Conventional Bispectrum Research Articles

Deep learning classification for improved bicoherence feature based on cyclic modulation and cross-correlation.

This paper aims to present an improved bicoherence spectrum (IBS) combined with cyclic modulation spectrum (CMS) and cross-correlation that is suitable for classification of hydrophone signals involving deep learning (DL). First, the proposed feature utilizes the all-phase fast Fourier transform to modify the spectrum leakage caused by CMS; this can be used to detect line spectra with low signal-to-noise ratios (SNRs). Second, the cross-correlation and bispectrum are both exploited to suppress non-periodic line spectra interference from CMS. Based on numerous numerical simulations and experimental verification, compared with CMS and conventional bispectrum, the prominent characteristics of IBS include: detecting higher-precision periodic harmonics without single-line interference, superior robustness under low SNR, and greatly reducing the data redundancy. In addition, to test the performance of IBS for DL application, three deep belief network (DBN)-based classifiers-DBN-softmax, DBN-support vector machine, and DBN-random forest-are introduced and employed for five experimental scenarios (including ships and underwater source). The results indicate that benefiting from DBN pre-training, the IBS classification accuracy of DBN-based models is generally higher than 80%.

A Performance Evaluation of Two Bispectrum Analysis Methods Applied to Electrical Current Signals for Monitoring Induction Motor-Driven Systems

This paper investigates the performance of the conventional bispectrum (CB) method and its new variant, the modulation signal bispectrum (MSB) method, in analysing the electrical current signals of induction machines for the condition monitoring of rotor systems driven by electrical motors. Current signal models which include the phases of the various electrical and magnetic quantities are explained first to show the theoretical relationships of spectral sidebands and their associated phases due to rotor faults. It then discusses the inefficiency of CB and the proficiency of MSB in characterising the sidebands based on simulated signals. Finally, these two methods are applied to analyse current signals measured from different rotor faults, including broken rotor bar (BRB), downstream gearbox wear progressions and various compressor faults, and the diagnostic results show that the MSB outperforms the CB method significantly in that it provides more accurate and sparse diagnostics, thanks to its unique capability of nonlinear modulation detection and random noise suppression.

A new method of accurate broken rotor bar diagnosis based on modulation signal bispectrum analysis of motor current signals

Motor current signature analysis (MCSA) has been an effective way of monitoring electrical machines for many years. However, inadequate accuracy in diagnosing incipient broken rotor bars (BRB) has motivated many studies into improving this method. In this paper a modulation signal bispectrum (MSB) analysis is applied to motor currents from different broken bar cases and a new MSB based sideband estimator (MSB-SE) and sideband amplitude estimator are introduced for obtaining the amplitude at (1±2s)fs (s is the rotor slip and fs is the fundamental supply frequency) with high accuracy. As the MSB-SE has a good performance of noise suppression, the new estimator produces more accurate results in predicting the number of BRB, compared with conventional power spectrum analysis. Moreover, the paper has also developed an improved model for motor current signals under rotor fault conditions and an effective method to decouple the BRB current which interferes with that of speed oscillations associated with BRB. These provide theoretical supports for the new estimators and clarify the issues in using conventional bispectrum analysis.

Influence of Gauge Artifact on Adiabatic and Entropy Perturbations during Inflation

In recent publications we proposed one way to calculate gauge-invariant variables in a local observable universe which is limited to a portion of the whole universe. To provide a theoretical prediction of the observable fluctuations, we need to preserve the gauge-invariance in the local universe, which is referred to the genuine gauge-invariance. The importance of the genuine gauge invariance is highlighted in the study of primordial fluctuations in the infrared (IR) limit. The stability against IR loop corrections to primordial fluctuations is guaranteed in requesting the genuine gauge invariance. The genuine gauge-invariance also gives impacts on the detectable fluctuations. We showed that at observable scales the bi-spectrum calculated in the conventional perturbation theory vanishes in the squeezed limit, if we request the genuine gauge invariance. This indicates that the conventional bi-spectrum is, in this limit, dominated by a gauge artifact, which cannot be observed. These studies have been elaborated in single-field models of inflation. In this paper we generalize our argument to multi-field models of inflation, where, in addition to the adiabatic field, the entropy field can participate in the generation of primordial fluctuations. We will find that the entropy field can generate the observable fluctuations, which cannot be eliminated by gauge transformations in the local universe.

Electrical motor current signal analysis using a modified bispectrum for fault diagnosis of downstream mechanical equipment

This paper presents the use of the induction motor current to identify and quantify common faults within a two-stage reciprocating compressor based on bispectrum analysis. The theoretical basis is developed to understand the nonlinear characteristics of current signals when the motor undertakes a varying load under different faulty conditions. Although conventional bispectrum representation of current signal allows the inclusion of phase information and the elimination of Gaussian noise, it produces unstable results due to random phase variation of the sideband components in the current signal. A modified bispectrum based on the amplitude modulation feature of the current signal is then adopted to combine both lower sidebands and higher sidebands simultaneously and hence characterise the current signal more accurately. Based on this new bispectrum analysis a more effective diagnostic feature, namely normalised bispectral peak, is developed for fault classification. In association with the kurtosis value of the raw current signal, the bispectrum feature gives rise to reliable fault classification results. In particular, the low feature values can differentiate the belt looseness from the other fault cases and different degrees of discharge valve leakage and inter-cooler leakage can be separated easily using two linear classifiers. This work provides a novel approach to the analysis of stator current for the diagnosis of motor drive faults from downstream driving equipment.

Performance Study of Adaptive Filtering in Bispectrum Signal Reconstruction

The problem of reconstructing a signal waveform when the observed realizations are corrupted by intensive noise and random shifts is considered in this paper. Several ways of performing bispectrum filtering are proposed and investigated. First, it is shown that the signal reconstruction is more efficient if one applies smoothing to the recovered real and imaginary parts of the Fourier spectrum separately instead of filtering the magnitude and phase spectra recovered from a bispectrum estimate. Second, several nonadaptive filters are studied, and it is demonstrated that the proper choice of the filter type and its parameters is critical. Some adaptive filtering techniques based on the Z-parameter and on local polynomial approximation (LPA)-intersection of confidence intervals (ICI) are discussed. The performances of nonadaptive and adaptive filtering techniques in the bispectrum-based signal reconstruction are studied using the mean-squared error as the criterion. It is shown that the use of LPA-ICI and other adaptive filters provides improvement of signal reconstruction in comparison to the conventional bispectrum method and the combined bispectrum filtering methods proposed earlier for nonadaptive filters. The benefits achieved are mainly observed for low (smaller than unity) signal-to-noise ratios.

Asymptotic Bias and Variance of Conventional Bispectrum Estimates for 2-D Signals

In this paper, we derive the asymptotic bias and variance of conventional bispectrum estimates of 2-D signals. Two methods have been selected for the estimation: the first one -- the indirect method -- is the Fourier Transform of the weighted third order moment, while the second one -- the direct method -- is the expectation of the Fourier component product. Most of the developments are known for 1-D signals and the first contribution of this paper is the rigorous extension of the results to 2-D signals. The calculation of the bias of the direct method is a totally original contribution. Nevertheless, we did all calculations (bias and variance) for both method in order to be able to compare the results. The second contribution of this paper consists of the comparison of the theoretical bispectrum estimate bias and variance with the measured bias and variance for two 2-D signals. The first studied signal is the output of a non-minimal phase linear system driven by a non-symmetric noise. The second signal is the output of a non-linear system with Gaussian input data. In order to assess the results, we performed the comparison for both methods with different sets of parameters. We show that the maximum bias coefficient is the one of the 1-D case multiplied by the dimensionality of the signal for both methods. We also show that the estimate variance coefficient is the 1-D case coefficient with a power equal to the signal dimensionality.

Time delay estimation of non-Gaussian signal in unknown Gaussian noises using third-order cumulants

For correlated Gaussian noises, a generalised cross correlation (GCC) type of processing and a parametric method is applied to one slice of the third-order cumulants to estimate time delay, with better performance than SCOT, the conventional bispectrum method (CBM) and the parametric bispectrum method (PBM). For uncorrelated Gaussian noises, HOS-SCOT using multiple slices of cumulants also outperforms SCOT, CBM and PBM. Simulation examples are given.

ORDER BISPECTRUM: A NEW TOOL FOR RECIPROCATED MACHINE CONDITION MONITORING

Vibrations and sounds generated by reciprocated machines or by their parts strongly depend on the rotation speed of the main shaft of the tested reciprocating system. At the testing or at common performance of the reciprocated machines, their rotation speed is usually changing. With regard to this fact, signals produced by reciprocating machines are non-stationary ones. Therefore, conventional time-invariant methods of their spectral or bispectral analysis are frequently unable to provide meaningful results. In order to solve this problem in the field of polyspectral signal analysis, the order bispectrum analysis is proposed in this contribution. This approach is based on the bispectrum estimation from the signal which is a function of the angle of roll of the main shaft of reciprocated machine. A digital representation of this signal can be obtained by resampling of the signal conveniently sampled in the time domain. The advantages of the order bispectrum application in comparison with that of the conventional bispectrum approach is illustrated based on the example of an engine set classification.

Detection of non-Gaussian signals by bispectrum-Udetector

A method for detecting non-Gaussian stationary signals in additive Gaussian noise using a bispectrum-U test is presented. The performance of the proposed detection statistic is compared to the conventional bispectrum χ2 detector.