Download pdf
Applications of Fourier transforms in engineering
- 1 Shanghai Experimental Foreign Language School
* Author to whom correspondence should be addressed.
Abstract
The Fourier transform was proposed by Fourier in 1807. Fourier transform is a method of analyzing signals, which can analyze the components of the signal or synthesize the signal using these components. Many waveforms can be used as signal components, such as sine waves, square waves, sawtooth waves, etc. The Fourier transform uses sine waves as components of the signal. Due to its excellent properties, the Fourier transform has a wide range of applications in physics, number theory, combinatorial mathematics, signal processing, probability, statistics, cryptography, acoustics, optics, and other fields. This paper focuses on the study of fractional-order Fourier transform in the engineering field, for the equipment of the tiny fault diagnosis method, and according to some existing diagnostic methods, put forward the idea of diagnostic method enhancement.
Keywords
fractional-order Fourier transform, tiny fault diagnosis
[1]. Ren L, Xu Z Y, Yan X Q. Single-sensor incipient fault detection [J]. IEEE Sensors Journal, 2011,11(9): 2102-2107.
[2]. Amar M, Gondal I, Wilson C. Vibration spectrum imaging: a novel bearing fault classification approach [J]. IEEE Transactions on Industrial Electronics, 2015, 62(1): 494-502.
[3]. Li B, Chow M Y, Tipsuwan Y, et al. Neural-network-based motor rolling bearing fault diagnosis[J]. IEEE Transactions on Industrial Electronics, 2000, 47(5): 1060-1069.
[4]. Demetriou M A, Polycarpou M M. Incipient fault diagnosis of dynamical systems using online approximators[J]. IEEE Transactions on Automatic Control, 1998, 43(11): 1612-1617.
[5]. Naderi M S, Gharehpetian G B, Abedi M, et al. Modeling and detection of transformer internal incipient fault during impulse test [J]. IEEE Transactions on Dielectrics and Electrical Insulation,2008, 15(1): 284-291
[6]. Huimin ZHAO, Zhiqiang ZHANG, Jianmin MEI, et al. Early fault diagnosis of transmission gears based on FRFT and LSTM[J]. Journal of Military Transportation Institute,2020,22(04):36-41.
[7]. Wu X. Open circuit fault diagnosis of inverter circuit based on fractional order Fourier transform and pattern recognition [D]. Nanjing University of Aeronautics and Astronautics,2013.
[8]. P. Zhang. Research on mechanical fault diagnosis method based on fractional order time-frequency analysis [D]. Nanchang aviation university,2017.
[9]. H. Luo, Y. R. Wang, J. Cui. A new method for fault feature extraction in analog circuits based on optimal fractional order Fourier transform[J]. Journal of Instrumentation, 2009, 30(05):997-1001.
[10]. Wiener N, Hermitian. Polynomials and Fourier Analysis [M]. Cambridge: Journal of Mathematics Physics, 1929: 70-73
[11]. Ozaktas H M, Arikan O, Kutay M A, et al. Digital Computation of the Fractional Fourier Transform [J]. IEEE Transactions on Signal Processing, 1996, 44(9): 2141-2150.
[12]. Xinghao, ZHAO, TAO R, Yue WANG, et al. A new method for fast computation of fractional-order Fourier transform[J]. Journal of Electronics,2007,35(6):1089-1093
[13]. Alghazzawi A, Lennox B. Monitoring a complex refifining process using multivariate statistics[J]. Control Engineering Practice, 2008, 16(3): 294-307.
[14]. Wang X, Kruger U, Irwin G W. Process monitoring approach using fast moving window pca [J]. Industrial & Engineering Chemistry Research, 2005, 44 (15): 5691-5702.
[15]. Zhao C, Wang F, Lu N, et al. Stage-based soft-transition multiple pca modeling and on-linemonitoring strategy for batch processes [J]. Journal of Process Control, 2007, 17(9): 728-741.
[16]. Kruger U, Chen Q, Sandoz D J, et al. Extended pls approach for enhanced condition monitoringof industrial processes [J]. AIChE Journal, 2001, 47(9): 2076-2091.
[17]. Morud T E. Multivariate statistical process control; example from the chemical process industry[J]. Journal of Chemometrics, 1996, 10(5-6): 669-675.
[18]. Zhang J, Zhao S J, Xu Y M. Performance monitoring of processes with multiple operating modesthrough multiple pls models [J]. Journal of Process Control, 2006, 16(7): 763-772.
[19]. Ge Z, Song Z. Process monitoring based on independent component analysis-principal component analysis (ica-pca) and similarity factors [J]. Industrial & Engineering Chemistry Research, 2007, 46(7): 2054-2063.
[20]. Lee J M, Qin S J, Lee I B. Fault detection and diagnosis based on modified independent component analysis [J]. AIChE Journal, 2006, 52(10): 3501-3514.
[21]. Liu X, Xie L, Kruger U, et al. Statistical-based monitoring of multivariate non-Gaussian systems [J]. AIChE Journal, 2008, 54(9): 2379-2391.
[22]. Mika S, Schölkopf B, Smola A J, et al. Kernel PCA and De-noising in feature spaces [C]. Proceedings of the 1998 Conference on Advances in Neural Information Processing Systems II, 1999(11): 536-542.
Cite this article
Lu,Y. (2024). Applications of Fourier transforms in engineering. Theoretical and Natural Science,43,26-32.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
Disclaimer/Publisher's Note
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
About volume
Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license. Authors who
publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons
Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this
series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published
version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial
publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and
during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See
Open access policy for details).