Nonstationary Processes Research Articles

Assessing decarbonization: a comparison of the green sacrifice ratio for China and India

ABSTRACT Carbon mitigation and net-zero targets have an important place on the political agenda for all countries. Countries have been seeking to decouple economic growth and carbon emissions to achieve decarbonization. However, there is a cost of the decarbonization of economies, which can be called as Green Sacrifice Ratio (GSR), and this is critical for developing countries because they have been in the growing stage. By considering the critical role of GSR in achieving net-zero emissions by decarbonizing economies, the study comparatively examines how much environmental quality should be sacrificed for per capita economic growth in China and India. In line with this purpose, the study uses the Fourier-Shin cointegration test and various time series estimators with Fourier approximations for the period from 1989/Q1 to 2022/Q4. Estimation results are as follows: (i) all variables follow the non-stationary process, (ii) the long-run relationship exists between variables, and (iii) Estimation results show that GSR is 0.65% for China and 0.78% for India. Therefore, China and India sacrifice a significant amount of environmental quality for a 1% increase in per capita income level. Also, the ecological cost of increasing economic welfare in India is higher with regard to China. Besides, the results are robust according to the alternative method. Thus, the study recommends that both Chinese and Indian policymakers should revise the economic expansion structure with green growth strategies to prevent irreversible environmental degradation due to higher economic growth.

A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Processes

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameter estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is , exact recovery of true change-points is possible in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to the U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method.

Анализ фильтрационного процесса в угольном пласте, отрабатываемом длинными столбами по простиранию

The underground coal field mining is inevitably associated with coal oxidation process accompanied with the thermal energy emission and the formation of coal self-heating spots. The self-heating spots can emerge in both coal dust accumulations deposited in the excavations and in the excavated coal seams. It is known that self-heating is caused by both chemical processes accompanied with heat emission and physical processes, primarily the filtration of gas-air mixtures through porous and fractured layers of rocks and coal seams. Although the filtration processes accompanying oil and gas field exploration have been thoroughly studied, similar processes accompanying coal mining have been studied less. The article focuses on the mathematic problem concerning the filtration process in the coal seam when excavated by long pillars. In this system, both fresh airflows and worked out flows move in opposite directions and under different pressures along the mine roadway and the ventilation opening. This causes so-called air suctions due to air infiltration through the coal seam. In theory, this problem has not been solved yet and thus is considered urgent. Based on the classic filtration theories and assumptions regarding the coal seam isotropy and homogeneity, the one-dimensional initial value problem describing the non-stationary air filtration process through the coal seam was formulated. The solution provided explicit formulas to determine the pressure and rate of air-gas mixture filtration and identified several regularities of the filtration process in the coal seam. Particularly, it was established that the filtration rate increases significantly in the direction towards the ventilation opening, especially at the initial stages of filtration. In process of time, however, the filtration rate aligns and after 5 days, the rate difference is not so significant.

Online Detection Method for Capacitor Voltage Transformer Measurement Error Adapted to Non-Stationary Random Processes

Online Detection Method for Capacitor Voltage Transformer Measurement Error Adapted to Non-Stationary Random Processes

NON-STATIONARY WAVES IN A FUNCTIONALLY GRADED VISCOELASTIC PLANE-PARALLEL LAYER2

The propagation of nonstationary disturbances in a plane-parallel layer of infinite extent, which arise as a result of normal dynamic loading of one of its surfaces when the other surface is stationary, is investigated. The material of the layer is assumed to be functionally graded and, at the same time, viscoelastic. The hereditary properties of such a material are taken into account using linear integral Boltzmann–Volterra relations with regular kernels in the form of partial sums of the Prony's series. The peculiarity of this work is that here the parameters of the relaxation kernels are considered continuous functions of the transverse coordinate in the same way as other physical and mechanical characteristics. A method was used for the study, which consists in replacing a functionally graded material with an approximating layered homogeneous structure with continuity conditions at the contact of homogeneous layers. The solution of the nonstationary dynamic linear viscoelasticity problem for a package of plane homogeneous viscoelastic layers is presented in a special form, which greatly simplifies its numerical implementation, especially with a large number of layers with different hereditary properties. This made it possible to successfully apply this method and carry out a series of calculations using an efficient algorithm. Transient wave processes are investigated in the case when the parameters of a functionally graded material are non-monotonic functions of the transverse coordinate, symmetrical with respect to the middle surface of the layer. A comparison of transient wave processes for different types of these functions is carried out. The convergence of the calculation results with an increase in the number of approximating homogeneous layers with a continuous dependence of the external load on time is confirmed. The significant influence of both heterogeneity and viscosity of the material on nonstationary wave processes has been established.

Thermophysical model of a thermonic cathode with induction heating

A thermophysical model was built and the temperature field of a cylindrical thermionic cathode with induction heating was calculated, taking into account the initial and boundary conditions, based on the adoption of assumptions to simplify the mathematical model. During the induction heating of the cathode, a non-stationary heat conduction process is established, which is described by the differential equation of heat conduction with internal sources of Joule heat. The distribution of internal heat sources in the volume of the cathode is determined by the distribution of the ring induced current. The cylindrical design of the inductive thermionic cathode, due to spatial symmetry, allows to reduce the number of spatial variables, significantly simplify functional dependencies, and limit the algorithm for solving the problem. The problem was solved in the cylindrical coordinate system. The obtained approximate solutions were assessed for the correctness of the accepted simplifications when finding the distribution of the temperature field with a sufficient degree of accuracy. Despite the high thermal conductivity of the cathode material, when the cathode is inductively heated, there can be a significant temperature difference between its outer and inner surfaces. The article shows the permissible temperature difference on the surface of the cathode, which limits the choice of geometric dimensions of the cathode. The temperature difference on the surfaces of the induction thermionic cathode is most affected on the end (annular) surfaces of the cathode, so it is better to apply emitting coatings to the side surfaces of the cylindrical cathode, thus complicating the design of the cathode. The application of induction heating of the thermionic cathode allows to simplify the heating unit, increase the reliability and service life of powerful electronic devices. The obtained results are planned to be used in further research as test data for the analysis of more complex problems of numerical calculation of the thermal regimes of the cathode unit with heat shields and focusing elements of thermoelectron flows.

Численное моделирование термогазодинамических процессов в модельных РДТТ с помощью трехмерного параллельного кода

An approach for calculating non-stationary thermo-gasdynamic processes in model chambers of solid rocket engines is described. A three-dimensional mathematical model of viscous multicomponent gas mixture is an extended system of Navier-Stokes equations with the component diffusion equations. The computational model and the computer code are based on the developed original mathematical methodology that combines the advantages of splitting method by physical processes, robustness of Godunov's scheme for the convective stage and efficiency of explicit iterative Chebyshev’s scheme for diffusion stage. The code is written in C++ and uses a hybrid three-level parallel structure, including the use of MPI, OpenMP and CUDA technologies.

Review of methods and devices for determining the resistance to heat transfer under natural conditions

The purpose of this study is to review modern methods of determining the resistance to heat transfer of building envelopes under natural conditions using experimental equipment. Methods for experimental determination of the resistance to heat transfer given in regulatory documents have been considered. Golunov S.V. and co-authors developed a method of determining the resistance to heat transfer based on thermal imaging examination with the placement of sensors on the surfaces of the building envelopes. Abramova E.V. together with other researchers created a method of thermal non-destructive testing using a thermal imaging system, temperature and heat flow sensors. The possibility of experimentally determining the reduced resistance to heat transfer of external building envelopes under summer operating conditions using the device developed by A.E. Rusanov’s with co-authors has been described. Wang Xin et al. proposed a device for determining the resistance to heat transfer of building envelopes with improved accuracy. As a result of the analytical review, it was concluded that the presented methods make it possible to measure the resistance to heat transfer of external building envelopes when modeling various stationary and non-stationary heat transfer processes.

Penetration of a Silicon Vapor through Residual Gaseous Medium during Siliconizing of a Carbon Composite Material

A new physical and mathematical approach is proposed for the description of a silicon vapor high-temperature transfer from the melt mirror to the surface of absorbing carbon porous medium in an atmosphere of residual gas under moderate vacuum conditions. The general hydrodynamic equations are simplified as much as possible and lead to the model, which is intended for further numerical implementation in the course of simulation the non-stationary three-dimensional process of high-temperature siliconizing of porous carbon products of arbitrary shape and under the condition of complex distribution of silicon sources and sinks. The physical and mathematical model of transport consists of only one non-linear differential equation in partial derivatives for the silicon vapor concentration in the atmosphere of argon or any other residual gas. The main achievement consists of obtaining two stationary analytical solutions for plane and cylindrical geometry in one-dimensional formulation of the problem, which explain the anomalously large silicon vapor flux into the porous material in full-scale experiments. The exact solutions for the studied gas mixtures are expressed in terms of the well-known verified values of material parameters. The high degree of the model usability is supported by numerical simulation in a non-steady two-dimensional case. It has shown that despite the low saturation density of gaseous silicon, the vapor-liquid phase process of high-temperature siliconizing of the carbon material is physically possible in a reasonable time.

Bayes synthesis of multidimensional stochastic system with high availability by wavelet canonical expansions

Paper in devoted to methodological and instrumental software synthesis support for multidimensional stochastic systems with high availability (StSHA). For modeling of nonstationary stochastic processes (StP) it is supposed to implement wavelet canonical expansions (WLCE), based on coefficients of canonical expansions of covariance matrix using two dimensional orthonormal wavelet basis with compact carrier. Vector StSHA input and output are nonlinear on vector of random parameters with known probability density and Gaussian (normal) noise. Noises do not depend upon random parameters. Functional Bayes criterion (FBC) is presented by linear functional. Optimal system is synthesized using conditional risk criterion. General StSHA synthesis method and algorithm contains 4 steps and 7 positions. FBC optimal estimate is calculated by WLCE method. Special software is developed for scalar nonlinear StSHA. Results of computer experiments are given and discussed. His shown that high efficiency of method at 8 WLCE items. Directions of future investigations are presented.

A Novel Multiscale Gated Structure Model for Soft Sensing of Nonstationary Process With Randomly Missing Data

A Novel Multiscale Gated Structure Model for Soft Sensing of Nonstationary Process With Randomly Missing Data

The effect of porous coatings obtained by various methods on heat transfer and crisis phenomena during nitrogen boiling including non-stationary heating and cooling

The paper presents the main results of experimental investigation of the influence of porous coatings obtained by various methods on heat transfer and crisis phenomena during nitrogen boiling, including unsteady heating and cooling regimes. Modification of heater surfaces was carried out by the methods of directed plasma spraying, additive 3D printing and micro-arc oxidation. For all types of porous coatings, a significant intensification of heat transfer at atmospheric pressure relative to smooth heaters was obtained (maximum degree of heat transfer increase up to 6 times). The mechanisms playing a determining role in the process of heat transfer coefficients increase are suggested. The essential influence of structured capillary-porous bronze coatings on the dynamics of transient processes and development of crisis phenomena of non-stationary processes is shown, leading to degeneration of the heat transfer crisis at pulse supply of heat load and significantly reducing the time of complete cooling of the heater in the process of rewetting.

Studying electrical activity of the brain within the concept of coordination of rhythmic processes

Purpose of this work is to study the effects of one-day sleep deprivation using the concept of coordination between brain rhythms as a complex network. The research method is the cross-correlation analysis of non-stationary processes, which is an extension of fluctuation analysis to the case of two signals. Recordings of electrocorticograms of mice in two states are considered: before and after sleep deprivation. As a result of the studies carried out, differences have been established between functional states, the diagnosis and quantitative description of which can be carried out using local scaling exponent. Conclusion. Additional possibilities for analyzing the complex dynamics of electrical activity of the brain within the framework of the concept of rhythm coordination are illustrated.

Optimized Distributed Nonstationary Process Monitoring Approach Based on Fault-Related Information and Partial Correlation Fusion

Optimized Distributed Nonstationary Process Monitoring Approach Based on Fault-Related Information and Partial Correlation Fusion

Causal Inference From Slowly Varying Nonstationary Processes

Causal Inference From Slowly Varying Nonstationary Processes

Continual Learning-Based Probabilistic Slow Feature Analysis for Monitoring Multimode Nonstationary Processes

A novel continual learning-based probabilistic slow feature analysis algorithm is introduced for monitoring multimode nonstationary processes. Multimode slow features are extracted and an elastic weight consolidation (EWC) is adopted for sequential modes. EWC was originally introduced in the setting of machine learning of sequential multi-tasks with the aim of avoiding catastrophic forgetting issue, which equally poses as a major challenge in multimode nonstationary process monitoring. When a new mode arrives, a small set of data are collected for continual learning by the proposed algorithm. A regularization term is introduced to prevent new data from significantly interfering with the learned knowledge, where the parameter importance measures are estimated. The proposed method is referred to as PSFA–EWC, which is updated continually and is capable of achieving excellent performance. PSFA–EWC furnishes backward and forward transfer ability by a single model. The significant features of previous modes are retained while consolidating new information, which may contribute to learning new relevant modes. The effectiveness of the proposed method is demonstrated via a continuous stirred tank heater and a practical coal pulverizing system. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Since industrial systems operate in varying modes and data are nonstationary within each mode, multimode nonstationary process monitoring is increasingly important. Traditional multimode monitoring methods generally need complete data from all possible modes and may need to be retrained from scratch when a new mode arrives, which require expensive computation and storage resources. Besides, it is difficult to distinguish real faults from normal variations in multimode nonstationary processes. This paper proposes a novel continual learning-based probabilistic slow feature analysis, where elastic weight consolidation is employed to consolidate the previously learned knowledge while extracting multimode slow features. The monitoring model is updated sequentially and provides backward as well as forward transfer learning ability for successive modes. It is able to separate real faults from normal dynamics, which is beneficial to identifying a new mode for multimode nonstationary processes. In addition, the proposed approach delivers excellent model interpretability and deals with missing data as well as uncertainty. In industrial applications, such as power plants and intelligent manufacturing processes, the proposed method can provide excellent monitoring performance.

On the stability of a nonlinear nonautonomous scalar equation with variable delay

The stability problem of a scalar functional differential equation is a classical one. It has been most fully studied for linear equations. Modern research on modeling biological, infectious and other processes leads to the need to determine the qualitative properties of the solutions for more general equations. In this paper we study the stability and the global limit behavior of solutions to a nonlinear one-dimensional (scalar) equation with variable delay with unbounded and bounded right-hand sides. In particular, our research is reduced to a problem on the stability of a non-stationary solution of a nonlinear scalar Lotka-Volterra-type equation, on the stabilization and control of a non-stationary process described by such an equation. The problem posed is considered depending on the delay behavior: is it a bounded differentiable function or a continuous and bounded one. The study is based on the application of the Lyapunov-Krasovsky functionals method as well as the corresponding theorems on the stability of non-autonomous functional differential equations of retarded type with finite delay. Sufficient conditions are derived for uniform asymptotic stability of the zero solution, including global stability, for every continuous initial function. Using the theorem proven by one of the co-authors on the limiting behavior of solutions to a non-autonomous functional differential equation based on the Lyapunov functional with a semidefinite derivative, the properties of the solutions’ attraction to the set of equilibrium states of the equation under study are obtained. In addition, illustrative examples are provided.

Non-equilibrium Onsager–Machlup theory

This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or ‘piecewise’) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein–Uhlenbeck stochastic process (which is globally stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager–Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager–Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the non-equilibrium self-consistent generalised Langevin equation (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model.

A Two-Step Estimation Method for a Time-Varying INAR Model

This paper proposes a new time-varying integer-valued autoregressive (TV-INAR) model with a state vector following a logistic regression structure. Since the autoregressive coefficient in the model is time-dependent, the Kalman-smoothed method is applicable. Some statistical properties of the model are established. To estimate the parameters of the model, a two-step estimation method is proposed. In the first step, the Kalman-smoothed estimation method, which is suitable for handling time-dependent systems and nonstationary stochastic processes, is utilized to estimate the time-varying parameters. In the second step, conditional least squares is used to estimate the parameter in the error term. This proposed method allows estimating the parameters in the nonlinear model and deriving the analytical solutions. The performance of the estimation method is evaluated through simulation studies. The model is then validated using actual time series data.

NEURAL ORDINARY DIFFERENTIAL EQUATIONS FOR TIME SERIES RECONSTRUCTION

Context. Neural Ordinary Differential Equations is a deep neural networks family that leverage numerical methods approaches for solving the problem of time series reconstruction, given small amount of unevenly distributed samples.&#x0D; Objective. The goal of the following research is the synthesis of a deep neural network that is able to solve input signal reconstruction and time series extrapolation task.&#x0D; Method. The proposed method exhibits the benefits of solving time series extrapolation task over forecasting one. A model that implements encoder-decoder architecture with differential equation solving in latent space, is proposed. The latter approach was proven to demonstrate outstanding performance in solving time series reconstruction task given a small percentage of noisy and uneven distributed input signals. The proposed Latent Ordinary Differential Equations Variational Autoencoder (LODE-VAE) model was benchmarked on synthetic non-stationary data with added white noise and randomly sampled with random intervals between each signal.&#x0D; Results. The proposed method was implemented via deep neural network to solve time series extrapolation task.&#x0D; Conclusions. The conducted experiments have confirmed that proposed model solves the given task effectively and is recommended to apply it to solving real-world problems that require reconstructing dynamics of non-stationary processes. The prospects for further research may include the process of computational optimization of proposed models, as well as conducting additional experiments involving different baselines, e. g. Generative Adversarial Networks or attention Networks.