scholarly journals Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Model Parameters ◽  
Geometrical Parameters ◽  
Parameter Uncertainties ◽  
Flame Response ◽  
Mode Stability

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain-based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible flow computations. They result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters, etc. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the problem is using adjoint perturbation theory. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo (MC) simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz, it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental data are available.

scholarly journals Methods for the Calculation of Thermoacoustic Stability Margins and Monte Carlo-Free Uncertainty Quantification

2017 ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Factor Analysis ◽  
Risk Factor ◽  
Uncertainty Quantification ◽  
Frequency Domain ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Risk Factor Analysis ◽  
Model Parameters

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible CFD computations. Frequency-domain approaches result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Nonlinear functions of the frequency are, for example, the n–τ model, impedance boundary conditions, etc. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, which are obtained by experiments with some uncertainty, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. It quantifies the uncertainty of a set of parameters in terms of the probability of a mode to become unstable. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters etc. Assessing also the influence of all possible combinations of these parameters on the risk factor is a numerically very costly task. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the eigenfrequency problem is using adjoint perturbation theory. Though adjoint perturbation methods were recently applied to accelerate the risk factor analysis, its potential to improve the theory has not yet been fully exploited. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental validation is available.

scholarly journals Bayesian estimation of parameters in a regional hydrological model

2002 ◽  
Vol 6 (5) ◽  
pp. 883-898 ◽  
Author(s):  
K. Engeland ◽  
L. Gottschalk
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Hydrological Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Daily Streamflow ◽  
Likelihood Model ◽  
Simulation Errors

Abstract. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1) process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

Parametric uncertainty quantification in the Rothermel model with randomised quasi-Monte Carlo methods

2015 ◽  
Vol 24 (3) ◽  
pp. 307 ◽  
Author(s):  
Yaning Liu ◽  
Edwin Jimenez ◽  
M. Yousuff Hussaini ◽  
Giray Ökten ◽  
Scott Goodrick
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
Monte Carlo Methods ◽  
Wildland Fire ◽  
Parametric Uncertainty ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Quasi Monte Carlo ◽  
Control Variate ◽  
Fuel Model

Rothermel's wildland surface fire model is a popular model used in wildland fire management. The original model has a large number of parameters, making uncertainty quantification challenging. In this paper, we use variance-based global sensitivity analysis to reduce the number of model parameters, and apply randomised quasi-Monte Carlo methods to quantify parametric uncertainties for the reduced model. The Monte Carlo estimator used in these calculations is based on a control variate approach applied to the sensitivity derivative enhanced sampling. The chaparral fuel model, selected from Rothermel's 11 original fuel models, is studied as an example. We obtain numerical results that improve the crude Monte Carlo sampling by factors as high as three orders of magnitude.

Uncertainty Quantification of Aeroacoustic Power Sources in Corrugated Pipes

2015 ◽  
Author(s):  
Maharudrayya Swamy ◽  
Pejman Shoeibi Omrani ◽  
Nestor Gonzalez Diez
Keyword(s):  
Uncertainty Quantification ◽  
Input Parameter ◽  
Distribution Functions ◽  
Geometrical Parameters ◽  
Acoustic Source ◽  
Parameter Uncertainties ◽  
Source Power ◽  
Power Sources ◽  
Edge Radius ◽  
Onset Velocity

Gas transport in corrugated pipes often exhibit whistling behavior, due to periodic flow-induced pulsations generated in the pipe cavities. These aero-acoustic sources are strongly dependent on the geometrical dimensions and features of the cavities. As a result, uncertainties in the exact shape and geometry play a significant role in determining the singing behavior of corrugated pipes. While predictive modelling for idealized periodic structures is well established, this paper focusses on the sensitivity analysis and uncertainty quantification (UQ) of uncertain geometrical parameters using probabilistic models. The two most influential geometrical parameters varied within this study are the cavity width and downstream edge radius. Computational Fluid Dynamics (CFD) analysis was used to characterize the acoustic source. Stochastic collocation method was used for propagation of input parameter uncertainties. The analysis was performed with both full tensor product grid and sparse grid based on level-2 Clenshaw-Curtis points. The results show that uncertainties in the width and downstream edge radius of the cavity have an effect on the acoustic source power, peak Strouhal number and consequently the whistling onset velocity. Based on the assumed input parameters distribution functions, the confidence levels for the prediction of onset velocity were calculated. Finally, the results show the importance of performing uncertainty analysis to get more insights in the source of errors and consequently leading to a more robust design or risk-management oriented decision.

Design for Thermo-Acoustic Stability: Modeling of Burner and Flame Dynamics

2013 ◽  
Author(s):  
Stefanie Bade ◽  
Michael Wagner ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer ◽  
Bruno Schuermans
Keyword(s):  
Optimization Procedure ◽  
Parametric Models ◽  
Design Parameters ◽  
Model Parameters ◽  
Geometrical Parameters ◽  
Flame Dynamics ◽  
Stability Model ◽  
Flame Response ◽  
Burner Design ◽  
Acoustic Stability

A Design for Thermo-Acoustic Stability (DeTAS) procedure is presented, that aims at selecting a most stable burner geometry for a given combustor. It is based on the premise that a thermo-acoustic stability model of the combustor can be formulated and that a burner design exists, which has geometric design parameters that sufficiently influence the dynamics of the flame. Describing the flame dynamics in dependence of the geometrical parameters an optimization procedure involving a linear stability model of the target combustor maximizes the damping and thereby yields the optimal geometrical parameters. To demonstrate the procedure on an existing annular combustor a generic burner design was developed that features a significant variability of dynamical flame response in dependence of two geometrical parameters. In this paper the experimentally determined complex burner acoustics and complex flame responses are described in terms of physics based parametric models with excellent agreement between experimental and model data. It is shown that these model parameters correlate uniquely with the variation of the burner geometrical parameters, allowing to interpolate the model with respect to the geometrical parameters. The interpolation is validated with experimental data.

SPUX - a Scalable Package for Bayesian Uncertainty Quantification

2020 ◽  
Author(s):  
Jonas Sukys ◽  
Marco Bacci
Keyword(s):  
Bayesian Inference ◽  
Uncertainty Quantification ◽  
High Performance ◽  
Performance Metrics ◽  
Expert Knowledge ◽  
Simple Random Walk ◽  
Scientific Workflow ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Computational Performance

<div> <div>SPUX (Scalable Package for Uncertainty Quantification in "X") is a modular framework for Bayesian inference and uncertainty quantification. The SPUX framework aims at harnessing high performance scientific computing to tackle complex aquatic dynamical systems rich in intrinsic uncertainties,</div> <div>such as ecological ecosystems, hydrological catchments, lake dynamics, subsurface flows, urban floods, etc. The challenging task of quantifying input, output and/or parameter uncertainties in such stochastic models is tackled using Bayesian inference techniques, where numerical sampling and filtering algorithms assimilate prior expert knowledge and available experimental data. The SPUX framework greatly simplifies uncertainty quantification for realistic computationally costly models and provides an accessible, modular, portable, scalable, interpretable and reproducible scientific workflow. To achieve this, SPUX can be coupled to any serial or parallel model written in any programming language (e.g. Python, R, C/C++, Fortran, Java), can be installed either on a laptop or on a parallel cluster, and has built-in support for automatic reports, including algorithmic and computational performance metrics. I will present key SPUX concepts using a simple random walk example, and showcase recent realistic applications for catchment and lake models. In particular, uncertainties in model parameters, meteorological inputs, and data observation processes are inferred by assimilating available in-situ and remotely sensed datasets.</div> </div>

Monte-Carlo Simulation of the Theoretical Site Response Variability at Turkey Flat, California, Given the Uncertainty in the Geotechnically Derived Input Parameters

1993 ◽  
Vol 9 (4) ◽  
pp. 669-701 ◽  
Author(s):  
Edward H. Field ◽  
Klaus H. Jacob
Keyword(s):  
Monte Carlo ◽  
Physical Model ◽  
Site Response ◽  
Input Parameter ◽  
Model Parameters ◽  
Spectral Ratios ◽  
Parameter Uncertainties ◽  
Theoretical Predictions ◽  
High Degree ◽  
Geotechnical Studies

In the weak-motion phase of the Turkey Flat blind-prediction effort, it was found that given a particular physical model of each sediment site, various theoretical techniques give similar estimates of the site response. However, it remained to be determined how uncertainties in the physical model parameters influence the theoretical predictions. We have studied this question by propagating the physical parameter uncertainties into the theoretical site-response predictions using monte-carlo simulations. The input-parameter uncertainties were estimated directly from the results of several independent geotechnical studies performed at Turkey Flat. While the computed results generally agree with empirical site-response estimates (average spectral ratios of earthquake recordings), we found that the uncertainties lead to a high degree of variability in the theoretical predictions. Most of this variability comes from poor constraints on the shear-wave velocity and thickness of a thin (∼2m) surface layer, and on the attenuation of the sediments. Our results suggest that in site-response studies which rely exclusively on geotechnically based theoretical predictions, it will be important that the variability resulting from input-parameter uncertainties is recognized and accounted for.

scholarly journals Uncertainty quantification in subject-specific estimation of local vessel mechanical properties

2021 ◽  
Author(s):  
Bruno V Rego ◽  
Dar Weiss ◽  
Matthew R Bersi ◽  
Jay D Humphrey
Keyword(s):  
Mechanical Properties ◽  
Uncertainty Quantification ◽  
Inverse Modeling ◽  
Quantitative Estimation ◽  
Small Animal ◽  
Image Correlation ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Local Point ◽  
Subject Specific

Quantitative estimation of local mechanical properties remains critically important in the ongoing effort to elucidate how blood vessels establish, maintain, or lose mechanical homeostasis. Recent advances based on panoramic digital image correlation (pDIC) have made high-fidelity 3D reconstructions of small-animal (e.g., murine) vessels possible when imaged in a variety of quasi-statically loaded configurations. While we have previously developed and validated inverse modeling approaches to translate pDIC-measured surface deformations into biomechanical metrics of interest, our workflow did not heretofore include a methodology to quantify uncertainties associated with local point estimates of mechanical properties. This limitation has compromised our ability to infer biomechanical properties on a subject-specific basis, such as whether stiffness differs significantly between multiple material locations on the same vessel or whether stiffness differs significantly between multiple vessels at a corresponding material location. In the present study, we have integrated a novel uncertainty quantification and propagation pipeline within our inverse modeling approach, relying on empirical and analytic Bayesian techniques. To demonstrate the approach, we present illustrative results for the ascending thoracic aorta from three mouse models, quantifying uncertainties in constitutive model parameters as well as circumferential and axial tangent stiffness. Our extended workflow not only allows parameter uncertainties to be systematically reported, but also facilitates both subject-specific and group-level statistical analyses of the mechanics of the vessel wall.

Uncertainty Quantification of NEPTUN Analysis Using Wilks’ Formula With an Extended Number of Calculations

2006 ◽  
Author(s):  
Moonkyu Hwang ◽  
Young-Jin Lee ◽  
Bub-Dong Chung
Keyword(s):  
Monte Carlo ◽  
Uncertainty Quantification ◽  
System Analysis ◽  
Sensitivity Study ◽  
Mean Value ◽  
Model Parameters ◽  
Phase System ◽  
Two Phase ◽  
Mars Model ◽  
Calculation Results

The two-phase system analysis code MARS [1] has been used for the uncertainty quantification of NEPTUN reflood test [2] analysis. By performing 10,000 calculations based on a random variation of the MARS model parameters and measured data, a mean value, and the 95% upper bounds are traced along the number of calculations. The CPU-intensive calculations were performed using the 11 node PC-cluster under Linux platform. The Monte-Carlo calculation results suggest a total number of 2,000 calculations would be sufficient to determine the stable mean and 95% upper bound values. The peak temperatures predictions are also used to find the 95% bounding values by using the Wilks’ method. For the 1st order one-sided formula, every 59 peak temperatures are examined to locate the bounding temperature, with a 95% confidence. The 2nd and 3rd order values were found in a similar way. The uncertainty band by the Wilks’ formula, when compared with the true 95% bounding value, is observed to be quite broad, especially in the case of the 1st order. The 2nd or 3rd orders or a full Monte-Carlo method would be necessary to demonstrate that the safety of the plant is ensured with a sufficient margin. A supplementary sensitivity study, for the nine uncertain parameters selected for the NEPTUN analysis, is also performed to find the degree of influence of each parameter on the peak rod temperature.

Design for Thermo-Acoustic Stability: Modeling of Burner and Flame Dynamics

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
S. Bade ◽  
M. Wagner ◽  
C. Hirsch ◽  
T. Sattelmayer ◽  
B. Schuermans
Keyword(s):  
Optimization Procedure ◽  
Parametric Models ◽  
Design Parameters ◽  
Model Parameters ◽  
Geometrical Parameters ◽  
Flame Dynamics ◽  
Stability Model ◽  
Flame Response ◽  
Burner Design ◽  
Acoustic Stability

A design for thermo-acoustic stability (DeTAS) procedure is presented that aims at selecting the most stable burner geometry for a given combustor. It is based on the premise that a thermo-acoustic stability model of the combustor can be formulated and that a burner design exists, which has geometric design parameters that sufficiently influence the dynamics of the flame. Describing the flame dynamics in dependence of the geometrical parameters, an optimization procedure involving a linear stability model of the target combustor, maximizes the damping and thereby yields the optimal geometrical parameters. To demonstrate the procedure on an existing annular combustor a generic burner design was developed that features significant variability of dynamical flame response in dependence of two geometrical parameters. In this paper the experimentally determined complex burner acoustics and complex flame responses are described in terms of physics-based parametric models with excellent agreement between experimental and model data. It is shown that these model parameters correlate uniquely with the variation of the burner geometrical parameters, allowing interpolating the model with respect to the geometrical parameters. The interpolation is validated with experimental data.

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