan pemodelan kondisi lalu lintas secara makroskopik untuk suatu ruas jalan x saat t berdasarkan pada hukum kekekalan arus kendaraan 1,2) sesuai Persamaan (1).…”

Section: Parameter Makroskopik Utamaunclassified

“…Selanjutnya, apabila dinamika kondisi lalu lintas didekati sesuai prinsip hidrodinamik untuk arus pergerakan partikel atau gaskinetik 3) yang terbatas pada satu ruas jalan x tertentu, maka diperoleh hubungan matematis untuk parameter makroskopik yang ketiga berdasar Persamaan (2). …”

Section: Parameter Makroskopik Utamaunclassified

PENDEKATAN PEMODELAN Â€DIAGRAM FUNDAMENTAL POLINOMIALâ€ UNTUK RUAS JALAN BEBAS HAMBATAN = MODELING APPROACH OF Â€œPOLYNOMIAL FUNDAMENTAL DIAGRAMâ€ FOR FREE WAY SEGMENTS

Harjono¹,

Aspar²

2023

Majalah Ilmiah Pengkajian Industri

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AbstrakPerilaku pergerakan banyak kendaraan pada ruas jalan bebas hambatan menjadi dasar bagi pengembangan banyak pemodelan lalu-lintas. Pengembangan pemodelan lalu-lintas jumlah kendaraan secara makroskopik dipergunakan pada jaringan jalan yang luas. Penelitian ini bertujuan untuk menemukan hubungan antara tingkat pelayanan jalan dengan diagram fundamental. Dengan demikian hubungan ini dapat dimanfaatkan untuk mengembangkan sistem informasi bagi pemangku kepentingan transportasi ataupun pengendalian aliran arus pada jalan bebas hambatan. Tujuan penelitian berikutnya menitik beratkan pada penentuan kecepatan rata-rata banyak kendaraan efektif berdasarkan tingkat pelayanan jalan. Hubungan spesifik antar parameter makroskopik untuk kondisi lalu lintas tertentu pada satu ruas jalan tunggal terjadi pada saat kondisi keadaan mantab dan kondisi equilibrium. Kondisi lalu lintas rata-rata secara praktis diambil pengukuran parameter makroskopik setelah kondisi stabil tercapai dan valid. Pemodelan yang diperoleh berdasarkan pada pemetaan kondisi equilibrium. Pada diagram antar parameter makroskopik tersebut disebut sebagai Diagram Fundamental Lalu-Lintas bagi ruas jalan. Hasil penelitian menunjukkan bahwa pada kondisi aliran arus kendaraan tertinggi diperoleh kepadatan kendaraan maksimum. Apabila kecepatan rata-rata banyak kendaraan pada kondisi arus bebas (free flow) ditetapkan sesuai kecepatan maksimum desain yaitu 120 km/jam, maka diperoleh headway dan gap masing-masing kendaraan adalah 1,5 detik dan 50 meter. Diagram Fundamental Polinomial yang terjadi dapat membantu bagi pengambil kebijakan untuk menentukan pola aliran arus kendaraan, pengendalian optimal dan rekayasa transportasi.

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Numerical Stability of Conservation Equation for Bus Travel Time Prediction Using Automatic Vehicle Location Data

2020

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State Estimation for the discretized LWR PDE using explicit polyhedral representations of the Godunov scheme

Cited by 12 publications

References 22 publications

State estimation for polyhedral hybrid systems and applications to the Godunov scheme

State estimation for polyhedral hybrid systems and applications to the Godunov scheme

PENDEKATAN PEMODELAN Â€DIAGRAM FUNDAMENTAL POLINOMIALâ€ UNTUK RUAS JALAN BEBAS HAMBATAN = MODELING APPROACH OF Â€œPOLYNOMIAL FUNDAMENTAL DIAGRAMâ€ FOR FREE WAY SEGMENTS

Numerical Stability of Conservation Equation for Bus Travel Time Prediction Using Automatic Vehicle Location Data

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State Estimation for the discretized LWR PDE using explicit polyhedral representations of the Godunov scheme

Cited by 12 publications

References 22 publications

State estimation for polyhedral hybrid systems and applications to the Godunov scheme

State estimation for polyhedral hybrid systems and applications to the Godunov scheme

PENDEKATAN PEMODELAN Â€DIAGRAM FUNDAMENTAL POLINOMIALâ€ UNTUK RUAS JALAN BEBAS HAMBATAN = MODELING APPROACH OF Â€œPOLYNOMIAL FUNDAMENTAL DIAGRAMâ€ FOR FREE WAY SEGMENTS

Numerical Stability of Conservation Equation for Bus Travel Time Prediction Using Automatic Vehicle Location Data

Contact Info

Product

Resources

About

PENDEKATAN PEMODELAN Â€DIAGRAM FUNDAMENTAL POLINOMIALâ€ UNTUK RUAS JALAN BEBAS HAMBATAN = MODELING APPROACH OF Â€œPOLYNOMIAL FUNDAMENTAL DIAGRAMâ€ FOR FREE WAY SEGMENTS