Detecting Nonlinearity in Experimental Data

Small, Michael; Judd, Kevin

doi:10.1142/s0218127498000966

Cited by 31 publications

(14 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case, the surrogate data generated by shuffling individual cycles within the time series, referred to as the cycle surrogate data, are useful for testing the determinism in the case of slow amplitude modulation. Referring to previous studies, 32,33 we postulate a null hypothesis that each cycle is independent of its adjacent cycles and that no determinism is visible in the pitch fluctuations of the time series. Under this null hypothesis, we generate a 20 cycle surrogate time series.…”

Section: Surrogate Data Methodsmentioning

confidence: 97%

“…26,30 Nevertheless, we do not use this algorithm in this study. We instead apply the amplitude adjusted Fourier transform surrogate method 31 and the cycle surrogate method, 32,33 to evaluate the statistical significance of our estimates for the translation error in the Wayland test. On the basis of the extracted deterministic nature of the dynamic behavior, the availability of the nonlinear forecasting method, proposed by Sugihara and May, 34 is also discussed to predict the short-term dynamic behavior of the combustion instability from a practical viewpoint.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor

Gotoda

Nikimoto

Miyano

et al. 2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

178

117

View full text Add to dashboard Cite

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics. Periodic and chaotic behavior in combustion dynamics that can be observed as a result of combustion instabilities in fundamental and practical combustion systems are of importance to present-day combustion physics and nonlinear science research. In this paper, we experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. As the equivalence ratio / increases from 0.43 to 0.55, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. This is clearly demonstrated by a nonlinear time series analysis in combination with a surrogate data method, which has not been reported in details in previous fundamental combustion research. On the basis of the deterministic nature of the dynamic behavior extracted by the nonlinear time series analysis, a nonlinear forecasting method was performed to predict the time series of the pressure fluctuations. The short-term predicted pressure fluctuations obtained by updating the data library of the phase space coincide very closely with the measured pressure fluctuations, which shows that the nonlinear forecasting method we applied in this work has potential use for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor.

show abstract

Section: Surrogate Data Methodsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor

Gotoda

Nikimoto

Miyano

et al. 2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

178

117

View full text Add to dashboard Cite

show abstract

“…This method is based on the well-known local-linear modeling methods described by Mees [2] and Sugihara and May [3]. Previously, Small and Judd advocated [4] and implemented [5] nonlinear radial basis modeling routines [6,7] as a form of surrogate hypothesis testing. The method we describe here is simpler and tests a more specific null hypothesis.…”

mentioning

confidence: 99%

Surrogate Test for Pseudoperiodic Time Series Data

2001

Self Cite

View full text Add to dashboard Cite

For time series exhibiting strong periodicities, standard (linear) surrogate methods are not useful. We describe a new algorithm that can test against the null hypothesis of a periodic orbit with uncorrelated noise. We demonstrate the application of this method to artificial data and experimental time series, including human electrocardiogram recordings during sinus rhythm and ventricular tachycardia. DOI: 10.1103/PhysRevLett.87.188101 PACS numbers: 05.45.Tp, 05.10. -a, 87.19.Nn The method of surrogate data [1] is widely applied to test the null hypothesis that an observed time series is a typical realization of the output of a specific class of dynamical systems. This method is widely used in the analysis of experimental time series and provides a powerful tool in the search for determinism in apparently stochastic data. However, the current surrogate techniques have very limited utility when applied to a time series with a strong pseudoperiodic behavior.The surrogate algorithm we describe in this Letter generates pseudoperiodic surrogates (PPS). This method is based on the well-known local-linear modeling methods described by Mees [2] and Sugihara and May [3]. Previously, Small and Judd advocated [4] and implemented [5] nonlinear radial basis modeling routines [6,7] as a form of surrogate hypothesis testing. The method we describe here is simpler and tests a more specific null hypothesis. This method may be applied to test against the null hypothesis of a periodic orbit with uncorrelated noise in the very large number of experimental systems that exhibit pseudoperiodic behavior.By contrast, the three most successful, and widely applied, algorithms test for membership of the class of (i) independent and identical distributed (IID) noise processes, (ii) linearly filtered noise processes, and (iii) static monotonic nonlinear transformation of linearly filtered noise processes [1,8]. For time series data exhibiting strong pseudoperiodic behavior, the null hypotheses of IID or colored noise are obviously false. Therefore, apart from serving as a "sanity check," these existing algorithms are of limited use for such data.For a pseudoperiodic time series, Theiler and Rapp suggested an alternative algorithm [9]: cycle shuffled surrogates. Analogously to IID noise surrogates, cycle shuffled surrogates are produced by shuffling the individual cycles within a time series. Hence, intracycle dynamics are preserved but intercycle dynamics are not. However, even with this new approach Theiler noted spurious long term correlations in the autocorrelation plot [9] for cycle shuffled surrogates. Furthermore, if the peak or troughs do not occur at precisely the same values, surrogates generated by this method are not able to preserve both stationarity and continuity. By shifting individual cycles vertically, individual cycles can be matched and continuity will be preserved. However, such a transformation introduces nonstationarity in the surrogates that is absent in the original.Each of these techniques is commonly applied to...

show abstract

“…It measures the freedom degree and complexity of the system. For the raw data and all data of φ F F ∈ , in the case of the same embedding dimension, the corresponding test results will be obviously significant [42]. Here, the correlation dimension is used as a test statistic to analyze the surface EMG signal.…”

Section: Study Of Surrogate Data Test Methods Based On Correlation Dimmentioning

confidence: 99%