Quantification of the Impact of Uncertainties in Operating Conditions on the Flame Transfer Function With Nonintrusive Polynomial Chaos Expansion

Nonintrusive polynomial chaos expansion (NIPCE) is used to quantify the impact of uncertainties in operating conditions on the flame transfer function (FTF) of a premixed laminar flame. NIPCE requires only a small number of system evaluations, so it can be applied in cases where a Monte Carlo simulation is unfeasible. We consider three uncertain operating parameters: inlet velocity, burner plate temperature, and equivalence ratio. The FTF is identified in terms of the finite impulse response (FIR) from computational fluid dynamics (CFD) simulations with broadband velocity excitation. NIPCE yields uncertainties in the FTF due to the uncertain operating conditions. For the chosen uncertain operating bounds, a second-order expansion is found to be sufficient to represent the resulting uncertainties in the FTF with good accuracy. The effect of each operating parameter on the FTF is studied using Sobol indices, i.e., a variance-based measure of sensitivity, which are computed from the NIPCE. It is observed that in the present case, uncertainties in the FIR as well as in the phase of the FTF are dominated by the equivalence-ratio uncertainty. For frequencies below 150 Hz, the uncertainty in the gain of the FTF is also attributable to the uncertainty in equivalence-ratio, but for higher frequencies, the uncertainties in velocity and temperature dominate. At last, we adopt the polynomial approximation of the output quantity, provided by the NIPCE method, for further uncertainty quantification (UQ) studies with modified input uncertainties.

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Quantification of the Impact of Uncertainties in Operating Conditions on the Flame Transfer Function With Non-Intrusive Polynomial Chaos Expansion

Volume 4A: Combustion, Fuels, and Emissions ◽

10.1115/gt2018-75476 ◽

2018 ◽

Cited By ~ 1

Author(s):

Alexander Avdonin ◽

Wolfgang Polifke

Keyword(s):

Transfer Function ◽

Impulse Response ◽

Equivalence Ratio ◽

Polynomial Chaos ◽

Finite Impulse Response ◽

Operating Parameter ◽

Polynomial Chaos Expansion ◽

Operating Conditions ◽

Chaos Expansion ◽

The Impact

Non-intrusive polynomial chaos expansion (NIPCE) is used to quantify the impact of uncertainties in operating conditions on the flame transfer function of a premixed laminar flame. NIPCE requires only a small number of system evaluations, so it can be applied in cases where a Monte Carlo simulation is unfeasible. We consider three uncertain operating parameters: inlet velocity, burner plate temperature, and equivalence ratio. The flame transfer function (FTF) is identified in terms of the finite impulse response from CFD simulations with broadband velocity excitation. NIPCE yields uncertainties in the FTF due to the uncertain operating conditions. For the chosen uncertain operating bounds, a second-order expansion is found to be sufficient to represent the resulting uncertainties in the FTF with good accuracy. The effect of each operating parameter on the FTF is studied using Sobol indices, i.e. a variance-based measure of sensitivity, which are computed from the NIPCE. It is observed that in the present case uncertainties in the finite impulse response as well as in the phase of the FTF are dominated by the equivalence-ratio uncertainty. For frequencies below 150 Hz, the uncertainty in the gain of the FTF is also attributable to the uncertainty in equivalence-ratio, but for higher frequencies the uncertainties in velocity and temperature dominate. At last, we adopt the polynomial approximation of the output quantity, provided by the NIPCE method, for further UQ studies with modified input uncertainties.

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Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽

10.3390/w13131830 ◽

2021 ◽

Vol 13 (13) ◽

pp. 1830

Author(s):

Gullnaz Shahzadi ◽

Azzeddine Soulaïmani

Keyword(s):

Polynomial Chaos ◽

Complex Structure ◽

Uncertainty Propagation ◽

Surrogate Models ◽

Polynomial Chaos Expansion ◽

Soil Parameters ◽

Chaos Expansion ◽

Rockfill Dam ◽

Parametric Studies ◽

The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

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Modified Polynomial Chaos Expansion for Efficient Uncertainty Quantification in Biological Systems

Applied Mechanics ◽

10.3390/applmech1030011 ◽

2020 ◽

Vol 1 (3) ◽

pp. 153-173

Author(s):

Jeongeun Son ◽

Dongping Du ◽

Yuncheng Du

Keyword(s):

Uncertainty Quantification ◽

Polynomial Chaos ◽

Biological Systems ◽

Parametric Uncertainty ◽

Polynomial Chaos Expansion ◽

High Dimensional ◽

Chaos Expansion ◽

Deterministic Models ◽

Generalized Dimension ◽

The Impact

Uncertainty quantification (UQ) is an important part of mathematical modeling and simulations, which quantifies the impact of parametric uncertainty on model predictions. This paper presents an efficient approach for polynomial chaos expansion (PCE) based UQ method in biological systems. For PCE, the key step is the stochastic Galerkin (SG) projection, which yields a family of deterministic models of PCE coefficients to describe the original stochastic system. When dealing with systems that involve nonpolynomial terms and many uncertainties, the SG-based PCE is computationally prohibitive because it often involves high-dimensional integrals. To address this, a generalized dimension reduction method (gDRM) is coupled with quadrature rules to convert a high-dimensional integral in the SG into a few lower dimensional ones that can be rapidly solved. The performance of the algorithm is validated with two examples describing the dynamic behavior of cells. Compared to other UQ techniques (e.g., nonintrusive PCE), the results show the potential of the algorithm to tackle UQ in more complicated biological systems.

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Tackling random fields non-linearities with unsupervised clustering of polynomial chaos expansion in latent space: application to global sensitivity analysis of river flooding

Stochastic Environmental Research and Risk Assessment ◽

10.1007/s00477-021-02060-7 ◽

2021 ◽

Author(s):

Siham El Garroussi ◽

Sophie Ricci ◽

Matthias De Lozzo ◽

Nicole Goutal ◽

Didier Lucor

Keyword(s):

Sensitivity Analysis ◽

Water Depth ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Polynomial Chaos Expansion ◽

Divide And Conquer ◽

Chaos Expansion ◽

Global Sensitivity ◽

Numerical Solver ◽

The Impact

AbstractA surrogate model is developed to accurately approximate a two-dimensional hydrodynamics numerical solver in order to conduct a reduced-cost variance-based global sensitivity analysis of the hydraulic state. The impact of uncertainties in river bottom friction and boundary conditions on the simulated water depth is analyzed for quasi-unsteady flows. An autoencoder technique adapted to non-linear variable dimension reduction is used to reduce the multi-dimensional model output so that the formulation of the surrogate remains computationally parsimonious. In addition, following the divide-and-conquer principle, a mixture of local polynomial chaos expansions is proposed to deal with non-linearity in the hydraulic state with respect to uncertain inputs. Machine learning techniques are used to automatically partition the input space into clusters that are not affected by non-linearities and support accurate surrogates. This combined strategy is applied to a reach of the Garonne River where river and floodplains dynamics are simulated by the numerical solver Telemac-2D. The merits of this strategy are highlighted when the flood front reaches regions where the topography features a strong gradient and where, consequently, strong non-linearities occur between the water depth and friction as well as hydrologic input forcing. By applying this strategy, the $$Q_2$$ Q 2 metric improves by 90% compared to a classical polynomial chaos expansion surrogate, resulting in a much more reliable sensitivity analysis. This is particularly important in floodplain areas where human and economic activities are at stake.

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Robust Dynamic Optimization of a Dual-rotor System Based on Polynomial Chaos Expansion

10.21203/rs.3.rs-267936/v1 ◽

2021 ◽

Author(s):

bensheng xu ◽

chaoping zang ◽

Xiaowei Wang ◽

Genbei Zhang

Keyword(s):

Dynamic Optimization ◽

Polynomial Chaos ◽

Polynomial Chaos Expansion ◽

Rotor System ◽

Operating Conditions ◽

Design Parameters ◽

Direct Monte Carlo Simulation ◽

Chaos Expansion ◽

The Finite Element Method ◽

The Mean

Abstract A novel methodology of robust dynamic optimization of a dual-rotor system based on polynomial chaos expansion (PCE) is developed in this paper. The dual-rotor system model was built by the Timoshenko theory and the finite element method. Instead of the direct Monte Carlo simulation (MCS), the PCE of the present dual-rotor system under support stiffness uncertainty is generated to facilitate a rapid analysis of stochastic responses and yield desirable results in significantly less number of functional evaluations. The PCE is explored as a basis for robust optimization, focusing on the problem of minimizing the unbalance response at operating conditions while minimizing its sensitivity to uncertainty in the support stiffness. This strategy avoids the use of MCS in order to effectively increase the efficiency of the optimization and significantly reduce the computing cost and time spending. The robust dynamic optimization attempts to both optimize the mean performance and minimizes the variance of the performance simultaneously. The multi-objective optimization results show that vibration response can be decreased and is significantly less sensitive to the variation of design parameters compared with initial design case by matching of unbalance amplitude and phase angle differences. Implementation of the proposed robust dynamic optimization in the present dual-rotor system illustrates its potential for further complicated applications.

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