An adaptive least-squares global sensitivity method and application to a plasma-coupled combustion prediction with parametric correlation

Tang, Kunkun; Massa, Luca; Wang, Jonathan M.; Freund, Jonathan B.

doi:10.1016/j.jcp.2018.01.042

Cited by 8 publications

(9 citation statements)

References 56 publications

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“…Laser-induced plasmas find application over a wide range of engineering technologies. For propulsion applications, for instance, both electric and chemical propulsion devices may benefit from plasma properties given their ability of generating high specific impulses [7][8][9], and enhancing the reaction kinetics [10][11][12][13][14], respectively. Recently, plasma assisted ignition has drawn a lot of attention due to the potential of improving ignition reliability, enhancing flame stabilization and reduce pollutant emission [15].…”

Section: Introductionmentioning

confidence: 99%

Laser-induced non-equilibrium plasma kernel dynamics

Alberti

Munafò

Koll

et al. 2019

J. Phys. D: Appl. Phys.

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A non-equilibrium model for laser generated plasmas is validated and used to investigate plasma kernel dynamics. Breakdowns in quiescent air at different ambient conditions (e.g. pressure) for different laser parameters (e.g. power density and beam wavelength) are considered. The hydrodynamics is described based on the chemically reactive Navier–Stokes equations where non-equilibrium effects are accounted for using a three-temperature model. Laser-plasma interactions over nano-second time-scales are modeled with a radiative transfer equation (RTE), including both multiphoton ionization (MPI) and inverse Bremsstrahlung (IB). Validation is conducted by comparing absorbed energy and plasma emission with the corresponding experimental measurements, and by observations of the structure of the breakdown. The laser generated plasma exhibits a two-lobe structure, developing both in the forward and backward directions. An analysis of the dynamics suggests that the kernel evolution results from a radiation-driven wave that is: (i) triggered by MPI, (ii) sustained by energy deposition in IB interactions, which compensates for the energy lost by free-electrons in ionizing collisions, and (iii) guided by both MPI and ionization by electron impact (IE).

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Section: Introductionmentioning

confidence: 99%

Laser-induced non-equilibrium plasma kernel dynamics

Alberti

Munafò

Koll

et al. 2019

J. Phys. D: Appl. Phys.

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“…The selection criterions for retaining the basis functions are based on the determination coefficient R 2 and least angle regression technique . Later, many other attempts also have been made to develop sparse PCE model in the field of UQ, the common idea hold in these methods is that the PCE coefficients are sparse (ie, having only several dominant coefficients). Given the training sample { X , Y }, where X = { x 1 , …, x N } T is the input data, Y = { Y 1 , …, Y N } T is the corresponding model response and N is the size of sample, the dominant PCE coefficients can be recovered by solving the following optimization problem

{boldω}_{boldα} = \underset{ω_{α}}{\arg \min} {(‖‖, {boldω}_{boldα})}_{1} \begin{array}{c} subject to \end{array} ‖{boldΦω}_{boldα} - Y‖ \leq ϵ,

Section: Polynomial Chaos Approximationmentioning

confidence: 99%

“…Given the training sample { X , Y }, where X = { x 1 , …, x N } T is the input data, Y = { Y 1 , …, Y N } T is the corresponding model response and N is the size of sample, the dominant PCE coefficients can be recovered by solving the following optimization problem

{boldω}_{boldα} = \underset{ω_{α}}{\arg \min} {(‖‖, {boldω}_{boldα})}_{1} \begin{array}{c} subject to \end{array} ‖{boldΦω}_{boldα} - Y‖ \leq ϵ,

where ‖ ω α ‖ 1 is the l 1 norm of PCE coefficients, and ϵ is a tolerance parameter necessitated by the truncation error and Φ ( i , j ) = ψ j ( x i )( i = 1, …, N ; j = 1, …, P + 1) is the measure matrix. To solve above optimization problem, a large number of powerful algorithms have been proposed, such as some adaptive methods and l 1 minimization methods. The adaptive methods aim at selecting the significant basis functions from full PCE sequentially using only few samples based on the well‐defined selection criterion, such as the correlation criterion in References and the variance contribution criterion in Reference .…”

Section: Polynomial Chaos Approximationmentioning

confidence: 99%

“…To solve above optimization problem, a large number of powerful algorithms have been proposed, such as some adaptive methods and l 1 minimization methods. The adaptive methods aim at selecting the significant basis functions from full PCE sequentially using only few samples based on the well‐defined selection criterion, such as the correlation criterion in References and the variance contribution criterion in Reference . The l 1 minimization techniques aim at minimizing the l 1 norm of PCE coefficients while preserving the fitting accuracy using the compressed sensing algorithm, and it has been shown to be efficient to capture the dominant PCE coefficients.…”

Section: Polynomial Chaos Approximationmentioning

confidence: 99%

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Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Cheng

Lü

2020

Numerical Meth Engineering

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Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis.This learning function is developed under the framework of the variance-bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.

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“…Laser-induced breakdown of gases has been extensively studied over the last few decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and its applications are of interest for a number of engineering technologies such as spectroscopy, propulsion, ignition, and flow control [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In nano-second discharges, numerical and experimental studies have been performed (and still are) on air and other gases to understand the breakdown mechanism and its dependence on parameters such as ambient pressure, beam wavelength, and the optical details of the focusing system (e.g.…”

Section: Introductionmentioning

confidence: 99%

Collinear dual-pulse laser optical breakdown and energy deposition

Alberti¹,

Munafò²,

Pantano³

et al. 2020

J. Phys. D: Appl. Phys.

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A non-equilibrium model for laser-generated plasmas is used to represent collinear dual nano-second-pulse interactions. In the specific case considered, the breakdown is initiated with an ultraviolet (UV) laser pulse at 266 nm, which pre-ionizes the gas, and it is followed by a near-infrared (NIR) pulse at 1064 nm, which deposits significant energy into the ionized mixture. The model is validated against corresponding experiments, and simulation results are interrogated to understand key features of the plasma-kernel dynamics and the post-discharge hydrodynamics. The hydrodynamics of the non-equilibrium plasma is governed by the two-temperature Navier–Stokes equations accounting for both multiphoton ionization and inverse bremsstrahlung. The interaction between the laser beam and the plasma is modeled based on the radiative transfer equation. The temporal and spatial offsets of the two pulses can generate ionization kernels with different topology and dynamics. It is shown that the UV pre-ionization pulse can tailor the plasma region, leading to a larger ionized volume than would occur for a single-pulse breakdown, and it increases the efficiency of the energy deposition for the following NIR discharge. Vorticity in the early post-discharge phase is generated via baroclinic torque from the misalignment of the radial gradient of density (sudden gas expansion) and the strong pressure gradient (initiated by energy deposition from the laser beam). It is predicted that the collinear dual pulse can be designed to specify the plasma kernel size, shape, and maximum temperature in the breakdown phase, and the initial post-breakdown vorticity and plasma-core decay.

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An adaptive least-squares global sensitivity method and application to a plasma-coupled combustion prediction with parametric correlation

Cited by 8 publications

References 56 publications

Laser-induced non-equilibrium plasma kernel dynamics

Laser-induced non-equilibrium plasma kernel dynamics

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Collinear dual-pulse laser optical breakdown and energy deposition

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