Henrique Mohallem Paiva

Fractional Order Modeling of Large Three-Dimensional RC Networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Cross-validation for the selection of spectral variables using the successive projections algorithm

This work compares the use of a separate validation set and leave-one-out cross-validation to guide the selection of variables in the Successive Projections Algorithm (SPA) for multivariate calibration. Two case studies involving diesel and corn analysis by NIR spectrometry are presented. A graphical interface for SPA is available at www.ele.ita.br/~kawakami/spa/

Wavelet-packet identification of dynamic systems in frequency subbands

This work presents a technique for linear system identification in frequency subbands by using wavelet packets. The wavelet-packet decomposition tree is used to establish frequency bands where subband models are created. An algorithm is proposed to adjust the tree structure, in order to achieve a compromise between accuracy and parsimony of the model. In a simulated example involving the identification of an aircraft model, the results of the proposed technique are favourably compared with those of a standard time-domain method.

Adaptive wavelet EMG compression based on local optimization of filter banks

This paper presents an adaptive wavelet technique for compression of surface electromyographic signals. The technique employs an optimization algorithm to adjust the wavelet filter bank in order to minimize the distortion of the compressed signal. Orthogonality of the transform is ensured by using a restriction-free parametrization described elsewhere. A case study involving real-life isotonic and isometric electromyographic signals is presented for illustration. The results show that the proposed approach outperforms the standard non-optimized wavelet technique in terms of the percent residual difference for a given compression factor.

On the Space of Orthonormal Wavelets: Additional Constraints to Ensure Two Vanishing Moments

This letter extends the formulation developed by Sherlock and Monro for parameterization of orthonormal wavelet filter banks. Additional constraints are proposed to ensure that the resulting wavelets have at least two vanishing moments. The remaining degrees of freedom are re-parameterized in a convenient form, which results in a convex set of feasible parameter values. An example involving wavelet adaptation in the context of signal compression is presented for illustration. In this case, the additional constraints improve the outcome of the optimization algorithm employed to adjust the filter bank.

A Wavelet Band-Limiting Filter Approach for Fault Detection in Dynamic Systems

This paper presents a wavelet-based analytical redundancy method for the detection of faults in dynamic systems. In the proposed approach, consistency checks are carried out after band-limiting the signals under consideration to specific frequency ranges. For this purpose, the discrete wavelet transform is used to establish the frequency bands of analysis and a finite impulse response filter is employed to check the dynamic consistency of the data within each band. The filter weights can be adjusted by a simple parametric identification procedure on the basis of data acquired under normal operating conditions. The proposed method is illustrated by using experimental fault data from an analog computer, which was adjusted to emulate the dynamic response of a servomechanism, as well as simulated data representing a sensor fault scenario in the operation of a Boeing 747 aircraft. For comparison, a standard Luenberger observer fault detection scheme is also employed. The results show that the wavelet method compares favorably with the observer-based scheme in terms of sensitivity to the fault effect, false alarms, and nondetected faults.

Optimized orthonormal wavelet filters with improved frequency separation

This paper proposes an optimization-based method to design orthonormal wavelet filters with improved frequency separation. The proposed approach adopts a parameterization of orthogonal filter banks which ensures that the resulting wavelets have at least two vanishing moments. The filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to cut-off sharpness. In comparison with standard orthonormal filters, the proposed method is shown to provide better trade-off between frequency selectivity and time resolution. For illustration, the optimized filters are employed in an application example involving the use of a wavelet-packet system identification scheme. As a result, the identification errors are smaller than those obtained by using a non-optimized filter with the same length.

Fault detection in a laboratory helicopter employing a wavelet-based analytical redundancy approach

Wavelet-based techniques for fault detection usually employ one of two basic approaches, namely (a) decomposition of a measured signal containing fault-related information or (b) decomposition of a residue calculated as the difference between sensor readings and the output of a model. An alternative approach, which was recently proposed in [1], consists of employing the wavelet transform to identify a subband model for the normal dynamical behaviour of the system. The resulting subband model is then used to generate a residual signal. Such a fault detection approach was shown to provide good results in terms of sensitivity and false alarm rate. However, the examples presented for validation were previously restricted to simulation studies. The present work is concerned with the application of this wavelet-based fault detection technique to a more elaborate case study involving experimental data. The system at hand consists of a laboratory helicopter operating under closed-loop control in the presence of a persistent disturbance. The results indicate that the technique under consideration can successfuly detect a fault of small magnitude, consisting of a 10% reduction in the pitch sensor gain. Moreover, the wavelet approach is shown to outperform a time-domain detector with similar configuration.

A wavelet-based multivariable approach for fault detection in dynamic systems

This paper presents a multivariable extension to a recently proposed wavelet-based technique for fault detection. In the original formulation, the Discrete Wavelet Transform is used to carry out dynamic consistency checks between pairs of signals within frequency subbands. For this purpose, moving average models with an integrative term are employed to reproduce the dynamics of the system in each subband under consideration. The present work introduces a new architecture allowing the use of subband models with more general multivariable structures. More specifically, a multivariable ARX (autoregressive with exogenous input) structure is adopted for each subband model. The proposed technique is illustrated in a case study involving a nonlinear simulation model for an aircraft with a sensor fault. The results show that the multivariable approach outperforms the original formulation in terms of residue amplification following the fault onset.

A state-space description for perfect-reconstruction wavelet FIR filter banks with special orthonormal basis functions

This paper presents a state space description for wavelet FIR filter banks with perfect reconstruction using special orthonormal basis functions. The FIR structure guarantees the BIBO stability, robustness and improves the filter divergence problem while orthonormal basis functions have characteristics that make them attractive in the modeling of dynamic systems. The state space description presented in this paper has all of those advantages and is minimal.