Theory Of Random Processes Research Articles

Statistic, probabilistic, correlation and spectral analyses of regenerative braking current of dc electric rolling stock

Purpose. Defining and analysis of the probabilistic and spectral characteristics of random current in regenerative braking mode of DC electric rolling stock are observed in this paper. Methodology. The elements and methods of the probability theory (particularly the theory of stationary and non-stationary processes) and methods of the sampling theory are used for processing of the regenerated current data arrays by PC. Findings. The regenerated current records are obtained from the locomotives and trains in Ukraine railways and trams in Poland. It was established that the current has uninterrupted and the jumping variations in time (especially in trams). For the random current in the regenerative braking mode the functions of mathematical expectation, dispersion and standard deviation are calculated. Histograms, probabilistic characteristics and correlation functions are calculated and plotted down for this current too. It was established that the current of the regenerative braking mode can be considered like the stationary and non-ergodic process. The spectral analysis of these records and “tail part” of the correlation function found weak periodical (or low-frequency) components which are known like an interharmonic. Originality. Firstly, the theory of non-stationary random processes was adapted for the analysis of the recuperated current which has uninterrupted and the jumping variations in time. Secondly, the presence of interharmonics in the stochastic process of regenerated current was defined for the first time. And finally, the patterns of temporal changes of the correlation current function are defined too. This allows to reasonably apply the correlation functions method in the identification of the electric traction system devices. Practical value. The results of probabilistic and statistic analysis of the recuperated current allow to estimate the quality of recovered energy and energy quality indices of electric rolling stock in the regenerative braking mode. But the correlation and spectral analysis is required to determine the electromagnetic compatibility of the electric rolling stock in the regenerative braking mode with the subsystems and the electric traction devices.

A rice method proof of the null-space property over the Grassmannian

The Null-Space Property (NSP) is a necessary and sufficient condition for the recovery of the largest coefficients of solutions to an under-determined system of linear equations. Interestingly, this property governs also the success and the failure of recent developments in high-dimensional statistics, signal processing, error-correcting codes and the theory of polytopes. Although this property is the keystone of $\ell_{1}$-minimization techniques, it is an open problem to derive a closed form for the phase transition on NSP. In this article, we provide the first proof of NSP using random processes theory and the Rice method. As a matter of fact, our analysis gives non-asymptotic bounds for NSP with respect to unitarily invariant distributions. Furthermore, we derive a simple sufficient condition for NSP.

Multiple-Source Time-Reversal Transmissions in Random Media

The ability of time-reversed signals in reproducing a given time-dependence of the electromagnetic field within random media is investigated. A general setup consisting of multiple sources cooperating in providing the best transmission is considered, where the constructive interference of their individual contributions is meant to improve the quality of the field generation with respect to a single-source setup. The medium response is described by means of tools from random-process theory, for the case of stationary media complex enough to ensure a large number of multi-path contributions. It is shown that even a very weak spatial coherence in the medium is sufficient to significantly hinder the improvement expected from the use of multiple-source scenarios. Experimental results obtained in a reverberation chamber support the validity of the proposed theory. Direct applications of these results can be found in recent proposals about the potential benefits of time-reversed signals used in wireless communications, imaging techniques, as well as in pulsed-field generation devices based on energy compression through dispersive media.

The Application of the Level-crossing Theory of Multidimensional Random Processes to the Evaluation of Vehicle Operators’ Performance

The application of the level-crossing theory of multidimensional random processes to the evaluation of the vehicle operators’ performance allows not only evaluating the possible deviation from parameters, but also considering the dynamics of the parameter changes. The level-crossing intensity is acquired for normal distribution random process correlated by two dimensions, as well as for the multidimensional process when a maximum mutual correlation of parameters is considered. The criterion is defined that allows evaluating the possibility that none of the parameters will reach an unacceptable value.

Hydrodynamic Aspects on Vulnerability Criteria for Surf-Riding of Ships

For developing the International Maritime Organization (IMO) second-generation intact stability criteria regarding broaching, draft vulnerability criteria for surf-riding were agreed at the IMO in 2012. This paper describes their hydrodynamic backgrounds with captive model experiments for seven ships, a hydrodynamic theory and a random process theory. In the first level vulnerability criteria, a ship is required to reduce her Froude number of less than 0.3 in case of severe following waves. For predicting the surf-riding threshold in a global bifurcation theory, it is necessary to precisely estimate wave-induced surge force. Thus, the authors execute captive model experiments for three ships in model basins. As a result, we confirmed that the Froude-Krylov calculation overestimates the amplitude of wave-induced surge force so that an empirical formula for regulatory application is presented. For investigating the reason of this discrepancy, a slender body theory assuming low encounter frequency is applied to the situation where a ship runs with a wave. This theory suggests that change of wave-making resistance due to incident wave could reduce the amplitude of the wave-induced surge force and quantitative agreement with model experiment requires the use of CFD or an empirical formula. Thus, the authors can recommend the use of experimental correction formula for the vulnerability criteria. Based on sample calculation results of surf-riding probability of six ships in the North Atlantic, the safety level to be required in the criteria is proposed.

Robust filtering: Correlated noise and multidimensional observation

In the late seventies, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721–734, Sijthoff & Noordhoff] pointed out that it would be natural for $\pi_{t}$, the solution of the stochastic filtering problem, to depend continuously on the observed data $Y=\{Y_{s},s\in[0,t]\}$. Indeed, if the signal and the observation noise are independent one can show that, for any suitably chosen test function $f$, there exists a continuous map $\theta^{f}_{t}$, defined on the space of continuous paths $C([0,t],\mathbb{R} ^{d})$ endowed with the uniform convergence topology such that $\pi_{t}(f)=\theta^{f}_{t}(Y)$, almost surely; see, for example, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721–734, Sijthoff & Noordhoff], Clark and Crisan [Probab. Theory Related Fields 133 (2005) 43–56], Davis [Z. Wahrsch. Verw. Gebiete 54 (1980) 125–139], Davis [Teor. Veroyatn. Primen. 27 (1982) 160–167], Kushner [Stochastics 3 (1979) 75–83]. As shown by Davis and Spathopoulos [SIAM J. Control Optim. 25 (1987) 260–278], Davis [In Stochastic Systems: The Mathematics of Filtering and Identification and Applications, Proc. NATO Adv. Study Inst. Les Arcs, Savoie, France 1980 505–528], [In The Oxford Handbook of Nonlinear Filtering (2011) 403–424 Oxford Univ. Press], this type of robust representation is also possible when the signal and the observation noise are correlated, provided the observation process is scalar. For a general correlated noise and multidimensional observations such a representation does not exist. By using the theory of rough paths we provide a solution to this deficiency: the observation process $Y$ is “lifted” to the process $\mathbf{Y}$ that consists of $Y$ and its corresponding Lévy area process, and we show that there exists a continuous map $\theta_{t}^{f}$, defined on a suitably chosen space of Hölder continuous paths such that $\pi_{t}(f)=\theta_{t}^{f}(\mathbf{Y})$, almost surely.

Deterministic Chaos Concept and Invariance Problem in Discrete Dynamic Systems

In given article new models of the discrete mappings are offered and on their basis the further development of the K(E) transformation apparatus for discrete functions is given. On the basis of K(E) transformation a method of discrete dynamic systems synthesis is set that in combination with principles of the classic theory of random processes makes it possible to carry out compensation (invariance) of the deterministic chaos, and optimal filtration of stationary random perturbation.

Relationship between International Roughness Index and Power Spectral Density of Asphalt Pavements in China

In this paper, pavement roughness is assumed as random stationary variable and used as the exciting force of theoretical analyses of the quarter car model of International Roughness Index (IRI). From the frequency response function of the quarter car, the response function of the displacement difference between sprung and unsprung mass is obtained based on random process theory. Then the relationship between IRI and power spectral density (PSD) is established from statement characteristic of the response function. Finally, the longitudinal road profiles of typical asphalt roads in China are used to validate the proposed model.

Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications.

Extremely High-Dimensional Feature Selection via Feature Generating Samplings

To select informative features on extremely high-dimensional problems, in this paper, a sampling scheme is proposed to enhance the efficiency of recently developed feature generating machines (FGMs). Note that in FGMs O(mlogr) time complexity should be taken to order the features by their scores; the entire computational cost of feature ordering will become unbearable when m is very large, for example, m > 10(11) , where m is the feature dimensionality and r is the size of the selected feature subset. To solve this problem, in this paper, we propose a feature generating sampling method, which can reduce this computational complexity to O(Gslog(G)+G(G+log(G))) while preserving the most informative features in a feature buffer, where Gs is the maximum number of nonzero features for each instance and G is the buffer size. Moreover, we show that our proposed sampling scheme can be deemed as the birth-death process based on random processes theory, which guarantees to include most of the informative features for feature selections. Empirical studies on real-world datasets show the effectiveness of the proposed sampling method.

Micro–Macro-Shear-Displacement Behavior of Contacting Rough Solids

Interlocking asperities are shown to have a fundamental effect on the friction behavior of contacting solids through theoretically derived shear force–displacement relationship. The key aspect of this relationship is the asperity contact orientation probability distribution obtained using the random process theory in terms of measurable surface roughness parameters. Thus, the obliquity of surface asperity contact is included in the contact shear analysis in a fundamental manner. The interlocking asperities are found to result in a normal load-dependent friction coefficient for a contact. The interlocking also affects contact partial slip and the shear displacements that precede sliding. The derived relationship can be used to evaluate factors, such as asperity adhesion, plasticity, damage, normal-shear coupling and scale dependency, which are difficult to separate in experiments and atomistic simulations.

The Response of the Dines Anemometer to Gusts and Comparisons with Cup Anemometers

Abstract The Dines pressure tube anemometer was the primary wind speed recording instrument used in Australia until it was replaced by Synchrotac cup anemometers in the 1990s. Simultaneous observations of the gust wind speeds recorded using both types of anemometers during tropical cyclones have, however, raised questions about the equivalency of the gust wind speeds recorded using the two instruments. An experimental study of the response of both versions of the Dines anemometer used in Australia shows that the response of the anemometer is dominated by the motion of the float manometer used to record the wind speed. The amplitude response function shows the presence of two resonant peaks, with the amplitude and frequency of the peaks depending on the instrument version and the mean wind speed. Comparison of the gust wind speeds recorded using Dines and Synchrotac anemometers using random process and linear system theory shows that, on average, the low-speed Dines anemometer records values 2%–5% higher than those recorded using a Synchrotac anemometer under the same conditions, while the high-speed Dines anemometer records values 3%–7% higher, depending on the mean wind speed and turbulence intensity. These differences are exacerbated with the adoption of the WMO-recommended 3-s moving average gust wind speed when reporting the Synchrotac anemometer gust wind speeds, rising to 6%–12% and 11%–19% for low- and high-speed Dines anemometers, respectively. These results are consistent with both field observations and an independent extreme value analysis of simultaneously observed gust wind speeds at seven sites in northern Australia.

Shock dynamics of random structures

Predicting the response of a structure following an impact is of interest in situations where parts of a complex assembly may come into contact. Standard approaches are based on the knowledge of the impulse response function, requiring the knowledge of the modes and the natural frequencies of the structure. In real engineering structures the statistics of higher natural frequencies follows those of the Gaussian Orthogonal Ensemble, this allows the application of random point process theory to get a mean impulse response function by the knowledge of the modal density of the structure. An ensemble averaged time history for both the response and the impact force can be predicted. Once the impact characteristics are known in the time domain, a simple Fourier Transform allows the frequency range of the impact excitation to be calculated. Experimental and numerical results for beams, plates, and cylinders are presented to confirm the validity of the method.

The method of the correlation and dispersion defining of the total power components in the electric transport devices

Purpose. Development and theoretical ground of the analytical method for the calculation of the active, reactive and total powers in the electric traction devices, taking into consideration the non-stationary character of the stochastic processes change of the voltage and current in the elements of these systems. Methodology. The mathematical methods of the random processes theory and the “discrete electrical engineering” methods are used for solving the main problem of this paper. Findings. The Method of the Correlation and Dispersion is developed for definition of the active power, the reactive power by Fryse and the total power of the devices in the elements of the electric traction system of the main-line railways. The method is based on the well-known concepts of auto- and inter-correlation functions of the random processes which govern the feeder voltages and the currents in the traction power supply subsystem as well as the currents and voltages of the electric rolling stock. The method developed in this paper allows estimating the powers of both stationary and non-stationary processes. This method can be used for the analysis of both the traction mode and the regenerative braking mode of the electric rolling stock. The total power components were calculated for the one of the feeder areas of the Prydniprovsk railway using this method. The results show the significant flow of the reactive power in the traction power supply system. This fact is also confirmed by the high values of the reactive power coefficient. Originality. Scientific novelty of the research is consisted in the following. Firstly, for defining the active and reactive powers in elements of the traction power supply system the new method (the Method of Correlation and Dispersion) is created and grounded. This method is different from other existing methods because it takes into consideration the varying non-stationary character of the chance processes of the feeder and substation voltages and currents. Secondly, in the DC traction power supply system the large values of the exchange reactive power by Fryze were created for the first time. Practical value.The method and its technique allow calculating the main energy coefficients for the traction power systems such are the reactive power coefficient, the main and additional active power losses in the power circuit of the electric rolling stockand the traction power supply system.

Statistical control k eff for subcritical fused-salt transplutonium burner reactor

In an at-power subcritical reactor with an external source, a deviation of criticality from a prescribed value monitored by means of the neutron flux may not be detected when the source characteristics change concurrently. In this connection, the fundamental possibility of additional real-time criticality control on the basis of reactor noise is being studied for a subcritical, fused-salt, transplutonium, burner reactor. A simple computational model of a reactor with a self-consistent description of the change in the neutron and thermophysical parameters, taking account of the circulation of the fuel salt through a heat-exchanger, is used. The theory of stationary random processes is used to examine the behavior of the model under a perturbation due to white-noise fluctuations of the reactivity and source intensity. It is shown that when the reactor operates at constant power the effect of the subcriticality on the noise level in the reactor is not a unique function of the ratio of the source and reactivity fluctuations. Ways to improve the representativeness of the reactor noise as a subcriticality indicator are briefly discussed.

Scaling earthquake ground motions in western Anatolia, Turkey

In this study, we provide a complete description of the ground-motion characteristics of the western Anatolia region of Turkey. The attenuation of ground motions with distance and the variability in excitation with magnitude are parameterized using three-component 0.25–10.0Hz earthquake ground motions at distances of 15–250km. The data set is comprised of more than 11,600 three-component seismograms from 902 regional earthquakes of local magnitude (ML) 2.5–5.8, recorded during the Western Anatolia Seismic Recording Experiment (WASRE) between November 2002 and October 2003.We used regression analysis to relate the logarithm of measured ground motion to the excitation, site, and propagation effects. Instead of trying to reproduce the details of the high-frequency ground motion in the time domain, we use a source model and a regional scaling law to predict the spectral shape and amplitudes of ground motion at various source-receiver distances. We fit a regression to the peak values of narrow bandpass filtered ground velocity time histories, and root mean square and RMS-average Fourier spectral amplitudes for a range of frequencies to define regional attenuation functions characterized by piece-wise linear geometric spreading (in log–log space) and a frequency-dependent crustal Q(f). An excitation function is also determined, which contains the competing effects of an effective stress parameter Δσ and a high-frequency attenuation term exp(−πκf). The anelastic attenuation coefficient for the entire region is given by Q(f)=180f0.55. The duration of motion for each record is defined as the value that yields the observed relationship between time-domain and spectral-domain amplitudes, according to random process theory. Anatolian excitation spectra are calibrated for our empirical results by using a Brune model with a stress drop of 10MPa for the largest event in our data set (Mw 5.8) and a near-surface attenuation parameter of κ=0.045s.These quantities, together with the effective duration of ground motion in the region, are used to estimate the peak ground motion (PGA, PGV). Using stochastic ground motion simulations, we predict the absolute level of ground shaking and compare them with strong-motion data in the region. The attenuation of simulated ground motion is compared with recent global and regional ground motion prediction equations (GMPEs). The performance of the stochastic model is also tested against small and intermediate-sized earthquakes (the M3.9 11 November 2007, M5.9 17 October 2005 and M5.7 20 October 2005 Izmir-Urla earthquakes) recorded by strong motion stations in the National Strong Ground Motion Network (operated by the Earthquake Department of the Disaster and Emergency Management Presidency, AFAD).

The Function Space to Describe the Dynamics of Linear Systems

There are two models of a random stationary process with a continuous spectrum of Wiener and the discrete spectrum of E. Slutsky. The first model of Wiener is often used. It is shown that this assumption leads to the absurdity of the equation Wiener-Hopf. The contradictions disappear in the theory of random stationary processes in the transition to a different model of a random process with discrete spectrum. Random ergodic stationary processes have on the mean and do not have the ergodicity of the variance and correlation functions. The struggle is based on the correlation functions of random processes with interference on the Wiener. Correct correlation functions cannot be obtained. Therefore, frequency analysis of random processes is proposed instead of the correlation analysis. The frequency analysis results in a more effective method of combating additive noise. The new method was used to identify the dynamic characteristics of the Airbus on the data obtained during the automatic landing.

Parametric control of structural responses using an optimal passive tuned mass damper under stationary Gaussian white noise excitations

In this study, the structural control strategy utilizing a passive tuned mass damper (TMD) system as a seismic damping device is outlined, highlighting the parametric optimization approach for displacement and acceleration control. The theory of stationary random processes and complex frequency response functions are explained and adopted. For the vibration control of an undamped structure, the optimal parameters of a TMD, such as the optimal tuning frequency and optimal damping ratio, to stationary Gaussian white noise acceleration are investigated by using a parametric optimization procedure. For damped structures, a numerical searching technique is used to obtain the optimal parameters of the TMD, and then the explicit formulae for these optimal parameters are derived through a sequence of curve-fitting schemes. Using these specified optimal parameters, several different controlled responses are examined, and then the displacement and acceleration based control effectiveness indices of the TMD are examined from the view point of RMS values. From the viewpoint of the RMS values of displacement and acceleration, the optimal TMDs adopted in this study shows clear performance improvements for the simplified model examined, and this means that the effective optimization of the TMD has a good potential as a customized target response-based structural strategy.

Cauchy problem for a parabolic pseudodifferential higher-order equation with pulse action

UDC 517.956 We consider the Cauchy problem and the problem with pulse action for a pseudodifferential higherorder equation with respect to t . We construct solutions of these problems, study their properties, and prove a theorem on correctness. The theory of pseudodifferential operators and pseudodifferential equations, whose modern form was formed in the middle of the 1960s, is studied in many works [2–8, 11, 12]. After determination that pseudodifferential operators are closely connected with problems of analysis and contemporary mathematical physics, especially in the theory of elliptic boundary-value problems [10], the number of such works has considerably increased. Linear parabolic pseudodifferential equations with nonsmooth symbols were defined by Eidel’man, Drin’, and Iwasaki at the beginning of the 1970s in [2, 3, 8, 9, 11, 12]. The symbols of these pseudodifferential operators are nonsmooth at the point σ= 0 , σ∈ R n . For this reason, standard methods, which are used for pseudodifferential operators with smooth symbols, cannot be applied to the investigation of problems for these pseudodifferential equations. Investigation of these equations with constant (independent of the space coordinates x ∈R n and the time coordinate t ∈(0,T ]) homogeneous symbol was originated in [8]. The fundamental solution of the Cauchy problem for these equations was determined with the use of the Fourier transformation. In [7], Fedoryuk establishes that the exact asymptotics of the fundamental solution of the Cauchy problem as x →∞ is power rather than exponential as for differential equations. In [3], Schauder estimates are obtained and the correct solvability of the Cauchy problem in classes of Holder functions is established. For the subsequent development of this theory, Kochubei’s works [4, 11] were very important. In these works, for the first time, it is noted that pseudodifferential operators with nonsmooth symbols can be interpreted as hypersingular integral operations. This enabled one to use the well-developed theory of hypersingular integral operations for the investigation of the Cauchy problem. Kochubei constructed and studied fundamental solutions of the Cauchy problem, proved theorems on solvability of the Cauchy problem in classes of functions with power increase as x →∞ , and indicated connections of the obtained results with theory of random processes.

The Gaussian Mixture Probability Hypothesis Density Filter and Its Application to Multi-Target Tracking

A algorithm based on random sets and point process theory is proposed for jointly estimate the time-varying number of targets and their states.The main contributions include:(1) Analyze multi-target tracking model based on random finite sets;(2) The Probability Hypothesis Density recursive formulas are deduced based on random sets and point process theory;(3) A analytic implementation of the Probability Hypothesis Density Filter is proposed under the linear Gaussian assumptions;(4) Two simulation results validate GMPHD performance and then compare GMPHD and JPDA performance under clutter and detection probability change;(5) Point out some the algorithm's lack and research direction.