Uncertainty propagation of dam break flow using the stochastic non-intrusive B-splines Bézier elements-based method

Abdedou, Azzedine; Soulaïmani, Azzeddine; Tchamen, Georges Williams TchamenG.W.

doi:10.1016/j.jhydrol.2020.125342

Cited by 11 publications

(10 citation statements)

References 61 publications

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“…In this whole process, the flow discharge is clearly a prominent parameter. Thus, there are numerous models and formulas for predicting discharge variation and peak discharge [41][42][43][44]. Existing emergency measures are also used to immediately return the main channel streamflow to normal parameters [36,40,45].…”

Section: Discussionmentioning

confidence: 99%

Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation

Wang

Tan

Shu

et al. 2021

Water

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Barrier lakes are secondary disasters with associated landslides and debris flow that can cause serious damage to the downstream populations and areas. Existing studies are lacking in comprehensive descriptions of the rescue process, where the main channel streamflow varies and topographic erosion develops, as well as engineering disposal performs. This paper aimed to theoretically investigate the formation and emergency responses to barrier lakes using on-the-spot investigation and calculus theory. The results showed that the formation of a barrier lake led to a sudden variation in the flow-change rate (normal to infinite). However, after implementing emergency measures, this rate returned to normal. The whole rescue process could be regarded as the accumulation of disposal effects. Volume changes in the main streams were expressed by a differential equation of the lake surface area and water level variations. In addition, a corresponding theoretical description of flow discharges was also given when engineering measures such as the excavation of diversion channels and engineering blasting were adopted. Specifically, the theoretical expressions of flow discharge were given respectively in the developing stage and breach stable stage after the excavation of diversion channels. The flow discharge through certain sections was also described theoretically when engineering blasting was chosen to widen and deepen the cross-section of the diversion channels. Overall, this paper mathematicizes and theorizes the existing emergency measures, which helps to better understand their implementation principles and application requirements.

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Section: Discussionmentioning

confidence: 99%

Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation

Wang

Tan

Shu

et al. 2021

Water

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“…This approach belongs to the multi-element techniques that use local piecewise bases expressed as a function of input random parameters. It is worth noting that the basic framework of the BSBEM in its full-order version has been presented in detail in [33,34]. Thus, only a summary description of its fundamental aspects is outlined in the following.…”

Section: Regression-based Non-intrusive B-splines Bézier Elements Met...mentioning

confidence: 99%

“…where e stands for the e th Bézier element I e and p i denotes the polynomial order of the univariate B-splines basis function ψ i (ξ i ). Details of the construction of the B-splines basis and their extraction from the local Bernstein's functions can be found in [33,34,36]. In each Bézier element, a set of n e s ≥ n b collocation points are selected ξ e(r) ∈ I e ; r = 1, .…”

Section: Let Us Considermentioning

confidence: 99%

“…In addition to the sampling approaches such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS), the performance and accuracy of the proposed POD-BSBEM are also compared to the non-intrusive reduced-order model-based artificial neural network (POD-ANN) and the fullorder polynomial chaos expansion (Full-PCE). It should be noted that a detailed discussion of the development and implementation steps of these methods is beyond the scope of this work, and the reader is encouraged to consult the corresponding references [18,22,23] and [34,40,41],…”

Section: A Third Level Proper Orthogonal Decompositionmentioning

confidence: 99%

“…This work presents a non-intrusive reduced order model for stochastic time-dependent problems. The method, referred to as the POD-BSBEM, combines the advantages of the POD and the B-splines Bézier element method (BSBEM) [33,34] to extract the reduced basis and to build a stochastic expansion over the random space, respectively. A two-level POD is applied to the snapshot matrix obtained by the collection of time-trajectory high-fidelity solutions for each given value of the random parametric vector.…”

Section: Introductionmentioning

confidence: 99%

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A non-intrusive reduced-order modelling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and Proper Orthogonal Decomposition: application to dam-break flows

Abdedou,

Soulaïmani

2021

Preprint

Self Cite

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A proper orthogonal decomposition-based B-splines Bézier elements method (POD-BSBEM) is proposed as a non-intrusive reduced-order model for uncertainty propagation analysis for stochastic time-dependent problems. The method uses a two-step proper orthogonal decomposition (POD) technique to extract the reduced basis from a collection of high-fidelity solutions called snapshots.A third POD level is then applied on the data of the projection coefficients associated with the reduced basis to separate the time-dependent modes from the stochastic parametrized coefficients.These are approximated in the stochastic parameter space using B-splines basis functions defined in the corresponding Bézier element. The accuracy and the efficiency of the proposed method are assessed using benchmark steady-state and time-dependent problems and compared to the reducedorder model-based artificial neural network (POD-ANN) and to the full-order model-based polynomial chaos expansion (Full-PCE). The POD-BSBEM is then applied to analyze the uncertainty propagation through a flood wave flow stemming from a hypothetical dam-break in a river with a complex bathymetry. The results confirm the ability of the POD-BSBEM to accurately predict the statistical moments of the output quantities of interest with a substantial speed-up for both offline and online stages compared to other techniques.

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A non-intrusive reduced-order modeling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and proper orthogonal decomposition: Application to dam-break flows

Abdedou

Soulaïmani

2021

Computers & Mathematics with Applications

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Uncertainty propagation of dam break flow using the stochastic non-intrusive B-splines Bézier elements-based method

Cited by 11 publications

References 61 publications

Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation

Theoretical Description of the Hydrodynamic Process after Barrier Lake Formation and Emergency Responses Implementation

A non-intrusive reduced-order modelling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and Proper Orthogonal Decomposition: application to dam-break flows

A non-intrusive reduced-order modeling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and proper orthogonal decomposition: Application to dam-break flows

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