Fourier decomposition of sharply peaked phase functions: Legendre expansions versus trapezoidal rule

2009 ◽  
Author(s):  
Alain Sei
Keyword(s):  
Trapezoidal Rule ◽  
Fourier Decomposition ◽  
Phase Functions

Vibration analysis and combustion parameter evaluation of CI engine based on Fourier Decomposition Method

2021 ◽  
pp. 146808742098819
Author(s):  
Wang Yang ◽  
Cheng Yong
Keyword(s):  
Vibration Analysis ◽  
Decomposition Method ◽  
Combustion Process ◽  
Pressure Rise ◽  
Maximum Pressure ◽  
Vibration Signals ◽  
Loop Control ◽  
Fourier Decomposition ◽  
Surface Vibration ◽  
Rise Rate

As a non-intrusive method for engine working condition detection, the engine surface vibration contains rich information about the combustion process and has great potential for the closed-loop control of engines. However, the measured engine surface vibration signals are usually induced by combustion as well as non-combustion excitations and are difficult to be utilized directly. To evaluate some combustion parameters from engine surface vibration, the tests were carried out on a single-cylinder diesel engine and a new method called Fourier Decomposition Method (FDM) was used to extract combustion induced vibration. Simulated and test results verified the ability of the FDM for engine vibration analysis. Based on the extracted vibration signals, the methods for identifying start of combustion, location of maximum pressure rise rate, and location of peak pressure were proposed. The cycle-by-cycle analysis of the results show that the parameters identified based on vibration and in-cylinder pressure have the similar trends, and it suggests that the proposed FDM-based methods can be used for extracting combustion induced vibrations and identifying the combustion parameters.

Adaptive power spectrum Fourier decomposition method with application in fault diagnosis for rolling bearing

Measurement ◽  
2021 ◽  
pp. 109837
Author(s):  
Jinde Zheng ◽  
Siqi Huang ◽  
Haiyang Pan ◽  
Jinyu Tong ◽  
Chengjun Wang ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Power Spectrum ◽  
Decomposition Method ◽  
Rolling Bearing ◽  
Fourier Decomposition ◽  
Adaptive Power

Optimal Signal Extraction with Correlated Components

2014 ◽  
Vol 6 (2) ◽  
pp. 237-273 ◽  
Author(s):  
Tucker S. McElroy ◽  
Agustin Maravall
Keyword(s):  
Signal Extraction ◽  
Economic Time Series ◽  
Systematic Treatment ◽  
Finite Samples ◽  
Economic Time ◽  
The Mean ◽  
Phase Functions ◽  
Component Models ◽  
Correlated Components ◽  
Optimal Signal

AbstractWhile it is typical in the econometric signal extraction literature to assume that the unobserved signal and noise components are uncorrelated, there is nevertheless an interest among econometricians in the hypothesis of hysteresis, i.e. that major movements in the economy are fundamentally linked. While specific models involving correlated signal and noise innovation sequences have been developed and applied using state space methods, there is no systematic treatment of optimal signal extraction with correlated components. This paper provides the mean square error optimal formulas for both finite samples and bi-infinite samples and furthermore relates these filters to the more well-known Wiener–Kolmogorov (WK) and Beveridge–Nelson (BN) signal extraction formulas in the case of ARIMA component models. Then we obtain the result that the optimal filter for correlated components can be viewed as a weighted linear combination of the WK and BN filters. The gain and phase functions of the resulting filters are plotted for some standard cases. Some discussion of estimation of hysteretic models is presented, along with empirical results on an economic time series. Comparisons are made between signal extractions from traditional WK filters and those arising from the hysteretic models.

scholarly journals On the scattering behaviour of bullet-rosette and bullet-shaped ice crystals

1996 ◽  
Vol 14 (5) ◽  
pp. 566-573
Author(s):  
B. Strauss
Keyword(s):  
Ray Tracing ◽  
Ice Crystals ◽  
Asymmetry Factor ◽  
Model Calculations ◽  
Geometrical Features ◽  
The Asymmetry ◽  
Particle Length ◽  
Phase Functions ◽  
Tracing Method ◽  
Factor G

Abstract. The scattering behaviour of bullet-rosette and bullet-shaped ice particles is investigated using model calculations (ray tracing method) with special emphasis on the asymmetry factor g. Because the variability of the geometrical features of these particles is very large, some representative shapes are used in the calculations. The model is based on geometrical optics, and particles are assumed to be oriented randomly; a wavelength of 0.56 μm is considered; absorption is neglected. The scattering behaviour of bullet rosettes is compared to that of single branches out of the bullet rosette. It turns out that there are slight differences in the asymmetry factor values, depending on the lengths of the branches (∆g~0.02) and on the angles between the branches (∆g~0.01). Bullets show some special features in their phase functions due to the pyramid. The length of the particle influences the asymmetry factor (∆g~0.10), as does the shape of the pyramid (∆g~0.07). The influence of the pyramidal shape decreases with increasing particle length. Bullets were compared to hexagonally shaped columns. This was done for two columns, one as long as the columnar part of the bullet (length without pyramid), and one for a column as long as the bullet including the pyramid. Asymmetry factor values of bullets with a pyramidal angle of 28° deviate less than ∆g~0.01 from the range given by the two values of the columns.

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