Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss.

We apply nonlinear forecasting to the time series of the flame front instability induced by radiative heat loss to test for the short-term predictability and long-term unpredictability characteristic of deterministic chaos in flame front instability. Our results indicate that the flame front instability represents high-dimensional chaos generated via the period-doubling cascade process reported in our previous study [H. Gotoda, K. Michigami, K. Ikeda, and T. Miyano, Combust Theory Modell. 14, 479 (2010)], while its short-term behavior is predictable using a local nonlinear predictor based on the Sugihara-May method [H. Gotoda, H. Nikimoto, T. Miyano, and S. Tachibana, Chaos 20, 013124 (2011); G. Sugihara and R. M. May, Nature 344, 734 (1990)] as well as a generalized radial basis function network as a global nonlinear predictor. The feasibility of a new approach based on short-term prediction is also discussed in this work from the practical viewpoint of combustion systems.

[1]  Michael Small,et al.  Comparisons of new nonlinear modeling techniques with applications to infant respiration , 1998 .

[2]  David J. Wales,et al.  Calculating the rate of loss of information from chaotic time series by forecasting , 1991, Nature.

[3]  J. Elsner,et al.  Nonlinear prediction as a way of distinguishing chaos from random fractal sequences , 1992, Nature.

[4]  S. Chung,et al.  Instability-induced extinction of diffusion flames established in the stagnant mixing layer , 1999 .

[5]  S. Chung,et al.  Nonlinear evolution of diffusion flame oscillations triggered by radiative heat loss , 2000 .

[6]  Tomaso A. Poggio,et al.  Regularization Theory and Neural Networks Architectures , 1995, Neural Computation.

[7]  Yi Xiao,et al.  Nonlinear analysis of correlations in Alu repeat sequences in DNA. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[9]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[10]  Hiroki Hashiguchi,et al.  Bootstrap nonlinear prediction. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  K. Aihara,et al.  Time series analysis and prediction on complex dynamical behavior observed in a blast furnace , 2000 .

[12]  Hiroshi Gotoda,et al.  Orbital instability and prediction of a Bunsen flame tip motion with burner rotation , 2005 .

[13]  Harvinder S. Sidhu,et al.  An oscillatory route to extinction for solid fuel combustion waves due to heat losses , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  S. Margolis.  A New Route of Chaos In Gasless Combustion , 1993 .

[15]  Takaya Miyano,et al.  Dynamic properties of unstable motion of swirling premixed flames generated by a change in gravitational orientation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  P. L. Curto-Risso,et al.  Monofractal and multifractal analysis of simulated heat release fluctuations in a spark ignition heat engine , 2010 .

[17]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[18]  H. Abderrahmane,et al.  Applying nonlinear dynamic theory to one-dimensional pulsating detonations , 2011 .

[19]  Takaya Miyano,et al.  Chaotic oscillation in diffusion flame induced by radiative heat loss , 2010 .

[20]  H S Greenside,et al.  Characterization of the domain chaos convection state by the largest Lyapunov exponent. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Zhenghua Dai,et al.  Noise robust estimates of the largest Lyapunov exponent , 2005 .

[22]  T. Miyano,et al.  Characterization of complexities in Czochralski crystal growth by nonlinear forecasting , 1994 .

[23]  Kazuyuki Aihara,et al.  Difference correlation can distinguish deterministic chaos from 1/f^α type colored noise , 1997 .

[24]  M. Matalon,et al.  Heat loss and Lewis number effects on the onset of oscillations in diffusion flames , 1996 .

[25]  T. Miyano,et al.  Dynamic properties of combustion instability in a lean premixed gas-turbine combustor. , 2011, Chaos.

[26]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[27]  C H Lai,et al.  Improvement of the local prediction of chaotic time series. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Tohru Ikeguchi,et al.  Evaluation of nonlinearity and validity of nonlinear modeling for complex time series. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  K. Narayanan,et al.  On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis. , 1998, Chaos.

[30]  V. Volpert,et al.  Nonlinear dynamics in a simple model of solid flame microstructure , 2003 .

[31]  S. Datta †,et al.  An investigation of nonlinear dynamics of a thermal pulse combustor , 2009 .

[32]  Holger Kantz,et al.  Practical implementation of nonlinear time series methods: The TISEAN package. , 1998, Chaos.

[33]  M. Miklavcic.  Period doubling cascade in diffusion flames , 2007 .

[34]  P. Wahi,et al.  Bifurcations of Self-Excited Ducted Laminar Premixed Flames , 2012 .

[35]  G. Tombras,et al.  Chaotic operation by a single transistor circuit in the reverse active region. , 2010, Chaos.

[36]  N. Peters.  Turbulent Combustion: Subject Index , 2000 .

[37]  E. L. Fallen,et al.  Predictability of normal heart rhythms and deterministic chaos. , 1993, Chaos.

[38]  G. Litak,et al.  Multifractal and statistical analyses of heat release fluctuations in a spark ignition engine. , 2008, Chaos.

[39]  Nikolaos Nikiforakis,et al.  Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations , 2005 .

[40]  Martin Casdagli,et al.  Nonlinear prediction of chaotic time series , 1989 .

[41]  M Wendeker,et al.  Combustion process in a spark ignition engine: dynamics and noise level estimation. , 2003, Chaos.

[42]  C. Stuart Daw,et al.  Chaos in thermal pulse combustion. , 1995, Chaos.