Stationary Characteristics Research Articles

The study of the duration of transient processes in growing random graphs with a non-linear preferential attachment rule

A study of the duration of transients processes in random graphs with preferred attachment was carried out, during which it was found out that for some random graphs transient processes can last very long. For some known growing graphs the absence of stationary distribution of the vertices attachment degree has been found out for the first time. This makes the calculation methods and the techniques for analyzing transient processes up-to-date, because real networks modelled by this graphs, do not have stationary characteristics either. Real networks having stationary characteristics, can for a long time, even if they are too large, stay in the transient mode which does not let estimate these networks by stationary solutions. While modeling these networks, the methods for analyzing the transient modes are also urgent as they provide for controlling the errors of stationary solutions application. The paper gives the example of the stationary solution error control for a random graph, widely used in modeling of growing networks.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ОЦЕНКИ ДИНАМИЧЕСКИХ ПОКАЗАТЕЛЕЙ ДВИГАТЕЛЯ МТА ПРИ НЕУСТАНОВИВШЕЙСЯ НАГРУЗКЕ

The article provides an analysis of the existing methods and techniques for assessing the dynamic characteristics of engines of mobile machines, and also presents theoretical calculations for estimating the dynamic performance of an machine and tractor unit’s engine under unsteady load. The proposed mathematical model describes the change in the performance of the engine of machine and tractor unit with a linear law of loading and allows you to compare an engine’s operation at unsteady load with the ideal. The quasi-dynamic characteristic was laid as the theoretical basis for study to assess the dynamic performance of machine and tractor unit’s engine under unsteady load. Comparison of the dynamic performance of engines at unsteady load with ideal performance, which have no dynamic losses. It is proposed to apply the “quasi-dynamic” characteristics. The quasidynamic (ideal) characteristic is called - the change in the performance of machine and tractor unit’s engine, in the transition process, occurring in accordance with the change in the frequency of rotation of the crankshaft on the stationary characteristics. The mathematical model for estimating the dynamic performance of an machine and tractor unit’s engine using a correcting branch with an unsteady load is experimental equations for load buildup. Theoretical relationships have been developed for evaluating the dynamic performance of an engine with an unsteady load on the correcting branch of the regulatory characteristic. Using the proposed theoretical dependences, it is possible to carry out theoretical studies of the effect of load on the dynamic performance of an machine and tractor unit’s engine and determine the total dynamic losses.

Removal of temperature effect in impedance-based damage detection using the cointegration method

Electromechanical impedance technique has been widely used in the area of structural health monitoring. However, both damage and variation in environmental temperature can cause the changes in electromechanical impedance signature, which may cause false damage diagnosis. The temperature effect on the electromechanical impedance-based method has been one of its main drawbacks in practical application. This article proposes a new approach based on cointegration to eliminate temperature interference in the electromechanical impedance technique. The augmented Dickey–Fuller test is used to analyze the stationary characteristics of the time series and determine the degree of non-stationarity. The Johansen test is used to obtain the cointegrating residuals instead of the direct electromechanical impedance responses for damage detection. The proposed method is verified on the undamaged and damaged steel plates with the consideration of environmental temperature variations. The damage detection was based on the electromechanical impedance technique in which the peak frequency is chosen as a cointegrated variable. The experimental results show that the cointegration method can remove the temperature effect on the electromechanical impedance responses, and the cointegrating residuals are effective indices to indicate the occurrence of damage.

Identification of the electric starting system dynamic features

The article describes the starting systems of combustion engines and the conditions of their operation. Traditional stationary characteristics of the acid battery and the electric starter were discussed. Structural models of functional components of the starter system: battery and starter are presented as classic electrical circuits with typical RLC elements. The equations of structural components operation in dynamic conditions were formulated and their solutions and characteristics were presented. The results of tests of the functioning of the starting system and its components, battery and starter in the test stand conditions and while driving the crankshaft of the engine, showing the behaviour and the course of work parameters under dynamic conditions are presented.

PEMILIHAN INPUT MODEL ANFIS UNTUK DATA RUNTUN WAKTU MENGGUNAKAN METODE FORWARD SELECTION DILENGKAPI GUI MATLAB (Studi Kasus: Jumlah Penumpang Kereta Api di Wilayah Jawa Non Jabodetabek)

One of the methods that is commonly used to identify a time series model and input ANFIS (Adaptive Neuro Fuzzy Inference System) model is PACF plot. The PACF plot shows the correlation between current observations and previous observations visually. Formally there are several methods that are known to effectively identify ANFIS inputs, one of which is the Forward Selection regression method. With the same concept as PACF, the process of selecting ANFIS inputs using the Forward Selection method is based on the order of the correlatiom between the predictors of the response which is indicated by the magnitude of the correlation coefficient. This study discusses the Forward Selection method in simulation data that has stationary characteristics, stationary with outliers, non stationary, non stationary with outliers and implements data on the number of train passengers in the Non Jabodetabek Java region. ANFIS modeling on data of the number of train passengers in the Non Jabodetabek Java region produces AIC of 15,5617, MAPE of 8,5093% and RMSE of 571,33691. The result of this study is equipped with a GUI which is useful as a tool to facilitate users in processing data.Keywords : PACF Plot, Forward Selection, ANFIS, non stasionary, outlier

Stationary Characteristics of an Unreliable Multi-Server Queueing System with Losses and Time Redundancy

This paper considers an unreliable restorable multi-server queueing system with losses in which failures may occur during requests service; in case of such failures, requests are served using a random time redundancy. The incoming flow is assumed to be elementary and all other random variables in the system’s description are assumed to obey a generalform distribution. A semi-Markov model of system’s evolution over time is developed and a stationary distribution of the embedded Markov chain is found. Explicit-form expressions for determining the stationary probabilities and mean stationary sojourn times in different physical states of the system are obtained, which can be used to estimate the time redundancy effect for the stationary characteristics of the system.

A phenomenological theory of steady-state vertical geothermal systems: A novel approach

This paper proposes a novel approach for studying the stationary energy characteristics of vertical geothermal systems (VGS) using stationary two-dimensional phenomenological mathematical theory. T ...

ADAS Acceptability Improvement Based on Self-Learning of Individual Driving Characteristics: A Case Study of Lane Change Warning System

Low user acceptance is one of the fundamental problems for popularizing advanced driver assistance systems (ADAS). Systems that are developed for the majority of drivers have to possess stationary characteristics and be conservative for safety reasons. However, the drivers with disparate driving styles possess different risk cognition of lane change behavior; therefore, such systems with stationary characteristics may cause frequent interference to aggressive drivers or may be perceived as a radical system by conservative drivers. An ADAS that adapts to the characteristics of individual drivers during lane change maneuvers will be more effective and more acceptable to drivers. In this study, we developed an adaptive algorithm that learns the characteristics of individual drivers during lane changes and determines the optimal threshold online to adapt to different drivers. Signal detection theory (SDT) was employed and the results of the accuracy, false negative rate, and false positive rate were used to capture the drivers' lane change behavior characteristics. A learning stage and a threshold fluctuation stage were designed in the adaptive algorithm to determine the optimal warning threshold and amended the optimal warning threshold based on changes in the drivers' behaviors. We evaluated the proposed algorithm by conducting the actual vehicle tests with a total of three participants. The offline statistical analysis results of the participants' lane change characteristics were compared with the online results of the warning threshold adjustments from the adaptive algorithm; the comparison results indicated that the adaptive algorithm could effectively capture the drivers' lane change characteristics and determine an appropriate warning threshold. The findings provide an improvement in the performance of the lane change warning (LCW) system and enhance people's acceptance of intelligent systems.

Semi-Markov model of a multi-component energy system with component-wise storages

To increase the reliability and efficiency of the functioning of various purposes systems (in particular, energy systems), time redundancy is used. In this paper, a semi-Markov model of a multi- component system with component-wise storage devices, which are the sources of the time reserve, is constructed. The stationary characteristics of reliability and efficiency of the system under consideration are found. The analysis of the influence of storage capacities on the reliability and efficiency of the system is been.

Power quality analysis in solar PV integrated microgrid using independent component analysis and support vector machine

This paper presents wavelet transform, independent component based detection of the power quality disturbances in a microgrid. Wavelet transform (WT) is well known for its better time-frequency multi-resolution analysis because of selection of adaptive window size depending inversely with the frequency. This makes it suitable for identification of both stationary and non-stationary characteristics of the power quality disturbances. But, it is analyzed in the study that the detection capability of wavelet is degraded when the input voltage signal contains noise and completely fails when the noise level is increased to 25 dB. Of course, a wavelet-denoising technique is tested to improve the ability of wavelet transform under noisy conditions, but observed to increase the detection time. Hence, independent component analysis (ICA) is proposed for detection based on its property of finding the significant components which are statistically independent and non-Gaussian. In addition, the statistical features are extracted to formulate the input dataset for support vector machine (SVM) to classify different power quality disturbances like sag, swell, interruptions, harmonics, transients, and flickering. A comparative analysis is presented and it is observed from the study that ICA-SVM hybrid combination provides better classification accuracy as comparison to WT-SVM under different operating scenarios.

Education, and the balance between dynamic and stationary functional connectivity jointly support executive functions in relapsing-remitting multiple sclerosis.

Graphical network characteristics and nonstationary functional connectivity features, both derived from resting-state functional magnetic resonance imaging (rsfMRI) data, have been associated with cognitive performance in healthy subjects. How these features jointly relate to cognition in diseased states has not been investigated. In this study, 46 relapsing-remitting multiple sclerosis subjects underwent rsfMRI scans and a focused cognitive battery. With a sliding window approach, we examined six dynamic network features that indicated how connectivity changed over time as well as six measures derived from graph theory to reflect static network characteristics. Multiset canonical correlation analysis (MCCA) was then carried out to investigate the relations between dynamic network features, stationary network characteristics, cognitive testing, demographic, disease severity, and mood. Multiple sclerosis (MS) subjects demonstrated weaker connectivity strength, decreased network density, reduced global changes, but increased changes in interhemispheric connectivity compared to controls. The MCCA model determined that executive functions and processing speed ability measured by Wechsler Adult Intelligence Scale IV (WAIS-IV) Working Memory Index, WAIS-IV Processing Speed Index, and the Verbal Fluency Test were positively correlated with education, dynamic connectivity, and static connectivity strength; while poor task switching was correlated with disease severity, psychiatric comorbidities such as depression, anxiety, and fatigue, and static network density. Taken together, our results suggest that better executive functioning in MS requires maintenance of a continued coordination between stationary and dynamic functional connectivity as well as the support of education, and dynamic functional connectivity may provide an additional cognitive biomarker of disease severity in the MS population.

Performance Analysis of M2M Traffic in LTE Network Using Queuing Systems with Random Resource Requirements

We analyze a multiserver queuing system, in which customers require a server and a certain amount of limited resources for the duration of their service. For the case of discrete resources, we develop a recurrence algorithm to evaluate the model’s stationary probability distribution and its various stationary characteristics, such as the blocking probability and the average amount of occupied resources. The algorithm is applied to analysis of M2M traffic characteristics in a LTE network cell. We derive the cumulative distribution function of radio resource requirements of M2M devices and propose a sampling approach in order to apply the recurrence algorithm to the case of continuous resources.

Discrete Product Inventory Control System with Positive Service Time and Two Operation Modes

Consideration is given to the Markov inventory control system of a discrete product of maximum volume S under the strategies (s,Q) and (s, S) with a positive service time. Upon arrival, the order is queued if the inventory level is positive or, otherwise, leaves the system unserviced. One server handles the queued orders one-by-one in the sequence of their arrival. If the inventory level exceeds s, then the service time has the exponential distribution of intensity μ; otherwise, of intensity αμ, 0 < α ⩽ 1. The product in the inventory is consumed only at the instant when the service (of the order) ends. Inventory deficit is not allowed. When the inventory is empty new orders are not admitted into the system, and the service process of the queued orders (if any) is stopped. The lead time is assumed to be exponentially distributed. Analytical relations are established for the basic stationary performance characteristics of the system.

Performance analysis of an unreliable M/G/1 retrial queue with two-way communication

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where the single server, subject to active failures, primarily attends incoming calls and directs outgoing calls only when idle. The incoming calls arriving at the server follow a Poisson arrival process, while outgoing calls are made in an exponentially distributed time. On finding the server unavailable (either busy or temporarily broken down), incoming calls intrinsically join the virtual orbit from which they re-attempt for service at exponentially distributed time intervals. The system stability condition along with probability generating functions for the joint queue length distribution of the number of calls in the orbit and the state of the server are derived and evaluated numerically in the context of mean system size, server availability, failure frequency and orbit waiting time.

Stationary characteristics in bipolar diffusion charging of aerosols: Improving the performance of electrical mobility size spectrometers

Electrical mobility size spectrometers are widely used to measure particle number size distributions (PNSD) in the range of 1–1000 nm (Wang and Flagan 1990; Jiang et al. 2011). These instruments co...

An algorithmic approach to analysing the reliability of a controllable unreliable queue with two heterogeneous servers

We consider a Markovian queueing system with two unreliable heterogeneous servers and one common queue. The servers serve customers without preemption and fail only if they are busy. Customers are allocated to one or the other server via a threshold control policy which prescribes using the faster server whenever it is free and the slower server only when the number of waiting customers exceeds a specified threshold level that depends on the state of the faster server. This paper focuses on the reliability analysis of a system with unreliable heterogeneous servers. First, we obtain the stationary state distribution using a matrix-geometric solution method. Second, we analyse the lifetimes of the servers and of the system. We provide algorithms for calculating the stationary reliability characteristics, reliability functions in terms of the Laplace transform and the mean times to the first failure. A new reliability measure is introduced in the form of the discrete distribution function of the number of failures during a specified life time that is derived from a probability generating function. The effects of various parameters on these reliability characteristics are analysed numerically.

Hierarchical symbolic dynamic filtering of streaming non-stationary time series data

Abstract This paper proposes a hierarchical feature extractor for non-stationary streaming time series based on the concept of switching observable Markov chain models. The slow time-scale non-stationary behaviors are considered to be a mixture of quasi-stationary fast time-scale segments that are exhibited by complex dynamical systems. The key idea is to model each unique stationary characteristics without apriori knowledge (e.g., number of possible unique characteristics) at a lower logical level, and capture the transitions from one low-level model to another at a higher level. In this context, the concepts in the recently developed Symbolic Dynamic Filtering is extended, to build an online algorithm suited for handling quasi-stationary data at a lower level and a non-stationary behavior at a higher level without apriori knowledge. A key observation made in this study is that the rate of change of data likelihood seems to be a better indicator of change in data characteristics compared to the traditional methods that mostly consider data likelihood for change detection. Thus, an adaptive Chinese Restaurant Process (CRP) distribution is formulated to accommodate the rate of change of data likelihood in the learning algorithm. The algorithm also aims to minimize model complexity while capturing data characteristics (likelihood). Efficacy demonstration and comparative evaluation of the proposed algorithm are performed using time series data both from a simulated system that exhibit nonlinear dynamics as well as a real residential electrical energy disaggregation case study using the publicly available reference energy disaggregation dataset (REDD). We discuss results that show that the proposed hierarchical symbolic dynamic filtering (HSDF) algorithm can identify underlying features with significantly high degree of accuracy, even under very noisy conditions. Based on our validation experiments, we demonstrate better performance of the proposed fast algorithm compared to the baseline Hierarchical Dirichlet Process-Hidden Markov Models (HDP-HMM). The proposed algorithm’s low computational complexity also makes it suitable for on-board, real time operations.

Incipient Fault Detection for Complex Industrial Processes with Stationary and Nonstationary Hybrid Characteristics

For a nonstationary process which has a time-varying mean, a time-varying variance, or both, it can be difficult to detect incipient disturbances which may be hidden by the time-varying process variations. Besides, stationary and nonstationary characteristics may coexist in complex industrial processes which, however, have not been studied for process monitoring. In the present work, a triple subspace decomposition based dissimilarity analysis algorithm is developed to detect incipient abnormal behaviors in complex industrial processes with both stationary and nonstationary hybrid characteristics. The novelty is how to comprehensively separate the stationary and nonstationary process characteristics and describe them, respectively. First, a stationarity evaluation and separation strategy is proposed to decompose the data space into three subspaces, revealing the linear stationary process characteristics, the nonlinear stationary process characteristics, and the final nonstationary process characteristics....

Stochastic contagion models without immunity: their long term behaviour and the optimal level of treatment

In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker–Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour. Two types of models are analyzed here: The first one is a version of the SIS model with external parameter noise and saturated incidence. The second one is based on the Kramers–Moyal approximation of the simple SIS Markov chain model, which leads to a model with scaled additive noise. In both cases we analyze the asymptotic behaviour, which leads to limiting stationary distributions in the first case and limiting quasistationary distributions in the second case. Finally, we use the derived properties for analyzing the decision problem of choosing the cost-optimal level of treatment intensity.

Compressible Analysis of Bénard Convection of Magneto Rotatory Couple-Stress Fluid

Thermal Instability (Benard’s Convection) in the presence of uniform rotation and uniform magnetic field (separately) is studied. Using the linearized stability theory and normal mode analyses the dispersion relation is obtained in each case. In the case of rotatory Benard’s stationary convection compressibility and rotation postpone the onset of convection whereas the couple-stress have duel character onset of convection depending on rotation parameter. While in the absence of rotation couple-stress always postpones the onset of convection. On the other hand, magnetic field on thermal instability problem on couple-stress fluid for stationary convection couple-stress parameter and magnetic field postpones the onset of convection. The effect of compressibility also postpones the onset of convection in both cases as rotation and magnetic field. Graphs have been plotted by giving numerical values to the parameters to depict the stationary characteristics. Further, the magnetic field and rotation are found to introduce oscillatory modes which were non-existent in their absence and then the principle of exchange of stability is valid. The sufficient conditions for non-existence of overstability are also obtained.