Identification of quadratic systems using higher order cumulants and neural networks: Application to model the delay of video-packets transmission

Antari, Jilali; Chabaa, Samira; Iqdour, Radouane; Zeroual, Abdelouhab; Safi, Saïd

doi:10.1016/j.asoc.2010.03.007

Cited by 13 publications

(7 citation statements)

References 31 publications

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“…Now we will present a stability result for (34). Corollary 3.6: Suppose that Assumption 2.1 and (33) hold.…”

Section: B Stability Of Rnn With Various Kinds Of Multiple Delaysmentioning

confidence: 96%

“…Different stability results for RNNs with above delays have been established, for example, in the forms of M-matrix, algebraic inequality, spectral norm, and linear matrix inequality (LMI) [3], [6], [9]- [26]. Meanwhile, neutral-type neural networks [14], [27]- [33] and high-order neural networks [9], [34]- [41] have also been investigated in the literature, which extend the classical Hopfield-type neural networks to the RNNs with different structures. Many significant stability results have been established for the neutral-type and high-order neural networks in many different expressions.…”

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confidence: 99%

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LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures

Wang

Zhang

Jiang

2011

IEEE Trans. Neural Netw.

114

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Global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying Lebesgue-Stieljies measures on the basis of linear matrix inequality. The concerned network model includes many neural network models with various delays and structures as its special cases, such as the delays covering the discrete delays and distributed delays, and the network structures containing the neutral-type networks and high-order networks. Therefore, many new stability criteria for the above neural network models have also been derived from the present stability analysis method. All the obtained stability results have similar matrix inequality structures and can be easily checked. Three numerical examples are used to show the effectiveness of the obtained results.

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“…Now we will present a stability result for (34). Corollary 3.6: Suppose that Assumption 2.1 and (33) hold.…”

Section: B Stability Of Rnn With Various Kinds Of Multiple Delaysmentioning

confidence: 96%

mentioning

confidence: 99%

LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures

Wang

Zhang

Jiang

2011

IEEE Trans. Neural Netw.

114

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“…Actually, when Volterra series is employed to model and blindly identify a nonlinear system, it needs to often meet the situation in which higher order cumulants are used. Antari et al [20,21] considered the third-order and fourthorder cumulants to blindly identify a Hammerstein system. However, the expression of higher cumulants sometimes seems to be quite complicated [22].…”

Section: Introductionmentioning

confidence: 99%

HOC Based Blind Identification of Hydroturbine Shaft Volterra System

Bai¹,

Zhang

2017

Shock and Vibration

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In order to identify the quadratic Volterra system simplified from the hydroturbine shaft system, a blind identification method based on the third-order cumulants and a reversely recursive method are proposed. The input sequence of the system under consideration is an unobservable independent identically distributed (i.i.d.), zero-mean and non-Gaussian stationary signal, and the observed signals are the superposition of the system output signal and Gaussian noise. To calculate the third-order moment of the output signal, a computer loop judgment method is put forward to determine the coefficient. When using optimization method to identify the time domain kernels, we combined the traditional optimization algorithm (direct search method) with genetic algorithm (GA) and constituted the hybrid genetic algorithm (HGA). Finally, according to the prototype observation signal and the time domain kernel parameters obtained from identification, the input signal of the system can be gained recursively. To test the proposed method, three numerical experiments and engineering application have been carried out. The results show that the method is applicable to the blind identification of the hydroturbine shaft system and has strong universality; the input signal obtained by the reversely recursive method can be approximately taken as the random excitation acted on the runner of the hydroturbine shaft system.

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“…The linear models are not efficient for representing and modeling all systems, because the majority of systems are represented by non linear models [7,8]. However, when linear modeling of the channel is not adequate, the non linear modeling appeared like an alternative efficient solution in most real cases.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, cumulants based methods boost signal to noise ratio (SNR) when signals are corrupted by Gaussian measurement noise. Second, the HOC methods are useful in identifying non minimum phase systems and in reconstructing non minimum phase signals when the signals are non Gaussian.The linear models are not efficient for representing and modeling all systems, because the majority of systems are represented by non linear models [7,8]. However, when linear modeling of the channel is not adequate, the non linear modeling appeared like an alternative efficient solution in most real cases.…”

mentioning

confidence: 99%

Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

Zidane¹,

Safi²,

Sabri³

2016

IJEECS

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In this paper, we present an extension of linear communication channels identification algorithms to non linear channels using higher order cumulants (HOC). In the one hand, we develop a theoretical analysis of non linear quadratic systems using second and third order cumulants. In the other hand, the relationship linking cumulants and the coefficients of non linear channels presented in the linear case is extended to the general case of the non linear quadratic systems identification. This theoretical development is used to develop three non linear algorithms based on third and fourth order cumulants respectively. Numerical simulation results example show that the proposed methods able to estimate the impulse response parameters with different precision.Keywords: Higher order cumulants, Blind identification, Non linear quadratic systems. Copyright c 2016 Institute of Advanced Engineering and Science IntroductionApplications of higher order cumulants theory in the blind identification domain are widely used in various works [1]-[3], [6,7]. Several models are identified in the literature such as the linear and non linear systems. In the part of the linear case, we have important results established that the blind identification is possible only from the second order cumulants (autocorrelation function) of the output stationary signal, but these methods is not able to identify correctly the channel models excited by non Gaussian signal and affected by Gaussian noise, because the additive Gaussian noise will be vanish in the higher order cumulants domain. The sensitivity of the second order cumulants to the additive Gaussian noise appealed to other blind identification methods exploiting the cumulants of order superieur than two [4,5]. There are several motivations behind this interest, first the methods based on HOC are blind to any kind of a Gaussian process, whereas autocorrelation function (second order cumulants) is not. Consequently, cumulants based methods boost signal to noise ratio (SNR) when signals are corrupted by Gaussian measurement noise. Second, the HOC methods are useful in identifying non minimum phase systems and in reconstructing non minimum phase signals when the signals are non Gaussian.The linear models are not efficient for representing and modeling all systems, because the majority of systems are represented by non linear models [7,8]. However, when linear modeling of the channel is not adequate, the non linear modeling appeared like an alternative efficient solution in most real cases. Moreover, quadratic non linear systems are widely used in various engineering fields such as signal processing, system filtering, predicting, identification and equalization [9,10].In this contribution, firstly we present a theoretical development of non linear quadratic systems using higher order cumulants. Indeed, we develop the relationship linking third order cumulants and the coefficients of non linear channels, then the method developed [11] for linear channels, is extended to the general case ...

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Identification of quadratic systems using higher order cumulants and neural networks: Application to model the delay of video-packets transmission

Cited by 13 publications

References 31 publications

LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures

LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures

HOC Based Blind Identification of Hydroturbine Shaft Volterra System

Extension of Linear Channels Identification Algorithms to Non Linear Using Selected Order Cumulants

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