Detection of non-Gaussian signals in non-Gaussian noise using the bispectrum

Hinich, Melvin J.; Wilson, Gary R.

doi:10.1109/29.57541

Cited by 72 publications

(32 citation statements)

References 12 publications

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“…This approach avoids the need for baseline data from the undamaged structure. Variance distribution function thresholds of 95, 99, 99.5, 99.9, and 99.99 established the probability of false alarms (5, 1, 0.5, 0.1, and 0.01%, respectively) as described by Hinich and Wilson (1990). A minimum of 15 measurements spread over 3 days enabled the calculation of ROC curves for all 11 sensors, 4 damage levels, and 4 excitation levels at the highest damage level.…”

Section: Discussionmentioning

confidence: 99%

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Quantitative Detection of Low Energy Impact Damage in a Sandwich Composite Wing

Seaver

Aktaş

Trickey

2009

Journal of Intelligent Material Systems and Structures

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This work describes damage detection in a foam core composite wing (1320 mm Â 152.4 mm Â 13.4 mm) following a series of low energy impacts. Thirteen impacts (68 J deposited energy) were applied at adjacent locations approximately 1/4 of the way out from the wing center. Following every one or two impacts, the wing was tested using static tip deflection and dynamic vibrational excitation. Static and dynamic strains were measured using eight fiber Bragg grating sensors. Dynamic acceleration was also monitored using three conventional accelerometers. The estimated bicoherence was used to detect the presence of damage-induced non-linearity in time-series data recorded from each sensor. Receiver operating characteristic (ROC) curves were constructed for each sensor based on 15 or more dynamic measurements made for each damage case. The ROC curves provide a quantitative, statistical approach to evaluating the damage detection capabilities of the various sensors.

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Section: Discussionmentioning

confidence: 99%

“…It is necessary to multiply P a by the variance because our bicoherence data are not 1. When using this approach the choice of a represents the probability of false alarms (Hinich and Wilson, 1990). For these data, we chose a ¼ 95, 99, 99.5, 99.9, and 99.99 and used P a ¼ 2.995, 4.605, 5.300, 6.910, and 9.210, respectively.…”

Section: Bicoherencementioning

confidence: 99%

Quantitative Detection of Low Energy Impact Damage in a Sandwich Composite Wing

Seaver

Aktaş

Trickey

2009

Journal of Intelligent Material Systems and Structures

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“…Higher order techniques show promise in applications for stationary signals and also for short-time transients where only a single occurrence of a signal may be available for detection ͑Dwyer, 1984; Hinich and Wilson, 1990;Kletter and Messer, 1990;Sangfelt and Persson, 1993;Delaney, 1994;Tague et al, 1994;Baugh and Hardwicke, 1994;Nuttall, 1994͒. The latter case, for correlation detectors, has been investigated in previous papers by the authors using both computer simulations ͑Pflug et al., 1992b, 1994b͒ and more recently for unknown source detection, using theoretical performance predictions for the case of uncorrelated noise ͑Pflug et al, 1995b͒.…”

Section: Introductionmentioning

confidence: 99%

Known source detection predictions for higher order correlators

Pflug

Ioup

1998

The Journal of the Acoustical Society of America

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The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. ͓S0001-4966͑98͒01805-0͔

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“…It is shown in Hinich and Wilson (1990) that if a signal with bispectrum Bs(fj,fk) and power spectrum PS(f) is processed in the presence of additive Gaussian noise with power spectrum pN(f), the normalized bispectrum estimate of signal-plus-noise is noncentral chi-square distributed with a noncentrality parameter given by X~~k =2 s(fj,fk) ,(4.8)…”

Section: Tun(q) = Npn(f)pn(fikpn(f+) T(d) (47) 2lmentioning

confidence: 99%

“…(4.8) is relevant for "narrowband" detection, i.e., detection at a single point in the bispectrum. One can also consider "broadband" detection in which the detection statistic is based on bispectrum values over the entire principal domain (Hinich and Wilson, 1990). and unnormalized bispectrum to the power spectrum for detecting harmonics in Gaussian noise.…”

Section: N (1 +Rl (Fj))(l +R-1()( +R (Fj+k))mentioning

confidence: 99%

Nonstationary Higher Order Spectral Analysis

Wilson¹,

Hardwicke²

1991

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Detection of non-Gaussian signals in non-Gaussian noise using the bispectrum

Cited by 72 publications

References 12 publications

Quantitative Detection of Low Energy Impact Damage in a Sandwich Composite Wing

Quantitative Detection of Low Energy Impact Damage in a Sandwich Composite Wing

Known source detection predictions for higher order correlators

Nonstationary Higher Order Spectral Analysis

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