Reduced Order Modelling and Uncertainty Propagation Applied to Water Distribution Networks

Abstract : Water distribution systems are large, spatially distributed infrastructures that ensure the distribution of potable water of sufficient quantity and quality. Mathematical models of these systems are characterized by a large number of state variables and parameter. Two major challenges are given by the time constraints for the solution and the uncertain character of the model parameters. The main objectives of this thesis are thus the investigation of projection based reduced order modelling techniques for the time efficient solution of the hydraulic system as well as the spectral propagation of parameter uncertainties for the improved quantification of uncertainties. The thesis gives an overview of the mathematical methods that are being used. This is followed by the definition and discussion of the hydraulic network model, for which a new method for the derivation of the sensitivities is presented based on the adjoint method. The specific objectives for the development of reduced order models are the application of projection based methods, the development of more efficient adaptive sampling strategies and the use of hyper-reduction methods for the fast evaluation of non-linear residual terms. For the propagation of uncertainties spectral methods are introduced to the hydraulic model and an intrusive hydraulic model is formulated. With the objective of a more efficient analysis of the parameter uncertainties, the spectral propagation is then evaluated on the basis of the reduced model. The results show that projection based reduced order models give a considerable benefit with respect to the computational effort. While the use of adaptive sampling resulted in a more efficient use of pre-calculated system states, the use of hyper-reduction methods could not improve the computational burden and has to be explored further. The propagation of the parameter uncertainties on the basis of the spectral methods is shown to be comparable to Monte Carlo simulations in accuracy, while significantly reducing the computational effort.
Document type :
Theses
Complete list of metadatas

Cited literature [130 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02278297
Contributor : Abes Star <>
Submitted on : Wednesday, September 4, 2019 - 11:56:08 AM
Last modification on : Saturday, September 7, 2019 - 1:25:55 AM

File

BRAUN_MATHIAS_2019.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-02278297, version 1

Collections

Citation

Mathias Braun. Reduced Order Modelling and Uncertainty Propagation Applied to Water Distribution Networks. Modeling and Simulation. Université de Bordeaux, 2019. English. ⟨NNT : 2019BORD0050⟩. ⟨tel-02278297⟩

Share

Metrics

Record views

93

Files downloads

13