Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response for Thermoacoustic Stability Analysis

2018 ◽  
Author(s):  
Shuai Guo ◽  
Camilo F. Silva ◽  
Abdulla Ghani ◽  
Wolfgang Polifke
Keyword(s):  
Growth Rate ◽  
Time Series ◽  
Stability Analysis ◽  
Impulse Response ◽  
Cfd Simulation ◽  
Finite Impulse Response ◽  
Dimensional Approximation ◽  
Fir Model ◽  
The Impact ◽  
Active Subspace

The thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools such as Helmholtz solvers or network models coupled with a model for the flame dynamic response. Within such a framework, the flame response to flow perturbations can be described by a Finite Impulse Response (FIR) model, which can be derived from LES time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to e.g., the statistical nature of the identification process, low signal-to-noise ratio or finite length of time series. Thus, a necessary step towards reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer CFD simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address the two issues, a dimensional reduction UQ methodology called “Active Subspace approach” is employed in the present study. For the first question, Active Subspace approach is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on Active Subspace approach is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response for Thermoacoustic Stability Analysis

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Shuai Guo ◽  
Camilo F. Silva ◽  
Abdulla Ghani ◽  
Wolfgang Polifke
Keyword(s):  
Growth Rate ◽  
Time Series ◽  
Stability Analysis ◽  
Impulse Response ◽  
Cfd Simulation ◽  
Finite Impulse Response ◽  
Original System ◽  
Dimensional Approximation ◽  
Fir Model ◽  
The Impact

The thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools such as Helmholtz solvers or network models coupled with a model for the flame dynamic response. Within such a framework, the flame response to flow perturbations can be described by a finite impulse response (FIR) model, which can be derived from large eddy simulation (LES) time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to, e.g., the statistical nature of the identification process, low signal-to-noise ratio, or finite length of time series. Thus, a necessary step toward reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer computational fluid dynamics (CFD) simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address the two issues, a dimensional reduction UQ methodology called “Active subspace approach (ASA)” is employed in the present study. For the first question, ASA is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on ASA is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

scholarly journals Response of a swirl flame to inertial waves

2017 ◽  
Vol 10 (4) ◽  
pp. 277-286 ◽  
Author(s):  
Alp Albayrak ◽  
Deniz A Bezgin ◽  
Wolfgang Polifke
Keyword(s):  
Steady State ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Reactive Flow ◽  
Inertial Waves ◽  
Mean Flow ◽  
Flow Equations ◽  
Flame Response ◽  
Inertial Wave ◽  
The Impact

Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier–Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton’s method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

scholarly journals Estimating the SARS-CoV-2 infected population fraction and the infection-to-fatality ratio: a data-driven case study based on Swedish time series data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andreas Wacker ◽  
Anna Jöud ◽  
Bo Bernhardsson ◽  
Philip Gerlee ◽  
Fredrik Gustafsson ◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Finite Impulse Response ◽  
Herd Immunity ◽  
Late Summer ◽  
Series Data ◽  
Rt Pcr ◽  
Filter Function ◽  
Study Results ◽  
Fir Model

AbstractWe demonstrate that finite impulse response (FIR) models can be applied to analyze the time evolution of an epidemic with its impact on deaths and healthcare strain. Using time series data for COVID-19-related cases, ICU admissions and deaths from Sweden, the FIR model gives a consistent epidemiological trajectory for a simple delta filter function. This results in a consistent scaling between the time series if appropriate time delays are applied and allows the reconstruction of cases for times before July 2020, when RT-PCR testing was not widely available. Combined with randomized RT-PCR study results, we utilize this approach to estimate the total number of infections in Sweden, and the corresponding infection-to-fatality ratio (IFR), infection-to-case ratio (ICR), and infection-to-ICU admission ratio (IIAR). Our values for IFR, ICR and IIAR are essentially constant over large parts of 2020 in contrast with claims of healthcare adaptation or mutated virus variants importantly affecting these ratios. We observe a diminished IFR in late summer 2020 as well as a strong decline during 2021, following the launch of a nation-wide vaccination program. The total number of infections during 2020 is estimated to 1.3 million, indicating that Sweden was far from herd immunity.

scholarly journals Pengaruh Ekspor, Impor, dan Investasi terhadap Pertumbuhan Sektor Pertanian Indonesia

2018 ◽  
Vol 35 (1) ◽  
pp. 49
Author(s):  
NFN Suharjon ◽  
Sri Marwanti ◽  
Heru Irianto
Keyword(s):  
Growth Rate ◽  
Time Series ◽  
Impulse Response ◽  
Agricultural Sector ◽  
Gdp Growth ◽  
Agricultural Export ◽  
Absolute Value ◽  
Gdp Growth Rate ◽  
Vector Auto Regression ◽  
Auto Regression

<p><strong>English</strong><br />Promoting agricultural sector is important for improving Indonesia economic performance. The objectives of the research are to determine the effects of levels and shocks of agricultural export, import, and investment on the growth (GDP) of the Indonesian agriculture sector. The research was conducted using quarterly time series data from 2000–2015. Vector Auto Regression analysis method was applied in this study. The causality analysis shows that the agricultural export, import, and investment levels do not significantly affect the agricultural GDP growth, but the agricultural GDP growth does significantly affect the level of agricultural export, import, and investment. The impulse response analysis shows that the investment response to GDP growth shocks is higher than that of export and import responses. The variance of decomposition analysis shows that the contribution of exports to agricultural GDP growth are larger than the contribution of imports and investments. This study concludes that the absolute value of the agricultural sector export, import, and investment do not affect the sector GDP growth rate, but the agricultural sector GDP growth rate affect the absolute value of the sector export, import, and investment in Indonesia.</p><p><br /><strong>Indonesian</strong><br />Mendorong pertumbuhan sektor pertanian Indonesia adalah penting untuk peningkatan kinerja perekonomian Indonesia. Tujuan penelitian adalah mengetahui pengaruh besaran dan goncangan (shock) ekspor, impor, dan investasi sektor pertanian terhadap pertumbuhan (GDP) sektor pertanian Indonesia. Penelitian dilakukan dengan menggunakan data time series triwulanan dari tahun 2000–2015. Penelitian menggunakan metode analisis Vector Auto Regression (VAR). Hasil analisis kausalitas menunjukkan bahwa ekspor, impor, dan investasi pertanian tidak berpengaruh nyata terhadap pertumbuhan PDB sektor pertanian, namun pertumbuhan PDB sektor pertanian berpengaruh nyata terhadap ekspor, impor, dan investasi pertanian. Hasil analisis impulse response menunjukkan bahwa respons investasi terhadap goncangan pertumbuhan PDB lebih besar dibandingkan respons besaran ekspor dan impor, Analisis variance decomposition menunjukkan kontribusi ekspor terhadap pertumbuhan PDB lebih besar dibandingkan dengan kontribusi impor dan investasi. Hasil penelitian ini menyimpulkan bahwa besaran absolut ekspor, impor, dan investasi pertanian tidak berpengaruh nyata terhadap laju pertumbuhan PDB sektor pertanian, namun pertumbuhan PDB sektor pertanian berpengaruh nyata terhadap besaran ekspor, impor, dan investasi pertanian di Indonesia.</p>

scholarly journals Impact of the Low-Price Medicine Policy on Medicine Supply in China: An Interrupted Time-Series Analysis

2021 ◽  
Vol 12 ◽  
Author(s):  
Mingyue Zhao ◽  
Ali Hassan Gillani ◽  
Duan Ji ◽  
Zhitong Feng ◽  
Yu Fang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Time Series ◽  
Interrupted Time Series ◽  
Interrupted Time Series Analysis ◽  
Average Growth Rate ◽  
Average Growth ◽  
Total Group ◽  
Increasing Trend ◽  
Trend Coefficient ◽  
The Impact

Objectives: The primary objective of the study was to assess the impact of the Low-Price Medicine Policy (LPMP) on the supply of low-price medicines (LPMs) in China. The secondary objective of the study was to describe the supply situation of LPMs from 2005 to 2018.Methods: The LPMP was launched in the third quarter of 2014 (2014Q3). An interrupted time series analysis was used to evaluate the impact of LPMP on the supply of LPMs in China. Ordinary least squares and Poisson regression models were utilized to estimate the effect of LPMP on LPMs’ supply growth rate and the number of supplied LPMs. All the LPMs were divided into two subgroups: intermittent supply and continuous supply. The trend and level changes of the quarterly average growth rate and number of quarterly supplies for different LPM groups were analyzed from 2005 to 2018.Findings: For the quarterly average growth rate, before the intervention, a significant increasing trend was observed in the total group and the continuous supply subgroup; after the introduction of LPMP, the increasing trend was ceased and a significant decrease in the trend and level was noted for both the total group (trend coefficient: β3= −0.0132, p &lt; 0.01; level coefficient: β2 = −0.1510, p &lt; 0.05) and the continuous supply subgroup (trend coefficient: β3 = −0.0133, p &lt; 0.01; level coefficient: β2 = −0.1520, p &lt; 0.05); whereas it had no significant effect for intermittent supply subgroup. For the number of quarterly supplies, after the intervention of LPMP, decline of the supply number was observed (trend coefficient: β3 = −0.0027, p &lt; 0.001; level coefficient: β2 = −0.0584, p &lt; 0.001); whereas the LPMP was associated with an upward trend and level (trend coefficient: β3 = 0.0715, p &lt; 0.001; level coefficient: β2 = 0.174) for the intermittent supply subgroup.Conclusion: For most of the LPMs, LPMP did not meet the goal of stimulating LPM production. However, for severely shortage medicines (the intermittent supply subgroup), the effect of LPMP was positive. Comprehensive policies rather than just deregulating medicine price should be introduced to alleviate the situation of medicine shortage in China.

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

2018 ◽  
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.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties, and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a 1-D model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function. By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a one-dimensional (1D) model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function (FTF). By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

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