Theory Of Random Processes Research Articles

On random spatial distribution of active crowds on grandstands and their effects on dynamic response

Active spectators on grandstands can induce wide palette of loads ranging from hand-clapping or swaying to bobbing or synchronized jumping. Each of these loads may differ in its intensity, frequency range, and level of synchronization. All these aspects render the process of predicting the behaviour and performance of grandstands difficult, requiring proper modelling techniques. Although grandstands themselves can be successfully modelled by finite element method, the situation with human-induced loading is less transparent, and mathematical description of load have evolved over the years from equivalent static load through deterministic approximations in time and frequency domain to Monte Carlo (MC) generators. In this contribution, the most intensive kind of human activity exercised on grandstands—synchronized jumping—is focused on. In particular, the response of grandstands loaded by jumping active crowds that are randomly distributed in space is investigated. For simplicity, no passive spectators are considered. Two modelling approaches are used. First, direct MC simulation provides a reference solution. Second, a semi-analytical formulation employing theory of random processes provides response estimates and simplifying formulas. Finally, both approaches are demonstrated and compared on a simple example.

Reliability estimation of fatigue crack growth prediction via limited measured data

In view of limited uncertainty information, a time-dependent reliability estimation procedure that combines the determined crack growth model with interval mathematics is presented as a theoretical basis for structural damage tolerance design. Firstly, by virtue of the theory of non-probabilistic interval process, an interval process model of fatigue crack propagation is investigated, in which we describe uncertain crack length a(N) at any load cycle N as interval variable and define the corresponding auto-covariance function and the correlation coefficient function to further characterize the correlation of a(N) at different cycles. By comparison of the critical crack length acritical, the uncertainty properties of the time-varying limit-state function can be given as well. Furthermore, inspired by the first-passage approach in random process theory, a new measure index of non-probabilistic time-dependent reliability is proposed as a feasible way for precisely evaluating the safe life of in-service engineering structures with crack. The corresponding solution algorithm is further discussed. Some application examples demonstrate the usage, efficiency and accuracy of the developed methodology eventually.

Stability analysis in Gram‐Schmidt QR decomposition

In this study, important aspects concerning the stability of the QR decomposition (QRD) through the modified Gram-Schmidt (GS) orthogonalisation procedure with application in multiple-input–multiple-output (MIMO) detection are investigated. In particular, the numerical stability of GS-QRD is analysed through the condition number, considering a matrix with Gaussian entries, which is a very special class of matrix, especially for telecommunication systems in general and for MIMO system in particular. The condition number is analysed in the average sense, aided by random processes theory, including in special the central limit theorem, random variable transformation and moment generating functions. An analytical bound for the condition number is found and corroborated by numerical simulations.

Calculation of the Kinetics of Processes in the Separation of Granular Materials in Multi-Tier Classifiers and Optimization of Their Operation

A method of calculating the kinetics of the separation of granular materials in a multi-tier classifier on the basis of the theory of random processes is considered and a kinetic model is identified. A problem of optimal hardware design of the classification process in a multi-criteria statement is formulated and solved. The performance of the apparatus and the efficiency of separation are selected as the optimization criteria.

"The Theory was Beautiful Indeed": Rise, Fall and Circulation of Maximizing Methods in Population Genetics (1930-1980).

Describing the theoretical population geneticists of the 1960s, Joseph Felsenstein reminisced: "our central obsession was finding out what function evolution would try to maximize. Population geneticists used to think, following Sewall Wright, that mean relative fitness, W, would be maximized by natural selection" (Felsenstein 2000). The present paper describes the genesis, diffusion and fall of this "obsession", by giving a biography of the mean fitness function in population genetics. This modeling method devised by Sewall Wright in the 1930s found its heyday in the late 1950s and early 1960s, in the wake of Motoo Kimura's and Richard Lewontin's works. It seemed a reliable guide in the mathematical study of deterministic effects (the study of natural selection in populations of infinite size, with no drift), leading to powerful generalizations presenting law-like properties. Progress in population genetics theory, it then seemed, would come from the application of this method to the study of systems with several genes. This ambition came to a halt in the context of the influential objections made by the Australian mathematician Patrick Moran in 1963. These objections triggered a controversy between mathematically- and biologically-inclined geneticists, with affected both the formal standards and the aims of population genetics as a science. Over the course of the 1960s, the mean fitness method withered with the ambition of developing the deterministic theory. The mathematical theory became increasingly complex. Kimura re-focused his modeling work on the theory of random processes; as a result of his computer simulations, Lewontin became the staunchest critic of maximizing principles in evolutionary biology. The mean fitness method then migrated to other research areas, being refashioned and used in evolutionary quantitative genetics and behavioral ecology.

Application of three-dimensional printing to pavement texture effects on rubber friction

Despite the significant attention gained by the three-dimensional (3D) printing technology in many research fields, it has not yet found application in tyre–road friction and pavement engineering. To better understand the impact of different roughness length scales on rubber friction, the feasibility of utilising 3D printing for replicating pavement texture and the strength of this technology in creating customised roughness patterns are investigated. An image-stitching algorithm was developed for a common portable optical profiler in order to obtain a large topography of an asphalt specimen for friction experiments. The printed topography showed a replication efficacy down to 0.5 mm in wavelength. Printed samples with artificial surface patterns were then generated by random process theory and fractal modelling. Rubber sliding tests implied different frictional behaviour between the asphalt specimen and its printed replica, which was mainly attributed to severe wear of rubber on rougher asphalt specimen. For artificial geometries, friction increased as the Hurst exponent (H) increased. Results also suggested that reducing roll-off wavevector (q0), that is, increasing maximum aggregate size, reduces friction coefficient of a fractal surface.

On a recent stickiness criterion using a very simple generalization of DMT theory of adhesion

In the contact of rough surfaces, contact occurs on smaller and smaller scales, the well-known Tabor adhesion parameter decreases and the so-called Derjaguin–Muller–Toporov (DMT) theory is the appropriate limit. Fuller and Tabor developed 40 years ago a model based on asperities and JKR theory, and more recently the author developed an asperity theory using asperities and DMT theory in the form given by Maugis. Both lead to adhesion parameters which do not depend on the range of attractive forces, in contrast to the parameter recently suggested by Pastewka and Robbins (PNAS, 111(9), 3298–3303, 2014). As it is well known from random process theory that contact of rough surfaces can be described reasonably well by asperity summits at least for low bandwidths, the Pastewka–Robbins DMT model and stickiness criterion should correspond in the limit case of a spherical contact. We therefore consider this limit case, and show that Pastewka–Robbins DMT model introduces a dependence on range of attractive forces, or on Tabor parameter, which is not correct for the sphere, and therefore may be incorrect also in general.

A Modified Discreet Particle Swarm Optimization for a Multi-level Emergency Supplies Distribution Network

Currently, the research of emergency supplies distribution and decision models mostly focus on deterministic models and exact algorithm. A few of studies have been done on the multi-level distribution network and matheuristic algorithm. In this paper, random processes theory is adopted to establish emergency supplies distribution and decision model for multi-level network. By analyzing the characteristics of the model, a modified discrete particle swarm optimization matheuristic algorithm (MBPSO) is proposed to solve the problem. In MBPSO, appropriate degradation mechanism and parallel global search structure is designed. Through a instance, MBPSO has capability of global optimuml search and fast convergence property for hybrid integer programming model with multi-constrained and weighted single objective.

Simulation of Fast-Ion motion in nanotubes with random bending

A model describing the random smooth bending of carbon nanotubes within the theory of random processes is proposed. The degree of influence of random deviations of the nanotube axis from a straight line on particle channeling is studied for a definite choice of the specific form of random processes.

Simulation Of Mine Water Inflow: Case Study Of The Štavalj Coal Mine (Southwestern Serbia)

Abstract The inflow of mine water to mining operations is often caused by random events such as precipitation. Consequently, the mine water inflow regime can be defined as a function of random events applying the theory of random processes. Regression models of the multiple linear correlation type have been used to simulate the inflow of mine water into mining operations, produce short-range predictions and facilitate rapid response inside the mine. The significance of such models lies in the ability to simulate and predict the consequences (mine water inflow), caused by events of a random nature (meteorological parameters: precipitation and air temperature). The presented prognostic models have been calibrated for mine water inflow to the Štavalj Coal Mine in southwestern Serbia. Mathematical dependencies were defined based on daily mine water inflow rates recorded during the period from 2003 to 2011, which can be used to generate short-range (1-7 day) predictions of mean daily mine water inflow rates to the Štavalj Coal Mine. A strong correlation (coefficient of correlation r = 0.93, Sig. = 0.00) was derived for the one-day forecast. The coefficients of correlation for predictions of mean daily mine water inflow rates related to time periods of two, three...seven days gradually declined to 0.63 (7-day mean daily inflow rate).

Cyclic Linear Random Process As A Mathematical Model Of Cyclic Signals

Abstract In this study the cyclic linear random process is defined, that combines the properties of linear random process and cyclic random process. This expands the possibility describing cyclic signals and processes within the framework of linear random processes theory and generalizes their known mathematical model as a linear periodic random process. The conditions for the kernel are given and the probabilistic characteristics of generated process of linear random process in order to be a cyclic random process. The advantages of the cyclic linear random process are presented. It can be used as the mathematical model of the cyclic stochastic signals and processes in various fields of science and technology.

A New Method for Rough Surface Profile Simulation Based on Peak–Valley Mapping

Starting from random process theory and taking peaks and valleys as reconstruction carriers to replace surface height distribution and autocorrelation function (ACF), a new method for rough surface simulation is proposed based on the peak–valley mapping principle. The proposed method is used to simulate rough surfaces with different correlation lengths. The simulated roughness parameters and ACF are examined. Comparisons of simulation precision and simulation efficiency between the proposed method and fast Fourier transform (FFT) are provided. Finally, the applications of the method are discussed briefly.

Formulae of roughness peak distribution parameters with standard deviation and correlation length

Principle error exists when peak distribution parameters are calculated based on the random process theory, and the microtopography simulation with desired peak distributions still cannot be realized. To solve these problems, the relationship between peak distribution parameters and surface statistical distribution parameters is studied through lots of rough surface reconstructions. The effects of high-pass filtering with different cut-off lengths are analyzed. In addition, formulae of peak distribution parameters with standard deviation and correlation length are constructed by mathematical fitting. The formulae are verified with experimental data and compared with classical literature. Finally, an example of application of the formulae to microtopography simulation is provided.

Fast ions channeling in nanotubes of weak chaotic curvature

The model of random smooth curvature for carbon nanotubes within the framework of the theory of random processes is proposed for describing the particle channeling in carbon nanotubes. The degree of influence of random nanotube axis deviation from the straight line on the particle channeling has been investigated with a specific choice for particular type of random processes. The conditions, at which the inaccuracy in given random type can be neglected at channeling, have been examined.

Fokker-Planck equations for stochastic diffusion associated with Markovian electrochemical noise

The theoretical analysis of quadratic correlations of equilibrium electrical fluctuations in the Markovian electrochemical ac circuit is accomplished. The modified Fokker-Plank equation which allows one to follow the time evolution of 2nd-order correlators of electrochemical stochastic diffusion associated with the Markovian electrochemical ac circuit (Eq. (7)) is obtained. Due to interdisciplinary significance of the random process theory, the resulting Fokker-Planck equation is also of certain interest for the general theory of stochastic phenomena occurring near the equilibrium state. The derived modified Fokker-Planck equation can be used in the electrochemical noise diagnosis as the Markovian standard of electrochemical stochastic diffusion.

Nonlinear Distortion in Wireless Systems [Book\/Software Reviews

This book focuses on nonlinear distortion in wireless communication systems whereby the author pulled from 140 references and melted together all the information on nonlinear system characteristics to derive a model and use it in MATLAB simulations. In today’s radiofrequency (RF) nonlinear simulations, deterministic signals are used that face a problem with predicting system performance when the input to the system is real-world communication signals, which have a random nature. The author introduces modeling and simulation of nonlinear distortions from both a deterministic and a stochastic point of view and uses random process theory to develop simulation tools for predicting system performance.

Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?

The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cut-offs or bi-fractality in the power-law power-spectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what was expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted for by fractal modeling.

Time-Dependent Reliability Modeling and Analysis Method for Mechanics Based on Convex Process

The objective of the present study is to evaluate the time-dependent reliability for dynamic mechanics with insufficient time-varying uncertainty information. In this paper, the nonprobabilistic convex process model, which contains autocorrelation and cross-correlation, is firstly employed for the quantitative assessment of the time-variant uncertainty in structural performance characteristics. By combination of the set-theory method and the regularization treatment, the time-varying properties of structural limit state are determined and a standard convex process with autocorrelation for describing the limit state is formulated. By virtue of the classical first-passage method in random process theory, a new nonprobabilistic measure index of time-dependent reliability is proposed and its solution strategy is mathematically conducted. Furthermore, the Monte-Carlo simulation method is also discussed to illustrate the feasibility and accuracy of the developed approach. Three engineering cases clearly demonstrate that the proposed method may provide a reasonable and more efficient way to estimate structural safety than Monte-Carlo simulations throughout a product life-cycle.

Reliability analysis of a ship hull structure under combined loads including slamming loading

During the last decades, much attention has been paid to long-term structural reliability analyses applied to design and maintenance planning of ships. However, many extreme loads occur in short time periods in particular severe sea conditions. In this paper, a random process model of the ship hull girder subjected to still-water, wave- and slamming-induced loads is formulated based on the random process theory covering a short time period during extreme seas in the short time duration of slamming. The correlation of the peak value of slamming- and wave-induced loads is considered according to the fact that the wave and the velocity of the ship are the dominating causes of the slamming. Through the analysis of the stochastic process of limit state function, the reliability is evaluated by means of up-crossing analysis and parallel system reliability method. In a numerical example, the influences of the damping ratio, slamming rate and correlation coefficient on the failure probability are analysed, considering different failure modes. The results show that the buckling failure of the deck under compression is the most dangerous case and the damping ratio influences the impact of the slamming load on the reliability.

Gust durations, gust factors and gust response factors in wind codes and standards

This paper discusses the appropriate duration for basic gust wind speeds in wind loading codes and standards, and in wind engineering generally. Although various proposed definitions are discussed, the 'moving average' gust duration has been widely accepted internationally. The commonly-specified gust duration of 3-seconds, however, is shown to have a significant effect on the high-frequency end of the spectrum of turbulence, and may not be ideally suited for wind engineering purposes. The effective gust durations measured by commonly-used anemometer types are discussed; these are typically considerably shorter than the 'standard' duration of 3 seconds. Using stationary random process theory, the paper gives expected peak factors, g w, as a function of the non-dimensional parameter (T/τ), where T is the sample, or reference, time, and τ is the gust duration, and a non-dimensional mean wind speed, U. T/L w, where U is a mean wind speed, and L w is the integral length scale of turbulence. The commonly-used Durst relationship, relating gusts of various durations, is shown to correspond to a particular value of turbulence intensity I u, of 16.5%, and is therefore applicable to particular terrain and height situations, and hence should not be applied universally. The effective frontal areas associated with peak gusts of various durations are discussed; this indicates that a gust of 3 seconds has an equivalent frontal area equal to that of a tall building. Finally a generalized gust response factor format, accounting for fluctuating and resonant along-wind loading of structures, applicable to any code is presented.