# The device estimates the actual value of the unit of physical quantity digital reference group

The invention relates to automation and computer engineering and can be used in Metrology for creating digital group standards. The technical result is to increase the accuracy of estimating the actual value of the unit of physical quantity digital group standard and the formation of the output device estimates the actual value of the unit of physical quantity obtained by the maximum likelihood method taking into account the actual value of the unit of physical quantity digital group benchmark in the preceding time. The technical result is achieved due to the fact that the device contains registers, dividers, power converters, multipliers, adders, Comparators, Quad, inverters and functional Converter. 2 Il. The invention relates to automation and computer engineering and can be used in Metrology for creating digital group standards.Known devices for determining the actual value of the unit of physical quantity. For example, the device [1] to determine the average value of the measured unit of physical quantity containing the pulse the pulse is. The principle of operation of this device is based on analog-to-digital functional transformation of the measured physical quantities. Its output is formed by the arithmetic average of the actual value of the unit of physical quantity without regard to the actual value of the unit of physical quantity digital group benchmark in earlier times.A disadvantage of this device is the low accuracy of the estimates the actual value of the unit of physical quantity.Closest to the proposed device is the device [1], determines the average value of the measured unit of physical quantity on the basis of functional Converter containing a multiplier d / a Converter, a register, a control unit and an analog-to-digital adder. The principle of operation of this device is based on a fast analog-to-digital functional transformation of the measured physical quantities. Its output is formed by the arithmetic average of the actual value of the unit of physical quantity without regard to the actual value of the unit of physical quantity digital group benchmark in earlier times.The disadvantage of the prototype is standard.The purpose of the invention is to improve the accuracy of estimating the actual value of the unit of physical quantity.The essence of the invention is that a device estimates the actual value of the unit of physical quantity digital group standard containing functional Converter. Unlike the prototype, it added p-1 Comparators, 3n+2 adders, 4n+1 registers, 2n+1 multipliers, n Quad, 2n+1 divisors of n power converters and two inverter. Thus the outputs of the first register connected to the first inputs of the first dividers, respectively, the second inputs of which are connected with the output of the second register, and the outputs from the inputs of the power converters, respectively, the outputs of which are connected with the first inputs of the first multiplier, the second inputs of which are connected to the outputs of the third registers, respectively, and the outputs to the inputs of the first adder, the output of which is connected to the input of the first inverter, the output of which is connected to the n-th functional input of the inverter whose output is connected to the input of the second inverter, and from the first to the n-1 inputs - outputs of the Comparators, respectively, and the first inputs of the second adders, the second inputs of which with 2-th to n-th third adders. The second third inputs of the adders are connected to the outputs of the fourth registers, respectively, and the outputs from the first to the second inputs of multipliers, respectively, whose outputs are connected to inputs of the fourth adder, the output of which is connected to the first input of the second divider, a second input connected to the output of the fifth adder, the inputs of which are connected with the second inputs of the second multipliers, respectively, and outputs the third voltage dividers, respectively, the second inputs of which are connected with the output of the third multiplier, the input of which is connected with the first inputs of the third dividers, respectively, and outputs Quad accordingly, the inputs of which are connected respectively to the outputs of the sixth adders, the first inputs of which are connected to the outputs of the fifth registers, respectively, and second inputs with the first input of the third adders, respectively. The first inputs of the Comparators are the first input device and second inputs and other input devices. The output of the second divider is the output of the claimed device.In Fig.1 shows a structural diagram of the device and the following notation: 1

_{1}-1

_{n}the first registers, 2

_{1}-2

_{n}first divisors,b>-6

_{n}third registers, 7 - the first adder 8 to the first inverter, 9 - functional Converter, 10 - second inverter 11

_{1}-11

_{n}Comparators, 12

_{1}-12

_{n-1}the second adders, 13

_{1}-13

_{n}third adders, 14

_{1}-14

_{n}fourth registers 15

_{1}-15

_{n}the second multipliers, 16 - fourth adder 17 - second divider 18 - the fifth adder 19

_{1}-19

_{n}third dividers, 20 - third multipliers, 21

_{1}-21

_{n}- Quad, 22

_{1}-22

_{n}sixth adders, 23

_{1}-23

_{n}- fifth registers.In Fig. 2 presents a graph of the basic error of frequency digital group benchmark and adopted the following notation: curve 1 - actual value curve; 2 - evaluation algorithm, implemented in the proposed device; curve 3 - evaluation algorithm, implemented in the prototype; direct 4 - main maximum allowable value.The invention is illustrated in Fig.1.The outputs of the first register 1 is connected with the first inputs of the first divider 2, respectively. Second input of the first divider 2 is connected to the output of the second register 3, and the outputs from the inputs of the power converters 4, respectively. The outputs of the power converters 4 of the of Gustrow 6, respectively, and outputs with the inputs of the first adder 7. The output of the first adder 7 is connected to the input of the first inverter 8. The output of the first inverter 8 is connected to the n-th functional input of the inverter 9. Output functional Converter 9 is connected to the input of the second inverter 10, and from the first to the n-1 inputs - outputs of the Comparators 11, respectively, first and second inputs of the adders 12. The second inputs of the second adders 12 is connected to the output of the second inverter 10 and the first input 1 of the third adders 13 and outputs - first inputs from the 2nd to n-th third adders 13. The second inputs of the third adders 13 are connected to the outputs of the fourth register 14, respectively, and the outputs from the first to the second inputs of the multipliers 15, respectively. The outputs of the second multipliers 15 is connected to the inputs of the fourth adder 16. The output of the fourth adder 16 is connected to the first input of the second divider 17. The second input of the second divider 17 is connected to the output of the fifth adder 18. The input of the fifth adder 18 is connected with the second inputs of the second multiplier 15, respectively, and the outputs of the third dividers 19, respectively. The second inputs of the third divider 19 is connected to the output of the third multiplier 20. The third inputs of the multiplier 20 is connected with the first inputs Treadstone with sixth outputs of the adders 22. The first inputs of the sixth adders 22 are connected to the outputs of the fifth registers 23, respectively, and second inputs with the first input of the third adders 13, respectively. The first inputs of the comparator 11 is connected to the first input device. The second inputs of the Comparators 11 - other input devices. The output of the second divider 17 is the output of the claimed device.The device operates as follows.Before applying signals to the inputs of the device from guardian digital group standard digital group benchmark in registers 1, 3, 6, 14, 23 recorded a priori information about the parameters of each of the guardians digital group benchmark in time comparisons guardian digital group benchmark with the original working pattern t

_{0}in the first registers 1 - values of the calibration interval of the corresponding custodians of digital group benchmarkin the second register 3 - value of the point in time that intra-group comparisons digital group standard, t

_{1}; in the third registers 6 - the values of allowable error of the corresponding custodians of digital group benchmark

_{d(i)}; in the fourth registers straps t

_{0}X

_{i}(t

_{0}); in the fifth registers 23 - return error values corresponding custodians of digital group benchmark at time t

_{0}, -

_{i}(t

_{0}). When we receive information from the first register 1 and the second register 3 to the inputs of the first divider 2 on their outputs are formed relationships values of time carrying out intra-group comparisons of the guardians digital group reference to the corresponding values of the calibration interval of the guardians digital group standard t

_{1}/T

_{(i)}. These relationships come to the inputs of corresponding power converters 4, the output of which generates signals corresponding to the square root of the received input relationsThe signals from the respective power converters 4 and third registers 6 are received at the respective inputs of the first multiplier 5, the output of which is formed of the values of a priori error estimates corresponding custodians of digital group standardThe signals from the first multiplier 5 are fed to the inputs of the first adder 7, the output of which is formed Segal, appropriate will aristopet at first inverter 8, where it is inverted, thereby forming the signal, reverse the a priori estimate of the total error digital group standardAfter recording the necessary information in the appropriate registers 1, 3, 6, 14, 23 to corresponding inputs of the Comparators 11 signals from guardian digital group standard: on the first inputs of the Comparators 11 signal of the first Keeper of the digital group standard X

_{1}and on the second input signals other custodians digital group standardThe outputs of the Comparators 11 results of the respective comparisons of the guardians digital group standardThese signals are sent to the first through n-1st functional inputs of the inverter 9 and the first inputs of the second adders 12. The output function of the Converter 9 is formed a signal corresponding to a weighted sum of the results of the respective comparisons of the guardians digital group standardand the inverse of the a priori estimates of total error digital group standard

^{*}

_{Σ}coming from the output of the first inverter 8,

_{0}X

_{i}(t

_{0}), forming thereby the output of the third adders 13 the actual value of the unit of physical quantity corresponding custodians of digital group standard X

_{i}= X

_{i}(t

_{0})+

^{*}

_{i}served on the first respective inputs of the second multiplier 15. Simultaneously, the first inputs of the sixth adders 22 the signals from the fifth register 23, characterizing the inverse values of the errors of the corresponding custodians of digital Gruppo sixth adders 22 signals, characterizing the change of error of the corresponding custodians of digital group standard for the time interval [t

_{0}, t

_{1}],

^{*}

_{i}-

_{i}(t

_{0}). The output signals of the respective sixth adders 22 are fed to the inputs of the corresponding Quad 21, forming at their outputs signals characterizing the statistical dispersion of the errors of the corresponding custodians of digital group standard

^{2}

_{i}= (

^{*}

_{i}-

_{i}(t

_{0}))

^{2}. The signals from the respective Quad 21 serves to corresponding inputs of a third multiplier 20 and the first inputs of the respective third divider 19. The output of the third multiplier 20, a signal is generated that characterizes the work of the statistical dispersion of the errors of the guardians digital group standardThis signal is applied to the second input of the third divider 19, the outputs of which are signals that characterize the works of the statistical dispersion of the errors of the guardians digital group standard for statistical disperse

^{2}

_{3}...

^{2}

_{n},...,

^{2}

_{1}

^{2}

_{2}...

^{2}

_{n-1}. The signals from the outputs of the respective third dividers 19 serves to respective second inputs of the second multiplier 15 and the input of the fifth adder 18, the output of which a signal is generated that characterizes their sum

^{2}

_{2}

^{2}

_{3}...

^{2}

_{n},...,

^{2}

_{1}

^{2}

_{2}...

^{2}

_{n-1}. The outputs of the second multipliers 15 are formed signals characterizing the relevant works (X

_{1})

^{2}

_{2}

^{2}

_{3}...

^{2}

_{n},..., X

_{n})

^{2}

_{1}, is the quiet are fed to the inputs of the fourth adder 16. The output of the fourth adder 16, a signal is generated that characterizes the sum (X

_{1})

^{2}

_{2}

^{2}

_{3}...

^{2}

_{n}+...+(X

_{n})

^{2}

_{1}

^{2}

_{2}...

^{2}

_{n-1}. This signal is fed to the first input of the second divider 17, and at its second input the signal from the fifth adder 18, thereby forming the output of the second divider 17, the signal characterizing the estimation of the actual value of the unit of physical quantity digital group standard equal toTo confirm the possibility of the claimed invention, consider the mathematical justification of a computational algorithm that is implemented by the device estimates the actual value of the unit of physical quantity digital group standard.Consider the following mathematical model of the measurement. Let at time t

_{0}made a comparison of the guardian units of physical the firs:where

_{i}(t

_{0}- the error of the i-th guardian digital group benchmark at time t

_{0}; X

_{i}(t

_{0}- the value of the units of the physical quantities of the i-th guardian digital group benchmark at time t

_{0}; X

_{0}- the unit value of a physical quantity of the original work of reference; n is the number of keepers in the digital group standard.Then at time t

_{1}are comparisons of the guardians of the scheme mutual comparisons. In the General case, when the number of keepers is equal to n possible n(n-1)/2 comparisons. With regard to (1) write the equation of comparisons, here and in further lowering denote the time t

_{1}

whererespectively the values of the errors and values of units of physical quantities i, j-th guardian digital group benchmark at time t

_{1};

_{i(j)}the result of the comparison at time t

_{1}.Digital group pattern may be formed from ravnotochnykh and razmetochnyh measuring instruments. For the case neravnodushnyh measurements, let us introduce the matrix of weight coefficients of mutual comparisons [2]. Elements is /> where

_{dmin}- basic tolerance of the precision of the guardian digital group standard;

_{di},

_{dj}accordingly the basic allowable error of the i-th and j-th guardian, participating in a relevant comparison.We write equation (2) with respective weights of comparisonsmultiplying these equations on the left and right of the appropriate weighting factors (3)

In the system (4) n(n-)/2 linear equations are invariant only n-1. Selecting from (4) n-1 equations with large weights, which contain errors each guardian digital group standard, it is necessary to Supplement this system the expression for the total error digital group standard

_{}, having thus forced invariance of the system of n equations

where

_{i}- accuracy of the i-th guardian digital group standard at the time of comparisons t

_{1}.However, due to the fact that

^{*}

_{i}determine, based on the mathematical apparatus of Markov random processes for evaluating the maximum calibration interval digital group benchmark [3].Assume that the error values of physical units

_{i}, i=1, n are Markov, describes a Gaussian probability density and the following differential equation:

The task of determining the calibration interval T

_{n}for measuring, storing unit of the physical quantities in the composition of the digital group standard, we will decide on the basis of the equation of Kolmogorov-Poker-Planck random processes. Direct Kolmogorov equation for n measures will write in the following form:

where W(

_{1},...,

_{n}, t) is the density of probability of error values physical values in the confidence interval (-

_{d}; +

_{d});

K

_{2n}is the diffusion coefficient for the digital group standard.The solution of this equation is a function [3]

where K

_{2(i)To solve this problem it is necessary to find the density distribution of the actual values of the errors of the digital group standardi.e., W(t)The expression for W(, t) can be obtained by integrating the intermediate functions [3]obtained by replacing the variables in equation (6), whereJ is the Jacobian of the transformationThe General equation for W(,t) takes the formFor a given confidence interval (-d; +dand confidence probability P(-d; +d), taking into account the expression (7) and the expression for the probability of a random value in any finite interval, we can writeBy a change of variables given paginegialle expression in the formula (8) to view the error functions (functions Paws the definition of calibration interval Tnfor n measurement included in the digital group standard, in this case takes the formwhere f-1(P(-d,d) is the inverse function to f(P(-d,d)).Having solved a similar problem for a single measurement means, obtain the expression for the calibration interval of the guardian digital group standardwhere T(i)- calibration interval of the Keeper.The expression for the error estimates of the guardians*idigital group standard takes the formwhere t1- time intra-group comparisons digital group reference (year).The expression to determine the diffusion coefficient of the i-th guardian digital group standard K2(i)isTaking into account (11, 12) the expression for the error estimates of the guardians*idigital group standard takes the formThus, using (5, 11, 12), Dene evaluation data/61/618597.gif">Taking into account (4) we write the system of n equations in matrix formM*= N, (15)wherewhere*i- evaluation of the basic error i-x guardian digital group benchmarkMatrix of estimates*the basic errors of the guardian digital group benchmark at time t1we find from the equation*= M-1N. (16)The inverse matrix coefficients M-1(16) takes the formAssessment values unit of physical quantity digital group standard for results mutual comparisons get by the criterion of maximum likelihood.Let the actual value of the unit of physical quantity of the i-th Keeper in the digital group standard Xisubject to Gaussian law, then the likelihood function can be written aswhere X is the actual value of the unit of physical quantity digital group standard;2i- the variance of Xi.Effect ta/61/618602.gif">The equation for the optimal value estimation unit of physical quantity digital group standard X* by the criterion of maximum likelihood has the form [5]X*=arg max{p(X1,...,Xn/X)}.Let us write the equation of assessment in General, using the necessary conditions of extremumTaking into account (17) equation estimation takes the formwhereSince at time t1Xiand2iunknown, proposed final equation estimation value units physical quantity to record the statistical dispersions2icharacterizing the change of error guardians relative to previous calibration Xi(t0) (1)Xi= Xi(t0)+*i;2i=2i= (*i-i(t0))2, (19)where2i- statistical variance of the error of the i-th guardian digital group Etalon. the prologo group standard takes the formExample.A digital group frequency standard, which consists of five low precision signal generator G3-110 with an error of frequency settingf=3,010-7(fnom=1[MHz],fd=0,3[Hz]). According to the previous verification carried out at time t0and carried out on the original measures (standard frequency and time B1-74), the absolute error of the guardians of this digital group reference have the following meanings:1(t0)=0 [Hz],2(t0)=0,1 [Hz],3(t0)=0 [Hz],4(t0)=-0,1 [Hz],5(t0)=0,2 [Hz]. Since all custodians of this digital group standard one-class accuracy, the weights of mutual comparisons of identical and equal toAfter conducting mutual comparisons of the guardians of the values of the absolute differences of the frequencies1(2)=0 [Hz],1(3)=-0,5 [Hz] ,1(4)= and-0.6 [Hz],d,d) = 0,997 and calibration interval for each generator Ti= 1 year,the diffusion coefficients for each of the guardian digital group Etalon according to (12) will be equal to K(i)value =0.01 [Hz2/year]Comparisons are made within six months from the date of the last calibration (t1= 0,5), from (11) we obtain the values of the error estimates of the guardians*i=0,21 [Hz],Estimation of total error digital group reference in (14) is equal to*Σ= 1,05 [Hz] . Forced invariant system given this assessment will take the formSolving the system, we get estimates of the basic errors of the digital group reference:*1= 0,43 [Hz],*2=0,43 [Hz],*3=0,07 [Hz],*4=-0,17 [Hz],*5=0,43 [Hz]. The statistical dispersion of the guardians according to (19), respectively21= 0,185 [Hz2] ,2],24=4,9103[Hz2],25= 0,053 [Hz2] . From (20) we find the value of a unit of frequency, the stored digital group standard f*=999999,854 [Hz] (f*=1,4610-7).To test the developed device was conducted experiments to study the reproducibility of the unit frequency digital group reference group custodian which is formed on the basis of four certified standards of frequency and time B1-74 [6]. The estimates are valid values of the basic error of frequency was determined on the basis of comparison of the estimates obtained by the above algorithm and estimates obtained by the method of arithmetic mean values of the implemented prototype, with valid values of this parameter, which in turn were derived from comparisons of the guardians of the digital group benchmark with the original work frequency standard, which used hydrogen frequency standard B1-75.In Fig.2 shows a graph of the annual change actual values main otnositelnostn B1-75 (curve 1), estimates of this error, obtained by the algorithm implemented in the proposed device (curve 2), and estimates defined by the method of the arithmetic mean of measured values implemented in the prototype (curve 3), relative to the primary maximum permissible error on frequency standards B1-74 (line 4).As a result of field experiment established that the error estimates are valid values units frequency digital group pattern obtained by the method of arithmetic mean values of the implemented prototype, the time interval 1 year averaged1,510-10that two and a half times less than the maximum permissible error on frequency standards B1-74 (f=3,5610-10). Error estimates are valid values units frequency digital group pattern obtained by the algorithm implemented in the proposed device, averaged4,610-11that is seven times less than the maximum permissible error and three times more precise estimates obtained by the method, ready for digital group pattern as ravnotochnykh, and razmetochnyh keepers, much less valid.Thus, the proposed device can be accomplished with the use of modern element base - analog-to-digital converters, logic elements and compared with the prototype has a more accurate assessment of the actual value of the unit of physical quantity digital group standard.Sources of information1. Gelman M M Analog-to-digital converters for information-measuring systems. - M.: Publishing house of standards, 1989, 320 S.2. Bezuglov D. A., Pomorians P. M.// Measurement techniques. - 2001. - 1, - n-3.3. Bezuglov D. A., Pomorians P. M. // Measurement techniques. - 1998. - 11, a - C. 3.4. GOST 8.207-76. The CIO. Direct measurement with multiple observations. Processing methods of observation results. The main provisions.5. Wentzel E. C. probability Theory. - M.: Higher. HQ., 1998. 576 C.6. Bezuglov D. A., Pomorians P. M EN 2173856 C1, 10.7.2000. ClaimsThe device estimates the actual value of the unit of physical quantity digital group standard containing functional Converter, the output of which a signal is generated that corresponds to the averaged sum result and a total error of digital group reference characterized in that it additionally introduced n-1 Comparators, 3n+2 adders, 4n+1 registers, 2n+1 multipliers, n Quad, 2n+1 divisors of n power converters and two inverter and the outputs of the first register connected to the first inputs of the first dividers, respectively, the second inputs of which are connected with the output of the second register, and the outputs from the inputs of the power converters, respectively, the outputs of which are connected with the first inputs of the first multiplier, the second inputs of which are connected to the outputs of the third registers, respectively, and the outputs to the inputs of the first adder, the output of which is connected to the input of the first inverter, the output of which is connected to the n-th functional input of the inverter whose output is connected to the input of the second inverter, and the first to the n-1 inputs - outputs of the Comparators, respectively, first and second inputs of adders, a second input which is connected to the output of the second inverter and the first input 1 of the third adders, and the outputs from the first inputs 2 through n-th third adders, the second to the third inputs of the adders are connected to the outputs of the fourth registers, respectively, and the outputs from the first to the second inputs of multipliers, respectively, the outputs of which connection is which is connected to the output of the fifth adder, the inputs of which are connected with the second inputs of the second multipliers, respectively, and outputs the third voltage dividers, respectively, the second inputs of which are connected with the output of the third multiplier, the input of which is connected with the first inputs of the third dividers, respectively, and outputs Quad accordingly, the inputs of which are connected respectively to the outputs of the sixth adders, the first inputs of which are connected to the outputs of the fifth registers, respectively, and second inputs with the first input of the third adders, respectively, the first inputs of the Comparators are the first input device and second inputs and other input devices, the output of the second divider is the output of the claimed device. }

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