Detection of engine misfire using characteristic harmonics of angular acceleration

2019 ◽  
Vol 233 (14) ◽  
pp. 3816-3823
Author(s):  
Qixin Song ◽  
Wenzhi Gao ◽  
Pan Zhang ◽  
Jiankang Liu ◽  
Ziqing Wei
Keyword(s):  
Fourier Transform ◽  
Diesel Engine ◽  
Discrete Fourier Transform ◽  
Torsional Vibration ◽  
Fourier Transforms ◽  
Angular Acceleration ◽  
Operating Conditions ◽  
Discrete Fourier Transforms

A new torsional vibration–based method for the detection of engine misfires was proposed based on the discrete Fourier transform of angular acceleration of the crankshaft. By analysis of the sensitivity of the discrete Fourier transform to fluctuations in speed and load of the engine, the characteristic harmonics and characteristic discrete Fourier transforms of a cylinder were defined. Then cylinder misfires under any operating conditions were diagnosed by checking the characteristic discrete Fourier transforms of the cylinder at its characteristic harmonics. An experiment on a four-stroke, six-cylinder diesel engine showed that this method accurately identified misfire faults and the misfiring cylinders.

scholarly journals More on algebraic properties of the discrete Fourier transform raising and lowering operators

4open ◽  
2019 ◽  
Vol 2 ◽  
pp. 2 ◽  
Author(s):  
Mesuma K. Atakishiyeva ◽  
Natig M. Atakishiyev ◽  
Juan Loreto-Hernández
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Fourier Transforms ◽  
Difference Operators ◽  
Discrete Fourier Transforms ◽  
Raising And Lowering Operators ◽  
Integral Fourier Transform ◽  
Symmetrical Form ◽  
Algebraic Properties ◽  
Lowering Operators

In the present work, we discuss some additional findings concerning algebraic properties of the N-dimensional discrete Fourier transform (DFT) raising and lowering difference operators, recently introduced in [Atakishiyeva MK, Atakishiyev NM (2015), J Phys: Conf Ser 597, 012012; Atakishiyeva MK, Atakishiyev NM (2016), Adv Dyn Syst Appl 11, 81–92]. In particular, we argue that the most authentic symmetrical form of discretization of the integral Fourier transform may be constructed as the discrete Fourier transforms based on the odd points N only, while in the discrete Fourier transforms on the even points N this symmetry is spontaneously broken. This heretofore undetected distinction between odd and even dimensions is shown to be intimately related with the newly revealed algebraic properties of the above-mentioned DFT raising and lowering difference operators and, of course, is very consistent with the well-known formula for the multiplicities of the eigenvalues, associated with the N-dimensional DFT. In addition, we propose a general approach to deriving the eigenvectors of the discrete number operators N(N), that avoids the above-mentioned pitfalls in the structure of each even-dimensional case N = 2L.

scholarly journals Theoretical foundations of digital vector Fourier analysis of two-dimensional signals padded with zero samples

2021 ◽  
pp. 55-65
Author(s):  
Olga Ponomareva ◽  
Aleksey Ponomarev
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Discrete Fourier Transform ◽  
Fourier Transforms ◽  
Information Control ◽  
Two Dimensional ◽  
Negative Effects ◽  
Variable Parameters ◽  
Discrete Fourier Transforms ◽  
Fourier Matrix

Introduction: The practice of using Fourier-processing of finite two-dimensional signals (including images), having confirmed its effectiveness, revealed a number of negative effects inherent in it. A well-known method of dealing with negative effects of Fourier-processing is padding signals with zeros. However, the use of this operation leads to the need to provide information control systems with additional memory and perform unproductive calculations. Purpose: To develop new discrete Fourier transforms for efficient and effective processing of two-dimensional signals padded with zero samples. Method: We have proposed a new method for splitting a rectangular discrete Fourier transform matrix into square matrices. The method is based on the application of the modulus comparability relation to order the rows (columns) of the Fourier matrix. Results: New discrete Fourier transforms with variable parameters were developed, being a generalization of the classical discrete Fourier transform. The article investigates the properties of Fourier transform bases with variable parameters. In respect to these transforms, the validity has been proved for the theorems of linearity, shift, correlation and Parseval's equality. In the digital spectral Fourier analysis, the concepts of a parametric shift of a two-dimensional signal, and a parametric periodicity of a two-dimensional signal have been introduced. We have estimated the reduction of the required memory size and the number of calculations when applying the proposed transforms, and compared them with the discrete Fourier transform. Practical relevance: The developed discrete Fourier transforms with variable parameters can significantly reduce the cost of Fourier processing of two-dimensional signals (including images) padded with zeros.

scholarly journals There Is Only One Fourier Transform

2017 ◽  
Author(s):  
Jens V. Fischer
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Fourier Transforms ◽  
Periodic Functions ◽  
Distributional Sense ◽  
Integral Fourier Transform ◽  
The Fourier Transform

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributional sense.

scholarly journals Color image watermarking using multidimensional Fourier transforms

2021 ◽  
Author(s):  
Tsz Kin Tsui
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Fourier Transforms ◽  
Color Image ◽  
Image Watermarking ◽  
Color Image Watermarking ◽  
Quaternion Fourier Transform ◽  
Just Noticeable Distortion ◽  
Human Eyes

This thesis presents two vector watermarking schemes that are based on the use of complex and quaternion Fourier transforms and demonstrates, for the first time, how to embed watermarks into the coefficients consistent with our human visual systems (HVS). Watermark casting is performed by estimating the Just-Noticeable distortion (JND) of the images, to ensure watermark invisibility. The first method encodes the chromatic content of a color image as CIE a*b* chromaticity coordinates whereas the achromatic content is encoded as CIE L tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using Spatio Chromatic Discrete Fourier Transform (SCDFT). It first encodes a* and b* as complex values, followed by a single discrete Fourier Transform. The most interesting characteristic of the scheme is the possibility of performing watermarking in the frequency domain of chromatic components. The second method encodes the L*a*b* components of color images and color watermarks are embedded as vectors in the frequency domain of the channels by using the Quaternion Fourier Transform (QFT). The idea is twofold: Robustness is achieved by embedding a color watermark in the coefficient with positive frequency, which spreads it to all components in the spatial domain. On the other hand, invisibility is satisfied by modifying the coefficient with negative frequency, such that the combined effects of the two are insensitive to human eyes

scholarly journals Color image watermarking using multidimensional Fourier transforms

2021 ◽  
Author(s):  
Tsz Kin Tsui
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Discrete Fourier Transform ◽  
Fourier Transforms ◽  
Color Image ◽  
Image Watermarking ◽  
Color Image Watermarking ◽  
Quaternion Fourier Transform ◽  
Just Noticeable Distortion ◽  
Human Eyes

This thesis presents two vector watermarking schemes that are based on the use of complex and quaternion Fourier transforms and demonstrates, for the first time, how to embed watermarks into the coefficients consistent with our human visual systems (HVS). Watermark casting is performed by estimating the Just-Noticeable distortion (JND) of the images, to ensure watermark invisibility. The first method encodes the chromatic content of a color image as CIE a*b* chromaticity coordinates whereas the achromatic content is encoded as CIE L tristimulus value. Color watermarks (yellow and blue) are embedded in the frequency domain of the chromatic channels by using Spatio Chromatic Discrete Fourier Transform (SCDFT). It first encodes a* and b* as complex values, followed by a single discrete Fourier Transform. The most interesting characteristic of the scheme is the possibility of performing watermarking in the frequency domain of chromatic components. The second method encodes the L*a*b* components of color images and color watermarks are embedded as vectors in the frequency domain of the channels by using the Quaternion Fourier Transform (QFT). The idea is twofold: Robustness is achieved by embedding a color watermark in the coefficient with positive frequency, which spreads it to all components in the spatial domain. On the other hand, invisibility is satisfied by modifying the coefficient with negative frequency, such that the combined effects of the two are insensitive to human eyes

scholarly journals Four Particular Cases of the Fourier Transform

2018 ◽  
Author(s):  
Jens V. Fischer
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Fourier Transforms ◽  
Summation Formula ◽  
Periodic Functions ◽  
Tempered Distributions ◽  
Integral Fourier Transform ◽  
The Fourier Transform

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

scholarly journals Fast Fourier transform-based micromechanics of interfacial line defects in crystalline materials

2018 ◽  
Vol 03 (03n04) ◽  
pp. 1840007
Author(s):  
Stéphane Berbenni ◽  
Vincent Taupin
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Heterogeneous Media ◽  
Fourier Transforms ◽  
Type Equation ◽  
Critical Question ◽  
Present Contribution ◽  
Simultaneous Treatment ◽  
Discrete Fourier Transforms ◽  
Elastic Fields

Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics community. The present contribution addresses the critical question of determining local mechanical fields using the FFT method in the presence of interfacial defects. Precisely, the present work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of disclinations, i.e., rotational discontinuities, and inhomogeneities. A centered finite difference scheme for differential rules are first used for numerically solving the Poisson-type equations in the Fourier space to get the incompatible elastic fields due to disclinations and dislocations. Second, centered finite differences on a rotated grid are chosen for the computation of the modified Fourier-Green’s operator in the Lippmann–Schwinger–Dyson type equation for heterogeneous media. Elastic fields of disclination dipole distributions interacting with inhomogeneities of varying stiffnesses, grain boundaries seen as DSUM (Disclination Structural Unit Model), grain boundary disconnection defects and phase boundary “terraces” in anisotropic bi-materials are numerically computed as applications of the method.

Transient Synthesis Using a Fourier Transform Envelope: An Alternative to Swept-Sine Vibration Testing

1996 ◽  
Vol 39 (5) ◽  
pp. 17-22
Author(s):  
M. Hine
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Inverse Fourier Transform ◽  
Operating Conditions ◽  
Inverse Transformation ◽  
Vibration Test ◽  
Frequency Content ◽  
Structural Components ◽  
Test Program ◽  
Transient Vibration

Transient vibration test offer an alternative to the conventional swept-sine vibration test, with controllable conservatism. A method of deriving a single vibration test transient from several spacecraft flight transients is described. These transients were from different physical locations on the spacecraft. The test transient was derived by taking the inverse Fourier transform of an envelope of the Fourier transforms of the flight transients. The inverse transformation was performed using the real and imaginary parts of that Fourier transform forming the envelope amplitude at each frequency. The test transient therefore has the same frequency content and maximum amplitudes as the flight transients. A generic test transient was therefore produced that duplicates many operating conditions at separate physical locations. It could be applied to many different structural components of a spacecraft, simplifying a vibration test program. The transient vibration test produces significantly less overtest than a conventional swept-sine vibration test.

Probabilistic Torsional Vibration Analysis of a Motor Ship Propulsion Shafting System: The Input-Output Problem

1987 ◽  
Vol 31 (01) ◽  
pp. 41-52
Author(s):  
Efstratios Nikolaidis ◽  
Anastassios N. Perakis ◽  
Michael G. Parsons
Keyword(s):  
Fourier Transform ◽  
Diesel Engine ◽  
Torsional Vibration ◽  
Vibration Analysis ◽  
Linear Time ◽  
Probabilistic Approach ◽  
Statistical Properties ◽  
Input Output ◽  
Double Fourier Transform ◽  
Torsional Excitation

A probabilistic approach to the torsional vibration analysis of a marine diesel engine propulsion shafting system is developed. The diesel engine and propeller torsional excitation are modeled probabilistically. The statistical properties of the resulting torsional vibratory shear stress in each element of the shafting system are determined by solving the corresponding input-output problem. The shafting system is considered as a multi-input linear system with the propeller and the cylinder torsional excitation as inputs and the torsional vibratory stress as the output. Under the assumption that the nonresonant torsional vibratory stresses are negligible compared with those in resonance, the input-output problem reduces to determining the statistical properties of the output of a multi-input, linear, time-invariant system driven by Gaussian amplitude modulated (AM) processes with equal carrier frequencies. The problem is solved in its general form by deriving an expression relating the double Fourier transform of the output autocorrelation function with the double Fourier transform of the input autocorrelation and cross-correlation functions. The probabilistic approach is applied to calculate the stress statistics in each shafting element of existing low-speed and medium-speed diesel engine propulsion shafting systems.

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