The spectral analysis of impulse processes.
Impulse processes relative to random sampling of random processes, deriving expression for spectral density
Beutler, F. J.↗
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Random loading fatigue crack growth: Crack closure considerations
The prediction of fatigue crack growth is an important element of effective fracture control for metallic structures and mechanical components, especially in the aerospace industry. The prediction techniques available and applied today are mostly based on fatigue crack growth measurements determined in constant amplitude testing. However, while many service loadings are constant amplitude, many more loadings are random amplitude. An investigation to determine which statistics of random loadings are relevant to fatigue crack closure was conducted. The fundamentals of random processes and crack closure are briefly reviewed, then the relevance of certain random process parameters to the crack closure calculation are discussed qualitatively. A course for further research is outlined.
Ortiz, Keith↗
Square-root algorithm for evaluating mismodeled process noise
As the application of sequential filters has grown, the need has arisen to evaluate the sensitivity of these filters to mismodeling of the random process. A numerically reliable square-root algorithm is developed for calculating the covariances of estimates from a sequential filter which incorrectly models process noise. Mismodeling is restricted to the correlation time and standard deviation of a random process represented as a first-order Gauss-Markov sequence. Using a computer program which employs this algorithm, a sensitivity analysis was performed for several types of earth-based tracking data from an interplanetary spacecraft.
Thornton, C. L.↗
Three-level sampler having automated thresholds
A three-level sampler is described that has its thresholds controlled automatically so as to track changes in the statistics of the random process being sampled. In particular, the mean value is removed and the ratio of the standard deviation of the random process to the threshold is maintained constant. The system is configured in such a manner that slow drifts in the level comparators and digital-to-analog converters are also removed. The ratio of the standard deviation to threshold level may be chosen within the constraints of the ratios of two integers N and M. These may be chosen to minimize the quantizing noise of the sampled process.
Jurgens, R. F.↗
The human as a detector of changes in variance and bandwidth
The detection of changes in random process variance and bandwidth was studied. Psychophysical thresholds for these two parameters were determined using an adaptive staircase technique for second order random processes at two nominal periods (1 and 3 seconds) and damping ratios (0.2 and 0.707). Thresholds for bandwidth changes were approximately 9% of nominal except for the (3sec,0.2) process which yielded thresholds of 12%. Variance thresholds averaged 17% of nominal except for the (3sec,0.2) process in which they were 32%. Detection times for suprathreshold changes in the parameters may be roughly described by the changes in RMS velocity of the process. A more complex model is presented which consists of a Kalman filter designed for the nominal process using velocity as the input, and a modified Wald sequential test for changes in the variance of the residual. The model predictions agree moderately well with the experimental data. Models using heuristics, e.g. level crossing counters, were also examined and are found to be descriptive but do not afford the unification of the Kalman filter/sequential test model used for changes in mean.
Curry, R. E.↗
Generalizations and extensions of the Fokker- Planck-Kolmogorov equations.
Fokker-Planck-Kolmogoroff equations extended to cover conditional probability density functions of arbitrary random processes
RANDOM PROCESS↗
Optimal estimation for discrete time jump processes
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.
Vaca, M. V.↗
Optimal estimation for discrete time jump processes
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.
Vaca, M. V.↗
The Need for more Measurements in the ACTS Propagation Experiment
Attenuation by rain at frequencies above 10 GHz is a random process. The observed cumulative distribution of the time in a month or year an attenuation value is exceeded is a realization of the results of this random process. The distribution observed in one year may be a poor predictor of the distribution to be observed in the next year. Existing models are based on the extremely limited set of attenuation data that is available from more than a few years of observation on single, fixed propagation paths. The goal of the NASA Advanced Communication Technology Satellite (ACTS) propagation experiment is to expand the data base on which new attenuation prediction models can be developed or old models can be validated.
Crane, R. K.↗
Long-term persistence of solar activity
We examine the question of whether or not the non-periodic variations in solar activity are caused by a white-noise, random process. The Hurst exponent, which characterizes the persistence of a time series, is evaluated for the series of C-14 data for the time interval from about 6000 BC to 1950 AD. We find a constant Hurst exponent, suggesting that solar activity in the frequency range from 100 to 3000 years includes an important continuum component in addition to the well-known periodic variations. The value we calculate, H approximately 0.8, is significantly larger than the value of 0.5 that would correspond to variations produced by a white-noise process. This value is in good agreement with the results for the monthly sunspot data reported elsewhere, indicating that the physics that produces the continuum is a correlated random process and that it is the same type of process over a wide range of time interval lengths.
Ruzmaikin, Alexander↗
A chaotic attractor in timing noise from the Vela pulsar?
Fourteen years of timing residual data from the Vela pulsar have been analyzed in order to determine if a chaotic dynamical process is the origin of timing noise. Using the correlation sum technique, a dimension of about 1.5 is obtained. This low dimension indicates underlying structure in the phase residuals which may be evidence for a chaotic attractor. It is therefore possible that nonlinear dynamics intrinsic to the spin-down may be the cause of the timing noise in the Vela pulsar. However, it has been found that the stimulated random walks in frequency and frequency derivative often used to model pulsar timing noise also have low fractal dimension, using the same analysis technique. Recent work suggesting that random processes with steep power spectra can mimic strange attractors seems to be confirmed in the case of these random walks. It appears that the correlation sum estimator for dimension is unable to distinguish between chaotic and random processes.
Harding, Alice K.↗
Power spectra of quasi-periodic oscillations in luminous X-ray stars
A variety of partial random processes are considered in order to study the effects on the power-density spectrum of several physical phenomena that may occur in the beat-frequency modulated accretion (BFMA) model of QPOs. The relevant physical properties of BFMA model are summarized, and the class of random processes used to represent the X-ray intensity time series predicted by the model are introduced. The dependence of the power-density spectrum on pulse shape is discussed. Pulse-lifetime and orbital-frequency distributions are introduced, illustrating how these affect the power-density spectrum. The effect of nonuniform initial-pulse phase distributions and of nonuniform pulse-time distributions are considered. The effects of a particular type of pulse-to-pulse correlation that may be natural in the context of the BFMA model and that greatly increases the power of the oscillations relative to that in the red noise is analyzed.
Shibazaki, N.↗
The variance of the number of zeros of stationary normal processes
Probabilistic model for variance of number of zeros of a stationary random process
RANDOM PROCESS↗
Predicting initial trans-membrane pressure across cycles in the ultrafiltration process using random forest
With growing freshwater scarcity, direct potable reuse (DPR) systems that reclaim wastewater for drinking are becoming increasingly important for sustainable water supply. Reliable operation requires minimizing downtime in ultrafiltration (UF) units, where membrane fouling leads to elevated trans-membrane pressure (TMP). This study develops data-driven regression models based on random forest (RF) and autoregressive (AR) approaches to forecast the initial TMP at the start of each UF filtration cycle in a pilot-scale DPR system. The RF model consistently outperforms baseline methods, including historical mean, last observation carried forward, and AR models, across multiple forecast horizons, achieving the lowest root mean square error. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent input variables across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is assessed for both direct and recursive RF modelling approaches. The proposed RF framework establishes a robust foundation for predictive monitoring and real-time optimization of UF operations, supporting sustainable and reliable water reuse.
direct potable reuse↗
Nonstationary atmospheric boundary layer turbulence simulation
Report on a new and general technique for simulating atmospheric turbulence-like random processes which are statistically homogeneous along the horizontal and nonhomogeneous along the vertical. This technique is general in the sense that it can be used for a broad class of similar problems. Like the other presently available schemes, the techniques presented are based on the Dryden hypothesis and Taylor's frozen eddy hypothesis; however, they go a step further by utilizing certain self-similarity properties of the Dryden spectral density function which permits the development of height invariant filters. These filters are in turn used to generate vertically homogeneous (statistically) random processes from which turbulence at any specified level in the boundary layer can be simulated, thus facilitating the simulation of a nonstationary turbulence process along the flight path of an aircraft during take-off or landing.
Fichtl, G. H.↗
Estimation of correlation functions by stochastic approximation.
Consideration of the autocorrelation function of a zero-mean stationary random process. The techniques are applicable to processes with nonzero mean provided the mean is estimated first and subtracted. Two recursive techniques are proposed, both of which are based on the method of stochastic approximation and assume a functional form for the correlation function that depends on a number of parameters that are recursively estimated from successive records. One technique uses a standard point estimator of the correlation function to provide estimates of the parameters that minimize the mean-square error between the point estimates and the parametric function. The other technique provides estimates of the parameters that maximize a likelihood function relating the parameters of the function to the random process. Examples are presented.
Habibi, A.↗
Evolution of a meteorite crater as a process of random displacements
An examination of the ages and sizes of 114 terrestrial impact craters shows that their aging kinetics can be described by the diffusion laws. The macrodiffusion coefficient which determines random displacements of mineral masses on the Earth has a mean value of 0.02 sq m/year. The amount of matter in a crater that contains information about the impact event decreases with time according to the 1/T law. The basic characteristic parameter of a crater is its initial area, inasmuch as sufficiently large craters are nearly surficial formations. The relaxation time of a crater is proportional to its initial area.
Zotkin, I. T.↗
Approximate effect of parameter pseudonoise intensity on rate of convergence for EKF parameter estimators
When using parameter estimation methods based on extended Kalman filter (EKF) theory, it is common practice to assume that the unknown parameter values behave like a random process, such as a random walk, in order to guarantee their identifiability by the filter. The present work is the result of an ongoing effort to quantitatively describe the effect that the assumption of a fictitious noise (called pseudonoise) driving the unknown parameter values has on the parameter estimate convergence rate in filter-based parameter estimators. The initial approach is to examine a first-order system described by one state variable with one parameter to be estimated. The intent is to derive analytical results for this simple system that might offer insight into the effect of the pseudonoise assumption for more complex systems. Such results would make it possible to predict the estimator error convergence behavior as a function of the assumed pseudonoise intensity, and this leads to the natural application of the results to the design of filter-based parameter estimators. The results obtained show that the analytical description of the convergence behavior is very difficult.
Hill, Bryon K.↗