Delay Identification in Thermoacoustics

2021 ◽  
Author(s):  
Francesco Gant ◽  
Giulio Ghirardo ◽  
Alexis Cuquel ◽  
Mirko R. Bothien
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Additive White Gaussian Noise ◽  
A Priori ◽  
Accurate Estimate ◽  
Combustion Noise ◽  
Unknown Parameters ◽  
Acoustic Damping ◽  
The Stability ◽  
Low Order

Abstract The stability of thermoacoustic systems is often regulated by the time delay between acoustic perturbations and corresponding heat release fluctuations. An accurate estimate of this value is of great importance in applications, since even small modifications can introduce significant changes in the system behavior. Different studies show that the nonlinear delayed dynamics typical of these systems can be well captured with low-order models. In the present work, a method is introduced to estimate the most likely value of the time delay of a single thermoacoustic mode from a measured acoustic pressure signal. The mode of interest is modeled by an oscillator equation, with a nonlinear delayed forcing term modeling the deterministic flame contribution and an additive white Gaussian noise to embed the stochastic combustion noise. Additionally, other thermoacoustic relevant parameters are estimated. The model accounts for a flame gain, for a flame saturation coefficient, for a linear acoustic damping and for the background combustion noise intensity. The pressure data time series is statistically analyzed and the set of unknown parameters is identified. Validation is performed with respect to synthetically generated time series and low order model simulations, for which the underlying delay is known a priori. A discussion follows about the accuracy of the method, in particular a comparison with existing methods is drawn.

Delay Identification in Thermoacoustics

2021 ◽  
Author(s):  
F. Gant ◽  
G. Ghirardo ◽  
A. Cuquel ◽  
M. R. Bothien
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Additive White Gaussian Noise ◽  
A Priori ◽  
Accurate Estimate ◽  
Combustion Noise ◽  
Unknown Parameters ◽  
Acoustic Damping ◽  
The Stability ◽  
Low Order

Abstract The stability of thermoacoustic systems is often regulated by the time delay between acoustic perturbations and corresponding heat release fluctuations. An accurate estimate of this value is of great importance in applications, since even small modifications can introduce significant changes in the system behavior Different studies show that the nonlinear delayed dynamics typical of these systems can be well captured with low-order models. In the present work, a method is introduced to estimate the most likely value of the time delay of a single thermoacoustic mode from a measured acoustic pressure signal. The mode of interest is modeled by an oscillator equation, with a nonlinear delayed forcing term modeling the deterministic flame contribution and an additive white Gaussian noise to embed the stochastic combustion noise. Additionally, other thermoacoustic relevant parameters are estimated. The model accounts for a flame gain, for a flame saturation coefficient, for a linear acoustic damping and for the background combustion noise intensity. The pressure data time series is statistically analyzed and the set of unknown parameters is identified. Validation is performed with respect to synthetically generated time series and low order model simulations, for which the underlying delay is known a priori. A discussion follows about the accuracy of the method, in particular a comparison with existing methods is drawn.

The ILRS Contribution to ITRF2020

2021 ◽  
Author(s):  
Vincenza Luceri ◽  
Erricos C. Pavlis ◽  
Antonio Basoni ◽  
David Sarrocco ◽  
Magdalena Kuzmicz-Cieslak ◽  
...  
Keyword(s):  
Time Series ◽  
Tracking System ◽  
A Priori ◽  
Systematic Errors ◽  
Novel Approach ◽  
Priori Information ◽  
The Stability ◽  
The Individual ◽  
Stability And Consistency

<p>The International Laser Ranging Service (ILRS) contribution to ITRF2020 has been prepared after the re-analysis of the data from 1993 to 2020, based on an improved modeling of the data and a novel approach that ensures the results are free of systematic errors in the underlying data. This reanalysis incorporates an improved “target signature” model (CoM) that allows better separation of true systematic error of each tracking system from the errors in the model describing the target’s signature. The new approach was developed after the completion of ITRF2014, the ILRS Analysis Standing Committee (ASC) devoting almost entirely its efforts on this task. The robust estimation of persistent systematic errors at the millimeter level permitted the adoption of a consistent set of long-term mean corrections for data collected in past years, which are now applied a priori (information provided by the stations from their own engineering investigations are still taken into consideration). The reanalysis used these corrections, leading to improved results for the TRF attributes, reflected in the resulting new time series of the TRF origin and especially in the scale. Seven official ILRS Analysis Centers computed time series of weekly solutions, according to the guidelines defined by the ILRS ASC. These series were combined by the ILRS Combination Center to obtain the official ILRS product contribution to ITRF2020.</p><p>The presentation will provide an overview of the analysis procedures and models, and it will demonstrate the level of improvement with respect to the previous ILRS product series; the stability and consistency of the solution are discussed for the individual AC contributions and the combined SLR time series.</p>

Protection and Identification of Thermoacoustic Azimuthal Modes

2020 ◽  
Author(s):  
G. Ghirardo ◽  
F. Gant ◽  
F. Boudy ◽  
M. R. Bothien
Keyword(s):  
Acoustic Field ◽  
Invariant Manifolds ◽  
Pressure Sensors ◽  
Fourier Component ◽  
Combustion Noise ◽  
Order Problem ◽  
Acoustic Damping ◽  
Protection Scheme ◽  
Flame Response ◽  
Low Order

Abstract This paper first characterizes the acoustic field of two annular combustors by means of data from acoustic pressure sensors. In particular the amplitude, orientation, and nature of the acoustic field of azimuthal order n is characterized. The dependence of the pulsation amplitude on the azimuthal location in the chamber is discussed, and a protection scheme making use of just one sensor is proposed. The governing equations are then introduced, and a low-order model of the instabilities is discussed. The model accounts for the nonlinear response of M distinct flames, for system acoustic losses by means of an acoustic damping coefficient α and for the turbulent combustion noise, modelled by means of the background noise coefficient σ. Keeping the response of the flames arbitrary and in principle different from flame to flame, we show that, together with α and σ, only the sum of their responses and their 2n Fourier component in the azimuthal direction affect the dynamics of the azimuthal instability. The existing result that only this 2n Fourier component affects the stability of standing limit-cycle solutions is recovered. It is found that this result applies also to the case of a non-homogeneous flame response in the annulus, and to flame responses that respond to the azimuthal acoustic velocity. Finally, a parametric flame model is proposed, depending on a linear driving gain β and a nonlinear saturation constant κ. The model is first mapped from continuous time to discrete time, and then recast as a probabilistic Markovian model. The identification of the parameters {α, β, κ, σ} is then carried out on engine timeseries data. The optimal four parameters {α, σ, β, κ} are estimated as the values that maximize the data likelihood. Once the parameters have been estimated, the phase space of the identified low-order problem is discussed on selected invariant manifolds of the dynamical system.

scholarly journals Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 924-941
Author(s):  
Mei Li ◽  
Ruoxun Zhang ◽  
Shiping Yang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Adaptive Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Chaotic Neural Networks ◽  
Controlled Systems ◽  
The Stability ◽  
Complex Valued

The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity.

DEVELOPMENT OF STREAMFLOW DROUGHT INDICES IN THE MORAVA RIVER BASIN

2020 ◽  
Author(s):  
Ondrej Ledvinka ◽  
◽  
Pavel Coufal ◽  
Keyword(s):  
Time Series ◽  
Kendall Test ◽  
Drought Indices ◽  
Drought Period ◽  
Left Hand ◽  
Low Flows ◽  
Current Period ◽  
Catchment Size ◽  
Morava River ◽  
The Stability

The territory of Czechia currently suffers from a long-lasting drought period which has been a subject of many studies, including the hydrological ones. Previous works indicated that the basin of the Morava River, a left-hand tributary of the Danube, is very prone to the occurrence of dry spells. It also applies to the development of various hydrological time series that often show decreases in the amount of available water. The purpose of this contribution is to extend the results of studies performed earlier and, using the most updated daily time series of discharge, to look at the situation of the so-called streamflow drought within the basin. 46 water-gauging stations representing the rivers of diverse catchment size were selected where no or a very weak anthropogenic influences are expected and the stability and sensitivity of profiles allow for the proper measurement of low flows. The selected series had to cover the most current period 1981-2018 but they could be much longer, which was considered beneficial for the next determination of the development direction. Various series of drought indices were derived from the original discharge series. Specifically, 7-, 15- and 30-day low flows together with deficit volumes and their durations were tested for trends using the modifications of the Mann– Kendall test that account for short-term and long-term persistence. In order to better reflect the drivers of streamflow drought, the indices were considered for summer and winter seasons separately as well. The places with the situation critical to the future water resources management were highlighted where substantial changes in river regime occur probably due to climate factors. Finally, the current drought episode that started in 2014 was put into a wider context, making use of the information obtained by the analyses.

On the stability of a class of nonlinear time delay systems

1999 ◽  
Author(s):  
Dan Ivancscu ◽  
Silviu-Iulian Niculcscu ◽  
Jcan-Michcl Dion ◽  
Luc Dugard
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Time Delay Systems ◽  
The Stability

Graphic method for assessing the margins of resistance to acoustic vibrations in the chambers of rocket engines by combustion noise

2020 ◽  
pp. 15-21
Author(s):  
R.A. Tsarapkin ◽  
V.N. Ivanov ◽  
V.I. Biryukov
Keyword(s):  
Rocket Engine ◽  
Spectral Characteristics ◽  
Combustion Process ◽  
Combustion Noise ◽  
Rocket Engines ◽  
Acoustic Vibrations ◽  
Statistical Regression ◽  
Unknown Parameters ◽  
Damping Decrement ◽  
Resonance Frequencies

An experimental method is proposed for estimating the damping decrements of pressure fluctuations in the combustion chambers of forced rocket engines. The method is based on the statistical processing of noise pressure pulsations in the vicinity of natural resonance frequencies for normal modes of acoustic vibrations of the reaction volume and the subsequent prediction of the instability of the combustion process relative to acoustic vibrations. Based on the theory of statistical regression for multidimensional experimental data, the problem of predicting unknown parameters of sample distributions is solved by asymptotic determination of the correlation coefficient of the damping decrement of pressure vibrations through optimal linear predictors and the Kolmogorov distribution. Keywords rocket engine, combustion chamber, acoustic vibrations, combustion noise, spectral characteristics, Kolmogorov criterion, damping decrement. [email protected]

scholarly journals Constructing Adaptive Deformation Models for Estimating DEM Error in SBAS-InSAR Based on Hypothesis Testing

2021 ◽  
Vol 13 (10) ◽  
pp. 2006
Author(s):  
Jun Hu ◽  
Qiaoqiao Ge ◽  
Jihong Liu ◽  
Wenyan Yang ◽  
Zhigui Du ◽  
...  
Keyword(s):  
Time Series ◽  
Hypothesis Testing ◽  
Surface Deformation ◽  
A Priori ◽  
Least Square ◽  
Deformation Model ◽  
Phase Time ◽  
Testing Theory ◽  
Sbas Insar ◽  
Deformation Models

The Interferometric Synthetic Aperture Radar (InSAR) technique has been widely used to obtain the ground surface deformation of geohazards (e.g., mining subsidence and landslides). As one of the inherent errors in the interferometric phase, the digital elevation model (DEM) error is usually estimated with the help of an a priori deformation model. However, it is difficult to determine an a priori deformation model that can fit the deformation time series well, leading to possible bias in the estimation of DEM error and the deformation time series. In this paper, we propose a method that can construct an adaptive deformation model, based on a set of predefined functions and the hypothesis testing theory in the framework of the small baseline subset InSAR (SBAS-InSAR) method. Since it is difficult to fit the deformation time series over a long time span by using only one function, the phase time series is first divided into several groups with overlapping regions. In each group, the hypothesis testing theory is employed to adaptively select the optimal deformation model from the predefined functions. The parameters of adaptive deformation models and the DEM error can be modeled with the phase time series and solved by a least square method. Simulations and real data experiments in the Pingchuan mining area, Gaunsu Province, China, demonstrate that, compared to the state-of-the-art deformation modeling strategy (e.g., the linear deformation model and the function group deformation model), the proposed method can significantly improve the accuracy of DEM error estimation and can benefit the estimation of deformation time series.

Stable Calibrations of Six-DOF Serial Robots by Using Identification Models with Equalized Singular Values

Robotica ◽  
2021 ◽  
pp. 1-22
Author(s):  
Zhouxiang Jiang ◽  
Min Huang
Keyword(s):  
Industrial Robot ◽  
Singular Values ◽  
Calibration Method ◽  
Identification Accuracy ◽  
Condition Numbers ◽  
Measurement Instruments ◽  
Unknown Parameters ◽  
Calibration Methods ◽  
Six Dof ◽  
The Stability

SUMMARY In typical calibration methods (kinematic or non-kinematic) for serial industrial robot, though measurement instruments with high resolutions are adopted, measurement configurations are optimized, and redundant parameters are eliminated from identification model, calibration accuracy is still limited under measurement noise. This might be because huge gaps still exist among the singular values of typical identification Jacobians, thereby causing the identification models ill conditioned. This paper addresses such problem by using new identification models established in two steps. First, the typical models are divided into the submodels with truncated singular values. In this way, the unknown parameters corresponding to the abnormal singular values are removed, thereby reducing the condition numbers of the new submodels. However, these models might still be ill conditioned. Therefore, the second step is to further centralize the singular values of each submodel by using a matrix balance method. Afterward, all submodels are well conditioned and obtain much higher observability indices compared with those of typical models. Simulation results indicate that significant improvements in the stability of identification results and the identifiability of unknown parameters are acquired by using the new identification submodels. Experimental results indicate that the proposed calibration method increases the identification accuracy without incurring additional hardware setup costs to the typical calibration method.

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