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Function of calculation of the schedule of machining of images of indicators of the panel of devices

Function of calculation of the schedule of machining

Defines the schedule in the form of assemblage Since the time moments

In which supply of a set of test signals for definition of correctness of indications of//th displayed parametre [59] is carried out.

Function input parametres are:

1) n - number of displayed parametres;

2) G - assemblage of displayed parametres of the panel of devices;

3) Tλp - assemblage of values tflp ι, each of which represents

Itself a time of determination of a dynamic regime for displayed parametrat.e. znachenieopisyvaet a change time

Inwardness of the panel of devices under the influence of a set of the test signals, necessary for scaling of the displayed parametre

4) Tp  - assemblage of values tpπi, each of which represents a time of recognition of the indication of the displayed parametre

I.e. value tописывает a time demanded for definition displayed parametras by use of algorithms of machining

strelochnyh, liquid crystal or light indicators;

5) A - a two-dimensional file of dimensions of a quantity (n, n), coding function of an admissibility of simultaneous machining of images of two indicators, in
Which elementesli the displayed parametre giвозможно

To compute simultaneously with the displayed parametre g, aij = 0 otherwise, i, j = 1, n \

6) B - assemblage of restrictions predshestvovanija an aspect

Defining sequence of machining of images of separate indicators of the panel of devices.

For schedule calculation parametre Tв an aspect of assemblage of the values matching dlitelnostjam of machining is defined

Images of the displayed parametres, thus each element ti assemblage Tрассчитывается as the sum of two components:

- Time of removal of the image tc ∏;

- Time of determination of a dynamic regime of the indicator tffpi.

After determination of a dynamic regime the image matching to i displayed parametre, is processed during computing time of the displayed parametre tс by use of algorithms of definition of indications strelochnyh, liquid crystal or light indicators.

Thus, Value tси is installed on

To basis of the analysis of experimental data.

For scaling the schedule is required to find a criterion function minimum f (t) an aspect

Defining the least time demanded for the parallel control all displayed parametres

Entrance parametryiopredeljajutsja on the basis of the analysis of technical datas of the device of parallel machining of images of indicators of the panel of devices.

As each displayed parametre is characterised by a time of recognition of the indications, depending on indicator type, and also from time responses of applied algorithm of recognition, are defined necessary and sufficient coditions for realisation of simultaneous parallel recognition of several displayed parametres on the basis of the analysis of range of values of criterion function (3.1).

Let for recognition of indications of the displayed parametre of each type (strelochnyj, the liquid crystal or light indicator) is used unique computing knot. Then the total time of loading of computing knot pays off as

Condition performance

Provides performance of operations of scaling of all displayed parametres in time smaller or equal to general counted processing time Tmin.

Thus, realisation of parallel machining of images of indicators with use of unique computing knot was possiblly at satisfaction of a condition where - a critical way to the counted schedule, w -

Length of a critical way. In this case the diagramme of loading of computing knot will look like, analogous resulted in drawing 3.1. Function L (t) defines percent of loading of computing knot, function Q (t) - quantity in parallel diagnosed

Displayed parametres.

Drawing 3.1. An instance of the diagramme of loading of computing knot

If the condition (3.4) is not carried out, for maintenance of parallel recognition of several displayed parametres demanded quantity of distinguishing computing knots - more than one.

Thus, a problem of a finding of minimum Tminописывается mathematical model Mm = (With, T, G, A, B,).

For a finding of minimum Tminв to dissertational work methods of the theory of schedules as the problem of minimisation of processing time of images of indicators of the panel of devices represents a special case more the general problem of construction of the schedule of the design taking into account restriction on resources with an inhibition of interruption of process of service (Resource-Constrained Project Scheduling Problem, RCPSP) were used.

The problem of construction of the schedule of the design is presented by mathematical model Ms = (j, R, P, K) which includes:

1) assemblage Jиз Nработ for which are defined their duration dj∈Z +. It is supposed, that the planning problem dares in a discrete time scale: t = 0,1.... As the Schedule is called the assemblage

The moments of starts of works. Thus work is considered active (carried out) during the moments

2) assemblage Rиз M vozobnovimyh (renewable) discrete resources for which their quantities are defined

3) assemblage Pограничений predshestvovanija (job order, precedence constraints). Each restriction is set by the four (j1, j2, t, l), where t ∈ {‘start­finish ’, ‘ start-start ’, ‘ finish-finish ’, ‘ finish-start ’}, - a time gap (log) between works j1и j2. Define a technological sequence of works: if, for example, t = ’ finish-start ’ work j2не can begin earlier, than through lединиц a time after the termination

The sense of other types is analogous.

4) assemblage Kназначений of resources to works (assignments)

Define following restriction: during each moment of a time and for each resource the sum of requirements of all works which are carried out during this moment of a time should not exceed quantity of this resource: where - assemblage active during the moment tработ.

In a case when a matrix (kjr) rarefied to set these appointments in the form of the list of three (Job, Resource, Capacity) more economically.

Between mathematical models of Mm and the M exists following conformity:

1. To assemblage with in Mm model is univocal there matches assemblage J in model M.

2. To assemblage Tв of model Mоднозначно there matches assemblage dlitelnostej dj∈Z+работ in model Ms.

3. To assemblage Gв of model of Mm is univocal there matches assemblage N of works in model Ms.

4. To assemblage Bв of model Mоднозначно there matches assemblage P of restrictions predshestvovanija in model M.

5. To two-dimensional file Aв of model of Mm is univocal there matches assemblage Kназначений of resources to works in model M.

Let's observe in more details resulted conformity 4 and 5.

In case of full absence of resources (and, hence, and type 4 restrictions) all restrictions of a problem contain in oriented graph predshestvovanija G = (J, P). In this case the length of the optimum schedule is equal to length critical, that is the longest way in G. The sum of scales of all apexes is meant a path length (dlitelnostej sootyovetstvujushchih works) and scales of all arches entering into this way. In this schedule the time of start of any work is defined as length of a critical way before this work.

Let's find early and late starts of works for bezresursnoj problems by means of a method of a critical way [27]. Let T - assemblage of early times of works - assemblage of late starts of works

The following algorithm of direct pass is offered:

And algorithm of return pass:

Besides restrictions predshestvovanija in problem RCPSP there are resource restrictions. In this case problem RCPSP is NP-difficult, it comprises, in particular, such known NP-difficult class-room of problems, as Job Shop.

Let's observe assemblage R consisting from Mвозобновимых of discrete resources. The quantity of subsets of an aspect {q, z} q, z∈J, q ≠ zиз two various works is quantity of resources M, that is

47

Where n - number of works.

Taking into account the formula (3.8) assemblage Rбудет to have the following appearance

Let's accept kolichestvokazhdogo a resource for the constant

Magnitude K = 1. Thus, if any two works compete for the general divided resource (are not executed

Simultaneously with each other) that the condition (3.5) was satisfied, it is necessary to set requirements of each of works q, zв a resource pкак If two rabotyne compete for

p ∈R (their simultaneous modification is is possible), for performance of a condition (3.5) it is necessary and to accept a resource enough

Input parametre of algorithm of definition of resource restrictions (initialization of assemblage R, K) is two-dimensional file A.

The offered algorithm for definition of resource restrictions will have the following appearance.

Definition of an input information of a problem of construction of the schedule of the design, presented mathematical model M, has allowed to apply the known

Methods of the theory of schedules for the solution of a problem of definition of minimum Tmin as special case of problem RCPSP.

As it has been noted earlier, problem RCPSP is NP-difficult, therefore there are no effective algorithms of reception of its optimum solution. However for difficult designs good result is the finding of the admissible schedule of comprehensible length (for example, on 10­30 than % is longer optimum). Now in this direction the assemblage of algorithms [28-30] is developed.

For the solution of problem RCPSP the method serial scheduling scheme, developed by Robert Kolishem (R has been chosen. Kolish) [30], differing the simplicity, a generality and having quadric labour content. Inherently the given method is so-called consecutive greedy algorithm.

Algorithm work consists from Nэтапов, on each of which the time of performance of one of works (that is, after to stages there is a partial schedule for to the works, fulfilling to all restrictions) is fixed.

Let's mark out through S (scheduled set) assemblage of the works already fixed by the moment of the beginning of a stage n (thus, ∣S = n-1). Through Dn (decision set) we will mark out assemblage yet not fixed works at which all their predecessors are fixed, that is

From assemblage Sвыбирается the work fixed at a stage n. This sampling is made according to a heuristic rule which can be defined in one way or another according to some reasons answering to common sense.

Instance of such heuristic rule is LST-corrected (latest start time): from all works Dnвыбирать that, for which start time in the late schedule for matching bezresursnoj problems the least. It is meaned, that by this work, most likely, has the longest chain 49

Followers, and it is favourable to put it in the schedule as soon as possible. Having chosen h ∈Dn, we fix it in the schedule, choosing the earliest time on which it is possible to put this work, having fulfilled all restrictions predshestvovanija and resource restrictions. The formal algorithm for a serial method is published in-process [30] and looks like:

The schedule gained by algorithm also is early: no of works can be shifted for earlier term, not shifting other works. It is easy to notice, that among early schedules of problem RCPSP there is an optimum solution. Really, if to take any optimum not the early schedule from it it is possible to gain simple serial shift of works for earlier term the early schedule which length will be no more, than length of the initial schedule; hence, it also will be optimum. All early schedules can be gained, if at each stage to overhaul all alternatives of sampling h ∈Dn. Thus, there is a circuit design of the full search, allowing to find the optimum solution of a problem. The optimum branch and bound method is based on this circuit design [27]. Naturally, this method is not vychislitelno effective as the solved problem of search of the optimum schedule NP-is difficult. The chosen serial method [30] looks through only one branch from this tree of search, finding one feasible solution.

Thus, the solution of problem RCPSP is represented in an aspect
Assemblage Since the time moments.i simultaneously

Is the solution of a problem of minimisation of function (3.1).

Hence, the target parametre of function of calculation of the schedule represents the schedule of supply of sets of test signals on entries of the panel of devices in the form of assemblage Cмоментов vremenigeneratsii

The test signals matching to the displayed parametre i.

3.1

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A source: Lysenko JAn Aleksandrovich. MODEL, the METHOD And the OPTIKO-ELECTRONIC DEVICE of PARALLEL MACHINING of IMAGES of INDICATORS of the PANEL of DEVICES. The dissertation on competition of a scientific degree of a Cand.Tech.Sci. Kursk - 2019. 2019

More on topic Function of calculation of the schedule of machining of images of indicators of the panel of devices:

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  2. MATHEMATICAL MODEL OF PROCESS OF MACHINING OF IMAGES OF INDICATORS OF THE PANEL OF DEVICES
  3. THE METHOD OF DEFINITION OF THE ORDER OF MACHINING OF IMAGES OF INDICATORS OF THE PANEL OF DEVICES AND THE APPARATUS-ORIENTED ALGORITHMS OF MACHINING OF IMAGES
  4. the apparatus-oriented algorithms of machining of images of indicators of the panel of devices
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  6. Synthesis of the structurally functional circuit design of the device of parallel machining of images of indicators of the panel of devices
  7. the Experimental research of the device of parallel machining of images of indicators of the panel of devices
  8. SYNTHESIS OF THE STRUCTURALLY FUNCTIONAL CIRCUIT DESIGN OF THE DEVICE OF PARALLEL MACHINING OF IMAGES OF INDICATORS OF THE PANEL OF DEVICES AND ITS EXPERIMENTAL RESEARCH
  9. Lysenko JAn Aleksandrovich. MODEL, the METHOD And the OPTIKO-ELECTRONIC DEVICE of PARALLEL MACHINING of IMAGES of INDICATORS of the PANEL of DEVICES. The dissertation on competition of a scientific degree of a Cand.Tech.Sci. Kursk - 2019, 2019
  10. Localization of indicators on the image of the panel of devices
  11. the Analysis of methods and processing devices of images of indicators of panels of devices
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