E. A. Gopalakrishnan

Detecting deterministic nature of pressure measurements from a turbulent combustor

Identifying nonlinear structures in a time series, acquired from real-world systems, is essential to characterize the dynamics of the system under study. A single time series alone might be available in most experimental situations. In addition to this, conventional techniques such as power spectral analysis might not be sufficient to characterize a time series if it is acquired from a complex system such as a thermoacoustic system. In this study, we analyze the unsteady pressure signal acquired from a turbulent combustor with bluff-body and swirler as flame holding devices. The fractal features in the unsteady pressure signal are identified using the singularity spectrum. Further, we employ surrogate methods, with translational error and permutation entropy as discriminating statistics, to test for determinism visible in the observed time series. In addition to this, permutation spectrum test could prove to be a robust technique to characterize the dynamical nature of the pressure time series acquired from experiments. Further, measures such as correlation dimension and correlation entropy are adopted to qualitatively detect noise contamination in the pressure measurements acquired during the state of combustion noise. These ensemble of measures is necessary to identify the features of a time series acquired from a system as complex as a turbulent combustor. Using these measures, we show that the pressure fluctuations during combustion noise has the features of a high-dimensional chaotic data contaminated with white and colored noise.

Influence of system parameters on the hysteresis characteristics of a horizontal Rijke tube

The influence of system parameters such as heater power, heater location and mass flow rate on the hysteresis characteristics of a horizontal Rijke tube is presented in this paper. It is observed that a hysteresis zone is present for all the mass flow rates considered in the present study. A power law relation is established between the non-dimensional hysteresis width and the Strouhal number, defined as the ratio between convective time scale and acoustic time scale. The transition to instability in a horizontal Rijke tube is found to be subcritical in all the experiments performed in this study. When heater location is chosen as the control parameter, period-2 oscillations are found for specific values of mass flow rate and heater power

Stochastic Bifurcations In A Prototypical Thermoacoustic System

We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.

Early warning signals for critical transitions in a thermoacoustic system

Dynamical systems can undergo critical transitions where the system suddenly shifts from one stable state to another at a critical threshold called the tipping point. The decrease in recovery rate to equilibrium (critical slowing down) as the system approaches the tipping point can be used to identify the proximity to a critical transition. Several measures have been adopted to provide early indications of critical transitions that happen in a variety of complex systems. In this study, we use early warning indicators to predict subcritical Hopf bifurcation occurring in a thermoacoustic system by analyzing the observables from experiments and from a theoretical model. We find that the early warning measures perform as robust indicators in the presence and absence of external noise. Thus, we illustrate the applicability of these indicators in an engineering system depicting critical transitions.

Recurrence networks to study dynamical transitions in a turbulent combustor

Thermoacoustic instability and lean blowout are the major challenges faced when a gas turbine combustor is operated under fuel lean conditions. The dynamics of thermoacoustic system is the result of complex nonlinear interactions between the subsystems-turbulent reactive flow and the acoustic field of the combustor. In order to study the transitions between the dynamical regimes in such a complex system, the time series corresponding to one of the dynamic variables is transformed to an ε-recurrence network. The topology of the recurrence network resembles the structure of the attractor representing the dynamics of the system. The transitions in the thermoacoustic system are then captured as the variation in the topological characteristics of the network. We show the presence of power law degree distribution in the recurrence networks constructed from time series acquired during the occurrence of combustion noise and during the low amplitude aperiodic oscillations prior to lean blowout. We also show the absence of power law degree distribution in the recurrence networks constructed from time series acquired during the occurrence of thermoacoustic instability and during the occurrence of intermittency. We demonstrate that the measures derived from recurrence network can be used as tools to capture the transitions in the turbulent combustor and also as early warning measures for predicting impending thermoacoustic instability and blowout.

Accurate Estimation of Glottal Closure Instants and Glottal Opening Instants from Electroglottographic Signal Using Variational Mode Decomposition

The objective of the proposed work is to accurately estimate the glottal closure instants (GCIs) and glottal opening instant (GOIs) from electroglottographic (EGG) signals. This work also addresses the issues with existing EGG-based GCI/GOI detection methods. GCIs are the instants at which excitation to the vocal tract is maximum and GOIs, on the other hand, have minimum excitation compared to GCIs. Both these instants occur instantaneously with a fundamental frequency defined for each glottal cycle in a given EGG signal. Accurate detection of these instants from the EGG signal is essential for the performance evaluation of GCIs and GOIs estimated from the speech signal directly. This work proposes a new method for accurate detection of GCIs and GOIs from the EGG signal using variational mode decomposition (VMD) algorithm. The EGG signal has been decomposed into sub-signals using the VMD algorithm. It is shown that VMD captures the center frequency close to the fundamental frequency of the EGG signal through one of its modes. This property of the corresponding mode helps to estimate GCIs and GOIs from the same. Besides, instantaneous pitch frequency is estimated from the obtained GCIs. The proposed method has been evaluated on the CMU-arctic database for GCI/GOI estimation and the Keele pitch extraction reference database for instantaneous pitch frequency estimation. The effectiveness of the proposed method is confirmed by comparison with state-of-the-art methods. Experimental results show that the proposed method has better accuracy and identification rate compared to state-of-the-art methods.

Instantaneous heart rate as a robust feature for sleep apnea severity detection using deep learning

Automated sleep apnea detection and severity identification has largely focused on multivariate sensor data in the past two decades. Clinically too, sleep apnea is identified using a combination of markers including blood oxygen saturation, respiration rate etc. More recently, scientists have begun to investigate the use of instantaneous heart rates for detection and severity measurement of sleep apnea. However, the best-known techniques that use heart rate and its derivatives have been able to achieve less than 85% accuracy in classifying minute-to-minute apnea data. In our research reported in this paper, we apply a deep learning technique called LSTM-RNN (long short-term memory recurrent neural network) for identification of sleep apnea and its severity based only on instantaneous heart rates. We have tested this model on multiple sleep apnea datasets and obtained perfect accuracy. Furthermore, we have also tested its robustness on an arrhythmia dataset (that is highly probable in mimicking sleep apnea heart rate variability) and found that the model is highly accurate in distinguishing between the two.

Experimental investigation on preconditioned rate induced tipping in a thermoacoustic system

Many systems found in nature are susceptible to tipping, where they can shift from one stable dynamical state to another. This shift in dynamics can be unfavorable in systems found in various fields ranging from ecology to finance. Hence, it is important to identify the factors that can lead to tipping in a physical system. Tipping can mainly be brought about by a change in parameter or due to the influence of external fluctuations. Further, the rate at which the parameter is varied also determines the final state that the system attains. Here, we show preconditioned rate induced tipping in experiments and in a theoretical model of a thermoacoustic system. We provide a specific initial condition (preconditioning) and vary the parameter at a rate higher than a critical rate to observe tipping. We find that the critical rate is a function of the initial condition. Our study is highly relevant because the parameters that dictate the asymptotic behavior of many physical systems are temporally dynamic.

Epoch Estimation from Emotional Speech Signals Using Variational Mode Decomposition

This paper presents a novel approach for the estimation of epochs from the emotional speech signal. Epochs are the locations of significant excitation in the vocal tract during the production of voiced sound by the vibration of vocal folds. The estimation of epoch locations is essential for deriving instantaneous pitch contours for accurate emotion analysis. Many well-known algorithms for epoch extraction are found to show degraded performance due to the varying nature of excitation characteristics in the emotional speech signal. The proposed approach exploits the effectiveness of a new adaptive time series decomposition technique called variational mode decomposition (VMD) for the estimation of epochs. The VMD algorithm is applied on the emotional speech signal for decomposition of the signal into various sub-signals. Analysis of these signals shows that the VMD algorithm captures the center frequency close to the fundamental frequency defined for each glottal cycle of emotional speech utterance through its modes. This center frequency characteristic of the corresponding mode signal helps in the accurate estimation of epoch locations from the emotional speech signal. The performance evaluation of the proposed method is carried out on six different emotions taken from the German emotional speech database with simultaneous electroglottographic signals. Experimental results on clean emotive speech signals show that the proposed method provides identification rate and accuracy comparable to that of the best performing algorithm. Besides, the proposed method provides better reliability in epoch estimation from emotive speech signals degraded by the presence of noise.