Search

An important process characteristic is process maxima as it is often an important quality or performance parameter. Such measurements often play a vital role in process analysis and have to be monitored carefully. In this paper, we consider the problem of monitoring process maxima when the process exhibits a kind of periodicity. A circle chart for periodical process maxima with or without seasonal patterns monitoring is developed and studied, by modeling the process maxima using the extreme value distribution. Mean normalization is applied for periodic process monitoring with seasonal patterns to facilitate comparison between different sections and periods. The average cycle run length is proposed to measure charting efficiency. Copyright © 2014 John Wiley & Sons, Ltd.

We introduce a new eddy-covariance method that uses a spectral decomposition algorithm called empirical mode decomposition. The technique is able to calculate contribu- tions to near-surface fluxes from different periodic components. Unlike traditional Fourier methods, this method allows for non-orthogonal contributions to the total flux, which are shown to be errors due to the undersampling of low-frequency processes. Inspection of the non-orthogonal terms with relation to sampling duration and periodicity reveals that a mea- sured periodic process requires approximately six cycles in order to be sufficiently sampled. This determines the maximum eddy size sufficiently measured given a particular sampling duration.

An interactive protocol for the control for a switched system of flow with process sharing is proposed. It is shown that the protocol suggested generates the required periodic process as a global attractor.

Musicians and nonmusicians synchronized drum-beating movements to sound sequences composed of 90 successive interonset intervals that increased or decreased continually by various amounts of time. After the end of a sequence, they continued to produce 30 beats without interruption. Synchronization appeared both smooth and accurate for all levels of changing tempo. In general, actions preceded sounds with increasing intervals and lagged behind sounds with decreasing intervals, indicating that the stimulus change was not fully predicted. There was a tendency for the continuation intervals to change in the reverse direction of the preceding synchronization intervals, suggesting that the system retains information about the tempo change. We discuss these results in terms of the demands tempo change makes on timing mechanisms, and what they reveal about participants� ability to create and sustain an internal nonisochronous periodic process.

We examine the problem of estimating the periods of interleaved periodic point processes. We are particularly interested in the case where times of arrival (TOAs) are either measured with noise or not measured at all. This can arise in communications surveillance, where communications signals of different bauds may lie within the same surveillance bandwidth, and likewise in Electronic Surveillance (ES), where pulses or scans from different radars are observed together. In [1], the authors developed a general asymptotic theory for the Bartlett point-process periodogram estimator of the period of a single periodic process. In this paper, we extend the model to multiple periodic processes, each with a distinct period. The TOAs are observed unlabelled and in time order, i.e., they are interleaved. The largest local maximizers of the periodogram are shown to be good estimators of the unknown periods, asymptotically, and central limit theorems are proved. Simulations highlight a number of practical problems, and some problems with outstanding solutions are suggested.

Although data is often used to estimate parameters for models in calculus and differential equations, the models themselves are seldom justified. In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.

The input of a multiserver loss system is assumed to be a periodic random marked point process which has, with probability one, infinitely many construction points. It is shown that, independently of the initial distribution, there exists a unique periodic process modeling the periodic steady-state behaviour of the loss system. In addition, practical sufficient conditions for the existence of enough construction points are derived.

The determination of periodic stationarity conditions for periodic autoregressive moving average (PARMA) processes is a prerequisite to their analysis. Means of obtaining these conditions in analytically simple forms are sought. It is shown that periodic stationarity conditions for univariate and multivariate PARMA processes can always be reduced to eigenvalue problems, which are computationally and analytically easier to deal with. Two different lumpings of the periodic process are considered along this line. The first is the common w-span lumping over all w periods. The second lumping considered is the p-span lumping of the pth order periodic autoregressive process over p periods, which is based on a recently introduced lumping technique. It is shown that p-span lumping may yield the periodic stationarity conditions in an analytically simpler form as compared to w-span lumping when p < w.

Analytical methods of assessing the periodic operation of chemical processes are reviewed. A recently introduced method of frequency response analysis is discussed as an efficient way of evaluating the stationary periodic behavior of nonlinear processes. The method is illustrated for two important generic problems: Rapid direct estimation of the time-average performance of periodic processes and the approximate estimation of the cyclic stationary state. The first problem arises when a periodic operation is considered for enhancing the performance of a steady-state process. Frequency response analysis can give a quick answer as to whether the periodic operation is advantageous. The second problem concerns inherent periodic processes. Nonlinear frequency response analysis provides an approximation of the complete periodic behavior. This can be used to optimize the periodic process with respect to the shape, amplitude and frequency of the input.

This paper presents a method for systematically adjusting the period lengths of periodic processes, such that the adjusted period lengths are as closely harmonically related to each other (having a smaller LCM value) as possible, in order to reduce the schedule length and the number of instances of new processes, and reduce storage requirements and system overhead, while at the same time ensuring that the adjusted period lengths are sufficiently close to the original period lengths, to satisfy the processor utilization level required by the application, and maximize the chances of finding a feasible schedule.

Here the problem is considered of obtaining a periodic description in state-space form of a linear process which can be modelled by linear difference equations with periodic coefficients. A polynomial time-invariant description of such a model is used, in order to characterize the order of the model and to introduce an equivalence relation between two models.

Periodic ARMA processes have seasonally varying parameters superimposed on a conventional ARMA structure. These varying parameters can arise when seasonality is incorporated into the theory of economic decision-making. Analogously to the aggregate of component ARMA processes having a unvariate representation, the periodic process has a corresponding ARMA representation. This unvariate representation may, however, imply high orders and substantial dynamic misspecification. In terms of forecast efficiency, the true periodic dynamic process dominates its unvariate counterpart.

Periodic (covariance) Stationarity conditions for multivariate periodic autoregressive moving average (PARMA) processes are investigated. It follows from a previous work that a necessary and sufficient condition for the periodic Stationarity of a multivariate periodic process is the (covariance) Stationarity of the “lumped” vector process which contains the periodic vectors as its elements. It is shown that for univariate and multivariate PARMA processes, even with periodically varying orders, the lumped process is a multivariate autoregressive moving average ARMA process, the Stationarity conditions of which are readily available. Periodic Stationarity conditions for the multivariate PARMA (1, 1) process are explicitly obtained, which apply for all PARMA (1, q) processes. It is shown that the periodic Stationarity of a periodic process always implies the Stationarity of the aggregated process, the sum of the periodic vectors. The reverse is yet to be proved or disproved. However, it is shown to be true for PAR(1) and PARMA (1, 1) processes.

The accessory minimization problem constructed from the second variation about a periodic extremal path with free period is investigated. Both necessary and sufficient conditions for a periodic path to be a weak local minimum are compactly established through a matrix inequality and the existence of a solution to the Riccati differential equation over the period. Extensions to the optimality conditions for the infinitely-repeated periodic processes are included. The existence of a real symmetric periodic solution to the Riccati differential equation is shown to be necessary for optimality, and this condition, plus some requirements on the eigenvalues of the monodromy matrix, imply sufficiency for optimality.

In this paper, the periodic solution for a class of Cohen-Grossberg neural networks with variable coefficients is discussed. By using inequality analysis technique and matrix theory, some new sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and exponential stability of the periodic solution. An example is given to show the effectiveness of the obtained results.

Dynamic parameters calculation and determination of optimum on response character of transition process in systems with periodic on phase coordinate by control actions.

In the previous chapter we have considered nonstationary VAR models with time invariant parameters. Nonstationarity, that is, time varying first and/or second moments of a process, can also be modeled in the framework of time varying parameter processes. Suppose, for instance, that the time series show a seasonal pattern. In that case a VAR(p) process with different intercept terms for each season may be a reasonable model: $$ y_t = v + A_1 y_{t - 1} + \cdots + A_p y_{t - p} + u_t $$ (12.1.1) Here v i is a (K × 1) intercept vector associated with the i-th season, that is, in (12.1.1) the time index t is assumed to be associated with the i-th season of the year. It is easy to see that such a process has a potentially different mean for each season of the year.

A sufficiency condition for a periodic process with free period to be a weak local minimum is given. By making detailed use of the properties of the monodromy matrix, the transition matrix calculated over a closed orbit, previous results are corrected, extended, and clarified. A necessary condition for a real valued periodic Riccati matrix to exist is that there be no distinct eigenvalues of the monodromy matrix on the unit circle. For local sufficiency, it is required that no eigenvalues of the monodromy matrix, except a double root at unity, lie on the unit circle.

When a periodic process is disturbed, control action may be necessary to maintain satisfactory performance. Regulating controls to achieve this objective can be synthesized by solving a linear-quadratic optimization problem with periodic coefficient's. Generalized proportional and proportional-integral feedback regulators developed in this manner are tested by simulating a cyclic reactor. Very satisfactory control is achieved for 10% step disturbances in reactor feed conditions although the results are sensitive to the choice of manipulated variables.

Conditions are given under which one can select the input signal of a system so that a given periodic process may be generated approximately. The problem invesdtigated here is related to the theory of programmed control [1, p. 231] since it considers the possibility of finding programming functions which all guarantee a stable periodic programming process. Under realistic conditions the programming functions can be given only approximately. This article presents estimates of the admissible errors of the required programming functions. From the strickly mathematical viewpoint, the problem can be reduced to the formulation of the conditions for stability of the periodic motion in the presence of constantly acting disturbances bounded in norm. An estimate of the absolute value, of the mean absolute value, and of the mean-square value of the above-indicated admissible error is given. The case when the constructed periodic motion is discontinuous is also considered. A part of the basic results is carried over to the case of non-periodic appriximate motion.

For the last few years, an enormous number of research publications on periodic processes have appared in the literature (see Fjeld [1], Guardabassi, Locatelli and Rinaldi [2] for the publications up to 1971). As the theory has reached a certain degree of growth and perfection, certain necessary and sufficient conditions have become available. Because of the peculiar behaviour of periodic processes, however, any extension of necessary and sufficient conditions of optimality for non-periodic processes to periodic processes is neither trivial nor straight-forward. The main difficulty is in the matching of the periodicity boundary conditions. This brings us to the problem of necessary and sufficient conditions for the existence and uniqueness of periodic solutions, a problem which was not severe in non-periodic cases. With this in mind, certain necessary and sufficient conditions for the existence and uniqueness of periodic solutions are first presented. Then the necessary conditions for optimality and the sufficient conditions, in particular the Hamilton-Jacobi theory, are covered. Certain conditions of relaxed controls are also briefly treated in the last section.

A short review of hypotheses on human time perception emphasises the distinction between endogenous and exogenous concepts. Methods are described, and the related problem of stationarity is discussed. A hypothesis is formulated which assumes oscillatory processes as the basis for the perception of short temporal intervals. Several experiments are described which test this hypothesis. The results of the first experiment suggest a temporal constant in the range of the conscious present. Periodic components in subjective random series which are demonstrated in another experiment, indicate a sequence of temporal units. The influence of physiological factors on time perception is illustrated; diurnal variations are discussed as an example. However, it is shown that the observed variations in time perception are not dependent on body temperature alone. The importance of informational cues is noted and an experiment is described which indicates the role of individual differences.

A Le Corbeiller oscillator having the Goodwin characteristic is one of the simplest two-stroke oscillator model, its periodic process was discussed by Le Corbeiller and de Figueiredo with the help of Lienard construction-a graphical method [5] in [1] and [2]. In this paper, the above problem is approached from analytic ways. Starting from the Lord Rayleigh type equation: x+f(x)+x=0 (1) by means of the piecewise linear method, the reduced characteristic F(x) is written as f(x)={-2h 1 x x 2 x-k x>b, where h 1 , h 2 ,b, k are constants. By using the point-transformation and sussesor-func-tion theory [3] , the author proves that when 0 1 2 1 2 , there is an unique and stable periodic solution of (1), and the oscillation has the soft-excitation character.The analytic expressions of the period and waveform for stable periodic solution are also given.