10,348 research outputs found
Estimation of Signal Coherence Threshold and Concealed Spectral Lines Applied to Detection of Turbofan Engine Combustion Noise
Combustion noise from turbofan engines has become important, as the noise from sources like the fan and jet are reduced. An aligned and un-aligned coherence technique has been developed to determine a threshold level for the coherence and thereby help to separate the coherent combustion noise source from other noise sources measured with far-field microphones. This method is compared with a statistics based coherence threshold estimation method. In addition, the un-aligned coherence procedure at the same time also reveals periodicities, spectral lines, and undamped sinusoids hidden by broadband turbofan engine noise. In calculating the coherence threshold using a statistical method, one may use either the number of independent records or a larger number corresponding to the number of overlapped records used to create the average. Using data from a turbofan engine and a simulation this paper shows that applying the Fisher z-transform to the un-aligned coherence can aid in making the proper selection of samples and produce a reasonable statistics based coherence threshold. Examples are presented showing that the underlying tonal and coherent broad band structure which is buried under random broadband noise and jet noise can be determined. The method also shows the possible presence of indirect combustion noise. Copyright 2011 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America
Aligned and Unaligned Coherence: A New Diagnostic Tool
The study of combustion noise from turbofan engines has become important again as the noise from other sources like the fan and jet are reduced. A method has been developed to help identify combustion noise spectra using an aligned and unaligned coherence technique. When used with the well known three signal coherent power method and coherent power method it provides new information by separating tonal information from random process information. Examples are presented showing the underlying tonal structure which is buried under broadband noise and jet noise. The method is applied to data from a Pratt and Whitney PW4098 turbofan engine
Maximum-likelihood estimation of lithospheric flexural rigidity, initial-loading fraction, and load correlation, under isotropy
Topography and gravity are geophysical fields whose joint statistical
structure derives from interface-loading processes modulated by the underlying
mechanics of isostatic and flexural compensation in the shallow lithosphere.
Under this dual statistical-mechanistic viewpoint an estimation problem can be
formulated where the knowns are topography and gravity and the principal
unknown the elastic flexural rigidity of the lithosphere. In the guise of an
equivalent "effective elastic thickness", this important, geographically
varying, structural parameter has been the subject of many interpretative
studies, but precisely how well it is known or how best it can be found from
the data, abundant nonetheless, has remained contentious and unresolved
throughout the last few decades of dedicated study. The popular methods whereby
admittance or coherence, both spectral measures of the relation between gravity
and topography, are inverted for the flexural rigidity, have revealed
themselves to have insufficient power to independently constrain both it and
the additional unknown initial-loading fraction and load-correlation fac- tors,
respectively. Solving this extremely ill-posed inversion problem leads to
non-uniqueness and is further complicated by practical considerations such as
the choice of regularizing data tapers to render the analysis sufficiently
selective both in the spatial and spectral domains. Here, we rewrite the
problem in a form amenable to maximum-likelihood estimation theory, which we
show yields unbiased, minimum-variance estimates of flexural rigidity,
initial-loading frac- tion and load correlation, each of those separably
resolved with little a posteriori correlation between their estimates. We are
also able to separately characterize the isotropic spectral shape of the
initial loading processes.Comment: 41 pages, 13 figures, accepted for publication by Geophysical Journal
Internationa
Validating Coherence Measurements Using Aligned and Unaligned Coherence Functions
This paper describes a novel approach based on the use of coherence functions and statistical theory for sensor validation in a harsh environment. By the use of aligned and unaligned coherence functions and statistical theory one can test for sensor degradation, total sensor failure or changes in the signal. This advanced diagnostic approach and the novel data processing methodology discussed provides a single number that conveys this information. This number as calculated with standard statistical procedures for comparing the means of two distributions is compared with results obtained using Yuen's robust statistical method to create confidence intervals. Examination of experimental data from Kulite pressure transducers mounted in a Pratt & Whitney PW4098 combustor using spectrum analysis methods on aligned and unaligned time histories has verified the effectiveness of the proposed method. All the procedures produce good results which demonstrates how robust the technique is
The statistical distribution of magnetotelluric apparent resistivity and phase
Author Posting. © The Authors, 2007. This article is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 171 (2007): 127-132, doi:10.1111/j.1365-246X.2007.03523.x.The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the GaussâMarkov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.This work was supported by NSF grant EAR0309584
Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals
There are three equivalent ways of representing two jointly observed
real-valued signals: as a bivariate vector signal, as a single complex-valued
signal, or as two analytic signals known as the rotary components. Each
representation has unique advantages depending on the system of interest and
the application goals. In this paper we provide a joint framework for all three
representations in the context of frequency-domain stochastic modeling. This
framework allows us to extend many established statistical procedures for
bivariate vector time series to complex-valued and rotary representations.
These include procedures for parametrically modeling signal coherence,
estimating model parameters using the Whittle likelihood, performing
semi-parametric modeling, and choosing between classes of nested models using
model choice. We also provide a new method of testing for impropriety in
complex-valued signals, which tests for noncircular or anisotropic second-order
statistical structure when the signal is represented in the complex plane.
Finally, we demonstrate the usefulness of our methodology in capturing the
anisotropic structure of signals observed from fluid dynamic simulations of
turbulence.Comment: To appear in IEEE Transactions on Signal Processin
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