Simulation Of Nonstationary Processes Research Articles

КОМП'ЮТЕРНЕ МОДЕЛЮВАННЯ НЕСТАЦІОНАРНОГО ПРОЦЕСУ РОЗВИТКУ НАДЗВУКОВОГО ПЕРЕРОЗШИРЕНОГО СТРУМЕНЮ

Questions of numerical simulation of non-stationary process of the development of a supersonic overexpanded jet are considered. Unsteady Reynolds-averaged Navier-Stokes equations (URANS) of compressible flows, written in an arbitrary coordinate system, along with the Spalart-Allmaras one-equation differential turbulence model are applied. The calculations of non-stationary formation of an air cold supersonic jet during the blowing through a conical Laval nozzle (simulation of engine start-up) were made. The physical features of the shock and acoustic waves generation and propagation are discussed. In the stationary phase an overexpanded free supersonic turbulent jet is formed, which includes a Mach disc in its structure. The obtained results were compared with experimental data and calculations by other authors based on the ANSYS Fluent and FloEFD CFD tools.

Efficient ground motion conditional simulation method for nonstationary multivariate processes based on Kriging method and orthogonal discrete wavelet transform

Conditional ground motion simulation methods preserve more physical features of actual ground motions than unconditional methods by including actual earthquake records. This study developed a conditional multivariate nonstationary process simulation method based on the combination of the Kriging method and the orthogonal discrete wavelet transform (DWT). The Kriging method is used to ensure the spectral coherences between simulations as prescribed and is extended to nonstationary random processes by applying it to the average power spectral density (APSD) of ground motions. The ground motions' DWT wavelet coefficients are assumed to be uniformly time-modulated stationary processes whose time-modulating functions are the envelopes of the seed record's wavelet coefficients. The APSD and the envelopes together outline the energy distribution of the random field in both the time and frequency domain features. The power spectral densities of the stationary random processes' DWT coefficients are derived and used to estimate the APSD of the ground motions' DWT coefficients. Approaches to realizing uniformly time-modulated stationary processes with prescribed APSDs and envelope functions are developed. Monte Carlo simulations were conducted to verify the new method's effectiveness. Results show that both the target APSD and coherences can be well approximated, but precise approximation cannot always be realized in the high-frequency range. The new approach possesses a simple structure, involves simple algorithms, and applies to time-independent spectral coherence models, making it an efficient method compared with existing methods.

Simulation of Nonstationary Process Using Ensemble Empirical Mode Decomposition and Empirical Envelope Methods

A simulation method for nonstationary process is proposed based on the ensemble empirical mode decomposition (EEMD) and the empirical envelope (EE) methods: the EEMD is used to decompose a nonstationary process into several mono-component signals, and then the EE method is utilized to calculate the instantaneous characteristics of these mono-component signals; a simulated process can be constructed based on the distributions of the instantaneous characteristics of the mono-component signals. An earthquake ground motion recorded in chi-chi earthquake and a nonstationary wind speed induced by typhoon Rammasun are utilized to verify the accuracy and efficacy of the newly-developed method. Results show that: the EE method performs much better than the Hilbert transform (HT)-based method in calculating the instantaneous frequency; the proposed method can successfully capture the global and transient energy distributions of a nonstationary process; the nonstationary wind speed can be modeled as a uniformly modulated nonstationary process, while the earthquake ground motion should be modeled as a non-uniformly modulated nonstationary process. The proposed method does not include any pre-assumed modulation function or inappropriate assumption such as piece-wise stationarity. The method is applicable to the simulation of various types of nonstationary processes, and it can be extended to simulate multivariate nonstationary processes.

Improving the Energy Efficiency of Heat-Technical Equipment on the Basis of Numerical Simulation of Non-Stationary Processes

In industrial heat-technological installations for accelerated hydration of concrete, which are the main element of the thermal power system of enterprises of concrete products, the modes of heat treatment and the organization of heat supply to the product processed in them are due to the required temperature distribution in the volume of the concrete body, providing a given product quality. In order to optimize the processes occurring in such thermal device, a nonstationary mathematical model of the hardening process of the concrete product subjected to heat treatment has been developed, which allows calculating the spatial distribution of its volume temperature and degree of hydration of the active part of the cement clinker. The proposed model is based on the use of a non-stationary three-dimensional heat equation that takes into account the internal heat release due to the exothermic reaction in a concrete body and determines the degree of its hydration and hardening. For a given mode of heat treatment with the use of the finite volume method, numerical simulation of the hardening process of a symmetric concrete object of cubic shape is performed. In the selected points of the object under study, depending on the time of heat treatment, the rates of temperature change and the degree of hydration were calculated and their analysis was carried out. When analyzing the graphs of the temperature change rate, the characteristic inflections consistent with the given thermal mode of the heater were revealed. By a given mode of heat treatment of the form of “temperature rise – isothermal exposure – temperature decrease” in the selected points of the object there is an increase in temperature compared with the specified maximum temperatures of isothermal exposure, which is associated with the exothermic effect of the hydration reaction. A temperature shift relative to the specified thermal mode of the heater due to the non-equilibrium of the concrete hardening process is observed. The proposed mathematical model allows determining the time of reaching a preset temperature for any point of the internal space of the product subjected to heat treatment that can be used in the when designing of new and modernizing of existing thermal technological installations of accelerated hydration of concrete, as well as systems for automated control of the concrete hardening process in these devices. The results obtained during the study are in satisfactory agreement with the experimental data of other authors.

Non-stationary turbulent wind field simulation of bridge deck using non-negative matrix factorization

Numerical simulation of turbulent wind field is essential for the time-domain buffeting analysis of long-span bridges. However, recent field measurements captured strong non-stationary features during extreme wind events, which may pose questions on the current bridge aerodynamic analysis based on the stationary assumption. Therefore, it is both necessary and realistic to perform non-stationary simulation of turbulent wind fields of long-span bridges. In this study, a spectral-representation-based non-stationary process simulation algorithm, which takes advantage of the FFT technique, is proposed using non-negative matrix factorization. In addition, an appropriate scheme is recommended to search the initial matrices for the factorization. After factorizing the decomposed spectrum, the FFT technique can be utilized to enhance the non-stationary simulation efficiency. Numerical examples demonstrate the feasibility and effectiveness of the factorization of the decomposed spectrum. Then, the non-stationary turbulent wind field on the long-span bridge deck is simulated. The computational efficiency, accuracy and applicability of the proposed method are compared with alternative approaches. Results show that the factorization and simulation agree well with the target ones. Therefore, the proposed approach can be used to simulate the non-stationary turbulent wind field in practice.

Моделирование нестационарных процессов в импульсных трубчатых ксеноновых лампах в условиях возврата в плазму отраженного излучения

Моделирование нестационарных процессов в импульсных трубчатых ксеноновых лампах в условиях возврата в плазму отраженного излучения

Numerical simulation of two-phase filtration in the near well bore zone

Abstract On the basis of the fundamental laws of energy conservation, nonstationary processes of filtration of two-phase liquids in multilayered reservoirs in the near well bore zone are considered. Number of reservoirs, fluid pressure in the given reservoirs, reservoir permeability, oil viscosity, etc. are taken into account upon that. Plane-parallel flow and axisymmetric cases have been studied. In the numerical solution, non-structured meshes are used. Closer to the well, the meshes thicken. The integration step over time is defined by the generalized Courant inequality. As a result, there are no large oscillations in the numerical solutions obtained. Oil production rates, Poisson’s ratios, D-diameters of the well, filter height, filter permeability, and cumulative thickness of the filter cake and the area have been taken as the main inputs in numerical simulation of non-stationary processes of two-phase filtration.

Fast simulation of multivariate nonstationary process and its application to extreme winds

Simulation of the devastating excitations such as the ground motion and transient extreme winds is an important task in the structural response analysis when it comes to the nonlinearity, system stochasticity, parametric excitations and so on. Although the classic spectral representation method (SRM) is widely used in the nonstationary process simulation, it suffers from lower efficiency due to the unavailability of use of fast Fourier transform (FFT). In this study, the classic SRM is extended to the nonstationary process with the time-varying coherence. Then, the FFT-aided and almost accurate simulation algorithm for the nonstationary process with the time-varying coherence is developed with the help of the proper orthogonal decomposition (POD) which is used to factorize the decomposed evolutionary spectra. Especially, the more efficient simulation for the nonstationary process with time-invariant coherence is also proposed, where the spectral matrix decomposition, use of POD and execution of FFT can be reduced significantly. Two examples including downburst and typhoon winds are employed to evaluate the accuracy and efficiency of the proposed method. Results show that the method has the good performance in terms of the efficiency and accuracy.

Application of Proper Orthogonal Decomposition in Fast Fourier Transform—Assisted Multivariate Nonstationary Process Simulation

AbstractThe classic spectral representation method (SRM)-based nonstationary process simulation algorithm is used extensively in the engineering community. However, it is less efficient owing to the unavailability of fast Fourier transform (FFT). In this paper, an efficient, almost accurate, and straightforward algorithm is developed for the simulation of the multivariate nonstationary process. In this method, an evolutionary spectral matrix is decomposed via Cholesky method, and then proper orthogonal decomposition (POD) is used to factorize decomposed spectra as the summation of the products of time and frequency functions. Because original time-dependent decomposed spectra are decoupled via factorization, FFT can be used to significantly expedite the simulation efficiency. This POD-based factorization is totally data-driven and optimal, and fewer items are required in matching decomposed spectra. Therefore, the accuracy and efficiency of the factorization can be guaranteed at the same time. Another att...

Predictive Modelling of the Warming up Times for Thermoelectric Converters

In the present article the question of simulation of nonstationary process of heat transport in a sensitive element of the thermoelectric transformer with an uninsulated seal is considered. The model allows defining and comparing the heating time of a thermocouple junction up to the given temperature for different types of thermocouples. In this article the values obtained by means of modelling the heat time of different thermocouples and also a temperature field in a sensitive element of the thermoelectric transformer are given.

An efficient simulation approach for multivariate nonstationary process: Hybrid of wavelet and spectral representation method

Currently, the classical spectral representation method (SRM) for nonstationary process simulation is widely used in the engineering community. Although this scheme has the higher accuracy, the time-dependent spectra results in unavailability of fast Fourier transform (FFT) and thus the simulation efficiency is lower. On the other hand, the approach based on stochastic decomposition can apply FFT in the simulation. However, the algorithm including the fitting procedure is relatively complicated and thus limits its use in practice.In this paper, the hybrid efficient simulation method is proposed for the vector-valued nonstationary process, which contains the spectra decomposition via wavelets and SRM. This method can take advantage of FFT and is also straightforward to engineering application. Numerical examples are employed to evaluate the proposed method. Results show that the method performs fairly well for the scalar process and vector-valued process with real coherence function. In the case of complex coherence function, the majority of the phase in the coherence function cannot be remained in the simulation. In addition, the validity of proper orthogonal decomposition (POD) in nonstationary process simulation via the decomposition of the time-dependent nonstationary spectra is studied. Analysis shows that the direct use of POD in nonstationary spectra decomposition may not be useful in nonstationary process simulations.

Modeling and Simulation of Nonstationary Processes Utilizing Wavelet and Hilbert Transforms

AbstractAn approach is proposed for modeling and simulating nonstationary earthquake ground motions that utilizes stationary wavelet and Hilbert transforms. The proposed model is based on the time-frequency representation of a process, which is essential for capturing the nonstationary characteristics of earthquake ground motions. Stationary wavelet transform is first utilized to decompose a sample of a multicomponent nonstationary random process into a set of monocomponent signals. These signals are subsequently transformed to analytic signals using the Hilbert transform, which yields the instantaneous amplitudes and frequencies. Without the customary assumption of piecewise stationarity or reliance on an assumed modulation function, this approach is able to simulate nonstationary random processes, such as earthquake ground motion, based on a sample realization of the process and its instantaneous features. The method is extended to the simulation of multivariate random processes utilizing the proper ort...

Research on Simulation Model of Nonstationary Stochastic Processes in Natural Disasters

Simulation of nonstationary processes has become an indispensable tool in study and prevention of natural disasters. A new method of simulation of nonstationary random processes is presented based on the orthogonal HHT spectra of sample observations and random phase. It takes advantage of orthogonal EMD, the instantaneous frequency, amplitude of the Hilbert transform and independent random phase angle, thus overcoming difficulties in the estimation of the frequency modulation and interdependence of frequency and amplitude modulation functions faced by most currently available methods. The new method extracts and preserves the true physical features of the process. The examples of earthquake ground motion and subway vibration, as low frequency and high frequency nonstationary process respectively, were simulated in the paper. The time history of sample, Fourier amplitude spectrum of sample, arithmetic average of sample, variance of sample, Wavelet time-frequency distribution of sample amd autocorrelation coefficient of sample compare well with those of the records. Scattering extent of the peaks of the sample processes is also analyzed in the paper. We can conclude that the method has great potential for engineering applications when dealing with nonstationary, nonlinear random peocesses exist in natural disasters, such as earthquake wave, vibration wave , wind wave and ocean wave.

Thermodynamic formalization of the fluid dynamics equations for a charged dielectric in an electromagnetic field

Minkowski’s classical work underlying modern electrodynamics is described. Primary attention is given to the mathematical refinements that are required if the parameters ɛ and μ depend on the properties of the dielectric fluid, i.e., the medium carrying charges in the field under study. It is shown that the motion of the medium and the accompanying evolution of the electromagnetic field are described by differential equations that are symmetric and hyperbolic in the sense of Friedrichs. This property guarantees their well-posedness. Note that this class of equations was not known in Minkowski’s time. At present, it plays an important role in the mathematical simulation of nonstationary processes and in the design of numerical algorithms. The author’s view of the mathematical foundations of Minkowski’s work is presented, which relates the latter to present-day insights into the theory of differential equations. This paper can possibly be of interest to physicists.

Synthesis of Vibration Waves Based on Wavelet Technology

A novel method to generate time series of vibration waves is proposed in the paper. Considering the frequency band energy as the criterion, synthesis formulas for fluctuating wind pressure and earthquake ground motion are developed in terms of Daubechies wavelet and Harr wavelet respectively. The wavelet reconstruction method is applicable to both stationary and non-stationary process simulation. Theoretically, for non-stationary (such as seismic) process synthesis, it has a better non-stationarity in time-frequency domain than the traditional trigonometric series. Influence of wavelet delamination number and wavelet function type is also analyzed. Numerical results show that the synthesis of vibration waves based on wavelet reconstruction method contains main components of vibration, and can reflect the main properties of practical vibrations.

Synthesis of vibration waves based on wavelet technology

A novel method to generate time series of vibration waves is proposed in the paper. Considering the frequency band energy as the criterion, synthesis formulas for fluctuating wind pressure and earthquake ground motion are developed in terms of Daubechies wavelet and Harr wavelet respectively. The wavelet reconstruction method is applicable to both stationary and non-stationary process simulation. Theoretically, for non-stationary (such as seismic) process synthesis, it has a better non-stationarity in time-frequency domain than the traditional trigonometric series. Influence of wavelet delamination number and wavelet function type is also analyzed. Numerical results show that the synthesis of vibration waves based on wavelet reconstruction method contains main components of vibration, and can reflect the main properties of practical vibrations.

Partially neutral two-component systems

The formation of high-current electron beams whose charge is partially neutralized by ions with currents exceeding the limiting Alfven current is analytically considered. The results of a measurement of the parameters of high-current electron beams formed in a partially neutralized state and a numerical simulation of nonstationary processes in different charge neutralization schemes are discussed.

Simulation of nonstationary processes in solid electrolyte electrochemical cells for the pulsed mode of gas composition variations

Studying processes that occur in solid electrolyte electrochemical cells when the working electrode is subjected to an impact of the reactive gas medium are of interest for both their practical application and the understanding of mechanisms of these processes. There are grounds to assume that the methods of studying the processes on electrodes by subjecting the latter to chemical pulses provide more information as compared with the conventional methods based on electric perturbations. A computer simulation of nonstationary processes in a solid electrolyte electrochemical cell of the flow-through kind is carried out. The model of these processes takes into account the transport of electrochemically active components in the gas phase, the kinetics and statics of adsorption of these substances on the gas/electrode interface, and the kinetics of electrode reactions including chemical and charge-transfer stages. Time dependences of concentration fields are calculated as well as the integral characteristics of flows, namely, the oxygen flow from the gas phase to the electrode, the oxygen flow from the electrode to the solid electrolyte, and the flow of the electrochemically active component at the cell outlet.

Electrodynamics of multifilament superconductors

A general scheme for electrodynamics of composite multifilament superconductors is presented. Our approach is based on an anisotropic continuum model for a multifilament wire taking into account smooth dependence of superconductor conductivity on temperature, magnetic field and current density. The electrodynamics equations are self-consistently treated together with heat transfer. On the base of this scheme, 2D codes were developed for simulation of non-stationary processes in composite superconductors. A comparison of current density dynamics in twisted and non-twisted multifilament wires is presented as an example. The dynamics of current density in a twisted wire proved to be determined by two characteristic times and differs from the predictions based on the critical state model.

Simulation of nonstationary processes in backward-wave tube with the self-modulation of emission (Carcinotrode)

The equations that describe nonlinear nonstationary processes in carcinotrode (backward-wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscillations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self-modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode-grid static field.