Stationary Ones Research Articles

Moderate deviation principles for unbounded additive functionals of distribution dependent SDEs

<p style='text-indent:20px;'>By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with non-degenerate and degenerate noises.</p>

Sustainability assessment of difficult-to-cut materials using rotary tools: a step towards sustainable machining environment

Difficult-to-cut materials offer superior properties such as high chemical stability, strength-to-weight ratio, and corrosion resistance. However, machining these materials is facing huge challenges due to localized high levels of temperature, especially when using traditional tools. Machining using rotary tools is a suitable technique that is used to machine difficult-to-cut materials which provides acceptable tool life, even under dry conditions. Rotary tools offer significant improvements compared to conventional tools especially in dry conditions, which makes this technology a good candidate to achieve a sustainable machining environment. Despite all attempts in modeling, analysis, and optimization of machining using rotary tools, it was found that no previous study has focused on the sustainability aspects related to the application of rotary tools in machining operations. Thus, in the current work, an attempt has been made to assess and prove the effectiveness of machining with rotary tools. Two different case studies are presented and discussed to evaluate and assess the sustainability effectiveness of rotary tools compared to stationary ones under different cooling and lubrication environments (i.e., flood, minimum quantity lubrication (MQL), and dry). The results showed that machining using SPRT under dry conditions provided higher total weighted sustainability index compared to the traditional approach for both case studies. Finally, a detailed mechanism for machining with a rotary tool is fully presented and discussed to physically prove the sustainability effectiveness of such technology. It was concluded from the sustainability assessment results that using self-propelled rotary tools under a dry environment showed significant results which proved the applicability of using rotary tools as a sustainable technology.

A nonlinear full condition process monitoring method for hot rolling process with dynamic characteristic

As a typical complex industrial process, hot rolling process (HRP) is different from chemical process. Strip steels are produced coil by coil, that means there is a long idle period between coils. The rolling speed is very high and the producing time of each coil is usually a few minutes. Previous researches mostly focus on fault detection in loaded condition and very few attempts have been made to exploit the monitoring of idle condition. In order to monitor the whole process, not only the loaded condition, but also the idle one, a novel nonlinear full condition process monitoring model is developed in this work. First, a dissimilarity index (DI) is defined for condition identification and a support data vector description (SVDD) model is established to monitor the idle condition. Second, t-distributed stochastic neighbor embedding (t-SNE) is used to extract nonlinear principal components (NPC) for slow feature analysis (SFA) and cointegration analysis (CA). Nonlinear cointegration analysis (NCA) can reveal the long-run dynamic relations of nonstationary parts, while nonlinear slow feature analysis (NSFA) can extract the latent temporal dynamic and static variations of stationary ones. Finally, the monitoring performance of the proposed model is verified through a real HRP.

Multiple Time-Frequency Curve Classification for Tacho-Less and Resampling-Less Compound Bearing Fault Detection Under Time-Varying Speed Conditions

Rotating machinery usually runs at time-varying speeds, which often brings failures, especially compound faults. However, currently, there is still a lack of satisfactory coupled fault diagnosis methods at variable speeds. Several methods have been developed, which try to eliminate rotational speed influences by converting nonstationary fault characteristic frequencies into stationary ones. But it brings new problems of computational efficiency and accuracy, and requires an auxiliary tachometer to measure the rotational speed. Time-frequency analysis can solve the problems, and extract time-frequency curves for fault diagnosis through time-frequency representation (TFR). However, for signals containing multiple faults at variable speeds, uninterested components will be generated when extracting multiple time-frequency curve (MTFC), which makes it difficult for compound fault diagnosis. To solve these problems, a novel MTFC classification method for tacho-less and resampling-less compound bearing fault detection under time-varying speed conditions is proposed in this paper. Here the TFR characteristics of a multi-fault vibration signal is analyzed, and a compound fault diagnosis strategy based on MTFC classification is developed. Firstly, MTFC is extracted by a local peak search method. Then, according to the relationship between instantaneous shaft rotational frequency, instantaneous fault characteristics frequency and their respective harmonics, two classification criteria for curves are proposed and MTFC is classified into interested curves and uninterested curves. Finally, the average ratios between interested curves are matched to theoretical fault characteristic coefficients to determine the fault type. Case studies on rolling bearing experiments verified the effectiveness and superiority of the proposed method.

A model of heat pulse induced limit-cycle-oscillations in the edge of magnetically confined plasmas

Limit-cycle-oscillation (LCO) is a ubiquitous feature in low to high confinement mode transition. We propose a double-source (heat and turbulence) prey-predator model of heat pulse induced LCOs in the edge plasmas. It is shown that the development of the radial electric field is a combined process of turbulent thermal and momentum transports. The causality relation between the turbulence intensity and the radial electric field reverses during the transport channel transfer. A numerical study reveals that the appearance of LCOs can be explained as a transition from a ‘forced’ oscillation to an ‘intrinsic’ oscillation of the edge plasmas. It is also found that there exists a critical equilibrium pressure gradient, above which the transient LCOs become stationary ones, i.e. a steady I-phase may be sustained.

Development of virtual analogues of nuclear facilities in virtual reality

Using virtual reality technology - a modern trend. The nuclear industry is no exception. This article provides an overview of mathematical models used to create virtual analogue of critical assembly Godiva in virtual reality. Godiva - there is a simple example that allows to hone techniques for creating more complex virtual analogues of nuclear reactors and nuclear facilities. Mathematical models include stationary and dynamic ones. The stationary model is based on data from calculations carried out using Monte Carlo programs such as MCU, Serpent and Geant4. An approach is also described that makes it possible to calculate the reverse multiplication from the values of the effective multiplication factor for various states of the subcritical assembly. The dynamic model allows one to calculate the neutron-physical characteristics of the supercritical assembly during fast processes such as a neutron burst. In conclusion, there are other examples of virtual analogs created using similar approaches.

Modeling high-dimensional unit-root time series

This paper proposes a new procedure to build factor models for high-dimensional unit-root time series by postulating that a p-dimensional unit-root process is a nonsingular linear transformation of a set of unit-root processes, a set of stationary common factors that are dynamically dependent, and some idiosyncratic white noise components. For the stationary components, we assume that the factor process captures the temporal dependence, and that the idiosyncratic white noise series explains, jointly with the factors, the cross-sectional dependence. The estimation of nonsingular linear loading spaces is carried out in two steps. First, we use an eigenanalysis of a nonnegative definite matrix of the data to separate the unit-root processes from the stationary ones, and a modified method to specify the number of unit roots. We then employ another eigenanalysis and a projected principal component analysis to identify the stationary common factors and the white noise series. We propose a new procedure to specify the number of white noise series and, hence, the number of stationary common factors. We establish asymptotic properties of the proposed method for both fixed and diverging p as the sample size n increases, and use a simulation and a real example to demonstrate the performance of the proposed method in finite samples. We also compare our method with some commonly used ones in the literature regarding the forecast ability of the extracted factors, and find that the proposed method performs well in out-of-sample forecasting of a 508-dimensional PM2.5 series in Taiwan.

Dissecting the Multivariate Extremal Index and Tail Dependence

A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the extremal index appears as a key parameter to capture the effect of temporal dependence on the limiting distribution of the maxima. The multivariate extremal index corresponds to a generalization of this concept to a multivariate context and affects the tail dependence structure within the marginal sequences and between them. As it is a function, the inference becomes more difficult, and it is therefore important to obtain characterizations, namely bounds based on the marginal dependence that are easier to estimate. In this work we present two decompositions that emphasize different types of information contained in the multivariate extremal index, an upper limit better than those found in the literature and we analyze its role in dependence on the limiting model of the componentwise maxima of a stationary sequence. We will illustrate the results with examples of recognized interest in applications.

Imbalance Fault Detection Based on the Integrated Analysis Strategy for Marine Current Turbines under Variable Current Speed.

The conversion of marine current energy into electricity with marine current turbines (MCTs) promises renewable energy. However, the reliability and power quality of marine current turbines are degraded due to marine biological attachments on the blades. To benefit from all the information embedded in the three phases, we created a fault feature that was the derivative of the current vector modulus in a Concordia reference frame. Moreover, because of the varying marine current speed, fault features were non-stationary. A transformation based on new adaptive proportional sampling frequency (APSF) transformed them into stationary ones. The fault indicator was derived from the amplitude of the shaft rotating frequency, which was itself derived from its power spectrum. The method was validated with data collected from a test bed composed of a marine current turbine coupled to a 230 W permanent magnet synchronous generator. The results showed the efficiency of the method to detect an introduced imbalance fault with an additional mass of 80–220 g attached to blades. In comparison to methods that use a single piece of electrical information (phase current or voltage), the fault indicator based on the three currents was found to be, on average, 2.2 times greater. The results also showed that the fault indicator increased monotonically with the fault severity, with a 1.8 times-higher variation rate, as well as that the method is robust for the flow current speed that varies from 0.95 to 1.3 m/s.

A Potential Orthogonal Matching Pursuit Algorithm for Device Free Moving Target Localization

Existing Compressive Sensing (CS) based Device-Free Localization (DFL) schemes focus on stationary targets. However, targets to be localized are always movable, whose positions are not the simple combination of the stationary ones. We investigate the moving target localization scheme in this letter and propose a novel approach named as Potential Orthogonal Matching Pursuit (POMP), which can recover the target positions in multiple time intervals simultaneously. Firstly, we transfer the moving characteristic to the relationship of the location vectors under the CS framework, which significantly reduces the possible location domain of the target. Secondly, we seek all the possible target traces using the tree searching operation and design a novel measure to select the most valuable columns of the sensing matrixes through iteration. Finally, the location vectors can be obtained by the Least-Square algorithm. Simulations show that the proposed POMP can significantly improve the recovery performance compared with the existing OMP algorithm.

Nonstationary Frequency Analysis of Censored Data: A Case Study of the Floods in the Yangtze River From 1470 to 2017

AbstractCensored data (CD) of floods, that is, the combination of systematic data (SD) and historical data, can help improve the robustness of flood frequency analysis, due to its temporal information expansion. However, in nonstationary flood frequency analysis, the approach to utilize the CD has rarely been investigated. In this study, a covariate‐based nonstationary flood frequency analysis framework based on various likelihood functions using the generalized extreme value (GEV) distribution was built to utilize the CD, with uncertainty considered. This framework was applied to the study of the annual maximum flood frequency of the Yichang gauging station 44 km downstream of the Three Gorges Dam over the period from 1470 to 2017. A summer precipitation anomaly and a reservoir index were used as covariates to explain the variation of the distribution parameters. The results show that for either the SD or CD, the nonstationary models are preferred to the stationary ones by the deviance information criterion, and these nonstationary models may prove to be practical in engineering application, due to the acceptable uncertainty range in flood quantiles derived from covariates. Compared to the stationary or nonstationary models based on the SD, the corresponding model based on the CD results in a higher posterior mean and a smaller posterior standard deviation for the shape parameter of the GEV distribution. It is concluded that the use of historical information under the nonstationary frequency analysis framework may be remarkable in reducing design flood uncertainty, especially for the very small exceedance probability at the tail.

Active Broken Rotor Bar Diagnosis in Induction Motor Drives

A new active fault diagnosis strategy for broken rotor bars (BRBs) in induction motor (IM) drives is proposed. The active scheme consists of injecting a zero-sequence signal online with a standard space vector pulsewidth modulation (PWM). The injected signal is obtained by applying the null vectors of the PWM, when the star point of the IM is connected to the dc-link midpoint. The response to the injected signal is acquired by using current derivative sensors, from which the diagnostic signals are obtained. BRB faults produce new components in the spectral distribution of the diagnostic signals, which are used as a fault indicator. These components are extracted by using a proposed algorithm, based on a simple reference frame transformation. Experimental results demonstrate the validity of our proposal not only at steady state, but also at transient conditions of speed and load. This is possible because a methodology to convert the diagnostic signals to a stationary ones by resampling it as a function of the rotor position is proposed.

METHOD OF UNCERTAIN COEFFICIENTS IN PROBLEMS OF OPTIMAL STABILIZATION OF TECHNOLOGICAL PROCESSES

Context. The equivalent transformation method is examined in the given article. Its essence lies in changing of a certain class of non-stationary systems with the stationary ones, for which optimization methods are well processed. Urgency of the method is determined by the fact that in most optimal control methods, developed for continuous systems, tasks are considered in the temporary space using the states space and the matrix theory. All real control objects are known to be non-linear and non-stationary in one way or another. Analysis and synthesis of control systems for such objects is a complex mathematical issue, and its solution is received for some separate occasions for now. As a result of using the suggested method, when the variable coefficients matrix is known, the task of the non-stationary system optimal control is reduced to the task of the equivalent stationary system optimal control for which solution methods are well-known and well processed.Objective. Reducing energy intensity and improving the quality of products of various technological processes is an urgent task of the national economy of Ukraine.Methods. To achieve this goal, we propose a method of modal synthesis of optimal stabilization laws using the method of uncertain coefficients, developed by the authorsResults. Algorithm of synthesis of the optimal controller in the absence and presence of delay in the control loop is developed. The method of selection and correction of the desired spectrum of roots is proposed. To eliminate self-oscillations in the presence of a delay in the control circuit, the R. Bass method is used.Conclusions. The modal synthesis of optimal laws of stabilization of technological processes is proposed on the basis of the original method of uncertain coefficients. The complexity of the choice of the desired eigenvalues is overcome by the proposed procedure of construction and correction of the spectrum of roots in a closed system of optimal control. To eliminate the occurrence of stable self-oscillations (in the presence of a delay) in the stabilization process near a given trajectory, the Bass’s method is proposed to be used. The simulation results confirm the correctness and effectiveness of the results.

Exact Solutions and Numerical Simulation of the Discrete Sawada–Kotera Equation

We investigated an integrable five-point differential-difference equation called the discrete Sawada–Kotera equation. On the basis of the geometric series method, a new exact soliton-like solution of the equation is obtained that propagates with positive or negative phase velocity. In terms of the Jacobi elliptic function, a class of new exact periodic solutions is constructed, in particular stationary ones. Using an exponential generating function for Catalan numbers, Cauchy’s problem with the initial condition in the form of a step is solved. As a result of numerical simulation, the elasticity of the interaction of exact localized solutions is established.

Inhaled drug airflow patterns and particles deposition in the paediatric respiratory tract

The effectiveness of inhaled drugs is strictly related to areas reachable by drug particles. Unless particles reach the desired part of the bronchial tree, their influence might not meet the expectations. Consequently, the disease progress might not be stopped or even slowed down. Therefore, the primary objective of this research was to analyze the airflow patterns and particle deposition of a standard inhaled drug using computational fluid dynamics. The study was devoted to the analysis of the particle diameter influence on their deposition areas within the entire respiratory tract. Two patient-specific respiratory tract models, for 6 and 12-year-old patients, were reconstructed based on the computed tomography examinations. Numerical analyses were carried out as stationary ones with the constant inflow of the particles of various diameters (within the range of 1-50 μm). It was proven that depending on the particle size, their deposition within the respiratory tract varies significantly. The vast majority of the particles with diameters over 20 μm is gathered on the walls of the throat, whereas particles of diameters 5-15 μm are accumulated mainly on the trachea walls, leaving the alveoli insufficiently supplied with the drug particles. The inhaled drug size cannot be treated as negligible factor during the drug spraying. An improper distribution of the particles might not inhibit the symptoms of the asthma. Numerical simulations may improve drugs selection and visualize their distribution along the airways, which might accelerate asthma treatment personalization.

Forecasting a Nonstationary Time Series with a Mixture of Stationary and Nonstationary Factors as Predictors

This paper develops a method for forecasting a nonstationary time series, such as GDP, using a set of high-dimensional panel data as predictors. To this end, we use what is known as a factor augmented regression [FAR] model that contains a small number of estimated factors as predictors; the factors are estimated using time series data on a large number of potential predictors. The validity of this method for forecasting has been established when all the variables are stationary and also when they are all nonstationary, but not when they consist of a mixture of stationary and nonstationary ones. This paper fills this gap. More specifically, we develop a method for constructing an asymptotically valid prediction interval using the FAR model when the predictors include a mixture of stationary and nonstationary factors; we refer to this as mixture-FAR model. This topic is important because typically time series data on a large number of economic variables is likely to contain a mixture of stationary and nonstationary variables. In a simulation study, we observed that the mixture-FAR performed better than its competitor that requires all the variables to be nonstationary. As an empirical illustration, we evaluated the aforementioned methods for forecasting the nonstationary variables, GDP and Industrial Production [IP], using the quarterly panel data on US macroeconomic variables, known as FRED-QD. We observed that the mixture-FAR model proposed in this paper performed better than its aforementioned competitors.

Dam Inflow Prediction by using Artificial Neural Network Reservoir Computing

A multipurpose dam serves multiple modalities like agriculture, hydropower, industry, daily usage. Generally dam water level and inflow are changing throughout the year. So, multipurpose dams require effective water management strategies in place for efficient utilization of water. Discrepancy in water management may lead to significant socio-economic losses and may have effect on agriculture patterns in surrounding areas. Inflow is one of the dynamic driving factors in water management. So accurate inflow forecasting is necessary for effective water management. For inflow forecasting various methods are used by researchers. Among them Auto Regressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) techniques are most popular. Both of these techniques have shown significant contribution in various domains in regards to forecasting. But they have a common drawback in handling non-stationary inflow patterns. To address this drawback, in this work neural Reservoir Computing technique is used. In this work, Context reverberation network, also known as reservoir computing approach, is applied for inflow forecasting. It comprises of a dynamic neural reservoir. As the nature of a neural reservoir is dynamic, it can easily model complex nonstationary patterns along with stationary ones. Proposed model is applied on daily inflow data of Srisailam Dam which is a multipurpose dam. Here ARIMA and ANN models are compared with Reservoir Computing model. On various evaluation parameters Reservoir computing is proved better than ARIMA and ANN.

THE EFFECT OF THYMOSIN β4 ON THE FUNCTIONAL ACTIVITY OF THE IMMUNE AND NERVOUS SYSTEM COMPONENTS

The data on properties of thymosin β4, a conserved multifunctional polypeptide of mammals is summarized. Attention has been focused on regulatory activity of thymosin β4 in regard to immune and nervous system components. In these systems thymosin β4 is present in different cell types both stationary and mobile ones. Besides intracellular localization thymosin β4 is also located in extracellular fluids. Inside cells, thymosin β4 has been postulated to regulate actin polymerization as a G-actin-sequestering molecule. But molecular mechanisms of thymosin β4 located extra cells on cell functions remain unclear. The structural-functional organization of thymosin β4 is also discussed. Thymosin β4 is a perspective medicine preparation for the therapy of diseases related to immune and neurological disturbances in patients.

On the definition and examples of cones and Finsler spacetimes

A systematic study of (smooth, strong) cone structures $\C$ and Lorentz-Finsler metrics $L$ is carried out. As a link between both notions, cone triples $(\Omega,T, F)$, where $\Omega$ (resp. $T$) is a 1-form (resp. vector field) with $\Omega(T)\equiv 1$ and $F$, a Finsler metric on $\ker (\Omega)$, are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures $\C$ are bijectively associated with classes of anisotropically conformal metrics $L$, and the notion of {\em cone geodesic} is introduced consistently with both structures. As a non-relativistic application, the {\em time-dependent} Zermelo navigation problem is posed rigorously, and its general solution is provided.

Transmitter polarization optimization for space-time adaptive processing with diversely polarized antenna array

This paper considers the performance optimization of space-time adaptive processing (STAP) based on a diversely polarized antenna (DPA) array. A transmitter polarization design to enhance the detection performance is proposed. Accounting for the special structure of the polarization signal, we formulate the problem as a quasi-convex form based on the block majorization-minimization (MM) principle and solve it in an iterative framework. Compared with several existing methods, the proposed method has a quasi-convex form and can achieve better clutter suppression performance. We analyze the performance of conventional STAP and polarization-STAP (PSTAP), which indicates that the polarization diversity can help improve the performance of STAP for targets with low velocities, especially stationary ones. Simulations are conducted for validating the proposed methods and demonstrating their high performance.