SU1547003A2 - Analog optimizer of number of standby units of process system - Google Patents

Abstract

The invention relates to computing and can be used in determining the optimal number of spare blocks of complex technical systems. The purpose of the invention is to expand the field of application of the device. The analog optimizer contains a failure rate incrementing node, a simple system time calculation node, subtraction blocks, division blocks, a simple technical system time shaping block, display blocks, a gradient specifier block, multiplication blocks, cost coefficients blocks, adders, comparison blocks, a switch , nodes of the formation of the present cost, the limitation setting unit, the switch, the total operating time setting unit, the system service intensity setting unit. The calculation of the optimal number of spare blocks of the system is carried out on the basis of an expanded volume of initial information and on a larger number of indicators, as a result of which the device can serve a wider class of technical systems. 6 Il.

Description

The invention relates to computing and can be used in determining the optimal number of spare blocks of complex technical systems.

The purpose of the invention is to expand the field of application of the device.

The essence of the invention lies in the fact that the calculation of the optimal number of spare blocks with given cost constraints is carried out according to two indicators: the system availability factor Kg and the functional significance of the elements of the technical system Z. Herewith, for the availability factor,

TO,

T - Tn

Where

Tp is the average time of a simple system due to the lack of spare blocks for a given interval or the entire estimated time of system operation}

T is the total (estimated) system operation time or a specified time interval during which the system availability for operation should be as high as possible.

Using Kg allows you to find the number of spare items

SP 1 1

Do

go

which, for a given time interval of the system operation, will exclude the practical possibility of its failure, that is, will provide. In the general case, this quantity of spare elements does not coincide with the quantity that is found by, since T var.

As a minimized indicator, Kg is of paramount importance for those systems that are not in duty, since, as a rule, the period of duty is short in comparison with the established service life, for this period the provision of Kg-I is not only relevant, but and the real challenge.

Mathematically, the task of choosing the optimal set of spare blocks is to search for a set of spare blocks 3 providing in a certain weight proportion;

T T1

Kg)

 L 21Zj (n;) - max

(ABOUT

provided

and

with -ZXc ,,

NlTi

where Tn 2ZT, (n,) is the average time of a simple system due to spare spare blocks,. (and T; (n; q.-PjT; j

B .

g

h g n nj) - No. lg

C - the total cost of the cost C - the cost of the spare

i-ro type, n - the number of spare blocks

1st type;

TV t is the failure rate of the technical system failures for the 1st type of blocks;

Z - the total value of the spare blocks} Z - the importance of the spare block

1st type;

.UT is the service parameter corresponding to the selected type of spare units; Tg is the intensity of service (restoration) of the system;

T - the total estimated time of the system.

The device solves the problem (1) by the gradient method by choosing for each 1st type of blocks the smallest value of n- for which the condition

h.fn - 7j (n J - T; (n.4i) M, y

&t; (n.),

nh

(2)

five

0

five

0

five

0

five

0

five

where h is an arbitrarily selected gradient;

P C; p (+ Z; PT. - reduced

the cost of costs With nnoZ.

FIG. 1 shows a block diagram of the device; in fig. 2 is a diagram of the unit for determining the probability of failure in FIG. 3 is a diagram of a site for calculating the time of a technical system; FIG. 4 is a diagram of the second node forming the present value of the costs; FIG. 5 is a switch diagram; in fig. 6 is a block diagram of the formation of a system service parameter.

The analog optimizer contains a node 1 for incrementing the probability of failures, a node 2 for calculating the time of a simple system, a first subtraction unit 3, a first division 4 unit a time shaping unit 5 is just a technical system, the first is a sixth display unit 6-1J, multiplication unit 13, first 4c and second blocks of setting cost coefficients, first and second l ,, - 7 (h blocks multiplying by a constant coefficient, first 18 and second 19 adders, first 20 and second 21 comparison blocks, switch 22, source 23 constant voltage the first 24 and second 25 nodes of the formation of the present value of costs, the block 26 for specifying the limitation, the second block 27 for dividing the switch 28.

The unit for forming the increment probability of failures contains switching contacts 29-32, a unit for forming a service parameter of the system including multipliers 33-1s 33-2, 33-3, a scale unit 34, a unit 35 for summing, a division unit 36, a switch 37 for switching contacts 38 ,, s 38.2. and 38j, button 39,

portioned Z; , on block 26 - voltage corresponding to the value of C "op; on block 65 - voltage proportional to the total expected system operation time; on block 66 - voltage proportional to service intensity | ty 5 on blocks 47, - 47 ,, - voltages proportional to the failure rate; , on blocks 50 ,, - 50 | j - voltages, proportional to the parameter T ;, on block 54, the value of the chosen decision step.

At each step of solving a task, a step-by-step procedure is carried out to determine the optimal number of spare elements of all types for the selected gradient h. At each ith step, the number of one of the N types of spare elements is determined. To do this, switch 28 is set to the position corresponding to the i-th type of spare elements, at block 63 - the value of the unit voltage “. Button 39 is pressed, resulting in the first output of node 1 (output

relays 40 and blocks 41-46 of memory one to six.

The time calculating node 2 of a simple technical system contains blocks 47, -47 for setting failure rates, block 48 for summing, block 49 for dividing, blocks for setting time for just systems, blocks 51 and 52 for multiplying, and switch 53.

The second cost-of-cost unit 25 contains a decision task setting unit 54, a constant multiplication unit 55, first 56 and second 57 inverters, first 58, second 59 and third 60 summation units, first 61 and second 62 multipliers, source 63 unit voltage and switch 64.

The device circuit also includes a block 65 for setting the total (estimated) operating time, block 66 for setting the system service intensity, second block 67 for subtraction, and third block 68 for dividing.

The device works as follows.

In block 12, a voltage proportional to the value of the gradient h 0 is set, on blocks 14, -14 c - the voltages proportional to Cj, on blocks 15j, 15 c - the voltage

block 45), a voltage value proportional to P (OЈ, 0) is generated, and at the second output, a value proportional to P (vol, 1). These values are applied to the corresponding inputs of node 2, the outputs of which form signals proportional to the values of T; (0) and T; (1). The value of T; (0) is fed to the input of the block 3 to be reduced, and the signal proportional to () is fed to its input of the subtracted. From the output of block 3, a signal proportional to & T (0) is removed, which is fed r to the input of the numerator of block 4, to the input of the denominator of which the value of the present value of the output from the node 25 is fed.

0

0

five

The signal is proportional to the value of h; (0), which is compared with the set gradient of block 12. This comparison occurs in block 20. If h (0) h, then switch 22 does not operate and indicator 10 lights up. Increase p. Then switch 37 is translated to the next position, corresponding to an increase in the number of spare elements of the 1st type per element, and the solution proceeds similarly until b | (n) h turns out, then the switch 22 is triggered by disconnecting the unit 10 from the voltage source 23 , and connects to it block 9 Install n-1. In this case, the switch 22 connects the first output of node 2 to the input of block 5. As a result, the voltage on block 5 increases by an amount proportional to T- (n-1). The number of spare blocks of each type is determined similarly.

After performing N steps of the solution, the total value C is formed at the output of the adder 18, and at the output

5, the adder 19 is the maximum value of Z, the value of which is displayed by the block 8. Based on the indications of the block 11, it is visually determined whether the restriction is fulfilled. If it is done, then

0 by the signal at the second control input, the switch 22 connects the output of block 65 to the input of the reduced block 67 and to the input of the denominator of block 68. To the input of the subtracted block 87 is fed

e signal from the output of block 5, proportional to the minimum time of the system. From the output of block 67, a signal is taken proportional to the difference in T-TP, and is fed to the input of the numerator

0

block 68 division. At the output of block 68, a signal is generated that is proportional to the value of K g ",,,", which is mapped

display unit 7. The problem is solved. Otherwise, the circuit is returned to its original position, at block 12 a new value of h s determined by the indication of block 6 is set, and the decision procedure is repeated,

The new value of h is defined as follows. The value of hs previously set in block 12E is multiplied in block 13 with the value of Psch, obtained by the step, the decision that comes from the output of node 25. The obtained value of L-Psch is fed to the input of the numerator of block 7, to the input of the denominator of which the value of the present value is given Fcdp from block 24 (i.e., the value including Sdop). At the output of block 27, the value hp-PM / Pd011 is generated, displayed by block 6.

As a result of solving the problem, a signal proportional to (7 (, at the output of block 19, a signal proportional to the value Z, which is displayed by display unit 8), is formed at the output of block 68, and the coefficients on blocks 16f - 16N are equal to the optimal number of spare blocks.

The principle of operation of the Formovova unit 1 — without increasing the probability of failure, is as follows.

Before starting operation, switch 37 is set to zero. At block 65, a voltage proportional to the total estimated system operation time is set, at block 66 a voltage proportional to the intensity of service {corresponding to the selected type (i-th) of spare blocks.

A button 395 is pressed and Uin is supplied to the input of blocks 35 and 33. In block 33, the service parameter O is formed (UT. A voltage proportional to s is removed from the output of block 33 and through the switch 37 it is fed to the input of scale unit 34, Output voltage output of block 34, proportional to Oij, is applied to the input of block 41 of the input of block 35 of summation. From the output of block 35 of summation, a voltage proportional to 1 + oЈ is removed, and fed to the input of block 43, Output voltages from blocks 41 and 43 through pe15470038

The switching contacts 31 and 32 are fed to the input of dividing unit 36, the output of which relieves a voltage proportional to od / 1 + vol, and is stored in block 45. This voltage corresponds to the probability of failure of the technical system due to the lack of spare units selected ( i-th) type, when the number of spare blocks of this (1-st) type is zero. In the second step, switch 37

ten

15

20

25

is shifted to position 1, the relay 40 is activated and switches its contacts 29-32, 38 to the opposite position. The voltages proportional to oi and + oL from the outputs of blocks 41 and 43 through the switching contacts 29 and 30 are fed to the inputs of blocks 33 and 35, respectively. From the output of block 33, the voltage proportional to x is removed and through the switch 37 to the input of scale unit s 34, the output of which is removed voltage proportional to about 2/2. The output voltage from block 34 is fed to the input of block 42 and to the first input of block 35 summation. From the output of block 35, the summation is removed, the voltage proportional to 64/2 + (1-i-ot), and fed to the input of block 44. Voltages proportional to Ob2 / 2 and V2 + (l + ci) from the outputs of blocks 42 and 44 through the switching contacts 31 and 32 are supplied to a dividing unit 36, from which output a signal proportional to h

)

35

40

45

50

55

on

Y

2 oCa / 2 + (1-H)

which corresponds to the probability of failure of the (simple) technical system due to the lack (shortage) of spare blocks of the selected (1st) type, when the number of spare blocks of this (1st) type is equal to one. This voltage is set to the input of block 46, the outputs of blocks 45 and 46 are removed voltage proportional to P (o6.0) and P (oi, l), respectively, and fed to the corresponding inputs of the time calculation node 2 just technical system. i

In the future, the work of the scheme is similar. Thus, from the outputs of blocks 41 and 42, we obtain voltages proportional to {/ п / п, that corresponds to the realization of the first factor in the formula

0

five

is shifted to position 1, the relay 40 is activated and switches its contacts 29-32, 38 to the opposite position. The voltages proportional to oi and + oL from the outputs of blocks 41 and 43 through the switching contacts 29 and 30 are fed to the inputs of blocks 33 and 35, respectively. From the output of block 33, the voltage proportional to x is removed and through the switch 37 to the input of scale unit s 34, the output of which is removed voltage proportional to about 2/2. The output voltage from block 34 is fed to the input of block 42 and to the first input of block 35 summation. The output of summation block 35 is removed, the voltage proportional to 64/2 + (1-i-ot) is removed, and is fed to the input of block 44. Voltages proportional to O2 / 2 and V2 + (l + ci) from the outputs of blocks 42 and 44 through the switching contacts 31 and 32 are supplied to a dividing unit 36, from which output a signal proportional to h

)

five

on

Y

2 oCa / 2 + (1-H)

which corresponds to the probability of failure of the (simple) technical system due to the lack (shortage) of spare blocks of the selected (1st) type, when the number of spare blocks of this (1st) type is equal to one. This voltage is set to the input of block 46, the outputs of blocks 45 and 46 are removed voltage proportional to P (o6.0) and P (oi, l), respectively, and fed to the corresponding inputs of the time calculation node 2 just technical system. i

In the future, the work of the scheme is similar. Thus, from the outputs of blocks 41 and 42, we obtain voltages proportional to {/ п / п, that corresponds to the realization of the first factor in the formula

s

zi- o

S to

(3)

and from the outputs of blocks 43 and 44

nor, proportional. - g, which corresponds to the realization of the second factor of this formula. From the outputs of blocks 45 and 46, we obtain the voltages proportional to P (oi, h-l) and P (ei, n), respectively.

The principle of operation of node 2 for calculating the time of a mere technical system is as follows.

The switch 53 operates synchronously with the switch 37. On the blocks 47 c, voltages proportional to ft are set; (2, ..., N), and in blocks 50, -50ts - voltages proportional to T; (i 1,2, ..., N). Voltages proportional to ft are supplied to the input of summation block 48; from blocks 47.-47N, and from its output a voltage proportional to N is removed

 21. ft; and is fed to the input of the denominator i-i

block 49 division. At the input of the numerator

dividing unit .49 is energized

from block 47-d. proportional to ft; a

the voltage is removed from its output

N

proportional q ft; / ft; s co; - (

The second is applied to the input of multiplication unit 51, The second input of multiplication unit 51 is supplied with voltage from block 50- proportional to Tj, the output of which is removed is voltage proportional to q; T ;, which is fed to input of multiplication unit 52.

Voltages from the output of blocks 45 and 46 of node 1, proportional to P (tf, K,) and P (tf ;, K + 1), respectively, are fed to the inputs (to the other two inputs) of multiplication unit 52, from whose outputs voltage proportional to respectively

T (K;) q; P (ot, K;) T; and t (K; +1) qjP (, K; +1) -t; ; K 0, l, 2, ..., h

The operation of the block 33 in the composition of the node 1 is as follows.

Before operation, the switch 37 is set to the zero position. At block 65, a voltage is established that is proportional to the total

five

Q

Q

five

0

five

five

0

0

five

The estimated time of operation of the system T, block 66, is a voltage proportional to the intensity of service C, corresponding to the selected (i-th) type of spare blocks.

The button 39 and U m is pushed to the input of blocks 33 and 35. In block 33, the multiplication of fU and T leads to the formation of the service parameter oi U T. From the output of block 33, the voltage proportional to ei is removed, and through switch 37 it is fed to the input of the scaled block 34. The output voltage from the output of block 34. proportional to r, is fed to the input of block 41 and the input of block 35 summation. Voltage output proportional to 1 + o6 is removed from the output of block 35, and supplied to the input of block 43. The output voltages from blocks 41 and 43 through the switching contacts 31 and

32 are fed to the input of block 36, from the output of which voltage is removed proportional to b / 1 + vol,

and is memorized in block 45. The first step of the work is completed.

In the second step, the switch is turned to position I, in which case the relay 40 is activated and switches its contacts 29-32, 38 to the opposite state. Voltages proportional to cЈ and 1 + oi from the outputs of blocks 4 and 43 through the switching contacts 29 and 30 are fed to the inputs of blocks 33 and 35, respectively. From the output of block 33, a voltage proportional to oi1 is removed, and through switch 37 it is applied to the input of scale unit 34.

In the future, the work of the scheme is similar. Thus, from the output of the block

33 get voltages proportional to oL,

Claims (1)

Invention Formula Analog optimizer of the number of spare blocks of the technical system in accordance with the auth. No. 1285496, characterized in that, in order to expand the scope of application, a second subtraction unit, a third division unit, a system service intensity setting unit and a unit for setting the total operating time of the system, the output of which is connected to the first information incrementing node, are introduced into it failure, the output of the time shaping unit of the technical system through the second subtraction unit and the third division unit is connected with the input of the display unit, the output of the total time setting unit, the system operation through the product contact of the switch is connected to the second inputs of the second subtraction unit and the third dividing unit, the output of the service intensity setting unit of the system is connected to the second information input of the failure rate incrementing node, and the second control input of the switch is connected to the output of the second comparison unit. 29 39 ABOUT 38, $ 5 U 51 45 K5Lzkd t 46 Fm.2 Fyu.Ch