SU845164A1 - Device for determining probability density - Google Patents

Description

one

The invention relates to the field of automation and computer technology, is intended to measure the probability density of extreme values of a random signal and the probability density of a random signal, and can be used in hardware systems for analyzing random vibrations, which require the simultaneous determination of the probability density of a random signal and probability density extreme values.

A device for determining the probability density L is known, comprising an adder, an adjustable constant voltage source, an amplifier-limiter, an auxiliary rectangular voltage source, a synchronous detector, and an integrator.

However, the device does not simultaneously measure the density distribution of the extreme values of the random signal and the density distribution of the random signal.

The closest in technical essence to the invention is a device for determining the density of probability 2, containing

block accumulation and registration, the first and second adders ,. the first inputs of which are combined and are the input of the device, the second and third inputs of the adders are connected respectively to the first and second inputs of the regulated constant voltage source, to the first and second inputs of the auxiliary direct line. .

10 coal voltage, the outputs of the adders, respectively, through the first and second double-sided limiters are connected to the first and second subtraction unit, the output of which

15 is connected to the first input of a synchronous detector, the second input of which is connected to the first output of an auxiliary rectangular voltage source, a sawtooth voltage generator, a survey pulse generator and, respectively, for the positive and negative voltages of the signal under investigation, two chains, each of which

25 of the series-connected And elements, modulator and analog-to-digital converter (ADC). The first inputs of the And element are combined and are the device input, the second inputs are combined and connected to the output of the synchronous detector, the input of the polling pulse generator, the first input of the registration accumulation unit and the first input of the sawtooth generator, the second and third inputs of which are connected to the outputs of the elements And, respectively, the first and second chains, and the output of the sawtooth voltage generator is connected to the input source ika regulated DC voltage, the third output is connected to the second storage unit and registering with the other inputs of the first and modulators .vtoroy chain. Other inputs of the ADC are combined and connected to the output of the impulse generator; v.; Survey OB, ADC bit outputs are connected to the first and second groups of inputs of the accumulation and recording unit, respectively. This device does not simultaneously measure the probability density of extremes and the probability density of a random signal, which leads to an increase in the analysis time. The aim of the invention is to enhance the functionality of the device by measuring the probability density of the extreme values of a random signal while simultaneously measuring the probability density of a random signal. The goal is achieved by the fact that the device for determining the probability DENSITY contains a two-way limiter, an accumulation and recording unit, two chains, respectively, for the positive and negative voltages of the signal under investigation, each of which consists of a series-connected element I, an ADC modulator the first inputs of the elements And are combined and are the input of the device, the second inputs are combined and connected to the first input of the accumulation and recording unit and to the control input of the saw generator shaped voltage, the first and second information inputs of which are connected to the outputs of the elements And, respectively, of the first and second circuits, and the output of the sawtooth generator is connected to the input of a source of adjustable constant voltage, the output of which is connected to the second input of the accumulation and recording unit and with the second inputs, the modulators of the first and second chains, the other inputs of the ADC are combined and connected to the first output of the interrogation pulse generator, and the bit output of the ADC is connected respectively to the first group and the second bit inputs of the accumulation and recording unit, a reversible counter, serially connected differential logging chain and limiter, and serially connected null indicator and trigger are introduced. The output of the two-way limiter is connected to the input of the null indicator, and the input is the input of the device. The trigger output is connected to the control input of the sawtooth generator and to the input of the differentiating chain. The output of the limiter is connected to the information input of the reversible counter, the information inputs of which are connected respectively to the bit inputs of the ADC of both chains, and the output of the reversible counter is connected to the third input of the accumulation and recording unit. The second output of the polling pulse generator is connected to the combined control inputs of the modulators of both chains. FIG. Figure 1 shows a block diagram of a device for determining the probability density, in Figure 2, timing diagrams explaining the operation of the device. The device for determining the probability density contains elements AND 1, 2, with outputs, respectively, connected to the first inputs of modulators 3, 4, which are connected to the first inputs of the first and second ADCs 5, b, respectively. Differentiating chain 7 output is connected to the input of the limiter 8. Two-sided limiter 9, the output is connected to the input of the null indicator 10, the output of which is connected to the input of the trigger 11, the output connected to the second inputs of the elements 1, 2 and the input of the differentiating chain 7, as well as the first input of the generator 12 sawtooth voltage. The generator 12 is connected to the output of the element I 1 by the second input, and to the output of the element 2 by the third input. A reversive counter -13, the first input of which is connected to the output of the ADC 5, and the second input - to the output of the ADC 6. The first and second inputs accumulation and recording unit 14 are respectively connected to the bit inputs of ADC 5 and 6. The first input of block 14 is connected to the input of the differentiating chain 7, the second input is connected to the second inputs of the modulators 3,4, respectively. The polling pulse generator 15 is connected to the second inputs of the A / D converters 5 and b, and the second input is connected to the third inputs of the modulators 3 and 4, respectively. The source 16 of the regulated constant voltage is connected to the output of the Mr.-12 trading system and the input is connected with the third inputs of modulators 3 and 4 and with the second input of block 14. Device input 17 is connected to the first inputs of the element; And to the limiter 9. The device operates as follows. The voltage of the investigated signal U-17 (t) (Fig. 2 a) is fed to the input 17 of the device and simultaneously to the first inputs of the elements I 1,2 of the limiter 9. Limiter 9 converts the signal under investigation t) (Fig. 2 a) into a random successor the strength of bipolar pulses bounded above and below. The positive spikes of the extreme values of the signal under study U 7- (i), exceeding the level of restrictions (t), are transformed by the limiters 9 into a positive sequence of pulses. Negative emissions of the extreme values of the signal under investigation, exceeding the level of the UQPP (t) limit, are converted by the limiter 9 into a negative pulse train. The total number of ne sections of the voltage ng of the signal under study U .-, (t) of the level of restriction (t) coincides with the number of zeros of the pulse signal at the output of the limiter 9. The durations of the positive spikes of the extremes of the signal under study coincide with the corresponding positive pulses from the output of the limiter 3 to the input of the indicator 10. For the negative spikes of the extreme values of the signal under study, one-to-one correspondence is observed, as well as for the positive values of the signal under study. The zero-indicator 10 fixes the moment of passing the zero level of the voltage of the pulse sequence entering its input, forming at the output positive impulses u, p (t) (Fig. 2 b), which control the trigger trigger 11. With the output 11 bipolar angular bipolar pulses 11,1 (t) trigger (Fig. 2c). The duration of itj corresponding to positive and D C corresponding to negative outliers extreme values of the signal under investigation, delivered to the second inputs of the And elements 1, 2, to the first inputs of the differentiating chains 7, generators 12 and at first input of accumulation and recording unit 14. Elements .Is 1 and 2 are fixed by the third inputs so that the realization of the signal under study and, -, and) remains in a given amplitude differential corridor - UT 2di, within which the extreme values are analyzed in a given time interval T. From the output of the elements 1, 2, the inputs of the modulators 3,4 and the second and third input of the generator 12 receive, respectively, positive and negative pulses, which repeat the form of the signal under study and If (t) (Fig. 2 a) within the time e t; d c. Generator 12 at the output, depending on the polarity of the signal under study, forms sawtooth pulses (Fig. 2 g), which are fed to the input of the source 16 of an adjustable constant voltage. This voltage varies in proportion to the change in the slope of the pulses of the generator 12, so that during the rise of the sawtooth voltage () (figure 2 g), it increases, and during the fall, it decreases. The modulators 3, 4 carry out pulse-amplitude modulation (AIM) (Fig. 2 d) when the second and third inputs have respectively a selection selection voltage from the second input, the generator 15 of the polling pulses and the voltage from the voltage source 16. ADCs 5, 6, when the pulses to are received from the first output of the generator 15 (FIG. 2, C), convert the DIM and CMM pulses and transmit information in parallel code on the discharge outputs to the 14-accumulation and registration unit (Fig. 2, w). At the same time, information from the A / D converter 5, b goes to the first and second inputs of the counter 13, respectively. Counter 13, depending on the increase or decrease in the voltage of the signal under study (c) Fig. 2, a) works on addition or subtraction. At the moment of reversal from the output of counter 1, the pulse U j (. T) appears (fig. 2 k) which fixes the moment of passage of the extreme value of the voltage of the signal under study. The counter 13 is reset when the pulse dC - decays (fig. 2 b) after differentiating it with differentiating chain 7 and limiting by limiter 8. The reset pulse from the output of limiter 8 enters the third input of counter 13 each time after analyzing the next voltage surge the investigated signal (t) (figure 2 a). From the output of the counter 13 to the third input of the accumulation and recording unit 14 a pulse is received of the mark of the N extreme value of the voltage of the signal under investigation (Fig. 2 K), and the second calibration input of the voltage is supplied to the second input of the voltage source 16. In block 14, the accumulation and recording is carried out by comparing the number determined by the number of bits of the ADC 5 or 6 at the time of the survey. pulses i with a number in the digital code, which is proportional to the change in the voltage value wa at the output of the voltage source 16 at the time of the appearance of the pulse of the extreme value of N, which is necessary to determine the probability density of the extreme values of the voltage of the signal under study U) (Fig .2 a)

In accumulation and recording unit 14, the number of cases marked by pulses of the N mark is counted, at which the voltage of the signal under investigation was in the range of levels corresponding to the calibrated voltage values of the voltage source 16.

The ratio of this number of cases to the total number of cases registered during the analysis serves as an estimate of the probability density of the extreme values of the voltage of the signal under study.

. The determination of the probability density in the accumulation and recording unit 14 of the signal under study is carried out similarly to the case discussed above, i.e. the number of all cases in which the voltage of the signal under investigation was calculated at the interval of levels corresponding to the calibrated values of the voltage of the source 16 of the voltage at the instants determined by the frequency of the interrogation pulses — C — this number of cases compared to the total number of cases recorded during the analysis Is an estimate of the probability density of the signal under investigation.

In principle, this is possible if the amplitude differential corridor 2uU is represented as a sum

2uU S and:), (2)

where and (-i) voltage value

j-ro of a calibrated fixed level within an amplitude differential corridor; Cfi - polling pulses of equal frequency, corresponding to the moment of analysis at this J-M level. The voltage analysis of the signal under investigation (t) (Fig. 2a) is performed at this level of analysis when equality of numbers is achieved.

, - () ()

in the analysis intervals

(t), uU (t), dL (t) ... uUj (t) ... dn (t),

where (} j ((i} -u.M

such that

& -imAUj (.i) (rn). (4) The probability density of the extreme values of the signal under study at a certain J-M fixed level is defined as the ratio of the number

hits of extreme values at a given level to the total number of polls marked by the impulse of a label by the formula

B, m% | & m mish

U)

Where

) ({NjCUti), (t)}

the number of cases in which the extreme value of the signal under investigation coincides with (t) in amplitude and their equality is achieved numerically

. N ruV-t j.M.ru, u, j,

where is the voltage of the experimental value of the signal under study in

the digital code at the time of the survey pulses

U | i, vi (b) - voltage of the signal

in digital code; - the number of all cases of extremes

Q values of the investigated signal in the analysis interval T.

The probability density of the signal under study is determined by the formula (5) taking into account the fact that the set of values of the signal being analyzed at time t contains a set of extreme values of the signal under study, Te (t) 0 (t) where eNj U (t) is all cases of voltage of the signal under study and U) at a predetermined calibrated level.

The proposed device makes it possible to simultaneously obtain the probability density of extreme values and the probability density of the signal under study, which expands its functionality while reducing the analysis time by a single time and increases the efficiency of application of the proposed device in hardware analysis systems of random processes.

Claims (1)

1. USSR author's certificate number 359670, cl. G About G 7/52, 1971. 2, USSR Copyright Certificate No. 2644529/24, cl. G About G 7/52, 1978 (prototype).