Principles of System Identification

Tangirala, Arun K.

doi:10.1201/9781315222509

Cited by 146 publications

(129 citation statements)

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“…Conversely, heat sources with large characteristic time scales tend to be detrimental for the stability of the thermoacoustic system. It is well known from control theory that systems with large delays are more difficult to control, 42 because a change in the delayed part of the system shows its effect only after some time lag. By the time the effect of a slow heat source is thus noticeable in a thermoacoustic configuration, damping mechanisms have already significantly diminished the amplitude levels of the acoustic field.…”

Section: Parameters Influencing Transient Growthmentioning

confidence: 99%

“…We further assume the response of the premixed flame to be linear and timeinvariant, such that its response behavior at any time t > 0 is fully characterized by its impulse response function hðtÞ : R þ ! R. 42 Consequentially, the fluctuating heat release rate of the flame _ q can be modeled as a convolution of its impulse response (IR) function h and the lagged acoustic velocity fluctuations at the flame base v F…”

Section: The Flame Subsystemmentioning

confidence: 99%

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A systems perspective on non-normality in low-order thermoacoustic models: Full norms, semi-norms and transient growth

Blumenthal

Tangirala

Sujith

et al. 2016

International Journal of Spray and Combustion Dynamics

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Non-normal transient growth of energy is a feature encountered in many physical systems. Its observation is intimately related to the norm used to describe the system dynamics. For a multi-physics problem such as thermoacoustics, where a heat source is in feedback with acoustic waves and a flow field, the appropriate metric is an ongoing matter of debate. Adopting a systemic perspective, it is argued in the present paper that an energy norm is, in principle, a matter of choice, but one that is critically tied to the dynamics described by the system model. To illustrate our arguments, it is shown that different norms exhibit the non-normal dynamics of thermoacoustic systems differently, but that this difference is fully explicable by the energy flux and source terms related to the formulation of the model. The non-normal dynamics as such is unaffected by the choice of norm, and transient growth merely results from a maximization of the flux and source terms governing the energy balance associated with the specific model formulation. Investigating transient growth for arbitrary energy norms requires the capability to handle semi-norm optimization problems. In the present study, we propose an approach to do so using the singular value decomposition. Non-normal transient growth around a stable fix point is then investigated for a low-order model of a simple thermoacoustic configuration of a premixed flame enclosed in a duct with non-zero mean temperature jump and bulk mean flow. The corresponding optimal mode shapes and pertinent parameters leading to transient growth are identified and discussed. For transient growth resulting from the interaction of the flame with the acoustic field, it is found that heat sources with a fast response lead to more transient growth than slow heat sources, because the system can bear a larger source term before becoming linearly unstable. Furthermore, the amount of transient energy growth does not increase monotonically with the amplitude of the initial perturbation of the flame.

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Section: Parameters Influencing Transient Growthmentioning

confidence: 99%

Section: The Flame Subsystemmentioning

confidence: 99%

A systems perspective on non-normality in low-order thermoacoustic models: Full norms, semi-norms and transient growth

Blumenthal

Tangirala

Sujith

et al. 2016

International Journal of Spray and Combustion Dynamics

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“…In addition, we introduce two new statistics, namely, the vector-valued ACF and partial ACF, for characterizing the correlation structure in multivariate stationary processes. These measures are useful in providing a collective picture of the correlation and can be thought of as multivariate analogues of the ACF and partial ACF (PACF) for the univariate process (Shumway and Stoffer, 2000;Tangirala, 2014). They possess similar properties as that of the univariate versions and aid in determining the order of VMA and VAR models, respectively.…”

Section: Introductionmentioning

confidence: 97%

Estimation of network connectivity strengths in linear causal dynamic systems

Kathari

Tangirala

2016

IFAC-PapersOnLine

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Identification of network structure and quantifying the connectivity strengths in multivariate systems is an important problem in many scientific areas. Data-driven approach to network reconstruction based on causality measures is an emerging field of research in this respect. Among several recently introduced data-driven causality measures, the partial directed coherence (PDC) and direct power transfer (DPT) have been shown to be very effective for linear systems. While the PDC is useful in reconstructing the network, DPT has been proved to be effective in both identifying the network structure as well as quantifying the strength of connectivity. In this work, we study the problem of obtaining efficient estimates of network connectivity strengths, which has hitherto not been addressed in the literature. To this end, we study two different estimation methods for network connectivity strengths and demonstrate that the goodness of estimates depends on nature of the data generating process (DGP). In order to characterize the multivariate DGP, we introduce two statistics, namely, the vectorvalued autocorrelation function (VACF) and the vector-valued partial autocorrelation function (VPACF), and estimators of the same. Our studies show that the parametric models used in estimating connectivity strengths should be commensurate with the dynamics of the process as characterized by the newly introduced VACF and VPACF. Simulation studies are presented under different scenarios to support our findings and the newly introduced measures.

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“…We propose to employ the EM algorithm based on the t-distribution for estimating the parameters of the robust local models and parameters of the weighting functions in the MLE framework. MLE approach [31][32][33], along with its effective variant, the EM algorithm, has also been commonly employed for system identification of LPV systems.…”

Section: Introductionmentioning

confidence: 99%