Статті в журналах: "Bispectrums"

1

Wang, Hongchao. "Fault diagnosis of rolling element bearing compound faults based on sparse no-negative matrix factorization-support vector data description." Journal of Vibration and Control 24, no. 2 (March 10, 2016): 272–82. http://dx.doi.org/10.1177/1077546316637979.

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The bispectrum of rolling element bearing compound faults contains abundant fault characteristic information, and how to extract the fault feature effectively is a key problem. The fault diagnosis method of rolling element bearing compound faults based on Sparse No-Negative Matrix Factorization (SNMF)-Support Vector Data Description (SVDD) is proposed in the paper. The figure handling method SNMF is used firstly in fault feature extraction of the bispectrums of rolling element bearing different kinds of compound faults and the sparse coefficient matrices of the bispectrums are obtained. The sparse coefficient matrices are used as training and test input vectors of SVDD. At last, the three kinds of rolling element bearing compound faults (inner race outer race compound faults, outer race rolling element compound faults and inner race outer race rolling element compound faults) are classified correctly. In order to verify the advantages of the proposed method, the diagnosis results of the same three kinds of rolling element bearing compound faults based on No-Negative Matrix Factorization (NMF)-SVDD is used as comparison. The proposed method provides a new idea for fault diagnosis of rolling element bearing compound faults.

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2

Li, Fu Cai, Lin Ye, Gui Cai Zhang, and Guang Meng. "Bearing Fault Detection Using Higher-Order Statistics Based ARMA Model." Key Engineering Materials 347 (September 2007): 271–76. http://dx.doi.org/10.4028/www.scientific.net/kem.347.271.

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Impulse response provides important information about flaws in mechanical system. Deconvolution is one system identification technique for fault detection when signals captured from bearings with and without flaw are both available. However effects of measurement systems and noise are obstacles to the technique. In the present study, a model, namely autoregressive-moving average (ARMA), is used to estimate vibration pattern of rolling element bearings for fault detection. The frequently used ARMA estimator cannot characterize non-Gaussian noise completely. Aimed at circumventing the inefficiency of the second-order statistics-based ARMA estimator, higher-order statistics (HOS) was introduced to ARMA estimator, which eliminates the effect of noise greatly and, therefore, offers more accurate estimation of the system. Furthermore, bispectrums of the estimated HOS-based ARMA models were subsequently applied to get clearer information. Impulse responses of signals captured from the test bearings without and with flaws and their bispectra were compared for the purpose of fault detection. The results demonstrated the excellent capability of this method in vibration signal processing and fault detection.

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3

Huang, Jin Ying, Hong Xia Pan, and Shi Hua Bi. "Your Bearing Fault Diagnosis Based on Bispectrum and Bispectrum Entropy Feature." Advanced Materials Research 159 (December 2010): 708–13. http://dx.doi.org/10.4028/www.scientific.net/amr.159.708.

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Fault feature extraction and application is the key technology of fault diagnosis. In this paper, a fault diagnosis method using bispectrum and bispectrum entropy as the fault feature parameters is put forward. Bispectrum entropy as the information entropy in bispectrum domain can reflect the complexity of information energy. When the structure is failed, the distribution of bispectrum will be changed. bispectrum entropy can reflect this change and achieve good separation of the different types of fault. Vibration signal in different bearing states of a secondary drive gearbox is compared and analyzed, bispectrum energy spetrum and bispectrum entropy are extracted. Feature vector is set up via bispectrum entropy for the fault pattern recognition and diagnosis by BP neural network. The analysis result proves that bispectrum entropy is more sensitive to fault characteristic and can separate the fault of bearing.

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4

Zhang, Gui Cai, Jin Chen, Fu Cai Li, and Wei Hua Li. "Extracting Gear Fault Features Using Maximal Bispectrum." Key Engineering Materials 293-294 (September 2005): 167–74. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.167.

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Bispectrum is a powerful tool for non-Gaussian signal processing and nonlinearity detection. However, it is difficult to use in practical applications due to that it is a 2-dimensional function. Bispectral slices are widely used reduction methods, and they can only represent a small part of the whole bispectral information. Integrated bispectrum contains more signal features than that of the bispectral slices, whereas the integration will lose the focus of some signal features. To overcome these problems, a new approach called maximal bispectrum is proposed to extract signal features. Maximal bispectrum is obtained by selecting the maximal values of every row of the magnitude bispectrum in the whole bispectral plane and it is a 1-dimensional function. Feature extraction based on maximal bispectrum is investigated and the maximal bispectrum is used to extract features of gear fault. Experimental results indicate that the maximal bispectrum is effective for diagnosing gear crack fault.

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5

Shaw, Abinash Kumar, Somnath Bharadwaj, Debanjan Sarkar, Arindam Mazumdar, Sukhdeep Singh, and Suman Majumdar. "A fast estimator for quantifying the shape dependence of the 3D bispectrum." Journal of Cosmology and Astroparticle Physics 2021, no. 12 (December 1, 2021): 024. http://dx.doi.org/10.1088/1475-7516/2021/12/024.

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Abstract The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have implemented an FFT based fast estimator for the three dimensional (3D) bin averaged bispectrum, and we demonstrate that it allows us to study the variation of the bispectrum across triangles of all possible shapes (and also sizes). The computational requirement is shown to scale as ∼ N g 3 log N g 3 where N g is the number of grid points along each side of the volume. We have validated the estimator using a non-Gaussian field for which the bispectrum can be analytically calculated. The estimated bispectrum values are found to be in good agreement (< 10 % deviation) with the analytical predictions across much of the triangle-shape parameter space. We also introduce linear redshift space distortion, a situation where also the bispectrum can be analytically calculated. Here the estimated bispectrum is found to be in close agreement with the analytical prediction for the monopole of the redshift space bispectrum.

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6

Morita, Koh-Ichiro. "The Bispectrum analysis technique in millimeter interferometry." International Astronomical Union Colloquium 131 (1991): 197–201. http://dx.doi.org/10.1017/s0252921100013300.

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AbstractWe propose an application of the bispectrum analysis technique in millimeter interferometry, which is used in the speckle masking technique. For the millimeter interferometry, in which atmospheric phase fluctuations are very serious, not only bispectrum phase but also bispectrum amplitude is good observable. We have developed an algorithm to reconstruct images directly from bispectrum. We have made good maps with this algorithm in the case of both simple and compact sources.

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7

Wang, Haibin, Junbo Long, Zeliang Liu, and Fang You. "Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods." Mathematical Problems in Engineering 2020 (December 31, 2020): 1–24. http://dx.doi.org/10.1155/2020/8823389.

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The generated signals generally contain a large amount of background noise when the mechanical bearing fails, and the fault signals present nonlinear and non-Gaussian feature, which have heavy tail and belong to α -stable distribution ( 1 < α < 2 ); even the background noises are also α -stable distribution process. Then it is difficult to obtain reliable conclusion by using the traditional bispectral analysis method under α -stable distribution environment. Two improved bispectrum methods are proposed based on fractional lower-order covariation in this paper, including fractional low-order direct bispectrum (FLODB) method, fractional low-order indirect bispectrum (FLOIDB) method. In order to decrease the estimate variance and increase the bispectral flatness, the fractional lower-order autoregression (FLOAR) model bispectrum and fractional lower-order autoregressive moving average (FLOARMA) model bispectrum methods are presented, and their calculation steps are summarized. We compare the improved bispectrum methods with the conventional methods employing second-order statistics in Gaussian and S α S distribution environments; the simulation results show that the improved bispectrum methods have performance advantages compared to the traditional methods. Finally, we use the improved methods to estimate the bispectrum of the normal and outer race fault signal; the result indicates that they are feasible and effective for fault diagnosis.

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8

Watkinson, Catherine A., Cathryn M. Trott, and Ian Hothi. "The bispectrum and 21-cm foregrounds during the Epoch of Reionization." Monthly Notices of the Royal Astronomical Society 501, no. 1 (November 28, 2020): 367–82. http://dx.doi.org/10.1093/mnras/staa3677.

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ABSTRACT Numerous studies have established the theoretical potential of the 21-cm bispectrum to boost our understanding of the Epoch of Reionization (EoR). We take a first look at the impact of foregrounds (FGs) and instrumental effects on the 21-cm bispectrum and our ability to measure it. Unlike the power spectrum for which (in the absence of instrumental effects) there is a window clear of smooth-spectrum FGs in which it may be detectable, there is no such ‘EoR window’ for the bispectrum. For the triangle configurations and scales we consider, the EoR structures are completely swamped by those of the FGs, and the EoR + FG bispectrum is entirely dominated by that of the FGs. By applying a rectangular window function on the sky combined with a Blackman–Nuttall filter along the frequency axis, we find that spectral, or in our case scale, leakage (caused by FFTing non-periodic data) suppresses the FG contribution so that cross-terms of the EoR and FGs dominate. While difficult to interpret, these findings motivate future studies to investigate whether filtering can be used to extract information about the EoR from the 21-cm bispectrum. We also find that there is potential for instrumental effects to seriously corrupt the bispectrum. FG removal using GMCA (generalized morphological component analysis) is found to recover the EoR bispectrum to a reasonable level of accuracy for many configurations. Further studies are necessary to understand the error and/or bias associated with FG removal before the 21-cm bispectrum can be practically applied in analysis of future data.

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9

Schmittfull, Marcel. "Large-scale structure non-Gaussianities with modal methods." Proceedings of the International Astronomical Union 11, S308 (June 2014): 67–68. http://dx.doi.org/10.1017/s1743921316009649.

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AbstractRelying on a separable modal expansion of the bispectrum, the implementation of a fast estimator for the full bispectrum of a 3d particle distribution is presented. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application, the time evolution of gravitational and primordial dark matter bispectra was measured in a large suite of N-body simulations. The bispectrum shape changes characteristically when the cosmic web becomes dominated by filaments and halos, therefore providing a quantitative probe of 3d structure formation. Our measured bispectra are determined by ∼ 50 coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. We also compare the measured bispectra with predictions from the Effective Field Theory of Large Scale Structures (EFTofLSS).

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10

Delgado, Paola C. M., Ruth Durrer, and Nelson Pinto-Neto. "The CMB bispectrum from bouncing cosmologies." Journal of Cosmology and Astroparticle Physics 2021, no. 11 (November 1, 2021): 024. http://dx.doi.org/10.1088/1475-7516/2021/11/024.

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Abstract In this paper we compute the CMB bispectrum for bouncing models motivated by Loop Quantum Cosmology. Despite the fact that the primordial bispectrum of these models is decaying exponentially above a large pivot scale, we find that the cumulative signal-to-noise ratio of the bispectrum induced in the CMB from scales ℓ<30 is larger than 10 in all cases of interest and therefore can, in principle, be detected in the Planck data.

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11

Vanhoff, Barry, and Steve Elgar. "Simulating Quadratically Nonlinear Random Processes." International Journal of Bifurcation and Chaos 07, no. 06 (June 1997): 1367–74. http://dx.doi.org/10.1142/s0218127497001084.

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A technique to generate realizations of quadratically nonlinear non-Gaussian time series with a desired ("target") power spectrum and bispectrum is presented. Specifically, by generating a Gaussian time series (using amplitude information from the target power spectrum and random phases) and passing it through a quadratic filter (that uses phase information from the target bispectrum), a realization of a quadratically nonlinear random process with a specified power spectrum and bispectrum can be produced. Second- and third-order statistics from many realizations of simulated nonlinear time series compare well to those from the original time series providing the target power spectrum and bispectrum, with deviations consistent with theory. The simulation technique is shown to simulate accurately ocean waves in shallow water, which are well known to be quadratically nonlinear.

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12

Agrawal, Aniket. "Non-Gaussianity of inflationary gravitational waves from the field equation." International Journal of Modern Physics D 28, no. 02 (January 2019): 1950036. http://dx.doi.org/10.1142/s0218271819500366.

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We demonstrate equivalence of the in–in formalism and Green’s function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, [Formula: see text], agrees with the results obtained previously using the in–in formalism exactly. Characterizing non-Gaussianity of the fluctuations using the ratio [Formula: see text] in the equilateral configuration, where [Formula: see text] is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green’s function, reproducing the results from in–in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.

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13

He, Guang Jin, Jin Fang Cheng, and Wei Zhang. "The Research on Bispectrum Detection of Underwater Target in Frequency Domain." Applied Mechanics and Materials 182-183 (June 2012): 1761–65. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1761.

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As the non-Gaussianity of ship-radiated noise reduces fast when the Signal-to-Noise Ratio (SNR) becomes low, a bispectrum detector in the frequency domain is proposed to ease the problem. First, FFT method is applied on the received data to calculate the power spectrum. Second, the non-Gaussianity of the power spectrum series is tested by Hinich-Wilson Gaussian Test rule. Last, the bispectrum detector based on non-Gaussianity is used to determine whether there are ship-radiated signals. The bispectrum detector in frequency domain is applied to detect simulated noise and real ship-radiated noise. The results are compared with the detector which is in the signal’s time domain. The comparison illustrates that the bispectrum detector based on the power spectrum series(in frequency domain) is much better in detecting low SNR signals, which is very valuable in far distance detection.

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14

Mondal, Rajesh, Garrelt Mellema, Abinash Kumar Shaw, Mohd Kamran, and Suman Majumdar. "The Epoch of Reionization 21-cm bispectrum: the impact of light-cone effects and detectability." Monthly Notices of the Royal Astronomical Society 508, no. 3 (October 8, 2021): 3848–59. http://dx.doi.org/10.1093/mnras/stab2900.

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ABSTRACT We study the spherically averaged bispectrum of the 21-cm signal from the Epoch of Reionization (EoR). This metric provides a quantitative measurement of the level of non-Gaussianity of the signal, which is expected to be high. We focus on the impact of the light-cone (LC) effect on the bispectrum and its detectability with the future SKA-Low telescope. Our investigation is based on a single reionization LC model and an ensemble of 50 realizations of the 21-cm signal to estimate the cosmic variance errors. We calculate the bispectrum with a new, optimized direct estimation method, DviSukta, which calculates the bispectrum for all possible unique triangles. We find that the LC effect becomes important on scales $k_1 \lesssim 0.1\, {\rm Mpc}^{-1}$, where, for most triangle shapes, the cosmic variance errors dominate. Only for the squeezed limit triangles, the impact of the LC effect exceeds the cosmic variance. Combining the effects of system noise and cosmic variance we find that ∼3σ detection of the bispectrum is possible for all unique triangle shapes around a scale of $k_1 \sim 0.2\, {\rm Mpc}^{-1}$, and cosmic variance errors dominate above and noise errors below this length-scale. Only the squeezed limit triangles are able to achieve a more than 5σ significance over a wide range of scales, $k_1\lesssim 0.8\, {\rm Mpc}^{-1}$. Our results suggest that among all the possible triangle combinations for the bispectrum, the squeezed limit one will be the most measurable and hence useful.

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15

Liguori, Michele, Emiliano Sefusatti, James R. Fergusson, and E. P. S. Shellard. "Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure." Advances in Astronomy 2010 (2010): 1–64. http://dx.doi.org/10.1155/2010/980523.

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The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum estimators are expected to continue to provide the best constraints on the non-Gaussian parameters in future observations. We review and compare the theoretical and observational problems, current results, and future prospects for the detection of a nonvanishing primordial component in the bispectrum of the Cosmic Microwave Background and large-scale structure, and the relation to specific predictions from different inflationary models.

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16

O’Brien, Michael J., Blakesley Burkhart, and Michael J. Shelley. "Studying Interstellar Turbulence Driving Scales Using the Bispectrum." Astrophysical Journal 930, no. 2 (May 1, 2022): 149. http://dx.doi.org/10.3847/1538-4357/ac6502.

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Abstract We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify nonlinear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence-driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large scales enhances phase coupling as compared to a pure hydrodynamic case. We therefore suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.

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17

Fang, Teng Fei, and Guo Fu Li. "Condition Feature Extraction of Machine Tools Based on Wavelet Packet Energy Spectrum Analysis and Bispectrum Analysis of Current Signal." Applied Mechanics and Materials 101-102 (September 2011): 847–50. http://dx.doi.org/10.4028/www.scientific.net/amm.101-102.847.

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Based on the study of the characteristics of load current signal, this article develops a method to extract features that can be use to distinguish the different working status of machine tools in real-time manner. The features are extracted from wavelet packet energy spectrum and bispectrum of the load current signal, and thus can take advantages of both wavelet packet transforms and bispectrum in signal analysis. Experimental results show that, compared with the features extracted from wavelet packet energy spectrum or bispectrum alone, the features extracted by applying the proposed method can provide better performance in term of identifying the machine working status.

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18

Lan, Xiaohong, and Domenico Marinucci. "The needlets bispectrum." Electronic Journal of Statistics 2 (2008): 332–67. http://dx.doi.org/10.1214/08-ejs197.

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19

Fergusson, J. R., M. Liguori, and E. P. S. Shellard. "The CMB bispectrum." Journal of Cosmology and Astroparticle Physics 2012, no. 12 (December 20, 2012): 032. http://dx.doi.org/10.1088/1475-7516/2012/12/032.

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20

Zhang, Lanyue, Yang Wang, and Desen Yang. "Bispectrum and cross-bispectrum feature extraction based on vector hydrophone." Journal of the Acoustical Society of America 131, no. 4 (April 2012): 3485. http://dx.doi.org/10.1121/1.4709154.

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21

Pyne, Susan, and Benjamin Joachimi. "Self-calibration of weak lensing systematic effects using combined two- and three-point statistics." Monthly Notices of the Royal Astronomical Society 503, no. 2 (February 12, 2021): 2300–2317. http://dx.doi.org/10.1093/mnras/stab413.

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ABSTRACT We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological parameters Ωm and σ8 by a factor of 90 and for the two parameters of a time-varying dark energy equation of state by a factor of almost 20, compared with the baseline approach of using the power spectrum alone and of imposing priors consistent with the accuracy requirements specified for Euclid. We also demonstrate that including the bispectrum self-calibrates all three systematic effects to the stringent levels required by the forthcoming generation of weak lensing surveys, thereby reducing the need for external calibration data.

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22

Zhang, Mingming, Jiangtian Yang, and Zhang Zhang. "Locomotive Gear Fault Diagnosis Based on Wavelet Bispectrum of Motor Current." Shock and Vibration 2021 (July 12, 2021): 1–12. http://dx.doi.org/10.1155/2021/5554777.

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The motor current signature analysis (MCSA) provides a nondestructive method for gear fault detection. The motor current in the faulty gear system not only involves the frequency information related to the fault but also the electric supply frequency and gear meshing-related frequency, which not only contaminates the fault characteristics but also increases the difficulty of fault extraction. To extract the fault characteristic frequency effectively, an innovative method based on the wavelet bispectrum (WB) is proposed. Bispectrum is an effective tool for identifying the fault-related quadratic phase coupling (QPC). However, it requires a large amount of data averaging, which is not suitable for short data analysis. In this paper, the wavelet bispectrum is introduced to motor current analysis and the problem of QPC extraction under variable speed conditions is preliminarily solved. Furthermore, a fault diagnostic approach for locomotive gears using the wavelet bispectrum and wavelet bispectral entropy is suggested. The presented method was effectively applied to the locomotive online running operations, and faults of the drive gear were successfully diagnosed.

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23

Li, Xue Mei. "A Novel Scheme for Time Delay Estimation in the Fractional Fourier Transform Domain." Applied Mechanics and Materials 385-386 (August 2013): 1425–28. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.1425.

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A time delay estimator based on the fractional bispectrum is proposed; and it is suitable for the chirp signal. The proposed time delay estimation technique can outperform the conventional time delay estimation methods associated with the bispectrum in the Fourier domain under the correlated Gaussian noises at lower SNR. Simulation results demonstrate the validity of this estimation method.

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24

Wen Yean, Choong, Wan Khairunizam Wan Ahmad, Wan Azani Mustafa, Murugappan Murugappan, Yuvaraj Rajamanickam, Abdul Hamid Adom, Mohammad Iqbal Omar, et al. "An Emotion Assessment of Stroke Patients by Using Bispectrum Features of EEG Signals." Brain Sciences 10, no. 10 (September 25, 2020): 672. http://dx.doi.org/10.3390/brainsci10100672.

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Emotion assessment in stroke patients gives meaningful information to physiotherapists to identify the appropriate method for treatment. This study was aimed to classify the emotions of stroke patients by applying bispectrum features in electroencephalogram (EEG) signals. EEG signals from three groups of subjects, namely stroke patients with left brain damage (LBD), right brain damage (RBD), and normal control (NC), were analyzed for six different emotional states. The estimated bispectrum mapped in the contour plots show the different appearance of nonlinearity in the EEG signals for different emotional states. Bispectrum features were extracted from the alpha (8–13) Hz, beta (13–30) Hz and gamma (30–49) Hz bands, respectively. The k-nearest neighbor (KNN) and probabilistic neural network (PNN) classifiers were used to classify the six emotions in LBD, RBD and NC. The bispectrum features showed statistical significance for all three groups. The beta frequency band was the best performing EEG frequency-sub band for emotion classification. The combination of alpha to gamma bands provides the highest classification accuracy in both KNN and PNN classifiers. Sadness emotion records the highest classification, which was 65.37% in LBD, 71.48% in RBD and 75.56% in NC groups.

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25

Bi, Xiaoyang, Shuqian Cao, and Daming Zhang. "Diesel Engine Valve Clearance Fault Diagnosis Based on Improved Variational Mode Decomposition and Bispectrum." Energies 12, no. 4 (February 19, 2019): 661. http://dx.doi.org/10.3390/en12040661.

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The evaluation and fault diagnosis of a diesel engine’s health conditions without disassembly are very important for diesel engine safe operation. Currently, the research on fault diagnosis has focused on the time domain or frequency domain processing of vibration signals. However, early fault signals are mostly weak energy signals, and the fault information cannot be completely extracted by time domain and frequency domain analysis. Thus, in this article, a novel fault diagnosis method of diesel engine valve clearance using the improved variational mode decomposition (VMD) and bispectrum algorithm is proposed. First, the experimental study was designed to obtain fault vibration signals. The improved VMD method by choosing the optimal decomposition layers is applied to denoise vibration signals. Then the bispectrum analysis of the reconstructed signal after VMD decomposition is carried out. The results show that bispectrum image under different working conditions exhibits obviously different characteristics respectively. At last, the diagonal projection method proposed in this paper was used to process the bispectrum image, and the fourth order cumulant is calculated. The calculation results show that three states of the valve clearance are successfully distinguished.

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26

Bharadwaj, Somnath, Arindam Mazumdar, and Debanjan Sarkar. "Quantifying the redshift space distortion of the bispectrum I: primordial non-Gaussianity." Monthly Notices of the Royal Astronomical Society 493, no. 1 (February 3, 2020): 594–602. http://dx.doi.org/10.1093/mnras/staa279.

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ABSTRACT The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors $\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3}$ with respect to the line of sight. Here, we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this, we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane-parallel approximation, only the first four even ℓ multipoles have non-zero values, and we present explicit analytical expressions for all the non-zero multipoles, that is, upto ℓ = 6 and m = 4. The ratio of the different multipole moments to the real-space bispectrum depends only on β1 the linear redshift distortion parameter and the shape of the triangle. Considering triangles of all possible shapes, we have studied how this ratio depends on the shape of the triangle for β1 = 1. We have also studied the β1 dependence for some of the extreme triangle shapes. If measured in future, these multipole moments hold the potential of constraining β1. The results presented here are also important if one wishes to constrain fNL using redshift surveys.

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Chen, Yanzhao, Yiqi Zhou, Xiangli Cheng, Xiaohua Fan, and Yuwei Zhang. "Bispectrum-based sEMG multi-domain joint feature extraction for upper limb motion classification." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 2 (May 28, 2015): 248–58. http://dx.doi.org/10.1177/0954406215588987.

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sEMG based motion pattern recognition is the focus in the rehabilitation medical engineering area. In order to get more information to characterize the sEMG signal of different upper limb motions, the signal data acquisition program is designed and the non-Gaussian characteristic of the sEMG signal is analyzed, the result shows that the sEMG signal collected is non-Gaussian signal. Bispectrum as a third-order statistics contains non-Gaussian information and the integral of bispectrum slice is extracted as feature. After that, the PCA method is adopted to reduce the bispectrum feature dimension. Then, the integral of bispectrum slice after PCA and the integral value of sEMG are combined as a multi-domain joint feature called BisIE. Finally, the experiment is executed to validate the effectiveness of the feature extraction method proposed by the SVM classifier compared with power spectrum-based multi-domain joint feature MMIE. The average classification accuracy of BisIE is about 97% and that of MMIE is about 93%. Besides, for the same subject, the classification accuracy of BisIE is higher than that of MMIE. The result shows that the proposed feature BisIE is effective in promoting sEMG-based upper limb motion recognition accuracy.

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28

Wang, Fei, and Liqing Fang. "Bispectrum Texture Feature Manifold for Feature Extraction in Rolling Bear Fault Diagnosis." Mathematical Problems in Engineering 2019 (February 26, 2019): 1–11. http://dx.doi.org/10.1155/2019/3805729.

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Effectively classify the fault types and the degradation degree of a rolling bearing is an important basis for accurate malfunction detection. A novel feature extract method - bispectrum image texture features manifold (BTM) of the rolling bearing vibration signal is proposed in this paper. The BTM method is realized by three main steps: bispectrum image analysis, texture feature construction and manifold feature dimensionality reduction. In this method, bispectrum analysis is employed to convert the mass vibration signals into bispectrum contour map, the typical texture features were extracted from the contour map by gray level co-occurrence matrix (GLCM), then the manifold dimensionality reduction method liner local tangent space alignment (LLTSA) is used to remove redundant information and reduce the dimension from the extracted texture features and obtain more meaningful low-dimensional information. Furthermore, the low-dimensional texture features were identified by support vector machine (SVM) which was optimized by genetic optimization algorithm (GA). The validity of BTM is confirmed by rolling bear experiments, the result show that the proposed feature extraction method can accurately distinguish different fault types and have a good performance to classify the degradation degree of inner race fault, outer race fault and rolling ball fault.

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29

Lei, Y., M. J. Zuo, and M. Hoseini. "The use of ensemble empirical mode decomposition to improve bispectral analysis for fault detection in rotating machinery." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 8 (January 12, 2010): 1759–69. http://dx.doi.org/10.1243/09544062jmes1827.

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Empirical mode decomposition (EMD) has been widely applied to analyse signals for the detection of faults in rotating machinery. However, sometimes, it cannot reveal signal characteristics accurately because of the mode mixing problem. Ensemble empirical mode decomposition (EEMD) was developed recently to alleviate the mode mixing problem of EMD. With EEMD, components that are physically meaningful can be extracted from the signals. Bispectrum, a third-order statistic, helps identify phase coupling effects, which are useful for detecting faults in rotating machinery. Utilizing the advantages of EEMD and bispectrum, this article proposes a joint method for detecting such faults. First, original vibration signals collected from rotating machinery are decomposed by EEMD and a set of intrinsic mode functions (IMFs) is produced. Then, the IMFs are reconstructed into new signals using the weighted reconstruction algorithm developed in this article. Finally, the reconstructed signals are analysed via bispectrum to detect faults. The simulation experiments and the physical experiments of two gears with a chipped tooth and a cracked tooth, respectively, demonstrate that the proposed method can detect faults more clearly than can directly performing bispectrum on the original vibration signals.

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30

Hillis, Andrew J., Simon A. Neild, Bruce W. Drinkwater, and Paul D. Wilcox. "Global crack detection using bispectral analysis." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2069 (February 8, 2006): 1515–30. http://dx.doi.org/10.1098/rspa.2005.1620.

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This paper describes a global non-destructive testing technique for detecting fatigue cracking in engineering components. The technique measures the mixing of two ultrasonic sinusoidal waves which are excited by a small piezoceramic disc bonded to the test structure. This input signal excites very high-order modes of vibration of the test structure within the ultrasonic frequency range. The response of the structure is measured by a second piezoceramic disc and the received waveform is analysed using the bispectrum signal processing technique. Frequency mixing occurs as a result of nonlinearities within the test structure and fatigue cracking is shown to produce a strong mixing effect. The bispectrum is shown to be particularly suitable for this application due to its known insensitivity to noise. Experimental results on steel beams are used to show that fatigue cracks, corresponding to a reduction in the beam section of 8%, can be detected. It is also shown that the bispectrum can be used to quantify the extent of the cracking. A simple nonlinear spring model is used to interpret the results and demonstrate the robustness of the bispectrum for this application.

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31

Wang, Guangbin, Fengshou Gu, Ibraham Rehab, Andrew Ball, and Long Li. "A Sparse Modulation Signal Bispectrum Analysis Method for Rolling Element Bearing Diagnosis." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/2954094.

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Modulation signal bispectrum (MSB) analysis is an effective method to obtain the fault frequency for rolling bearing, but harmonics make fault frequency dense and even frequency aliasing. Carrier frequency of bearing is generally determined by its structure and inherent characteristics and changes with the increase of the damage degree, so it is hard to be accurately found. To solve these problems, this paper proposes a sparse modulation signal bispectrum analysis method. Firstly the vibration signal is demodulated by MSB analysis and its bispectrum is obtained. After the frequency domain filtering, the carrier frequency is computed based on the characteristics of energy concentration at the carrier frequency on MSB. By shift-frequency MSB (SF-MSB), the carrier frequency is moved to the coordinate origin, the entire MSB is shifted for the same distance, and SF-MSB is obtained. At last, the bispectrum is shifted to the frequency zero point and diagonal slices are performed to obtain a sparse representation of MSB. Experimental results show that sparse MSB (S-MSB) method can not only eliminate the interference of harmonic frequency, but also make the extracted characteristic frequency of fault more obvious.

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32

Li, Ling Jun, Wen Ping Lei, Jie Han, and Wang Shen Hao. "Intelligent Fault Diagnosis Method Based on Vector-Bispectrum and SVDD." Advanced Materials Research 490-495 (March 2012): 1029–33. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1029.

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Support vector data description (SVDD) can be used to solve the problems of the insufficient fault samples in the fault diagnosis field. Vector-bispectrum is the bispectrum analysis method based on the full vector spectrum information fusion. It can be used to fuse the double-channel information of the rotary machines effectively and reflect the nonlinear properties in the signals more completely and accurately. In order to realize the aim that the faults of the machines can be diagnosed effectually and intelligently under the situation of the lack of the fault samples, the intelligent diagnosis method of the faults by combining the vector-bispectrum with SVDD is put forward. By using the vector-bispectrum to process the signals and extract the characteristic vectors, which can be used as the input parameters of SVDD. The classification model is set up and therefore the running states of the machines can also be classified. The method is applied to the gearbox fault diagnosis. The results indicate that the method can be effectively used to extract the characteristic information of the gearbox signals and increase the accuracy of SVDD in the fault diagnosis.

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33

Xiao, Ying, Xiao Mei Liu, and Jian Can Chen. "Fault Diagnosis of the Relief Valve Based on Fractal Box Dimension of Autoregressive Bispectrum Slices." Applied Mechanics and Materials 274 (January 2013): 70–73. http://dx.doi.org/10.4028/www.scientific.net/amm.274.70.

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After data preprocessing,the autoregressive(AR) bispectrum diagonal slices were figured and fractal box dimensions were calculated. The results show that the box dimensions are different in evidence under different conditions. So the fault pattern recognitions of the relief valve are effective by the method of using fractal box dimension of AR bispectrum diagonal slices, it provides a simple and accurate method for fault diagnosis of the relief valve.

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34

Sarkar, Debanjan, Suman Majumdar, and Somnath Bharadwaj. "Modelling the post-reionization neutral hydrogen (H i) 21-cm bispectrum." Monthly Notices of the Royal Astronomical Society 490, no. 2 (October 10, 2019): 2880–89. http://dx.doi.org/10.1093/mnras/stz2799.

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ABSTRACT Measurements of the post-reionization 21-cm bispectrum $B_{{\rm H\,{\small I}}\, }(\boldsymbol {k_1},\boldsymbol {k_2},\boldsymbol {k_3})$ using various upcoming intensity mapping experiments hold the potential for determining the cosmological parameters at a high level of precision. In this paper, we have estimated the 21-cm bispectrum in the z range 1 ≤ z ≤ 6 using seminumerical simulations of the neutral hydrogen (H i) distribution. We determine the k and z range where the 21-cm bispectrum can be adequately modelled using the predictions of second-order perturbation theory, and we use this to predict the redshift evolution of the linear and quadratic H i bias parameters b1 and b2, respectively. The b1 values are found to decrease nearly linearly with decreasing z, and are in good agreement with earlier predictions obtained by modelling the 21-cm power spectrum $P_{{\rm H\,{\small I}}\, }(k)$. The b2 values fall sharply with decreasing z, becomes zero at z ∼ 3 and attains a nearly constant value b2 ≈ −0.36 at z < 2. We provide polynomial fitting formulas for b1 and b2 as functions of z. The modelling presented here is expected to be useful in future efforts to determine cosmological parameters and constrain primordial non-Gaussianity using the 21-cm bispectrum.

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35

LANDRIAU, M. "ON THE BISPECTRUM OF COSMIC STRING SEEDED CMB FLUCTUATIONS." International Journal of Modern Physics D 22, no. 09 (June 26, 2013): 1350053. http://dx.doi.org/10.1142/s0218271813500533.

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I compute the bispectrum of maps of cosmic microwave background (CMB) fluctuations seeded by cosmic strings from large to 30 arcminute scales. Examining the distribution of triangle configurations and comparing with Gaussian realizations with the same power spectrum, I conclude that the CMB bispectrum cannot pick up the mild non-Gaussianity present in the maps and thus that it cannot characterize cosmic string induced non-Gaussianity produced in the regimes probed by these maps.

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36

Narita, Y., K. H. Glassmeier, P. M. E. Décréau, T. Hada, U. Motschmann, and Y. Nariyuki. "Evaluation of bispectrum in the wave number domain based on multi-point measurements." Annales Geophysicae 26, no. 11 (October 24, 2008): 3389–93. http://dx.doi.org/10.5194/angeo-26-3389-2008.

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Abstract. We present an estimator of the bispectrum, a measure of three-wave couplings. It is evaluated directly in the wave number domain using a limited number of detectors. The ability of the bispectrum estimator is examined numerically and then it is applied to fluctuations of magnetic field and electron density in the terrestrial foreshock region observed by the four Cluster spacecraft, which indicates the presence of a three-wave coupling in space plasma.

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37

Molchanov, Pavel, and Alexandr Totsky. "Application of Triple Correlation and Bispectrum for Interference Immunity Improvement in Telecommunications Systems." International Journal of Applied Mathematics and Computer Science 18, no. 3 (September 1, 2008): 361–67. http://dx.doi.org/10.2478/v10006-008-0032-9.

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Application of Triple Correlation and Bispectrum for Interference Immunity Improvement in Telecommunications SystemsThis paper presents a new noise immunity encoding/decoding technique by using the features of triple correlation and bispectrum widely employed in digital signal processing systems operating in noise environments. The triple correlation-and bispectrum-based encoding/decoding algorithm is tested for a digital radio telecommunications binary frequency shift keying system. The errorless decoding probability was analyzed by means of computer simulation for the transmission and reception of a test message in a radio channel disturbed by both additive white Gaussian noise (AWGN) and a mixture of an AWGN and an impulsive noise. Computer simulation results obtained for varying and less than unity signal-to-noise ratios at the demodulator input demonstrate a considerable improvement in the noise immunity of the technique suggested in comparison with the traditional redundant linear block encoding/decoding technique.

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38

Zhu, Jia, Zhangqin Zhu, and Zhongfu Ye. "An Efficient Profile Detection Method for Fiber Spectrum Images with Low SNR Based on Wigner Bispectrum." Publications of the Astronomical Society of Australia 28, no. 2 (2011): 144–49. http://dx.doi.org/10.1071/as11012.

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AbstractAnovel profile detection method is proposed for astronomical fiber spectrum data with low signalto-noise ratio. This approach can be applied to the pretreatment for 2-D astronomical spectrum data before the extraction of spectra. The Wigner bispectrum, a classical higher-order spectrum analysis method, is introduced and applied to deal with the spectrumsignal in this article.After analyzing the Wigner higher-order spectra distribution of the target profile signal, the combination of the Wigner bispectrum algorithm and the fast Fourier transform algorithm is used to weaken the effect of the noise to obtain more accurate information. Both the reconstruction method of the Wigner bispectrum and inverse fast Fourier transform are used to acquire the detection signal. At the end of this paper, experiments with both simulated and observed data based on the Large Sky Area Multi-Object Fiber Spectroscopy Telescope project are presented to demonstrate the effectiveness of the proposed method.

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39

Saidi, Lotfi, Mohamed Benbouzid, Demba Diallo, Yassine Amirat, Elhoussin Elbouchikhi, and Tianzhen Wang. "Higher-Order Spectra Analysis-Based Diagnosis Method of Blades Biofouling in a PMSG Driven Tidal Stream Turbine." Energies 13, no. 11 (June 5, 2020): 2888. http://dx.doi.org/10.3390/en13112888.

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Most electrical machines and drive signals are non-Gaussian and are highly nonlinear in nature. A useful set of techniques to examine such signals relies on higher-order statistics (HOS) spectral representations. They describe statistical dependencies of frequency components that are neglected by traditional spectral measures, namely the power spectrum (PS). One of the most used HOS is the bispectrum where examining higher-order correlations should provide further details and information about the conditions of electric machines and drives. In this context, the stator currents of electric machines are of particular interest because they are periodic, nonlinear, and cyclostationary. This current is, therefore, well adapted for analysis using bispectrum in the designing of an efficient condition monitoring method for electric machines and drives. This paper is, therefore, proposing a bispectrum-based diagnosis method dealing the with tidal stream turbine (TST) rotor blades biofouling issue, which is a marine environment natural process responsible for turbine rotor unbalance. The proposed bispectrum-based diagnosis method is verified using experimental data provided from a permanent magnet synchronous generator (PMSG)-based TST experiencing biofouling emulated by attachment on the turbine blade. Based on the achieved results, it can be concluded that the proposed diagnosis method has been very successful. Indeed, biofouling imbalance-related frequencies are clearly identified despite marine environmental nuisances (turbulences and waves).

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40

Heavens, Alan, Mario Santos, and Pedro Ferreira. "The bispectrum of MAXIMA." New Astronomy Reviews 47, no. 8-10 (November 2003): 815–20. http://dx.doi.org/10.1016/j.newar.2003.07.009.

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41

Jung, Gabriel, Filippo Oppizzi, Andrea Ravenni, and Michele Liguori. "The integrated angular bispectrum." Journal of Cosmology and Astroparticle Physics 2020, no. 06 (June 16, 2020): 035. http://dx.doi.org/10.1088/1475-7516/2020/06/035.

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42

Magueijo, João, and João Medeiros. "On the bispectrum ofCOBEandWMAP." Monthly Notices of the Royal Astronomical Society 351, no. 1 (June 2004): L1—L4. http://dx.doi.org/10.1111/j.1365-2966.2004.07912.x.

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43

Scoccimarro, Roman, Hume A. Feldman, J. N. Fry, and Joshua A. Frieman. "The Bispectrum ofIRASRedshift Catalogs." Astrophysical Journal 546, no. 2 (January 10, 2001): 652–64. http://dx.doi.org/10.1086/318284.

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44

Cooray, Asantha, and Wayne Hu. "Weak Gravitational Lensing Bispectrum." Astrophysical Journal 548, no. 1 (February 10, 2001): 7–18. http://dx.doi.org/10.1086/318660.

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45

Newman, Julian, Aleksandra Pidde, and Aneta Stefanovska. "Defining the wavelet bispectrum." Applied and Computational Harmonic Analysis 51 (March 2021): 171–224. http://dx.doi.org/10.1016/j.acha.2020.10.005.

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46

Sugimura, Kazuyuki, and Eiichiro Komatsu. "Bispectrum from open inflation." Journal of Cosmology and Astroparticle Physics 2013, no. 11 (November 29, 2013): 065. http://dx.doi.org/10.1088/1475-7516/2013/11/065.

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47

Hirlekar, S. G., R. S. Holambe, and T. K. Basu. "Phase Recovery from Bispectrum." IETE Journal of Research 46, no. 3 (May 2000): 139–45. http://dx.doi.org/10.1080/03772063.2000.11416149.

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48

Akrami, Y., F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, et al. "Planck 2018 results." Astronomy & Astrophysics 641 (September 2020): A9. http://dx.doi.org/10.1051/0004-6361/201935891.

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We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: fNLlocal = −0.9 ± 5.1; fNLequil = −26 ± 47; and fNLortho = −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is gNLlocal = (−5.8 ± 6.5) × 104 (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

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49

Feng, Yong Xin, Wei Peng Zhang, Tao Yang, Xiao Wen Deng, and Shi Liu. "Wind Turbine Planetary Gearbox Fault Analysis Based on Bispectrum." Advanced Materials Research 1070-1072 (December 2014): 1861–68. http://dx.doi.org/10.4028/www.scientific.net/amr.1070-1072.1861.

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Through researching the fault vibration signal characteristics of planetary gearbox, various forms of quadratic phase coupling phenomenon were found in the signals. Bispectrum has properties such as detecting the quadratic coupling phenomena and restraining gaussian noise signal, and it can be well used in the planetary gearbox fault diagnosis. Meanwhile, the sun gear distributed fault (gear wear) and partial fault (root crack, partial broken teeth) are simulated in the wind turbine test bench built in the laboratory. By analyzing the structure characteristics of its frequency through bispectrum, the fault of the gear is effectively diagnosed.

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50

Zheng, Yue Kun, and Yi Jian Huang. "High Order Spectrum Characteristics of the Elevator Fault." Advanced Materials Research 605-607 (December 2012): 739–43. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.739.

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Used the high order spectrum and slice analysis method, studied the elevator running vibration acceleration signals and calculated the trispectrum two dimensional slices, bispectrum and theirs diagonal slices, under different running conditions. The results show that: when the elevator normal operation the acceleration signal spectrum peaks concentration, otherwise the acceleration signal peaks dispersion; in fault condition, compared to bispectrum peaks trispectrum peaks is sharper. High order spectrum contains abundant information of different fault elevator running details. It is a suitable analysis tool for diagnosing the faults of elevator.

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