Short Data Sequences Research Articles

Recognition of chatter with neural networks

Chatter deteriorates surface finish, reduces tool life, and damages machine tools. A chatter development prediction procedure is proposed for the cylindrical turning of long slender bars. The procedure uses two synthetically trained neural networks to recognize the harmonic acceleration signals and their frequency, and based on these observations, the future vibration characteristics of the system are estimated. The developed neural networks are capable of identifying 98% of the harmonic signals with over 90% certainty and estimate their frequencies with less than ±5% error from very short data sequences (only 11 sampled points). The accuracy of the neural networks is equivalent to time domain time series method based approaches; however, the proposed procedure can be implemented very quickly by using commercially available neural network hardware and software, and can use the new neural network chips to make the estimations very quickly by using parallel processors. The validity of the chatter prediction procedure is also demonstrated on the experimental data.

Fast cross-correlation algorithm with application to spectral analysis

A method for transfer function calculation is described that derives its economy from the symmetry of the autocorrelation to double the number of lags. The imbalance in the number of lags between autocorrelations and cross-correlations is restored by calculating the negative lags of the cross-correlation without any extra computations. With both positive and negative lags available, the symmetry and periodicity constraints of the fast Fourier transform can be taken into account, and windowing the cross-correlation sequence is less ambiguous. This greatly increases the accuracy and convergence of the computed transfer function. Since the statistical significance of the transfer function estimate is higher, it is possible to obtain the transfer function using shorter data sequences. These last advantages more than outweigh the increase in resolution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High‐resolution velocity spectra using eigenstructure methods

Stacking spectra provide maximum‐likelihood estimates for the stacking velocity, or for the ray parameter, of well separated reflections in additive white noise. However, the resolution of stacking spectra is limited by the aperture of the array and the frequency of the data. Despite these limitations, parametric spectral estimation methods achieve better resolution than does stacking. To improve resolution, the parametric methods introduce a parsimonious model for the spectrum of the data. In particular, when the data are modeled as the superposition of wavefronts, the properties of the eigenstructure of the data covariance matrix can be used to obtain high‐resolution spectra. The traditional stacking spectra can also be expressed as a function of the data covariance matrix and directly compared to the eigenstructure spectra. The superiority of the latter in separating closely interfering reflections is then apparent from a simple geometric interpretation. Eigenstructure methods were originally developed for use with narrow‐band signals, while seismic reflections are wide‐band and transient in time. Taking advantage of the full bandwidth of seismic data, we average spectra from several frequency bands. We choose each frequency band wide enough, so that we can average over time estimates of the covariance matrix. Thus, we obtain a robust estimate of the covariance matrix from short data sequences. A field‐data example shows that the high‐resolution estimators are particularly attractive for use in the estimation of local spectra in which short arrays are considered. Several realistic synthetic examples of stacking‐velocity spectra illustrate the improved performance of the new methods in comparison with conventional processing.

Autocorrelation estimation using constrained iterative spectral deconvolution

Computing an autocorrelation conventionally produces a biased estimate, especially for a short data sequence. Windowing the autocorrelation can remove the bias but at the expense of violating the nonnegativity of the corresponding power spectrum. Constrained iterative deconvolution provides a basis for improving an autocorrelation estimate by reducing the bias while guaranteeing nonnegative definiteness. The length of the autocorrelation is increased in order to satisfy the nonnegativity constraints on the power spectral estimate. The constraints can also have significant effects on small, poorly determined values of the autocorrelation. The technique is applied to synthetic and real examples to show the improvements in the autocorrelation and power spectrum which are possible. The method is reasonably stable in the presence of noise and it approximately preserves the area of the power spectrum. Comparison to the maximum entropy technique shows that the iterative method gives power spectral resolution which is sometimes better and sometimes not as good, but that there are cases for which it is the more desirable approach.

Analysis of Robust Recursive Identification Algorithms

Abstract The problem of recursive robust identification of linear discrete-time dynamic stochastic systems is discussed. Supposing approximately Gaussian system disturbance samples, a general form of robustified recursive identification algorithms of stochastic approximation type, characterized by an adequate nonlinear residual transformation, is defined. In order to improve the convergence rate, especially on short data sequences, the weighting matrix of the algorithm is derived by performing step-by-step optimization of a predefined empirical criterion. The convergence of the estimates w.p.l. is established theoretically by using martingale theory. The theoretical results are followed by extensive Monte Carlo simulation results, providing a basis for making a precise judgement of real practical robustness of the algorithms. Important relationships between parameters describing the algorithms are pointed out.

Experimental comparison of three multichannel linear prediction spectral estimators

Single-channel spectral estimators based on linear prediction techniques, such as the maximum-entropy method, have been shown to often provide better spectral stability and resolution than standard FFT procedures for short data sequences. Based on this improved performance, a multitude of multichannel linear prediction techniques have been promoted for processing multichannel data sequences. Three of these are examined in the paper: a multichannel generalisation of the single-channel Burg algorithm by Nuttall, a maximum-entropy type of algorithm by Morf, Vieira, Lee and Kailath, and a multichannel extension of the covariance method of linear prediction implemented by Marple. For purposes of experimental comparison, various two-channel data sets were processed by the three methods to produce the two autospectra, the magnitude-squared coherence and the coherence phase associated with each data set. A possible deleterious effect of signal ‘feed-across’ between autospectra and in the coherence has been discovered in all three methods. The phenomenon, due to inexact pole-zero cancellation, is especially prominent for short data sequences. Based on the multichannel results given here, the Nuttall method generally produced the best spectral estimates.

The short-time behavior of a frequency-warping power spectral estimator

This paper investigates the behavior of a nonlinear frequency-warping power spectral estimator when it is used with short input data sequences. Expressions are derived for the mean, variance, and covariances of the estimate. Some discussion is also included on variance reduction methods.

Inferences drawn from atmospheric CO2 data

Detailed analyses of the atmospheric carbon dioxide concentration measurements from Mauna Loa Observatory have produced a model which describes most of the variability in the data. The final model is y(t) = a + deαt + Σi = 1 2Aisin[(2π/Ti)(t + ϕi)] + Σj = 12Fj sin[(2π/τj)(t + Θj)], where a is the preindustrial value, α is the exponential long‐term growth rate, i represents the annual cycle and its harmonics, and j represents longer‐term periodicities. The exponential growth rate is nearly identical to that calculated for the production of CO2 from fossil fuel burning. A long‐period component of about 44 months correlates with the southern oscillation index. Another long‐period oscillation—about 142 months—has tentatively been identified with the solar activity cycle and complicates the determination of α because the two sources of curvature interact in the fitting procedure, and the data record is not long enough to specify both of them independently. The generality of the model has been demonstrated by testing it against shorter data sequences from the South Pole and Australia.