scholarly journals Thermoacoustic instability – a dynamical system and time domain analysis

2014 ◽  
Vol 753 ◽  
pp. 448-471 ◽  
Author(s):  
Taraneh Sayadi ◽  
Vincent Le Chenadec ◽  
Peter J. Schmid ◽  
Franck Richecoeur ◽  
Marc Massot
Keyword(s):  
Time Series ◽  
Heat Source ◽  
Limit Cycle ◽  
Nonlinear Regime ◽  
Galerkin Projection ◽  
Nonlinear Flow ◽  
Mean Flow ◽  
Retarded Time ◽  
Thermoacoustic Instability ◽  
Linear And Nonlinear

AbstractThis study focuses on the Rijke tube problem, which includes features relevant to the modelling of thermoacoustic coupling in reactive flows: a compact acoustic source, an empirical model for the heat source and nonlinearities. This thermoacoustic system features both linear and nonlinear flow regimes with complex dynamical behaviour. In order to synthesize accurate time series, we tackle this problem from a numerical point of view, and start by proposing a dedicated solver designed for dealing with the underlying stiffness – in particular, the retarded time and the discontinuity at the location of the heat source. Stability analysis is performed on the limit of low-amplitude disturbances by using the projection method proposed by Jarlebring (PhD thesis, Technische Universität Braunschweig, 2008), which alleviates the problems arising from linearization with respect to the retarded time. The results are then compared with the analytical solution of the undamped system and with the results obtained from Galerkin projection methods commonly used in this setting. This analysis provides insight into the consequences of the various assumptions and simplifications that justify the use of Galerkin expansions based on the eigenmodes of the unheated resonator. We demonstrate that due to the presence of a discontinuity in the spatial domain, the eigenmodes in the heated case predicted by using Galerkin expansion show spurious oscillations resulting from the Gibbs phenomenon. Finally, time series in the fully nonlinear regime, where a limit cycle is established, are analysed and dominant modes are extracted. By comparing the modes of the linear regime to those of the nonlinear regime, we are able to illustrate the mean-flow modulation and frequency switching, which appear as the nonlinearities become significant and ultimately affect the form of the limit cycle. Analysis of the saturated limit cycles shows the presence of higher-frequency modes, which are linearly stable but become significant through nonlinear growth of the signal. This bimodal effect is not exhibited when the coupling between different frequencies is not accounted for. In conclusion, a dedicated solver for capturing thermoacoustic instability is proposed and methods for analysing linear and nonlinear regions of the resulting time series are introduced.

scholarly journals Bistability and Triggering Analysis of Thermoacoustic Instability in a Horizontal Rijke Tube

2019 ◽  
Vol 37 (1) ◽  
pp. 48-56
Author(s):  
Jianchang Feng ◽  
Wen Ao ◽  
Peijin Liu
Keyword(s):  
Nonlinear Dynamics ◽  
Limit Cycle ◽  
Time Lag ◽  
Damping Coefficient ◽  
Nonlinear Flow ◽  
Velocity Perturbation ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Heater Power ◽  
Bistable Region

Dynamical systems theory has been often employed to study nonlinear flow and flame dynamics in combustion systems. However, the corresponding studies using nonlinear dynamics to analyze the Rijke tube thermoacoustic system are still occasional. Little study has been performed to elucidate the characteristics of triggering phenomenon in the bistable region of the thermoacoustic system. In this regard, the main objectives of the present research are to contribute analysis for the lack of literature in these areas, especially to study the bistability and triggering properties of a thermoacoustic system. The thermoacoustic model of a horizontal Rijke tube is firstly established. The governing equations are expanded and solved by using Galerkin method. The analysis of the system is carried out by using nonlinear dynamics theory. Linear and nonlinear stability boundaries for the variation of non-dimensional heater power, damping coefficient and the relative heater location are obtained for different values of non-dimensional time lag in the system. Regions of global stability, global instability and bistability are characterized. The bistable region in the relative heater location is distributed symmetrically with xf=0.25. It is observed that the bistable region in the relative heater location firstly decreases with an increase in the non-dimensional time lag, reaching a minimum value at a certain critical value of τ, then increases. The situation for the bistable region in the damping coefficient presents a reverse variation, And the bistable region reach the maximum at τ=0.5. The triggering phenomenon and limit cycle of the system in the bistable region are studied. The critical triggering values are determined with the changes of the non-dimensional heater power, the damping coefficient and the relative heater location. The critical triggering value of velocity perturbation decreases with the increase of non-dimensional heater power, whereas an increasing trend is observed with the increase of damping coefficient. Interestingly, the critical triggering value firstly decreases and then increases with the increase of the relative heater location. The variation of critical triggering value for pressure perturbation is found to correspond with velocity perturbation. In the bistable region, the amplitude and frequency of the steady limit cycle oscillation of the system are independent of the initial perturbation values, but the perturbation value has strong effect on the duration needed to achieve the steady limit cycle, and the time required for the system to reach the limit cycle under the perturbation of U1=0.4 is about 3 times longer than that of U1=0.8.

scholarly journals Technical note: Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores

2019 ◽  
Vol 23 (10) ◽  
pp. 4323-4331 ◽  
Author(s):  
Wouter J. M. Knoben ◽  
Jim E. Freer ◽  
Ross A. Woods
Keyword(s):  
Time Series ◽  
Coefficient Of Variation ◽  
Ad Hoc ◽  
Model Performance ◽  
Technical Note ◽  
Mean Flow ◽  
Model Adequacy ◽  
Robust Model ◽  
The Mean ◽  
Adequacy Assessment

Abstract. A traditional metric used in hydrology to summarize model performance is the Nash–Sutcliffe efficiency (NSE). Increasingly an alternative metric, the Kling–Gupta efficiency (KGE), is used instead. When NSE is used, NSE = 0 corresponds to using the mean flow as a benchmark predictor. The same reasoning is applied in various studies that use KGE as a metric: negative KGE values are viewed as bad model performance, and only positive values are seen as good model performance. Here we show that using the mean flow as a predictor does not result in KGE = 0, but instead KGE =1-√2≈-0.41. Thus, KGE values greater than −0.41 indicate that a model improves upon the mean flow benchmark – even if the model's KGE value is negative. NSE and KGE values cannot be directly compared, because their relationship is non-unique and depends in part on the coefficient of variation of the observed time series. Therefore, modellers who use the KGE metric should not let their understanding of NSE values guide them in interpreting KGE values and instead develop new understanding based on the constitutive parts of the KGE metric and the explicit use of benchmark values to compare KGE scores against. More generally, a strong case can be made for moving away from ad hoc use of aggregated efficiency metrics and towards a framework based on purpose-dependent evaluation metrics and benchmarks that allows for more robust model adequacy assessment.

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

2009 ◽  
Vol 19 (02) ◽  
pp. 453-485 ◽  
Author(s):  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
LI LI ◽  
YULIN XU ◽  
HONGJV LIU ◽  
...  
Keyword(s):  
Time Series ◽  
Limit Cycle ◽  
Stochastic Dynamics ◽  
Nonlinear Time Series ◽  
Special Importance ◽  
Neuronal System ◽  
Neural Firing ◽  
Firing Patterns ◽  
Theoretical Simulation ◽  
Definition Of

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

2011 ◽  
Vol 680 ◽  
pp. 511-533 ◽  
Author(s):  
SATHESH MARIAPPAN ◽  
R. I. SUJITH
Keyword(s):  
Mach Number ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Heat Release ◽  
Acoustic Field ◽  
Release Rate ◽  
Governing Equations ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acceleration Term

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.

Empirical analysis of time series using feature selection algorithms

2021 ◽  
Author(s):  
Mikhail Kanevski
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Feature Selection ◽  
Dimensional Space ◽  
Multivariate Time Series ◽  
Feature Space ◽  
Real Data ◽  
Theoretical Concepts ◽  
Wide Range ◽  
Linear And Nonlinear

<p>Nowadays a wide range of methods and tools to study and forecast time series is available. An important problem in forecasting concerns embedding of time series, i.e. construction of a high dimensional space where forecasting problem is considered as a regression task. There are several basic linear and nonlinear approaches of constructing such space by defining an optimal delay vector using different theoretical concepts. Another way is to consider this space as an input feature space – IFS, and to apply machine learning feature selection (FS) algorithms to optimize IFS according to the problem under study (analysis, modelling or forecasting). Such approach is an empirical one: it is based on data and depends on the FS algorithms applied. In machine learning features are generally classified as relevant, redundant and irrelevant. It gives a reach possibility to perform advanced multivariate time series exploration and development of interpretable predictive models.</p><p>Therefore, in the present research different FS algorithms are used to analyze fundamental properties of time series from empirical point of view. Linear and nonlinear simulated time series are studied in detail to understand the advantages and drawbacks of the proposed approach. Real data case studies deal with air pollution and wind speed times series. Preliminary results are quite promising and more research is in progress.</p>

Complex Relationship Between Daily Partner Violence and Alcohol Use Among Violent Heterosexual Men

2020 ◽  
pp. 088626051989732 ◽  
Author(s):  
David Katerndahl ◽  
Sandra K. Burge ◽  
Robert L. Ferrer ◽  
Johanna Becho ◽  
Robert Wood
Keyword(s):  
Time Series ◽  
Alcohol Use ◽  
Partner Violence ◽  
Structural Equation ◽  
Equation Modeling ◽  
Group Level ◽  
Heterosexual Couples ◽  
Significant Group ◽  
Linear And Nonlinear ◽  
Unique Relationship

Although alcohol use and partner violence are consistently associated, the nature of the alcohol–violence relationship is still unclear. The purpose of this pilot study was to use longitudinal daily assessments of male partners’ alcohol use and violent events to identify the nature of the alcohol–violence relationship, employing both linear and nonlinear analyses. The participants were 20 adult heterosexual couples of whom the woman reported experiencing partner violence in the prior 30 days. Each partner provided a separate daily telephone report for 8 weeks via an automated interactive voice response (IVR), concerning the previous day’s violence, alcohol use, stressors, emotional reactions, and concerns for children. Individual IVR databases were merged to form a combined couple’s IVR time series. Time series were analyzed using graphic, linear, and nonlinear methods. Graphic analysis using state space grids found no consistent pattern across couples. Similarly, linear analysis using same-day cross-correlation and prior-day beta statistics found no significant group-level alcohol–violence relationship. Using cross-approximate entropy statistics and differential structural equation modeling, no nonlinear relationships between alcohol use and violence were noted either. Whether applying linear or nonlinear analytic methods, there is no group-level relationship between alcohol use by male perpetrators and their violent acts. The implications are significant. First, the alcohol–violence relationship may differ among subgroups. Second, couples need to be assessed thoroughly to determine their unique relationship with alcohol use, so that couple-specific interventions can be designed. Third, if perpetrators believe that their violence is facilitated by their alcohol use, then alcohol reduction should be encouraged despite any evidence suggesting a different alcohol–violence relationship. Finally, the accepted alcohol-causes-violence belief held by many providers needs to be reconsidered. Because the nature of the alcohol–violence relationship varies considerably across couples, clinicians should seek to understand their unique relationship applying across-the-board management approaches.

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