Determination of the classification characteristics of random processes

An algorithm for classifying random processes using a single sample, based on the use of nonparametric criteria, Hurst indicators, the Bayes classification procedure and fuzzy logic is proposed. __________ Translated from Izmeritel’naya Tekhnika, No. 4, pp. 7–10, April, 2008.     

On random characteristics of composite materials

Abstract

Theoretical formulation is described, which presents random characteristics in composite materials. The presented method is based on Poisson processes. Examples of random characteristics of composite materials are shown. The method presented can be used for evaluation of composite materials and the subsequent quantitative stochastic design as well as stochastic optimisation of composite materials.     

Modeling lifetimes with unknown initial age

The failure rate of a distribution, which describes a lifetime random variable with unknown initial age, is studied. A specific model of mixing formalizes this setting. In accordance with this model, it turns out that under certain assumptions the operation of mixing distributions with increasing failure rates can result in the mixture failure rate with a bathtub shape: decreasing in the initial interval of time and then increasing, asymptotically approaching the failure rate of the baseline distribution. Two specific cases of the baseline distribution are considered: the Weibull and the truncated extreme value distributions. A possibility of mixing via the mean residual lifetime function is discussed.     

Closed-form solutions for the time-variant spectral characteristics of non-stationary random processes

Spectral characteristics are important quantities in describing stationary and non-stationary random processes. In this paper, the spectral characteristics for complex-valued random processes are evaluated and closed-form solutions for the time-variant statistics of the response of linear single-degree-of-freedom (SDOF) and both classically and non-classically damped multi-degree-of-freedom (MDOF) systems subjected to modulated Gaussian colored noise are obtained. The time-variant central frequency and bandwidth parameter of the response processes of linear SDOF and MDOF elastic systems subjected to Gaussian colored noise excitation are computed exactly in closed-form. These quantities are useful in problems which require the use of complex modal analysis, such as random vibrations of non-classically damped MDOF linear structures, and in structural reliability applications. Monte Carlo simulation has been used to confirm the validity of the proposed solutions.     

Dynamic systems with random initial state

Summary A perturbation scheme is described to treat time variable cryptodeterministic systems. According to Moyal's degree of randomness criteria the method provides a complete stochastic characterization of the system response. Certain digital computational features, when the perturbation scheme is not applicable, are also outlined. For an assumed random initial state, the results are then applied to describe the transient flapping oscillations of a helicopter blade which in forward flight has periodically varying aerodynamic damping and spring parameters.     

Optimization of aqueous microgrinding processes for fibrous plant materials

Fibrous plant-based materials are characterized by inhomogeneous structure and composition, which further evolve during wet grinding processes and affect the surface functionality of micronized particles. Therefore, the performance of aqueous microgrinding operations in stirred media mills can be optimized by investigating the interaction between process conditions and material properties of heterogeneous fibrous plant materials.In this experimental study it is shown how particle size reduction, tendency of re-agglomeration and stability of the suspension of micronized particles are driven by the specific energy input, residence time, temperature and presence of surfactants during the milling process. A structured experimental approach is described to optimize the achievable particle size reduction, expressed by the top cut diameter d_90,3. It was found that the applied wet milling process determines the stability of particle suspensions throughout further downstream processing, making the grinding process the core unit operation with respect to the performance and formulation of food products containing micronized particles.     

Study of the processes of mechanical-thermal treatment of food dispersed materials

The paper presents experimental data for the processes of low-temperature vacuum drying and grinding of thermolabile materials in devices with spring members.     

Optimization by random search with jumps

We give a random optimization (RO) algorithm to optimize a real‐valued function of n real variables. During the optimization process, interpolation points are examined to follow valleys, and jumps to new starting points are executed to avoid numerous iterations in local minima. Convergence with probability one to the global minimum of a function is proved. The proposed RO method is a simple, derivative‐free and computationally moderate algorithm, with excellent performance compared to other RO methods. Seven functions, which are commonly used to test the performance of optimization methods, are used to evaluate the performance of the RO algorithm given here. Copyright © 2004 John Wiley & Sons, Ltd.     

Constructing models of random processes with specified properties in the frequency domain

Problems of constructing models of random processes with specified statistical properties are considered. Examples are given of the construction of such models in the frequency domain. __________ Translated from Izmeritel’naya Tekhnika, No. 8, pp. 47–50, August, 2006.     

Strongly non-linear stochastic response of a system with random initial imperfections

Strongly non-linear responses of structures with random imperfections of Gaussian type in their geometrical form under slowly increasing loading are investigated. Large displacements as a source of non-linearities are taken into account. Imperfections are considered as stochastic functions of space coordinates. The finite element method is supposed as a basis. A stochastic version of the arc length method of stochastic non-linear algebraic systems in linearised formulation is proposed. A closed interaction between deterministic and stochastic parts of response is demonstrated. Several numerical tests of theoretical results on simple Mieses frames modelling imperfect shallow shells have been carried out. Analytical and numerical results make it possible to demonstrate non-conventional properties typical for a randomly imperfect structure with a tendency to various types of snap-through effects.     

Numerical discretization of stationary random processes

The increasing interest of the research community to the probabilistic analysis concerning the civil structures with space-variant properties points out the problem of achieving a reliable discretization of random processes (or random fields in a multi-dimensional domain). Given a discretization method, a continuous random process is approximated by a finite set of random variables. Its dimension affects significantly the accuracy of the approximation, in terms of the relevant properties of the continuous random process under investigation. The paper presents a discretization procedure based on the truncated Karhunen–Loève series expansion and the finite element method. The objective is to link in a rational way the number of random variables involved in the approximation to a quantitative measure of the discretization accuracy. The finite element method is applied to evaluate the terms of the series expansion when a closed form expression is not available. An iterative refinement of the finite element mesh is proposed in this paper, leading to an accurate random process discretization. The technique is tested with respect to the exponential covariance function, that enables a comparison with analytical expressions of the approximated properties of the random process. Then, the procedure is applied to the square exponential covariance functions, which is one of the most used covariance models in the structural engineering field. The comparison of the adaptive refinement of the discretization with a non-adaptive procedure and with the wavelet Galerkin approach allows to demonstrate the computational efficiency of the proposal within the framework of the Karhunen–Loève series expansion. A comparison with the Expansion Optimal Linear Estimation (EOLE) method is performed in terms of efficiency of the discretization strategy.     

Stiffness tensor random fields through upscaling of planar random materials

Unique effective material properties are not possible for random heterogeneous materials at intermediate length scales, which is to say at some mesoscale above the microscale yet prior to the attainment of the representative volume element (RVE). Focusing on elastic moduli in particular, a micromechanical analysis based on the Hill–Mandel condition leads to the conclusion that two fields, stiffness and compliance, are required to bound the response of the material. In particular, we analyze means and correlation coefficients of a random planar material with a two-phase microstructure of random checkerboard type. We employ micromechanics, which can be viewed as an upscaling, smoothing procedure using the concept of a mesoscale “window”, and random field theory to compute the correlation structure of 4th-rank tensor fields of stiffness and compliance for a given mesoscale. Results are presented for various correlation distances, volume fractions, and contrasts in stiffness between phases. The main contribution of this research is to provide the data for developing analytical correlation functions, which can then be used at any mesoscale to generate micromechanically based inputs into analytical and computational mechanics models.     

Diffusion of decaying admixtures in materials with random spherical inclusions

We study the process of diffusion of admixtures in a layer of an inhomogeneous material with randomly located spherical inclusions modeling, e.g., the lavalike fuel-containing masses formed at nuclear power plants. The contact boundary-value problem of diffusion is reduced to a boundary-value problem of mass transfer in the entire body by the methods of the theory of generalized functions. We propose an equivalent integro-differential equation and obtain its solution by the method of successive approximations in the form of a Neumann integral series. The convergence of this series and the theorem of existence of the solution are proved. We deduce an approximate formula for the evaluation of the concentration of radionuclides averaged over the ensemble of phase configurations and perform its numerical analysis. It is shown that the characteristics of the material affect the behavior and concentration of admixtures in a body with randomly inhomogeneous structure. If the diffusion coefficient in the inclusions is lower than in the matrix, then the average concentration in the layer increases, and vice versa. As a result of the process of decay of foreign particles, their average concentration may become several times lower. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, pp. 28–38, March–April, 2006.     

Measurement of random processes at rough surfaces with digital speckle correlation

We present a detailed investigation of digital speckle correlation to measure small changes in the microstructure of random rough surfaces. The corresponding alterations in the scattered-light field are recorded by an electronic camera with subsequent numerical correlation. Among the classical theoretical approaches to describe the scattering at random rough surfaces, the composite-roughness model is advanced to calculate the speckle correlation in terms of parameters of the changes in surface microstructure. For an experimental verification, surfaces with similar microstructure are fabricated with a photolithographic technique. They are employed for comparative measurements with high-resolution scanning force microscopy and for correlation measurements under variation of experimental parameters. A good agreement between theoretically predicted and experimental correlation data can be observed. The results allow a quantitative whole-field monitoring of surface processes by remote optical means.