Nonstationary Systems Research Articles

Stabilization of a linear non-stationary system under conditions of delay and additive sinusoidal perturbation of the output

Stabilization of a linear non-stationary system under conditions of delay and additive sinusoidal perturbation of the output

Exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations of covariances or correlations

Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate amplitude distributions of such systems are of considerable interest. Extending previous work, we view a set of measured, non-stationary correlation matrices as an ensemble for which we set up a random matrix model. We use this ensemble to average the stationary multivariate amplitude distributions measured on short time scales and thus obtain for large time scales multivariate amplitude distributions which feature heavy tails. We explicitly work out four cases, combining Gaussian and algebraic distributions. The results are either of closed forms or single integrals. We thus provide, first, explicit multivariate distributions for such non-stationary systems and, second, a tool that quantitatively captures the degree of non-stationarity in the correlations.

Assessment of chlorinated ethenes degradation after field scale injection of activated carbon and bioamendments: Application of isotopic and microbial analyses

Over the last decade, activated carbon amendments have successfully been applied to retain chlorinated ethene subsurface contamination. The concept of this remediation technology is that activated carbon and bioamendments are injected into aquifer systems to enhance biodegradation. While the scientific basis of the technology is established, there is a need for methods to characterise and quantify the biodegradation at field scale. In this study, an integrated approach was applied to assess in situ biodegradation after the establishment of a cross sectional treatment zone in a TCE plume. The amendments were liquid activated carbon, hydrogen release donors and a Dehalococcoides containing culture. The integrated approach included spatial and temporal evaluations on flow and transport, redox conditions, contaminant concentrations, biomarker abundance and compound-specific stable isotopes. This is the first study applying isotopic and microbial techniques to assess field scale biodegradation enhanced by liquid activated carbon and bioamendments. The injection enhanced biodegradation from TCE to primarily cis-DCE. The Dehalococcoides abundances facilitated characterisation of critical zones with insufficient degradation and possible explanations. A conceptual model of isotopic data together with distribution and transport information improved process understanding; the degradation of TCE was insufficient to counteract the contaminant input by inflow into the treatment zone and desorption from the sediment. The integrated approach could be used to document and characterise the in situ degradation, and the isotopic and microbial data provided process understanding that could not have been gathered from conventional monitoring tools. However, quantification of degradation through isotope data was restricted for TCE due to isotope masking effects. The combination of various monitoring tools, applied frequently at high-resolution, with system understanding, was essential for the assessment of biodegradation in the complex, non-stationary system. Furthermore, the investigations revealed prospects for future research, which should focus on monitoring contaminant fate and microbial distribution on the sediment and the activated carbon.

Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity.

We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the "climate" associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as "regime transitions"). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.

Statistical properties of the detrended multiple cross-correlation coefficient

Cross-correlations are ubiquitous in nonstationary multivariable systems. By using detrended cross-correlation (DCCA) technique, recently a new multiple cross-correlation coefficient DMC was proposed to quantity the correlation between multivariate and a target variable. We studied the statistical properties of DMC in detail. More specifically, we first proved that 0≤DMC≤1, and then deduced that the DMC is approximately χ2 distributed for overlapping windows with different window size. In addition, the range of DMC was determined numerically by statistical test, where the multiple correlations can be regarded as statistically significant. Furthermore, we discussed the influence of the cross-correlation among the target variable and independent variables on DMC. Finally, by utilizing this statistical test on financial system and environment data, we found that the US dollar index affects international gold spot prices and West Texas Intermediate oil price greatly, and PM2.5 dominates in Beijing’s AQI system.

Investigation of transport properties and characteristics of a large karst aquifer system in southern China using correlation, spectral, and wavelet analyses

Karst aquifers are highly heterogeneous, and non-stationary systems in terms of hydrodynamic properties. The investigation of the different transport properties and characteristics of a karst aquifer system (KAS) is of great significance for the management and protection of karst aquifers. To investigate the response of discharge (Q), suspended sediment (SS), and temperature (T) to the precipitation (P), we performed correlation, spectral, and wavelet analyses on the hydrologic time series that included mean daily value from 2009/1/1 to 2015/12/31 from the Nandong underground river system (NURS), a large (> 1600 km2) karst-groundwater basin in southern China. The long memory effects can be determined from the autocorrelation functions of the Q, SS and T implied that the NURS has a significant amount of storage. The sharp and narrow cross-correlation function (CCF) peaks and the cross-wavelet transform (XT) power spectrum of the SS vs. P indicated that the response of the SS to P was shorter than that of the Q and T, and also indicated that the weak memory effect and small inertia of the karst systems with regard to SS. The CCF and XT power spectrum indicated that an increase in Q was the main factor triggering the increase in SS, not precipitation, which is contrary to results determined for other karst springs. Furthermore, the XT and cross-wavelet coherence (TC) of T vs. the air temperature (Ta) was used to demonstrate that Ta is not a direct control on the T in the NURS, which can be misinterpreted when using the traditional correlation and spectral analyses.

Nonstationary incompressible Navier-Stokes system governed by a quasilinear reaction-diffusion equation

In this paper, we consider a new class of a dynamic system which couplesa nonstationary incompressible Navier-Stokes equation involving nonmonotone and multivalued boundary 条件 of subdifferential type,and a generalized quasilinear reaction-diffusion equation with the Neumann boundary condition.The variational formulation of the system is provided in the form of an evolutionary hemivariational inequality coupled with the nonlinear parabolic equation. The main result concerning with the existence of global weak solutions to the system is proved.Firstly, the backward Euler technique and the feedback iterative method are used to develop a temporally semi-discrete approximate 问题. Next, invoking a surjectivity result for weakly-weakly upper semicontinuous multivalued operators, the existence and $a$ $priori$ estimates for the 解 to the semi-discrete approximate 问题 are established. Finally, using a limiting procedure for solutions to the approximate 问题, a 定理 on the existence of weak solutions to the system is obtained.

Hydrodynamics around long vibrating beams

The paper is devoted to the study of hydrodynamics around long cantilever beams that perform flexural vibrations in first natural mode in a viscous incompressible fluid. The study is based on the numerical three-dimensional simulation of flows induced by vibrations. The fluid motion is described by the full non-stationary system of Navier–Stokes equations and the oscillation profile of the beam is determined according to the Euler–Bernoulli theory. In the framework of the research, the analysis of the changes of hydrodynamics around the beams that are caused by an increase of the relative length, dimensionless frequency and amplitude of oscillations is made, in particular, the applicability of a quasi-two-dimensional theory is considered. According to the results of the study, the dynamic processes of vortex formation in a wide range of vibration frequencies and amplitudes are described, the map of the observed flow regimes is constructed, and analysis of the dependence of hydrodynamic forces on the vibration parameters is carried out.

A Tutorial Review on Time-Frequency Analysis of Non-Stationary Vibration Signals with Nonlinear Dynamics Applications

Time-frequency analysis (TFA) for mechanical vibrations in non-stationary operations is the main subject of this article, concisely written to be an introducing tutorial comparing different time-frequency techniques for non-stationary signals. The theory was carefully exposed and complemented with sample applications on mechanical vibrations and nonlinear dynamics. A particular phenomenon that is also observed in non-stationary systems is the Sommerfeld effect, which occurs due to the interaction between a non-ideal energy source and a mechanical system. An application through TFA for the characterization of the Sommerfeld effect is presented. The techniques presented in this article are applied in synthetic and experimental signals of mechanical systems, but the techniques presented can also be used in the most diverse applications and also in the numerical solution of differential equations.

Фізика геокосмічних бур

A review of our knowledge about the coupling of solar-terrestrial processes, manifestations of geospace storms, and variations in space weather is presented. Space weather effects are analyzed within the system paradigm concept. The system where geospace storms occur is a Sun–interplanetary medium–magnetosphere–ionosphere–atmosphere–Earth (interior spheres) aggregate (SIMMIAE). An early twenty-first- century geospace superstorm that occurred on November 7 – 10, 2004, is examined in detail. Clustered instrument observations of this storm effects are presented. The investigation of the physical effects of geospace storms is noted to be the most important field of study in space geophysics. The problem of subsystem coupling in the SIMMIAE system during a geospace storm is interdisciplinary in nature. Its solution requires an application of the system approach. The problem has a multifactor character. The subsystem response is determined by the simultaneous (synergetic) impact of a few disturbing factors. It is important to note that the SIMMIAE is an open, nonlinear, and nonstationary system. Within it, direct coupling and feedback processes, positive and negative linkages operate. Due to the myriads of manifestations of geospace storms, because of the unique nature of each storm, the investigation of occurring physical effects is far from complete. In addition to a thorough investigation of the storm’s physical effects, there is an urgent need to model and forecast the storms adequately and in detail. The solution to these problems will facilitate the survival and steady progress of our civilization, relying more and more on new state-of-the-art technology. The more technologically reliant our society is, the more vulnerable the civilization's infrastructure to solar and geospace storm impacts becomes. A classification of geostorms based on Akasofu's epsilon parameter has been advanced. Six types of geostorm have been introduced, and a geostorm index has been suggested. A classification of ionospheric storms and disturbances based on the magnitude of variations in the peak density of the F2 layer has been suggested. Five types of the ionospheric storm have been introduced. An ionospheric index characterizing the intensity of negative and positive ionospheric storms has been suggested. A classification of ionospheric storms and disturbances based on the magnitude of variations in the lower-ionosphere electron density has been proposed. Six types of the positive ionospheric storm have been introduced. The appropriate ionospheric index has been suggested. The physics-based model of the evolution of each group of ionospheric storms and disturbances has been determined. The linkages among magnetic, ionospheric, and atmospheric storms, as well as electric field disturbances, have been shown.

О методе построения линейной нестационарной дискретной системы с управлением полной размерности посредством изменения шага квантования

The method that allows one to reduce a stationary system with control of incomplete dimension to a non-stationary periodic system with control of full dimension is considered in this article. The paper proves the equivalence of these systems, and also that the optimal in terms of speed for a non-stationary system is also optimal for the original stationary system. A satellite attitude control system is considered as an example.

Synthesis of non-stationary continuous nonlinear control systems by the generalized Galerkin method

Synthesis of non-stationary continuous nonlinear control systems by the generalized Galerkin method

Efficient manufacturing processes and performance qualification via active learning: Application to a cylindrical plunge grinding platform

The industry invests significant resources towards qualification of its individual processes and machines to assure quality and productivity of the process chain. Process qualification traditionally involves employing elaborate experimental methods to find the response surface mapping the response to various process parameters and measurements. Most of the existing methods are passive experimental designs which take into account the limits of the parameter space and a design method (CCD, Taguchi, orthogonal etc.) to identify the points in the parameter space. More often than not, these methods need a lot of experiments to be conducted and do not take into account how the response changes with each experiment. Also, the number of experiments increase combinatorically to get a desired estimate of the response surface. The formulation of mathematical models for complex, high dimensional, inherently nonstationary, and stochastic systems like abrasive machining process and also catering to the process-machine interactions is challenging. In this work, to address the other alternative for cost-effective experimentation: we adapt a Query by Committee (QBC) based active learning approach where we sequentially find the next best experimental point to reduce the uncertainty of prediction of surface roughness over the sample space. The method uses a carefully curated list of committee members, (i.e., models) which predict the response surface at each instant and selects the next experimental point based on a metric called prediction deviation. We used a real-world dataset from a cylindrical plunge grinding platform to test if the QBC approach performs better than a passive CCD design. The machine tool used is the next generation precision grinder (NGPG) from IIT Madras which is capable to finishing components to an IT3 tolerance grade. We compared the QBC based active learning model to a previous random forest model built on a dataset which gave a test accuracy (R2) of 85% using 178 experimental points. It is demonstrated that similar prediction accuracies can be achieved by reducing the number of experiments by about 65%. The merits of the model in the choice of the members of the committee and the advantage of the current experimental design compared to random experimentation were presented.

Software tools for analysis and synthesis of stochastic systems with high availability (XII)

The article proceeds the thematic cycle dedicated to analysis and synthesis for mean square criteria software tools for vector nonstationary (e.g. shock disturbances) linear stochastic systems with high availability (StSHA). Methodological support is based on Haar wavelet expansions (WLE) and wavelet canonical expansions (WLCE). Sect.1 is dedicated to problems statements. General basic algorithm is given in Sect. 2. Algorithms for StSHA with linear parameters and additive noises based on WLE and WLCE are described in Sect.3. Software tools in MATLAB are considered in Sect. 4. For typical shock disturbances bank of algorithms is developed. Complex of examples is given in Sect.5. Some generalizations are presented.

Method for finding a solution to a linear nonstationary interval ОDЕ system

The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. Оn the basis of these conditions, the method of the steepest descent is applied to the original problem. Some examples illustrate the constructed algorithm realization.

Homogenization of nonstationary Maxwell system with constant magnetic permeability

Изучается нестационарная система Максвелла в $\mathbb{R}^3$ с диэлектрической проницаемостью $\eta(\varepsilon^{-1}{\mathbf x})$ и магнитной проницаемостью $\mu$. Здесь $\eta(\mathbf{x})$ - положительно определенная и ограниченная симметричная матрица-функция размера $3\times 3$, периодическая относительно некоторой решетки, а $\mu$ - постоянная положительная $(3 \times 3)$-матрица. Получены аппроксимации решений по норме в $L_2(\mathbb{R}^3;\mathbb{C}^3)$ при фиксированном времени с оценками погрешностей операторного типа.

Применение уравнения Больцмана для определения аэродинамических характеристик летательных аппаратов

In this paper we present the derivation of new one-dimensional non-stationary nonlinear system of moment equations and an approximation of the microscopic boundary condition when part of molecules reflect from the surface specularly and part diffusive with Maxwell’s distribution. Macroscopic boundary conditions for the system of moment equations depend on the evenness and oddness of the approximation , where is the partial sum of expansion of the distribution function of molecules  into eigenfunctions of the linearized collision operator. The formulation of the initial and boundary value problem for the system of moment equations in the third approximation under the Maxwell-Auzhan macroscopic boundary conditions is given. To analyze aerodynamic characteristics of aircraft in transient regime was used complete integro-differential Boltzmann equation, which contains a term depending on the moving speed of aircraft, and under Maxwell's microscopic boundary conditions, depending on the surface temperature.

Fluctuation-dissipation relations far from equilibrium: a case study.

Fluctuation–dissipation relations or “theorems” (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-from-equilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to equilibrium correlation functions, and the second FDT relates the memory friction kernel in the GLE to the stochastic force. We find that the validity of the first FDT depends strongly on the strength of the external driving: it is fulfilled close to equilibrium and breaks down far from it. In contrast, we observe that the second FDT is always fulfilled. We provide a mathematical argument why this generally holds for memory kernels reconstructed from a deterministic Volterra equation for correlation functions, even for non-stationary non-equilibrium systems. Motivated by the Mori–Zwanzig formalism, we therefore suggest to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation. Such GLEs automatically satisfy the second FDT and are unique, which is desirable when using GLEs for coarse-grained modeling.

ПОКРАЩЕННЯ БЕЗПЕКИ ДОРОЖНЬОГО РУХУ ЗА ДОПОМОГОЮ АВТОМАТИЗОВАНОГО УПРАВЛІННЯ ДОРОЖНІМ РУХОМ

The article considers automated traffic flow control systems, their classification and description. Based on the above, it can be argued that traffic control systems have the characteristics of distributed, discrete and non-stationary complex systems used to solve traffic control problems by modern means of information and computer technology. The object of research is to improve traffic control with the help of automated control systems Purpose - analysis of automated traffic management systems With the rapid growth of the car fleet, there is an overload of the street and road network of cities. Even today, the street and road network does not meet the requirements for the organization and safety of road traffic. A survey of traffic flows shows that the road network operates at the capacity limit, and in some places exceeds this limit. The main reason for this transport situation in cities is the mismatch between the level of motorization and the density of the road network. Therefore, to improve, improve traffic control, it is proposed to use automated traffic management systems. But first you need to analyze them in detail. It is noted that the efficiency of the street and road network depends entirely on the effective balanced operation of all its elements. KEYWORDS: CAR, AUTOMATED SYSTEMS, ROAD TRANSPORT MANAGEMENT SYSTEMS, TRANSPORT NETWORK, TRANSPORT FLOW.

Design of Production Systems. 3. Tool Design

A module for tool development (including design) is analyzed within the framework of the proposed design procedure for nonstationary production systems. Specifically, the tool considered is used for slipway machining of channels to be welded into submarine hulls.