Fourier nonlinear filters

Chaotic systems are widely studied in various research areas such as signal processing and secure communication. Existing chaotic systems may have drawbacks such as discontinuous chaotic ranges and incomplete output distributions. These drawbacks may lead to the defects of some chaos-based applications. To accommodate these challenges, this paper proposes a two-dimensional (2D) modular chaotification system (2D-MCS) to improve the chaos complexity of any 2D chaotic map. Because the modular operation is a bounded transform, the improved chaotic maps by 2D-MCS can generate chaotic behaviors in wide parameter ranges while existing chaotic maps cannot. Three improved chaotic maps are presented as typical examples to verify the effectiveness of 2D-MCS. The chaos properties of one example of 2D-MCS are mathematically analyzed using the definition of Lyapunov exponent. Performance evaluations demonstrate that these improved chaotic maps have continuous and large chaotic ranges, and their outputs are distributed more uniformly than the outputs of existing 2D chaotic maps. To show the application of 2D-MCS, we apply the improved chaotic maps of 2D-MCS to secure communication. The simulation results show that these improved chaotic maps exhibit better performance than several existing and newly developed chaotic maps in terms of resisting different channel noise.

Two-Dimensional Modular Chaotification System for Improving Chaos Complexity

A survey on active noise control in the past decade–Part II: Nonlinear systems

A method to detect and locate a high-impedance fault caused by a downed conductor on a distribution primary feeder cone is presented. The protection system in radial networks generally consists in placing current detectors along each feeder lenz. A down-conductor fault typically has a very low current values which is often not detectable by conventional overcurrent protection devices. The proposed method is not based on current measurement but instead on voltage measurements performed at MV/LV stations. This method may be particularly interesting if LV potential transformers are already present in the network. The method is divided into two steps. The first step consists in determining whether each sensor is above or below the fault. The second step consists in determining the fault section, from a purely topological method. EMTP simulations are presented to highlight the effectiveness of the proposed technique.

Down-conductor fault detection and location via a voltage based method for radial distribution networks

This article is concerned with the problem of state estimation for continuous-time polynomial nonlinear (CTPN) systems with unknown but bounded disturbances. The Taylor polynomial expansion technique is employed to realize the conversion from polynomial nonlinear systems to linear-parameter-varying systems related to the estimate. Moreover, for the purpose of saving the communication resources, an event-triggered sampling scheme is first introduced in the state estimation for CTPN systems, where the event-triggered condition is changed dynamically and the Zeno behavior is excluded. Based on the matrix inequality approach, a sufficient condition is derived in terms of the parameter-dependent linear matrix inequality (LMI) such that the estimation error system is input-to-state stable. Then, the desired estimator parameters can be obtained by solving the parameter-dependent LMI via the sum of squares decomposition technique. Finally, two examples with one concerning the permanent magnet synchronous motor systems are provided to demonstrate the usefulness of proposed method.

Dynamic Event-Triggered State Estimation for Continuous-Time Polynomial Nonlinear Systems With External Disturbances

This paper presents a detection and signaling system designed to identify and locate high impedance faults caused by broken conductors on distribution primary feeders. Unlike conventional protection systems, which perform current sensing, the working principle of the proposed system consists on monitoring the voltage unbalance along a feeder. This allows the system to detect a fault occurrence even in cases when the conductor touches a high impedance earth surface (for instance asphalt). This system has an additional advantage of giving an indication of the location of a fault since it involves measurements at multiple points on a feeder. In order to detect the voltage unbalance produced by a broken conductor, a new sensor was developed which is sensitive to the electric field generated by primary feeders. A carrier communication channel is associated to each sensor allowing the high impedance fault occurrence information to reach the protection equipment located closer to or at the substation.

Broken conductors protection system using carrier communication

Bilinear and Volterra models are important when dealing with nonlinear systems which arise in several signal processing applications. The former can approximate a large class of systems affine in the input with relatively low parametric complexity. Such an approximate bilinear model can be derived by means of Carleman bilinearization (CB). Then, a Volterra model can be computed from it, having the advantage of being linear in the parameters, but often involving a large number of them. In this paper, we develop efficient routines for CB and for computing the Volterra kernels of a bilinear system. We argue that they are useful for studying a class of systems for which a reference physical model is known. In particular, the so-derived kernels allow assessing the suitability of a Volterra filter and of other alternatives for modeling the system of interest. Techniques exploiting sparsity and low rank of involved matrices are proposed for alleviating computing cost. Several examples are given along the paper to illustrate their use, based on existing physical models of loudspeakers.

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Efficient Computation of Bilinear Approximations and Volterra Models of Nonlinear Systems

Despite their generality, conventional Volterra filters are inadequate for some applications, due to the huge number of parameters that may be needed for accurate modelling. When a state-space model of the target system is known, this can be assessed by computing its kernels, which also provides valuable information for choosing an adequate alternate Volterra filter structure, if necessary, and is useful for validating parameter estimation procedures. In this letter, we derive expressions for the kernels by using the Carleman bilinearization method, for which an efficient algorithm is given. Simulation results are presented, which confirm the usefulness of the proposed approach.

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Efficient Kernel Computation for Volterra Filter Structure Evaluation

An analysis of the local convergence speed of constant gain algorithms for direct form IIR adaptive filters is initially presented, showing the adverse effects that result from the proximity of the poles of the modelled system to the unit circle and, for complex poles, to the real axis. A global analysis of the reduced error surface in these cases is also presented, which shows that, away from the global minimum, there will be regions with an almost constant error, where the convergence of constant gain algorithms tends to be slow. A polyphase IIR adaptive filter is then proposed and its local and global convergence properties are investigated, showing it to be specially well suited for applications with underdamped low-frequency poles. The polyphase structure is tested with different constant gain algorithms in an echo-cancellation example, attaining a gain of 14 to 70 times in global convergence speed over the direct form, at the price of a relatively modest increase in computational complexity. A theorem concerning the existence of stationary points for the polyphase structure is also presented.

A polyphase IIR adaptive filter: error surface analysis and application

A parameterization of an adaptive infinite impulse response (IIR) filter's poles is developed, based on balanced realization theory. From this, we develop a local approximation of the actual adapted pole parameters, in which convergence speed is related to a certain eigenvalue spread. This, in turn, is shown to relate to the Hankel singular values of the system to be identified, as well as certain coefficient sensitivity functions of the adapted filter. The local approximation is not restricted to stationary points. At these points, however, it is equivalent to a Hessian approximation, with the benefit of decomposing the Hessian matrix into terms related to the aforementioned singular values and sensitivity functions. The description of the adaptation process by means of the developed approximation leads to a greater understanding of the effects on convergence speed of factors, such as the Hankel singular values of the system, its order, the distribution of its poles, and the choice of adapted parameters. In particular, the use of direct form and lattice parameters are compared in detail. Based on these properties, a new adaptive IIR algorithm with faster convergence and relatively low computational complexity has recently been proposed, which is briefly mentioned. Results also indicate a potential for variable gain algorithms.

P.M.S. Burt

Papers

Broken conductors protection system using carrier communication

Efficient Computation of Bilinear Approximations and Volterra Models of Nonlinear Systems

Efficient Kernel Computation for Volterra Filter Structure Evaluation

A polyphase IIR adaptive filter: error surface analysis and application

A new framework for convergence analysis and algorithm development of adaptive IIR filters