Non-Gaussianity of the Cosmic Infrared Background anisotropies I : Diagrammatic formalism and application to the angular bispectrum

We present the first halo model based description of the Cosmic Infrared Background (CIB) non-Gaussianity (NG) that is fully parametric. To this end, we introduce, for the first time, a diagrammatic method to compute high order polyspectra of the 3D galaxy density field. It allows an easy derivation and visualisation of the different terms of the polyspectrum. We apply this framework to the power spectrum and bispectrum, and we show how to project them on the celestial sphere in the purpose of the application to the CIB angular anisotropies. Furthermore, we show how to take into account the particular case of the shot noise terms in that framework. Eventually, we compute the CIB angular bispectrum at 857 GHz and study its scale and configuration dependencies, as well as its variations with the halo occupation distribution parameters. Compared to a previously proposed empirical prescription, such physically motivated model is required to describe fully the CIB anisotropies bispectrum. Finally, we compare the CIB bispectrum with the bispectra of other signals potentially present at microwave frequencies, which hints that detection of CIB NG should be possible above 220 GHz.Comment: 21 pages, 21 figures. Accepted by MNRA

Making Every Photon Count: A Quantum Polyspectra Approach to the Dynamics of Blinking Quantum Emitters at Low Photon Rates Without Binning

The blinking statistics of quantum emitters and their corresponding Markov models play an important role in high resolution microscopy of biological samples as well as in nano-optoelectronics and many other fields of science and engineering. Current methods for analyzing the blinking statistics like the full counting statistics or the Viterbi algorithm break down for low photon rates. We present an evaluation scheme that eliminates the need for both a minimum photon flux and the usual binning of photon events which limits the measurement bandwidth. Our approach is based on higher order spectra of the measurement record which we model within the recently introduced method of quantum polyspectra from the theory of continuous quantum measurements. By virtue of this approach we can determine on- and off-switching rates of a semiconductor quantum dot at light levels 1000 times lower than in a standard experiment and 20 times lower than achieved with a scheme from full counting statistics. Thus a very powerful high-bandwidth approach to the parameter learning task of single photon hidden Markov models has been established with applications in many fields of science

Simulation of non-Gaussian CMB maps

A simple method is presented for the rapid simulation of statistically-isotropic non-Gaussian maps of CMB temperature fluctuations with a given power spectrum and analytically-calculable bispectrum and higher-order polyspectra. The $n$th-order correlators of the pixel values may also be calculated analytically. The cumulants of the simulated map may be used to obtain an expression for the probability density function of the pixel temperatures. The statistical properties of the simulated map are determined by the univariate non-Gaussian distribution from which pixel values are drawn independently in the first stage of the simulation process. We illustrate the method using a non-Gaussian distribution derived from the wavefunctions of the harmonic oscillator. The basic simulation method is easily extended to produce non-Gaussian maps with a given power spectrum and diagonal bispectrum.Comment: 10 pages, 8 figures (3 coloured), replaced with version accepted by MNRAS. Figure 3 is not included but a complete version of the paper with high resolution figures can be downloaded from (http://www.mrao.cam.ac.uk/~graca/Ngsims/

Higher-order spectral analysis of stray flux signals for faults detection in induction motors

[EN] This work is a review of current trends in the stray flux signal processing techniques applied to the diagnosis of electrical machines. Initially, a review of the most commonly used standard methods is performed in the diagnosis of failures in induction machines and using stray flux; and then specifically it is treated and performed the algorithms based on statistical analysis using cumulants and polyspectra. In addition, the theoretical foundations of the analyzed algorithms and examples applications are shown from the practical point of view where the benefits that processing can have using HOSA and its relationship with stray flux signal analysis, are illustrated.This work has been supported by Generalitat Valenciana, Conselleria d'Educació, Cultura i Esport in the framework of the "Programa para la promoción de la investigación científica, el desarrollo tecnológico y la innovación en la Comunitat Valenciana", Subvenciones para grupos de investigación consolidables (ref: AICO/2019/224). J. Alberto Conejero is also partially supported by MEC Project MTM2016-75963-P.Iglesias Martínez, ME.; Antonino Daviu, JA.; Fernández De Córdoba, P.; Conejero, JA. (2020). Higher-order spectral analysis of stray flux signals for faults detection in induction motors. Applied Mathematics and Nonlinear Sciences. 5(2):1-14. https://doi.org/10.2478/amns.2020.1.00032S11452H. Akçay and E. Germen. Subspace-based identification of acoustic noise spectra in induction motors. IEEE Transactions on Energy Conversion, 30(1):32–40, 2015.J. Antonino-Daviu, M. Riera-Guasp, J. Roger-Folch, F. Martínez-Giménez, and A. Peris. Application and optimization of the discrete wavelet transform for the detection of broken rotor bars in induction machines. Applied and Computational Harmonic Analysis, 21(2):268–279, 2006.N. Arthur and J. Penman. Induction machine condition monitoring with higher order spectra. IEEE Transactions on Industrial Electronics, 47(5):1031–1041, 2000.T. P. Banerjee and S. Das. Multi-sensor data fusion using support vector machine for motor fault detection. Information Sciences, 217:96–107, 2012.G. Bin, J. Gao, X. Li, and B. Dhillon. Early fault diagnosis of rotating machinery based on wavelet packets—empirical mode decomposition feature extraction and neural network. Mechanical Systems and Signal Processing, 27:696–711, 2012.B. Boashash, E. J. Powers, and A. M. Zoubir. Higher-order statistical signal processing. Longman Cheshire, 1995.A. Ceban, R. Pusca, and R. Romary. Eccentricity and broken rotor bars faults-effects on the external axial field. In The XIX International Conference on Electrical Machines-ICEM 2010, pages 1–6. IEEE, 2010.I. Chernyavska and O. Vítek. Analysis of broken rotor bar fault in a squirrel-cage induction motor by means of stator current and stray flux measurement. In 2016 IEEE International Power Electronics and Motion Control Conference (PEMC), pages 532–537. IEEE, 2016.T. Chow and G. Fei. Three phase induction machines asymmetrical faults identification using bispectrum. IEEE Transactions on Energy Conversion, 10(4):688–693, 1995.X. Dai and Z. Gao. From model, signal to knowledge: A data-driven perspective of fault detection and diagnosis. IEEE Transactions on Industrial Informatics, 9(4):2226–2238, 2013.J. de Jesus Rangel-Magdaleno, H. Peregrina-Barreto, J. M. Ramirez-Cortes, P. Gomez-Gil, and R. Morales-Caporal. Fpga-based broken bars detection on induction motors under different load using motor current signature analysis and mathematical morphology. IEEE Transactions on Instrumentation and Measurement, 63(5):1032–1040, 2013.P. A. Delgado-Arredondo, D. Morinigo-Sotelo, R. A. Osornio-Rios, J. G. Avina-Cervantes, H. Rostro-Gonzalez, and R. de Jesus Romero-Troncoso. Methodology for fault detection in induction motors via sound and vibration signals. Mechanical Systems and Signal Processing, 83:568–589, 2017.M. Drif and A. J. M. Cardoso. Stator fault diagnostics in squirrel cage three-phase induction motor drives using the instantaneous active and reactive power signature analyses. IEEE Transactions on Industrial Informatics, 10(2):1348–1360, 2014.L. Frosini, C. Harlişca, and L. Szabó. Induction machine bearing fault detection by means of statistical processing of the stray flux measurement. IEEE Transactions on Industrial Electronics, 62(3):1846–1854, 2014.Z. Gao, C. Cecati, and S. X. Ding. A survey of fault diagnosis and fault-tolerant techniques—part i: Fault diagnosis with model-based and signal-based approaches. IEEE Transactions on Industrial Electronics, 62(6):3757–3767, 2015.M. Geethanjali and H. Ramadoss. Fault diagnosis of induction motors using motor current signature analysis: A review. In Advanced Condition Monitoring and Fault Diagnosis of Electric Machines, pages 1–37. IGI Global, 2019.T. Ghanbari and A. Farjah. A magnetic leakage flux-based approach for fault diagnosis in electrical machines. IEEE Sensors Journal, 14(9):2981–2988, 2014.A. Glowacz. Acoustic based fault diagnosis of three-phase induction motor. Applied Acoustics, 137:82–89, 2018.A. Glowacz, W. Glowacz, Z. Glowacz, and J. Kozik. Early fault diagnosis of bearing and stator faults of the single-phase induction motor using acoustic signals. Measurement, 113:1–9, 2018.T. Goktas, M. Zafarani, K. W. Lee, B. Akin, and T. Sculley. Comprehensive analysis of magnet defect fault monitoring through leakage flux. IEEE Transactions on Magnetics, 53(4):1–10, 2016.K. C. Gryllias and I. A. Antoniadis. A support vector machine approach based on physical model training for rolling element bearing fault detection in industrial environments. Engineering Applications of Artificial Intelligence, 25(2):326–344, 2012.F. Gu, Y. Shao, N. Hu, A. Naid, and A. Ball. Electrical motor current signal analysis using a modified bispectrum for fault diagnosis of downstream mechanical equipment. Mechanical Systems and Signal Processing, 25(1):360–372, 2011.C. Harlişca, L. Szabó, L. Frosini, and A. Albini. Diagnosis of rolling bearings faults in electric machines through stray magnetic flux monitoring. In 2013 8TH International Symposium on Advanced Topics in Electrical Engineering (Atee), pages 1–6. IEEE, 2013.R. Hoppler and R. A. Errath. Motor bearings, not must a piece of metal. In 2007 IEEE Cement Industry Technical Conference Record, pages 214–233. IEEE, 2007.R. M. Howard. Principles of random signal analysis and low noise design: The power spectral density and its applications. John Wiley & Sons, 2004.J.-N. Hwang and Y. H. Hu. Handbook of neural network signal processing. CRC press, 2001.M. E. Iglesias-Martínez, J. A. Antonino-Daviu, P. Fernández de Córdoba, and J. A. Conejero. Rotor fault detection in induction motors based on time-frequency analysis using the bispectrum and the autocovariance of stray flux signals. Energies, 12(4):597, 2019.M. E. Iglesias-Martinez, P. F. de Cordoba, J. Antonino-Daviu, and J. A. Conejero. Detection of nonadjacent rotor faults in induction motors via spectral subtraction and autocorrelation of stray flux signals. IEEE Transactions on Industry Applications, 55(5):4585–4594, 2019.M. E. Iglesias-Martínez, P. F. de Córdoba, J. A. Antonino-Daviu, and J. A. Conejero. Detection of bar breakages in induction motor via spectral subtraction of stray flux signals. In 2018 XIII International Conference on Electrical Machines (ICEM), pages 1796–1802. IEEE, 2018.M. E. Iglesias-Martínez, P. F. de Córdoba, J. A. Antonino-Daviu, and J. A. Conejero. Detection of adjacent and non-adjacent bar breakages in induction motors via convolutional analysis of sound signals. Preprint, 2020.F. Immovilli, A. Bellini, R. Rubini, and C. Tassoni. Diagnosis of bearing faults in induction machines by vibration or current signals: A critical comparison. IEEE Transactions on Industry Applications, 46(4):1350–1359, 2010.C. Jiang, S. Li, and T. G. Habetler. A review of condition monitoring of induction motors based on stray flux. In 2017 IEEE Energy Conversion Congress and Exposition (ECCE), pages 5424–5430. IEEE, 2017.L. Jiang, Y. Liu, X. Li, and S. Tang. Using bispectral distribution as a feature for rotating machinery fault diagnosis. Measurement, 44(7):1284–1292, 2011.Q. Jiang and F. Chang. A novel rolling-element bearing faults classification method combines lower-order moment spectra and support vector machine. Journal of Mechanical Science and Technology, 33(4):1535–1543, 2019.X. Jin and T. W. Chow. Anomaly detection of cooling fan and fault classification of induction motor using mahalanobis–taguchi system. Expert Systems with Applications, 40(15):5787–5795, 2013.J. Józwik. Identification and monitoring of noise sources of CNC machine tools by acoustic holography methods. Advances in Science and Technology Research Journal, 10(30), 2016.S. M. Kay. Fundamentals of statistical signal processing. Prentice Hall PTR, 1993.R. Liu, B. Yang, E. Zio, and X. Chen. Artificial intelligence for fault diagnosis of rotating machinery: A review. Mechanical Systems and Signal Processing, 108:33–47, 2018.Z. Liu, H. Cao, X. Chen, Z. He, and Z. Shen. Multi-fault classification based on wavelet svm with pso algorithm to analyze vibration signals from rolling element bearings. Neurocomputing, 99:399–410, 2013.J. M. Mendel. Tutorial on higher-order statistics (spectra) in signal processing and system theory: Theoretical results and some applications. Proceedings of the IEEE, 79(3):278–305, 1991.M. Mrugalski, M. Witczak, and J. Korbicz. Confidence estimation of the multi-layer perceptron and its application in fault detection systems. Engineering Applications of Artificial Intelligence, 21(6):895–906, 2008.V. Muralidharan and V. Sugumaran. A comparative study of naïve bayes classifier and bayes net classifier for fault diagnosis of monoblock centrifugal pump using wavelet analysis. Applied Soft Computing, 12(8):2023–2029, 2012.Y. Ono, Y. Onishi, T. Koshinaka, S. Takata, and O. Hoshuyama. Anomaly detection of motors with feature emphasis using only normal sounds. In Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on, pages 2800–2804. IEEE, 2013.R. H. C. Palácios, I. N. da Silva, A. Goedtel, and W. F. Godoy. A comprehensive evaluation of intelligent classifiers for fault identification in three-phase induction motors. Electric Power Systems Research, 127:249–258, 2015.P. Panagiotou, I. Arvanitakis, N. Lophitis, J. A. Antonino-Daviu, and K. N. Gyftakis. Analysis of stray flux spectral components in induction machines under rotor bar breakages at various locations. In 2018 XIII International Conference on Electrical Machines (ICEM), pages 2345–2351. IEEE, 2018.P. A. Panagiotou, I. Arvanitakis, N. Lophitis, J. Antonino-Daviu, and K. N. Gyftakis. A new approach for broken rotor bar detection in induction motors using frequency extraction in stray flux signals. IEEE Transactions on Industry Applications, 2019.K. Pandey, P. Zope, and S. Suralkar. Review on fault diagnosis in three-phase induction motor. MEDHA–2012, Proceedings published by International Journal of Computer Applications (IJCA), 2012.J. Rafiee, F. Arvani, A. Harifi, and M. Sadeghi. Intelligent condition monitoring of a gearbox using artificial neural network. Mechanical systems and signal processing, 21(4):1746–1754, 2007.A. Sadeghian, Z. Ye, and B. Wu. Online detection of broken rotor bars in induction motors by wavelet packet decomposition and artificial neural networks. IEEE Transactions on Instrumentation and Measurement, 58(7):2253–2263, 2009.L. Saidi, J. B. Ali, and F. Fnaiech. Application of higher order spectral features and support vector machines for bearing faults classification. ISA transactions, 54:193–206, 2015.L. Saidi, F. Fnaiech, G. Capolino, and H. Henao. Stator current bi-spectrum patterns for induction machines multiple-faults detection. In IECON 2012-38th Annual Conference on IEEE Industrial Electronics Society, pages 5132–5137. IEEE, 2012.L. Saidi, F. Fnaiech, H. Henao, G. Capolino, and G. Cirrincione. Diagnosis of broken-bars fault in induction machines using higher order spectral analysis. ISA Transactions, 52(1):140–148, 2013.M. Salah, K. Bacha, and A. Chaari. An improved spectral analysis of the stray flux component for the detection of air-gap irregularities in squirrel cage motors. ISA transactions, 53(3):816–826, 2014.B. Samanta. Gear fault detection using artificial neural networks and support vector machines with genetic algorithms. Mechanical systems and signal processing, 18(3):625–644, 2004.P. Sangeetha and S. Hemamalini. Dyadic wavelet transform-based acoustic signal analysis for torque prediction of a three-phase induction motor. IET Signal Processing, 11(5):604–612, 2017.J. Sanz, R. Perera, and C. Huerta. Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks. Applied Soft Computing, 12(9):2867–2878, 2012.Z. Shen, X. Chen, X. Zhang, and Z. He. A novel intelligent gear fault diagnosis model based on emd and multi-class tsvm. Measurement, 45(1):30–40, 2012.A. Singhal and M. A. Khandekar. Bearing fault detection in induction motor using fast fourier transform. In IEEE Int. Conf. on Advanced Research in Engineering & Technology, 2013.A. Soualhi, K. Medjaher, and N. Zerhouni. Bearing health monitoring based on hilbert–huang transform, support vector machine, and regression. IEEE Transactions on Instrumentation and Measurement, 64(1):52–62, 2014.A. Swami, G. B. Giannakis, and G. Zhou. Bibliography on higher-order statistics. Signal processing, 60(1):65–126, 1997.O. Vitek, M. Janda, and V. Hajek. Effects of eccentricity on external magnetic field of induction machine. In Melecon 2010–2010 15th IEEE Mediterranean Electrotechnical Conference, pages 939–943. IEEE, 2010.H. Wang, X. Bao, C. Di, and Z. Cheng. Detection of eccentricity fault using slot leakage flux monitoring. In 2015 9th International Conference on Power Electronics and ECCE Asia (ICPE-ECCE Asia), pages 2188–2193. IEEE, 2015.Y. Wang, J. Xiang, R. Markert, and M. Liang. Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications. Mechanical Systems and Signal Processing, 66:679–698, 2016.Z. Wang and C. Chang. Online fault detection of induction motors using frequency domain independent components analysis. In 2011 IEEE International Symposium on Industrial Electronics, pages 2132–2137. IEEE, 2011.Z. Wang, C. Chang, and Y. Zhang. A feature based frequency domain analysis algorithm for fault detection of induction motors. In 2011 6th IEEE Conference on Industrial Electronics and Applications, pages 27–32. IEEE, 2011.W. Wenbing and X. Jinquan. The application of coupled three order cumulants’ differential feature in fault diagnosis. In 2017 International Conference on Virtual Reality and Visualization (ICVRV), pages 374–375. IEEE, 2017.I. Zamudio-Ramirez, R. A. Osornio-Rios, M. Trejo-Hernandez, R. d. J. Romero-Troncoso, and J. A. Antonino-Daviu. Smart-sensors to estimate insulation health in induction motors via analysis of stray flux. Energies, 12(9):1658, 2019.X. Zhang and J. Zhou. Multi-fault diagnosis for rolling element bearings based on ensemble empirical mode decomposition and optimized support vector machines. Mechanical Systems and Signal Processing, 41(1–2):127–140, 2013.W. Zhao, T. Tao, and E. Zio. System reliability prediction by support vector regression with analytic selection and genetic algorithm parameters selection. Applied Soft Computing, 30:792–802, 2015.W. Zhao, Y. Zhang, and Y. Zhu. Diagnosis for transformer faults based on combinatorial Bayes Network. In 2009 2nd International Congress on Image and Signal Processing, pages 1–3. IEEE, 2009.F. Zidat, J.-P. Lecointe, F. Morganti, J.-F. Brudny, T. Jacq, and F. Streiff. Non invasive sensors for monitoring the efficiency of ac electrical rotating machines. Sensors, 10(8):7874–7895, 2010