Penalized Whittle-Likelihood Estimates of Spectral Density

A method has been developed for converting a discrete sequence of extrema into a continuous process. The relevancy of the problem is attributed to the necessity of an approximate estimation of spectral density in in testing materials and structures under random (irregular) loading. A great bulk of available experimental data thus can be used in development and validation of calculation methods for assessing durability in the multi-cycle region. Postulating the continuity of random stress processes and their first derivative we propose to connect piecewise the available starting points (namely, the extrema of the random process) with half-cosine functions under the condition of compatibility at the points of extrema. A distinctive feature of the method is the provision of 100% coincidence of the values and sequences of extrema in the initial discrete and simulated continuous processes. The issue of choosing the magnitude of half-periods for these half-cosine functions is addressed on the basis of information obtained from the analysis of real stress records in the form of a regression equation linking half-periods and half-ranges for some realizations of the random process for transport vehicles. The regression dependences of the half-periods and semi-ranges of bending stresses (part of a railway train) and torsion (torsion shaft of a tracked vehicle) are shown as an example. An analysis of the correlation of two random variables (half-periods and half-ranges) according to empirical data has shown that the correlation exists and is significant for the observed number of points thus providing the basis for using the regression formula for an approximate choice of the frequency composition of the process. Moreover, the lower restrictions are imposed on the number of points (at least 5) in the half-period. Since the extrema of the initial and simulated processes coincide in accordance with the principle of the proposed simulation, the distribution of the amplitudes of complete cycles, as well as the results of schematization by other known methods are identical, therefore, the estimate of the durability by hypotheses based on a linear one is also identical. The validation of the method consists in consideration of the chain: 1) the initial continuous process; 2) the discrete process of extrema; 3) simulated continuous process according to the proposed method. Auxiliary distributions, such as distributions of maximum, minimum and average cycle values also coincide in accordance with the principle of modeling. The method is proposed to be used in analysis of the comparability of two competing approaches in assessing the loading in the problems of assessing durability, namely: those that use cycle-counting methods and methods based on the spectral density of processes. Since the spectral densities of the processes can differ due to an approximate choice of the frequencies on the basis of a regression formula, methods on their base can give estimates of the durability that differ from those obtained by schematization methods. To study this phenomenon, further computational experiments are required. The developed method can be very useful for the experiment design.

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Fuzzy Modeling of Multi-Degree-of-Freedom Power Spectral Density Systems

Recent Patents on Mechanical Engineering ◽

10.2174/2212797610902010040 ◽

2009 ◽

Vol 2 (1) ◽

pp. 40-47

Author(s):

Montasser Tahat ◽

Hussien Al-Wedyan ◽

Kudret Demirli ◽

Saad Mutasher

Keyword(s):

Spectral Density ◽

Power Spectral Density ◽

Fuzzy Modeling ◽

Degree Of Freedom ◽

Power Spectral

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Power spectral density of on-off sources

Electronics Letters ◽

10.1049/el:19970417 ◽

1997 ◽

Vol 33 (7) ◽

pp. 559 ◽

Cited By ~ 2

Author(s):

K. Laevens

Keyword(s):

Spectral Density ◽

Power Spectral Density ◽

Power Spectral

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Research on Supply and Demand of Xi'an Real Estate Market

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.368-373.3078 ◽

2011 ◽

Vol 368-373 ◽

pp. 3078-3082

Author(s):

Zhou Ji Meng ◽

Tao Zhou ◽

Shu Hua Gao

Keyword(s):

Principal Component Analysis ◽

Spectral Analysis ◽

Real Estate ◽

Spectral Density ◽

Supply And Demand ◽

Principal Component ◽

Real Estate Market ◽

Medium Term ◽

Real Estate Price ◽

Synthetic Indicators

In the passage, the indicators of supply and demand of real estate market in Xi'an are established, and such indicators are synthesized into a class of synthetic indicators using “principal component analysis”. After the spectral analysis of synthetic indicators, periodic change of supply and demand of real estate through spectral density could be determined. Through the analysis, great randomness existed in supply and demand of real estate in Xi’an. Furthermore, in the medium term, a 3.3 years’ secondary cycle still existed in synthetic indicators of demand, while randomness existed in synthetic indicators of supply. Such findings suggest a declined trend existed in real estate price in medium term of Xi’an.

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