The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis

2020 ◽  
Author(s):  
Felicitas Schäfer ◽  
Shuai Guo ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Large Sets ◽  
Training Samples ◽  
Numerical Stability Analysis ◽  
Increased Sensitivity ◽  
Positive Growth Rate ◽  
Input Uncertainties ◽  
The Impact

Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.

The Impact of Exceptional Points On the Reliability of Thermoacoustic Stability Analysis

2020 ◽  
Author(s):  
Felicitas Schaefer ◽  
Shuai Guo ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Large Sets ◽  
Training Samples ◽  
Numerical Stability Analysis ◽  
Increased Sensitivity ◽  
Positive Growth Rate ◽  
Input Uncertainties ◽  
The Impact

Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.

Effect of the Condition Number of the Inverse Fourier Transform Matrix on the Solution Behavior of the Time Spectral Equation System

2020 ◽  
Author(s):  
Sen Zhang ◽  
Dingxi Wang ◽  
Yi Li ◽  
Hangkong Wu ◽  
Xiuquan Huang
Keyword(s):  
Fourier Transform ◽  
Stability Analysis ◽  
Condition Number ◽  
Inverse Fourier Transform ◽  
Real Life ◽  
Equation System ◽  
Time Instant ◽  
Transform Matrix ◽  
Spectral Equation ◽  
The Impact

Abstract The time spectral method is a very popular reduced order frequency method for analyzing unsteady flow due to its advantage of being easily extended from an existing steady flow solver. Condition number of the inverse Fourier transform matrix used in the method can affect the solution convergence and stability of the time spectral equation system. This paper aims at evaluating the effect of the condition number of the inverse Fourier transform matrix on the solution stability and convergence of the time spectral method from two aspects. The first aspect is to assess the impact of condition number using a matrix stability analysis based upon the time spectral form of the scalar advection equation. The relationship between the maximum allowable Courant number and the condition number will be derived. Different time instant groups which lead to the same condition number are also considered. Three numerical discretization schemes are provided for the stability analysis. The second aspect is to assess the impact of condition number for real life applications. Two case studies will be provided: one is a flutter case, NASA rotor 67, and the other is a blade row interaction case, NASA stage 35. A series of numerical analyses will be performed for each case using different time instant groups corresponding to different condition numbers. The conclusion drawn from the two real life case studies will corroborate the relationship derived from the matrix stability analysis.

scholarly journals Quantifying lower tropospheric methane concentrations using GOSAT near-IR and TES thermal IR measurements

2015 ◽  
Vol 8 (8) ◽  
pp. 3433-3445 ◽  
Author(s):  
J. R. Worden ◽  
A. J. Turner ◽  
A. Bloom ◽  
S. S. Kulawik ◽  
J. Liu ◽  
...  
Keyword(s):  
Near Infrared ◽  
Surface Fluxes ◽  
Vertical Profiles ◽  
Monthly Average ◽  
Near Ir ◽  
Surface Measurements ◽  
Increased Sensitivity ◽  
The Impact ◽  
Total Column ◽  
Methane Concentrations

Abstract. Evaluating surface fluxes of CH4 using total column data requires models to accurately account for the transport and chemistry of methane in the free troposphere and stratosphere, thus reducing sensitivity to the underlying fluxes. Vertical profiles of methane have increased sensitivity to surface fluxes because lower tropospheric methane is more sensitive to surface fluxes than a total column, and quantifying free-tropospheric CH4 concentrations helps to evaluate the impact of transport and chemistry uncertainties on estimated surface fluxes. Here we demonstrate the potential for estimating lower tropospheric CH4 concentrations through the combination of free-tropospheric methane measurements from the Aura Tropospheric Emission Spectrometer (TES) and XCH4 (dry-mole air fraction of methane) from the Greenhouse gases Observing SATellite – Thermal And Near-infrared for carbon Observation (GOSAT TANSO, herein GOSAT for brevity). The calculated precision of these estimates ranges from 10 to 30 ppb for a monthly average on a 4° × 5° latitude/longitude grid making these data suitable for evaluating lower-tropospheric methane concentrations. Smoothing error is approximately 10 ppb or less. Comparisons between these data and the GEOS-Chem model demonstrate that these lower-tropospheric CH4 estimates can resolve enhanced concentrations over flux regions that are challenging to resolve with total column measurements. We also use the GEOS-Chem model and surface measurements in background regions across a range of latitudes to determine that these lower-tropospheric estimates are biased low by approximately 65 ppb, with an accuracy of approximately 6 ppb (after removal of the bias) and an actual precision of approximately 30 ppb. This 6 ppb accuracy is consistent with the accuracy of TES and GOSAT methane retrievals.

The Numerical Stability Analysis of Pipelined Conjugate Gradient Methods: Historical Context and Methodology

2018 ◽  
Vol 40 (5) ◽  
pp. A3549-A3580 ◽  
Author(s):  
Erin C. Carson ◽  
Miroslav Rozložník ◽  
Zdeněk Strakoš ◽  
Petr Tichý ◽  
Miroslav Tůma
Keyword(s):  
Stability Analysis ◽  
Conjugate Gradient ◽  
Numerical Stability ◽  
Historical Context ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Numerical Stability Analysis

scholarly journals A numerical study into the longitudinal dynamic stability of the tailless aircraft

2019 ◽  
Vol 91 (3) ◽  
pp. 428-436 ◽  
Author(s):  
Agnieszka Kwiek
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Numerical Study ◽  
Aircraft Design ◽  
Content Type ◽  
Preliminary Stage ◽  
Longitudinal Dynamic ◽  
Stability Derivatives ◽  
The Impact ◽  
Tailless Aircraft

Purpose The purpose of this research is a study into a mathematical approach of a tailless aircraft dynamic stability analysis. This research is focused on investigation of influence of elevons (elevator) on stability derivatives and consequently on the aircraft longitudinal dynamic stability. The main research question is to determine whether this impact should be taken into account on the conceptual and preliminary stage of the analysis of the longitudinal dynamic stability. Design/methodology/approach Aerodynamic coefficients and longitudinal stability derivatives were computed by Panukl (panel methods). The analysis of the dynamic stability of the tailless aircraft was made by the Matlab code and SDSA package. Findings The main result of the research is a comparison of the dynamic stability of the tailless aircraft for different approaches, with and without the impact of elevator deflection on the trim drag and stability derivatives. Research limitations/implications This paper presents research that mostly should be considered on the preliminary stage of aircraft design and dynamic stability analysis. The impact of elevons deflection on the aircraft moment of inertia has been omitted. Practical implications The results of this research will be useful for the further design of small tailless unmanned aerial vehicles (UAVs). Originality/value This research reveals that in case of the analysis of small tailless UAVs, the impact of elevons deflection on stability derivatives is bigger than the impact of a Mach number. This impact should be taken into consideration, especially for a phugoid mode.

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

scholarly journals Dynamic Stability and Control of a Manipulating Unmanned Aerial Vehicle

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Yunping Liu ◽  
Xijie Huang ◽  
Yonghong Zhang ◽  
Yukang Zhou
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Dynamic Stability ◽  
Unmanned Aerial Vehicle ◽  
Impedance Control ◽  
System Stability ◽  
Constructive Method ◽  
Aerial Vehicle ◽  
And Control ◽  
The Impact

This paper focuses on the dynamic stability analysis of a manipulator mounted on a quadrotor unmanned aerial vehicle, namely, a manipulating unmanned aerial vehicle (MUAV). Manipulator movements and environments interaction will extremely affect the dynamic stability of the MUAV system. So the dynamic stability analysis of the MUAV system is of paramount importance for safety and satisfactory performance. However, the applications of Lyapunov’s stability theory to the MUAV system have been extremely limited, due to the lack of a constructive method available for deriving a Lyapunov function. Thus, Lyapunov exponent method and impedance control are introduced, and the Lyapunov exponent method can establish the quantitative relationships between the manipulator movements and the dynamics stability, while impedance control can reduce the impact of environmental interaction on system stability. Numerical simulation results have demonstrated the effectiveness of the proposed method.

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