RU2517322C1 - Adaptive digital predicting and differentiating device - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: adaptive digital predicting and differentiating device includes: a smoothing unit having an adder, first and second bidirectional counters, a single-channel smoothing subunit, a deviation ratio setting subunit, a real deviation subunit, a unit increment subunit, a dynamic characteristic control subunit, data, first control and clock inputs of the device and a prediction unit clocking unit.

EFFECT: broader functional capabilities by obtaining second derivative estimates using numerical differentiation formulae for equidistant points of the history of the input smoothed discrete sequence.

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Description

The invention relates to automation and computer technology and can be used to predict stationary and non-stationary random processes, improve the quality and accuracy of control in digital control systems and guidance of various (including ballistic) objects.

A digital predictive and differentiating device is known (according to RF patent No. 2470359, IPC G06F 17/17, 12/20/2012, bull. No. 35), which contains a smoothing unit and a forecast unit, which includes two subtractors, a forecast dynamics control unit, two subunits - quadratic and linear forecasts, three subunits of the calculation of the first derivative at the (n) th, (n-1) th and (n-2) th calculation points of the history of the input smoothed process. The device is functionally limited.

The closest in technical essence to the claimed device is selected as a prototype, an adaptive digital predictive and differentiating device (according to RF patent No. 2475831, IPC G06F 17/17, 02/20/2013, bull. No. 5), containing a smoothing unit and a forecast unit , which includes two subtractors, a forecast dynamics control unit, two sub-blocks - quadratic and linear forecasts, three sub-blocks for calculating the first derivative at the (n) -th, (n-1) -th and (n-2) -th calculation points the background of the input smoothed process and the adaptation block. This device is also functionally limited.

The technical problem for the proposed device is to expand the functionality by obtaining estimates of the second derivatives according to the formulas of numerical differentiation for equally spaced points (nodes) of the history of the input smoothed discrete sequence.

Therefore, in an adaptive digital predictive and differentiating device, which includes: a smoothing unit containing an adder, first and second reversible counters, a single-channel smoothing subunit from a series-connected adder and a register, a subunit for setting the deviation ratio containing a register, counter and delay element, a subunit actual deviations, containing a block of inverters, two comparators and an element And, a subunit of unit increments, containing two elements And and an inverter, a subunit of control dynam ical characteristic, containing two pulse shapers, an OR element, a counter, the first, second and third AND elements and a mode trigger, the information output of the smoothing unit, information, the first control and clock inputs of the device; a timing unit of a forecast block comprising a delay element, a trigger, a pulse generator, an AND element, and a shift register; a prediction block containing the first and second subtractors, each of which contains a register memory block, a multiplexer, an inverter block and an adder, a quadratic prediction block containing a inverter block, a first and second adder, a linear prediction sub block containing an adder and a inverter block, an evaluation unit of the first derivatives, containing the first subunit of calculating the first derivative in the first n-th (current) calculation point of the history of the predicted process from one adder, the output of which is the second information output for triads, the second subunit of calculating the first derivative in the second (n-1) -th calculation point of the history from one adder, the output of which is the third information output of the device and the third subunit of calculating the first derivative in the third (n-2) -th calculation point of the history from the block inverters, first and second adders, the output of the latter is the fourth information output of the device; a forecast dynamics control unit containing a register for storing the ordinates of the (input points) history of the input process, the input of which is the second control input of the device specifying the time (interval) of the forecast, a comparator, an inverter, an I element and an address counter whose information output is connected to the address buses of the multiplexers both subtractors; an adaptation unit containing the first and second elements of an EXCLUSIVE OR, an OR element, an inverter, the first and second elements of an AND, a trigger and a multiplexer, to both information inputs of which, respectively, the outputs of the sub-blocks of quadratic and linear forecasts are wound, and the output of the multiplexer is the first information output of the device , to solve the problem, a subunit for calculating the second derivative at the (n) th (current) historical settlement point has been introduced into the forecast block, containing a block of inverters and an adder, the first input of which is started the multiplexer output of the adaptation unit, to the second input, through the inverter unit, the output of the first subtractor multiplexer, the adder output is the fifth information output of the device, and the output of the first adder of the quadratic prediction subunit is connected to the sixth information output of the device to evaluate the second derivative in the second (n-1) - th design point of the history of the predicted process.

The invention is illustrated by drawings, which depict: in Fig.1 - a block diagram of the proposed device; figure 2 is a block diagram of a smoothing unit; figure 3 is a block diagram of a single-channel anti-aliasing subunit; Fig. 4 is a block diagram of a timing unit of a forecast block; figure 5 is a block diagram of a forecast block and an adaptation block.

Formulas of prediction operators are known that are obtained analytically using approximating polynomials in three points (ordinates) of the history of an input random discrete process using the least squares method (Milne V.E. Numerical analysis. M., IL, 1951, p. 212). The prediction operator for an approximating polynomial of the second degree (quadratic) over three historical points has the form:

y _{p + 1} = 3y _p -3y _p-1 + y _p-2 . (1) [KB3]

The prediction operator for an approximating polynomial of the first degree (linear) over three historical points has the form:

y _{p + 1} = ⅓ (4y _p + y _p-1 -2y _p-2 ), (2) [LN3]

or its simplified version:

y _{n + 1} = ½ (3y _n -y _n-2 ), (3) [LH3]

where y _p is the first (current) calculated point (ordinate),

y _p-1 , y _p-2 - respectively, the second and third calculated points (ordinates) of the two-level history of the input smoothed discrete sequence. In numerical analysis, this is a system of equally spaced points with a step h; in real time, h is the interval between points (ordinates), i.e. time (depth) of the forecast (N).

We denote Δy ₁ = (2y _p -y _p-1 ) as the biodiversity of the first level of the history of the input discrete sequence, i.e. the difference between the doubled current and previous ordinates of the process, respectively, Δy ₂ = (2y _p-1 -y _p-2 ) is the biodiversity of the second level of history.

After modifying equations (1) and (3), taking into account biodiversity, we obtain the following expressions for the quadratic [KB3] and linear [LH3] prediction operators implemented in the proposed device:

y _{p + 1} = (2y _p -y _p-1 ) + [y _p - (2y _p-1 -y _p-2 )] = (y _p -Δy ₂ ) + Δy ₁ = Z + Δy, (4) [KB3]

where Z = y _p -Δy ₂ and

y _{n + 1} = ½ (3y _n -y _n-2 ) = Δy ₁ -½ (y _n -Δy ₂ ) = Δy ₁ -½Z. (5) [LN3]

Formulas of numerical differentiation for equidistant points are known, expressed in terms of the function values at these points (J. Pollard. Handbook of Computational Methods of Statistics. M., “FS”, 1982, § 6.6, p. 61), in particular, for three points we have :

$$y_n^{\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left(y_{n-2}-\mathrm{four}{y}_{n-\mathrm{one}}+3y_n\right),\text{(6)}$$

$$y_{n-\mathrm{one}}^{\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left(-y_{n-2}+y_n\right),\text{(7)}$$

$$y_{n-2}^{\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left(-3y_{n-2}+\mathrm{four}{y}_{n-\mathrm{one}}-y_n\right),\text{(8)}$$

$$y_n^{\text{'}\text{'}\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$h^2$}\right.\left(y_{n+\mathrm{one}}-2y_n+y_{n-\mathrm{one}}\right),\text{(9)}$$

$$y_{n-\mathrm{one}}^{\text{'}\text{'}\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$h^2$}\right.\left(y_n-2y_{n-\mathrm{one}}+y_{n-2}\right).\text{(10)}$$

After transforming equations (6) ÷ (10) taking into account biodiversity, we obtain the following expressions for the calculation of derivatives implemented in the proposed device:

$$y_n^{\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left[\left(y_n-\Delta y_2\right)+\Delta y_{\mathrm{one}}-y_{n-\mathrm{one}}\right]=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left(Z+\Delta y_{\mathrm{one}}-y_{n-\mathrm{one}}\right)=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left(y_{n+\mathrm{one}}\left[\mathrm{TO}\mathrm{AT}3\right]-y_{n-\mathrm{one}}\right),\text{(eleven)}$$

$$y_{n-\mathrm{one}}^{\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left(y_n-y_{n-2}\right),\text{(12)}$$

$$y_{n-2}^{\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$2h$}\right.\left[2\Delta y_2-\left(y_n+y_{n-2}\right)\right],\text{(13)}$$

$$y_n^{\text{'}\text{'}\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$h^2$}\right.\left(y_{n+\mathrm{one}}-\Delta y_{\mathrm{one}}\right),\text{(fourteen)}$$

$$y_{n-\mathrm{one}}^{\text{'}\text{'}\text{'}\text{'}}=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$h^2$}\right.\left(y_n-\Delta y_2\right)=\raisebox{1ex}{$\mathrm{one}$}\!\left/ \!\raisebox{-1ex}{$h^2$}\right.Z.\text{(fifteen)}$$

The main typical elements of the device are adders (combinational) and inverter blocks, and the multiplication of the coefficients by the terms is carried out by the corresponding mounting shifts of the latter buses when entering the adder. Such operations on the block diagram (see figure 5) are indicated by a circle.

The value Z = y _n −Δy ₂ , as a polynomial and as an element of the circuit (inverter block and adder), participates in the calculations of estimates of the quadratic and linear forecasts (see equations (4) and (5)), estimates of the first derivative in (n) -th (current) calculation point of the history background (see equation (11)) and itself estimates the second derivative in the second (n-1) -th calculation point of the history of the predicted process (see equation (15)).

Using it as an independent information output in the proposed device meets the solution of the problem - the expansion of functionality.

The device contains (see Fig. 1) a smoothing unit 1, a forecast unit 2 and an adaptation unit 3. The smoothing unit 1 contains (see Fig. 2) an adder 4, a subunit 5 of actual deviations, containing an inverter unit 6, two comparators 7.1 and 7.2 and the element And 8, the first reversible counter 9, the subunit 10 sets the deviation ratio containing the register 11, the counter 12 and the delay element 13, the subunit 14 unit increments containing the inverter 15 and two elements And 16.1 and 16.2, the second reversible counter 17, the subunit 18 dynamic response control, containing two formovat A pulse 19.1 and 19.2, an OR gate 20, counter 21, three AND gates 22.1, 22.2, 22.3 and 23, trigger mode; information input 24 of the smoothing unit and the device, the first control 25 and clocking 26 inputs of the device and the smoothing unit; a single-channel anti-aliasing subunit 27, comprising (see FIG. 3) an adder 28 and a register 29 connected in series; information output 30. The timing unit 31 of the forecast block contains (see FIG. 4) a delay element 32, a trigger 33, a pulse generator 34, an And 35 element and a shift register 36. Prediction block 2 (see FIG. 5) contains the first 37 and the second 38 subtractors, each of which contains a block of register memory 39 from (A) series-connected registers 40, a multiplexer 41, a block of inverters 42 (assuming that the multiplexer does not have inverse outputs) and an adder 43; a quadratic prediction subunit 44 comprising an inverter unit 45, a first 46 and a second 47 adders; a sub-block 48 of a linear forecast comprising a block of inverters 49 and an adder 50; the first derivative evaluation unit 51 contains the first subunit 52 for calculating the first derivative in the first n-th calculation point of the process history from one adder 53, the output 54 of which is the second information output of the device, the second subunit 55 for calculating the first derivative in the second (n-1) -th the historical reference point from one adder 56, the output 57 of which is the third information output of the device, the third subunit 58 of the calculation of the first derivative at the third (n-2) -th historical reference point, which includes the first adder 59, to inverters 60 and a second adder 61, the output of which 62 is the fourth information output of the device; prediction dynamics control unit 63 containing a register 64 for storing the address (A) of the ordinates of the calculated points of the process history, input 65 of which is the second control input of the device that sets the forecast time H = AT (T is the cycle of the device, A is the maximum address of the 40 memory block register 39), comparator 66, inverter 67, AND element 68, and address counter 69; adaptation block 3 contains two elements EXCLUSIVE OR 70.1 and 70.2, element OR 71, inverter 72, two elements AND 73.1 and 73.2, trigger 74, multiplexer 75 and the first information output 76 of the device, subunit 77 for calculating the second derivative in the second (n-1) -th calculation point of the history from the block of inverters 78 and the adder 79, the output 80 of which is the fifth information output of the device, the sixth information output 81 of the device for evaluating the second derivative in the second (n-1) -th calculation point of the history of the predicted process.

The cycle of the device consists of 4 cycles. The smoothing unit 1 operates in two modes: stationary and dynamic (transitional), and all operations are performed in it in one (1st) cycle.

In stationary mode, the unit smooths the input random discrete process, the deterministic basis (median) of which can have a constant, linear or non-linear (quadratic) character of change in time. The smoothing unit 1 (see figure 2) implements the following modification of the operator of signature exponential smoothing:

y _n = y _n-1 + sign [1 / K (x _n -y _n-1 )], (16)

where x _n and y _n are the input and output discrete;

α = 1 / K is the smoothing parameter, K is the adaptation parameter;

Δx _n = (x _n -y _n-1 ) - current deviations from the median of the process.

As a criterion for the effectiveness (accuracy) of smoothing, the ratio d between zero and actual deviations Δx _{n is} chosen. The latter form the current unit increments of both signs of the output discrete in accordance with the signature function in (16):

sign [Δx _n / K] = 0 for [Δx _n -K] <0 (Δx _n are zero deviations),

sign [Δx _n / K] = 1 for [Δx _n -K]> 0 (Δx _n are the actual deviations).

In stationary mode (D = 0 - a sign of mode), block 1 smooths the input random sequence of discrete to the level specified by the relation d (real range d = 7 ÷ 190), which is entered before the device starts from input 25 into register 11 of subunit 10 of the deflection ratio . The latter is a controllable frequency divider, for example, with d = 7, every seventh clock pulse from input 26 appears at the output of direct transfer of counter 12, which, through delay element 13, overwrites inverse code d from register 11 to counter 12 (for the next cycle of the divider) and subtracts “1” from the first reversible counter 9 containing the adaptation parameter code K.

Adaptive control of the smoothing parameter, ensuring the constancy of the output value of the variance of the smoothed process, regardless of the degree of its variability at the input, is performed as follows. Let (for a certain code K in counter 9), the variance of the input discrete process increase, i.e. the number of actual deviations Δx _n (of both signs) increased. After comparing them with the adaptation parameter K at the output of the comparator blocks 7.1 and 7.2 of the subunit 5 (playing the role of negative feedback), logical “1” is set (the mode of operation of the comparators: [Δx _n > K] = “1”, [Δx _n <K] = "0") received at the input of element And 8. Since in the stationary mode the trigger of mode 23 is in the state "0" (D = 0), then from its inverse output to the first input of element And 8 of subunit 5, a logical "one". A high level of signals at all inputs of the And 8 element allows the passage of clock pulses from input 26 to the summing input of the first reverse counter 9 (the K code in the last increases) and to the second inputs of the And 16.1 and 16.2 elements of the subunit of unit increments 14. The signal from the output of one of them (depending on the sign of the deviation) is fed to the summing (or subtracting) input of the second reverse counter 17 of the smoothing result, i.e. the signature function (16) is realized. The growth process of K will lead to a decrease in the number of actual deviations and will continue until a dynamic equilibrium sets in, i.e. the number of pulses received from subunit 10 to the subtracting input of counter 9 will be equal to the number of pulses received at its summing input from subunit 5, and the variance of the output smoothed discrete sequence will remain unchanged (for d = 7: there must be seven zero deviations per actual deviation) .

Transient (dynamic) mode can be caused by starting, accelerating, bending, switching from one stationary mode to another, etc., i.e. an almost abrupt change in the process. To smooth the input discrete sequence in transient modes (D = 1), a single-channel smoothing subunit 27 is used (see Fig. 3), which implements the following exponential smoothing operator: y _n = ½ (x _n + y _n-1 ), i.e. . with a minimum degree of smoothing and, accordingly, with a minimum phase shift (delay) of the output discrete. Subunit 27 operates in both modes, is initiated by clock pulses from input 26 in register 29, but is used only in transition (dynamic) mode. For a stationary random process, the probability of a series, for example, of m = 8 (eight) deviations from the median (deterministic basis) of a single sign in a row, in accordance with the geometric law of probability distribution, is:

P (x = m) = (½) ^m = 1 / 256≈0.004,

those. so small that the appearance of such a series can be considered the beginning of a transitional regime. Subunit 18 captures such a series and works as follows. Since for the stationary mode the deviations of different signs are most likely, when the sign in the adder 4 changes from “plus” to “minus” and vice versa, the pulse shapers 19.1 or 19.2 are triggered and through the element OR 20 they reset counter 21 and trigger 23 to “0” (D = 0). In the dynamic mode (shapers 19 do not work), eight pulses will certainly come to the counter 21 (for example, 4-bit) from the clock input 26. At the output of the high-order bit of the counter 21, a logical “1” will be set, the high level of which will ensure passage through the first element And 22.1 clock pulse, which sets the trigger of mode 23 to "1" (D = 1). The last signal from the inverse output will block the operation of the subunit 5 of the actual deviations and, accordingly, the subunit of 14 unit increments, and by the high level of the direct output signal it will allow the discretion from the single-channel smoothing subunit 27 to the second reverse counter 17 of the smoothing result through the second element And 22.2. At the end of the transition mode, in the adder 4, deviations of different signs will inevitably occur, which will lead to the operation of the pulse shapers 19 and, accordingly, to the switching of the trigger of mode 23 to the state “0” (stationary smoothing mode, D = 0).

Prediction, differentiation and adaptation operations are performed in three cycles, respectively, 2nd, 3rd and 4th. They are formed by a series of three clock pulses from the clock node 31 (see figure 4). A clock pulse from input 26 resets trigger 33 and writes “1” to the least significant bit of the shift register 36. The same clock pulse, delayed by delay element 32, sets trigger 33 to “1”, thereby allowing pulses from generator 34 to pass through element I 35 in the shift register 36, on the tires of the least significant bits of which ("a", "b" and "c") the above series appears. In the 2nd step, the ordinate of the current (first) calculated point y _p is recorded in the first register 40 of the block 39 of the register memory of the first subtractor 37. At the same time, all previous ordinates are rewritten (shifted) to neighboring registers 40 (i.e., the input process history is formed ) At the address input of the multiplexer 41, the history ordinal address code (A) is received from the address counter 69, which is equal to the address code recorded from the second control input 65 in the address storage register 64 before the device starts operation and determines the forecast time (interval) Н = AT. In accordance with this address, the ordinate from the output of the multiplexer 41 (already as the second calculation point y _p-1 ) through the inverter block 42 is fed to the input of the second term of the adder 43, the first term of which is doubled the ordinate of the previous calculation point y _p . The output of the adder 43 of the first subtractor 37 sets the biodiversity of the 1st level of the history of the input discrete sequence. In the 3rd step, operations are performed similar to those described above, but already for the second 38 subtracters, at the output of which the biodiversity of the 2nd level of history is established. All adders in the device are combination. At the end of the third cycle, at the output of subunit 44, in accordance with formula (4), a quadratic (non-linear) prediction estimation code for a non-stationary discrete input sequence is set, at the output of subunit 48, in accordance with formula (5), a linear prediction estimation code for stationary or slowly varying input discrete sequence, and at the outputs 54, 57, 62, 80 and 81 of blocks 51 and 77, codes for evaluating the first and second derivatives in accordance with formulas (11) ÷ (15). In the 4th step, the signal from the output (“c”) of the shift register 36 of the clock unit 31, depending on the combination of the signs of the first derivatives, sets the trigger 74 of the adaptation unit 3 to the state “1” (quadratic forecast) or to “0” (linear forecast) . The direct output of the trigger 74, as the address input of the multiplexer 75, provides selection and transmission to its only output 76 of the multiplexer and the device of the corresponding forecast estimation code.

The prediction dynamics control unit 63 is designed to exclude the prediction operation on the dynamic (transient) modes (D = 1) of the device operation by resetting the address counter 69 to the O signal by a clock signal (U ₀ ) from the sub-block 18 of the dynamic characteristic control of the smoothing block. The zero address of the counter 69 on the address lines of the multiplexers 41 of both subtractors will ensure the calculation and installation of the current discrete code y _{n of a} minimally smoothed input process at the outputs of both prediction subunits 44 and 48. With the transition of the device to the stationary mode of operation (D = 0), the trigger of mode 23 of subunit 18 will allow the clock pulse to pass from input 26 through open element And 68 to the counting input (U _a ) of address counter 69. As the address grows in the latter, at the outputs of both subunits forecast 44 and 48 are set codes (y _{n + 1} ) of the predicted input process using information from a two-level history only for the new stationary mode. The growth of the address code h in the counter 69 (h = aT, a = 1,2,3, ... A), i.e. restoration of the specified forecast time H will continue with each cycle until it becomes equal to the value set in the storage register 64 h = H. Comparator 66 (operating mode: [Hh] ->"1", [H ≠ h] → "0") in this case, using the key 67 and the And 68 element, closes the counting input of the address counter 69. Introduction of the second derivatives calculation into the subunit device the first (n) -th and second (n-1) -th settlement points of the history (i.e., separated in time) makes it possible to analyze the nature (tendency) of changes in the parameters of the predicted process (growth - decrease, acceleration - deceleration, etc. .), which improves the quality of control, especially of fast-dynamic objects using well-known PID controllers.

Claims (1)

An adaptive digital predictive and differentiating device, which includes: a smoothing unit containing an adder, first and second reversible counters, a single-channel smoothing subunit from a series-connected adder and a register, a deviation ratio setting subunit containing a register, a counter and a delay element, a valid deviation subunit containing a block of inverters, two comparators and an element And, a subunit of unit increments, containing two elements And and an inverter, a subunit of control of dynamic x teristics, comprising two of the pulse, an OR gate, a counter, first, second and third AND elements and a trigger mode, a smoothing information output unit information, the first control inputs and the timing device; a timing unit of a forecast block comprising a delay element, a trigger, a pulse generator, an AND element, and a shift register; a prediction block containing the first and second subtractors, each of which contains a register memory block, a multiplexer, an inverter block and an adder, a quadratic prediction block containing a inverter block, a first and second adder, a linear prediction sub block containing an adder and a inverter block, an evaluation unit of the first derivatives, containing the first subunit of calculating the first derivative in the first n-th (current) calculation point of the history of the predicted process from one adder, the output of which is the second information output for triads, the second subunit of calculating the first derivative in the second (n-1) -th calculation point of the history from one adder, the output of which is the third information output of the device and the third subunit of calculating the first derivative in the third (n-2) -th calculation point of the history from the block inverters, first and second adders, the output of the latter is the fourth information output of the device; a forecast dynamics control unit containing a register for storing the ordinates of the (input points) history of the input process, the input of which is the second control input of the device specifying the time (interval) of the forecast, a comparator, an inverter, an I element and an address counter whose information output is connected to the address buses of the multiplexers both subtractors; an adaptation unit containing the first and second elements of an EXCLUSIVE OR, an OR element, an inverter, the first and second elements of an AND, a trigger and a multiplexer, to both information inputs of which, respectively, the outputs of the sub-blocks of quadratic and linear forecasts are wound, and the output of the multiplexer is the first information output of the device characterized in that a prediction block has a sub-block for calculating the second derivative at the (n) th (current) calculation point of the history, containing a block of inverters and an adder, the first input of which has a mul adapter of the adaptation unit, to the second input, through the inverter unit, the output of the first subtractor multiplexer, the adder output is the fifth information output of the device, and the output of the first adder of the quadratic prediction subunit is connected to the sixth information output of the device to evaluate the second derivative in the second (n-1) -th calculated point of the history of the forecasted process.

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