Defining the wavelet bispectrum

Newman, Julian; Pidde, Aleksandra; Stefanovska, Aneta

doi:10.1016/j.acha.2020.10.005

Cited by 12 publications

(12 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bicoherence is a very useful process in higher order spectral analysis to examine nonlinearities found in time domain signals [30], which makes this analysis strategy suitable for extracting quadratic phase coupling present within a particular signal. The theoretical expression followed to obtain bicoherence estimation is as shown in the following equation [30]:…”

Section: Bicoherence Resultsmentioning

confidence: 99%

“…These two frequencies are linked together by a third frequency 𝑓3 with the relation expressed as: Whereas, the physical explanation of equation 10 concept is that 𝑓 1 is a frequency corresponding to an event in cylinder pressure signal, 𝑓 2 to a manifold pressure event, while 𝑓 3 is corresponding an event in crank speed signal. The negative frequencies shown in the bispectrum plots are the complex conjugate of their reflections [18,30].…”

Section: Higher Order Spectral Analysismentioning

confidence: 99%

See 1 more Smart Citation

Frequency Coupling Analysis in Spark Ignition Engine Using Bispectral Method and Ensemble Empirical Mode Decomposition

Yacoubi¹,

Samuel²

2022

SAE Technical Paper Series

View full text Add to dashboard Cite

Internal combustion (IC) engines are the current dominant power source used in the automotive industry for hybrid vehicles. The combustion process of IC engines involves various parameters, which are linked to the overall performance of the driveline. Therefore, finding the frequency coupling between the manifold pressure, incylinder pressure and output crankshaft speed will provide an insight into the reasons for torque fluctuations and its effect on driveline performance. The present work introduces a methodology to analyze cylinder pressure, manifold pressure and instantaneous crank speed signals measured from a 4 cylinder, 1.6 Litre, Gasoline Direct Injection Engine at different speed conditions to identify the frequency coupling between these signals. This work uses Ensemble Empirical Mode Decomposition (EEMD) as a de-noising method and Bispectral analysis for examining the presence of a frequency coupling from the signals. This paper will demonstrate a systematic approach followed for employing EEMD and Bispectral analysis in a GDI engine for deriving frequency coupling details and its significance.

show abstract

Section: Bicoherence Resultsmentioning

confidence: 99%

Section: Higher Order Spectral Analysismentioning

confidence: 99%

Frequency Coupling Analysis in Spark Ignition Engine Using Bispectral Method and Ensemble Empirical Mode Decomposition

Yacoubi¹,

Samuel²

2022

SAE Technical Paper Series

View full text Add to dashboard Cite

show abstract

“…For the Morlet wavelet, the relation between the parameter σ and the frequency and time localization accuracy is known [399]:…”

Section: Decomposition Of Signals Into Components By Frequencymentioning

confidence: 99%

“…The Morlet wavelet is excellent for use in multi-signal interconnection techniques, such as the wavelet coherence technique [400][401][402] and bispectral analysis using wavelets [399,403], since, in these methods, the key criterion for the relationship between signals is the preservation of the relative phase shift of the oscillations. The disadvantages of the Morlet wavelet include the significant computational costs required for its calculation on discrete data series and the inconvenient form of the frequency response [128].…”

Section: Decomposition Of Signals Into Components By Frequencymentioning

confidence: 99%

Application of Spectral Methods of Analysis for Description of Ultradian Biorhythms at the Levels of Physiological Systems, Cells and Molecules (Review)

2023

View full text Add to dashboard Cite

The presence of biological rhythms is a characteristic of all living organisms. Over the past 60 years, scientists around the world have accumulated a huge amount of data on rhythmic processes in living systems at various levels. The acquired knowledge has found applications in human economic activity and medicine. The ultradian (less than a day) rhythms at the organismal, organ, and cellular levels are characterized by high diversity. Unfortunately, biorhythms in different systems are considered, most often, in isolation from each other. Much knowledge about biorhythms was obtained using expert evaluation methods, and later methods of spectral analysis were used to describe biorhythms. Ultradian rhythms have a relatively short duration; therefore, they can be characterized by spectral analysis methods. More and more researchers believe that in order to further expand the understanding of the nature and purpose of biorhythms, the use of more advanced methods of mathematical processing is required, and rhythms in different organs, tissues, and cells should be considered parts of a single system. This review is intended to provide the reader with the variety of ultradian rhythms in living systems (organismal, organ, cellular, molecular levels), the mechanisms of their generation, and their functions to give the reader a picture of the possible relationships between these rhythms. Further, the reader will be able to get acquainted with the variety of mathematical methods for analyzing biorhythms, including bispectral and cross-correlation analyses.

show abstract

“…It performs step-by-step multiscale refinement of the signal through scaling and translation operations, and finally realizes time subdivision at high frequencies and frequency subdivision at low frequencies. It can also automatically adapt to the requirements of time-frequency signal analysis, thereby focusing on any details of the signal (Newman et al, 2021). In recent years, wavelet transform theory has been gradually applied to wave analysis.…”

Section: Introductionmentioning

confidence: 99%

Experimental study on the effect of an oyster reef on the nonlinear characteristics of irregular waves

et al. 2022

View full text Add to dashboard Cite

As a “marine ecological engineer”, the oyster reefs not only perform important ecological functions, but also reduce the damage caused by waves to protective structures such as seawalls. However, oyster reefs in shallow water change the nonlinear characteristics of waves and affect sediment transport and coastal evolution. Based on Fourier spectrum and analysis of Wavelet Transform, the influence of artificial bag oyster reefs on the energy and nonlinear phase coupling of irregular waves are studied through physical experiment. The results show that oyster reefs have a substantial effect on the energy of primary harmonic, which transfer to higher harmonics through triad interactions, and a considerable reduction in primary harmonic energy and an increase in higher harmonics energy are reflected in the energy spectra. The transmission spectrum behind the oyster reefs shows three peaks at primary, secondary and third harmonics. The bicoherence spectrum indicates that the peaks at secondary and third harmonics mainly result from the self-coupling of the primary harmonics and phase coupling between the primary and secondary harmonics respectively. As the water depth increases, the degree of nonlinear coupling between wave components decreases, which leads to the energy of wave components at different frequencies increases. With increasing top width, the length of the shoaling region increases, and the growth of triad nonlinear interactions are observed in wavelet-based bicoherence spectra, resulting in the spectral peak energy decreasing while the secondary harmonics energy increasing in the spectrum. Finally, the potential application of an ecological system composed by “oyster reefs + mangroves” is discussed. As the effect of water depth on wave energy is much greater than that of top width, in artificial oyster reef construction, it is recommended that keep the oyster reefs non-submerged in terms of wave dissipation. Further studies should take the dynamic growth effect of oyster reefs into account.

show abstract

Defining the wavelet bispectrum

Cited by 12 publications

References 57 publications

Frequency Coupling Analysis in Spark Ignition Engine Using Bispectral Method and Ensemble Empirical Mode Decomposition

Frequency Coupling Analysis in Spark Ignition Engine Using Bispectral Method and Ensemble Empirical Mode Decomposition

Application of Spectral Methods of Analysis for Description of Ultradian Biorhythms at the Levels of Physiological Systems, Cells and Molecules (Review)

Experimental study on the effect of an oyster reef on the nonlinear characteristics of irregular waves

Contact Info

Product

Resources

About