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Study of techniques for all random process technology, including stationary, nonstationary, and Gaussian bivariate, aids digital data processing. It presents material on digital filtering, correlation function, optimal spectral smoothing, deterministic data processing, and nonstationary spectrum and correlation analyses.
Several random process models in the time domain are defined and discussed. Attention is given to the moving average model, the autoregressive model, and relationships between and combinations of these models. Consideration is then given to methods for investigating pulse structure, procedures of model construction, computational methods, and numerical experiments. A FORTRAN algorithm of time series analysis has been developed which is relatively stable numerically. Results of test cases are given to study the effect of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the light curve of the quasar 3C 272 is considered as an example.
Message estimation of sample function from continuous Gaussian random process, establishing and evaluating optimal bounds for procedure
Statistics of distribution of rises and falls in continuous random process, with application to gaussian processes
Statistics of distribution of rises and falls in continuous random process, with application to Gaussian processes
A simulation technique is described which directly synthesizes the extrema of a random process and is more efficient than the Gaussian simulation method. Such a technique is particularly useful in stochastic fatigue analysis because the required stress range moment E(R sup m), is a function only of the extrema of the random stress process. The family of autoregressive moving average (ARMA) models is reviewed and an autoregressive model is presented for modeling the extrema of any random process which has a unimodal power spectral density (psd). The proposed autoregressive technique is found to produce rainflow stress range moments which compare favorably with those computed by the Gaussian technique and to average 11.7 times faster than the Gaussian technique. The autoregressive technique is also adapted for processes having bimodal psd's. The adaptation involves using two autoregressive processes to simulate the extrema due to each mode and the superposition of these two extrema sequences. The proposed autoregressive superposition technique is 9 to 13 times faster than the Gaussian technique and produces comparable values for E(R sup m) for bimodal psd's having the frequency of one mode at least 2.5 times that of the other mode.
Stationarity conditions for a certain periodic random process
Algorithm applied to specific classes of random processes for calculating minimum channel capacity required by transmission system for sources in each class
Nonstationary random processes in nonreal-time applications - theories for nonreal-time correlation and spectrum analysis
Analog computer method for approximating stationary Gaussian random process depending only on position parameter
Random processes, filtering, and telemetry problems in space communications theory
Random process models provide a useful mathematical framework for analysis of the quasi-periodic oscillations (QPO) recently discovered in the X-ray emission from certain luminous Galactic X-ray stars. In this paper, consideration is given to the effects of the power spectrum of the decay of the amplitude of oscillation that is expected in some physical models for the QPO phenomena. The resulting changes in the power spectrum depend on the ratio of the decay time of the amplitude of oscillation to the lifetime of the shot envelope. For values of this ratio less than about 10, it is found that incoherent QPO peaks in the power spectrum are significantly reduced in height and total power and are broadened in width, making them more difficult to detect. Coherent terms in the power spectrum, if present, are reduced in height and total power, but their width is unaffected. The red noise component remains unchanged. The present results are applied to the beat-frequency modulated accretion model in order to set constraints on the physical properties of the boundary layer between the inner edge of the accretion disk and the neutron star magnetosphere.
A probability model of random processes is used to calculate the probability characteristics which exist in the random problem of vibroacoustic processes in machine operations.
Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al 0.5 CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.
This paper describes and illustrates two ways of performing time-correlated gust-load calculations. The first is based on Matched Filter Theory; the second on Random Process Theory. The two yield theoretically identical results and both employ novel applications of the theories and unconventional interpretations of the intermediate and final results. Both approaches are computationally fast and are general enough to be applied to dynamic-response problems other than gust loads. A brief mathematical development and example calculations using both Matched Filter Theory and Random Process Theory are presented.
Statistical distribution of first occurrence and recurrence of crossing of given level in continuous random process determined, using approximate forms and exponential distribution
Two ways of performing time-correlated gust-load calculations are described and illustrated. The first is based on Matched Filter Theory; the second on Random Process Theory. Both approaches yield theoretically identical results and represent novel applications of the theories, are computationally fast, and may be applied to other dynamic-response problems. A theoretical development and example calculations using both Matched Filter Theory and Random Process Theory approaches are presented.
Statistical probability distribution of first occurrence and first recurrence times of given level crossing in continuous random process