Jorge L. Aravena

A modular methodology for fast fault detection and classification in power systems

This paper presents a modular yet integrated approach to the problem of fast fault detection and classification. Although the specific application example studied here is a power system, the method would be applicable to arbitrary dynamic systems. The approach is quite flexible in the sense that it can be model-based or model-free. In the model-free case, we emphasize the use of concepts from signal processing and wavelet theory to create fast and sensitive fault indicators. If a model is available then conventionally generated residuals can serve as fault indicators. The indicators can then be analyzed by standard statistical hypothesis testing or by artificial neural networks to create intelligent decision rules. After a detection, the fault indicator is processed by a Kohonen network to classify the fault. The approach described here is expected to be of wide applicability. Results of computer experiments with simulated faulty transmission lines are included.

Triple matrix product architectures for fast signal processing

A procedure is introduced to determine highly concurrent representation of linear algorithms. The technique replaces matrix/vector operations by sums of small-size triple matrix products. A specially dedicated array architecture performs each triple product without intermediate I/O operations. The highly concurrent representation is shown to be possible for any linear algorithm. The special architecture features dual-mode operation for processing elements and closed-loop data circulation. Both characteristics increase the flexibility and speed of the configuration. >

2-D model reduction by quasi-balanced truncation and singular perturbation

This paper considers two-dimensional system model reduction using 2-D balanced truncation and singular perturbation. A new 2-D state space realization named quasi-balanced realization is proposed which is closely related to a pseudo-balanced realization and a structurally balanced realization. A unique feature of the new balanced realization is that it is numerically efficient when it exists and it reduces to the pseudo-balanced realization if the system is denominator separable. An improved frequency error bound is also derived for the pseudo-balanced (or quasi-balanced) realization model reduction for denominator separable systems. Finally, a new 2-D model reduction method together with stability analysis based on singular perturbation theory is studied. >

Recursive moving window DFT algorithm

A recursive algorithm is presented for computing the discrete Fourier transform (DFT). The algorithm is developed for a moving-window-type processing. The computational structure is fully concurrent and allows a vectorized updating of the DFT. The total time required for the updating could be as low as that of only one multiplication and two additions, regardless of the number of points. A possible structure for executing the computations is developed, and possible enhancements are analyzed. >

State models and stability for 2-D filters

A generalized 2-D discrete-time filter is considered. Using the concept of a wave advance process, the filter equation is converted to a 1-D recursive form. A 1-D state equation is then developed and a canonical form for the state equation is presented. A norm bound on state transitions is developed, which is then related to the coefficients of the underlying filter equation. The norm bound is used to specify asymptotic stability conditions; the resultant criteria are illustrated through examples. >

Weighted least mean square design of 2-D FIR digital filters: the general case

This paper solves the weighted least mean square (WLMS) design of two-dimensional (2-D) finite impulse response (FIR) filters with general half plane symmetric frequency responses and nonnegative weighting functions. The optimal solution is characterized by a pair of coupled integral equations, and the existence and uniqueness of the WLMS solution for 2-D FIR filter design are established. Two efficient numerical algorithms using a 2-D fast Fourier transform (FFT) are proposed to solve the WLMS solution. One is based on the contraction mapping and fix point theorem characterizing the coupled integral equation; the other uses conjugate gradient techniques, which guarantees finite convergence. The associated computational complexity is analyzed and compared with existing algorithms. Examples are used to illustrate the effectiveness of the proposed design algorithms. The selection of weighting functions to improve the minimax performance of the filter is also discussed.

Nonplanar switchable arrays

On-line signal processing and automatic control applications give rise to numerous examples of computationally intense algorithms. Architectures which are algorithmically specialized and provide massive parallelism are necessary to cope with such computational requirements. Systolic arrays, which feature parallelism, local communications, and VLSI compatability appear to match up well with these computational requirements.This paper summarizes recent research on a general class of nonplanar systolic arrays. These arrays feature closed-loop data flow. The arrays may be switched dynamically to facilitate I/O simplicity and to accommodate iterative calculations without intermediate I/O interdiction. The closed-loop data flows also facilitate restructuring of the array to accommodate specific algorithmic requirements. The potential for multiuser, multialgorithm operation is also enhanced.Matrix operations are used as examples in the development. Algorithms as diversified as the Riccati equation, LU factorization, the Faddeev algorithm, FFT calculation, and controllability Grammians can be implemented on the nonplanar architectures.

Fast Construction of Robustness Degradation Function

We develop a fast algorithm to construct the robustness degradation function, which describes quantitatively the relationship between the proportion of systems guaranteeing the robustness requirement and the radius of the uncertainty set. This function can be applied to predict whether a controller design based on an inexact mathematical model will perform satisfactorily when implemented on the true system.

Nonstationary signal classification using pseudo power signatures: The matrix SVD approach

This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. This independence is a requirement in common classification problems like stratigraphic analysis, which was a motivation for this research. We achieve this objective by developing the notion of an approximation to the continuous wavelet transform, which is separable in the time and scale parameters, and using it to define power signatures, which essentially characterize the scale energy density, independent of time. We present a simple technique which uses the singular value decomposition to compute such an approximation, and demonstrate through an example how it is used to perform the classification. The proposed classification approach has potential applications in areas like moving target detection, object recognition, oil exploration, and speech processing.

Weighted least mean square design of 2-D FIR digital filters

This paper is concerned with weighted least mean square design of two-dimensional (2-D) zero-phase FIR filters with quadrantally symmetric and antisymmetric frequency responses. The optimal solutions are first characterized by certain integral equations, and the existence, and uniqueness of the weighted least mean square solution for 2-D FIR filter design are then established using contraction mapping, and fixed point theorem. Explicit solution in closed form for discretized weighted least mean square error is obtained for 2-D zero-phase FIR filters, which can be considered as an extension of the methods of Ahmed and Wang (1989) and Tufts and Francis (1970). Further, two numerical algorithms are proposed to iteratively solve the weighted least mean square solution. Convergence of the iterative algorithms is established, and estimates of the convergence rate are also derived. Examples are used to illustrate the effectiveness of the proposed design algorithms. >