# Device for detecting and eliminating anomalous measurements with fixed value of false alarm probability

FIELD: physics; computer engineering.

SUBSTANCE: invention relates to computer engineering and can be used in control and signal processing systems. Technical outcome is achieved due to that, the device contains a unit for storing measurement results, commutators, interval division unit, random number generator, unit for eliminating associated values, ranking unit, storage register for random number samples, approximation units, subtracting units, remainder storage units, units for obtaining an ordered series on intervals, truncated sampling units, units for calculating mean-square deviation, multiplier units, coefficient storage register, coefficient evaluator, unit for setting false alarm probability, comparators, penalty storage units, arithmetic adder, threshold evaluator, comparator, penalty storage register, unit for eliminating anomalous measurements, storage register, delay unit and a clock pulse generator.

EFFECT: detection and elimination of anomalous measurements with a fixed value of false alarm probability.

1 dwg

The invention relates to the field of computer engineering and can be used in control systems and signal processing.

The observed time series is a sequence of y_{1}, y_{2},..., y_{n}measurement results obtained at equidistant points in time t_{1}, t_{2}, ..., t_{n}where y(t_{k})=y_{k},.

A mathematical model of the measurement results can be presented in General form

where S_{k}- a useful component; u_{k}additive noise component; η_{k}- anomalous component.

The values of the additive noise component u_{k}are uncorrelated, have zero mean and are implementing ergodic random process.

The purpose of this invention is the detection and elimination of anomalous dimensions in the original discrete implementation of the results of measurements at a fixed probability of false alarm.

Anomalous dimensions we will consider the sequence values of the measurement results, which are very different in magnitude and statistical properties on the background of the main group of values implementation. The problem of detecting anomalous measurements may occur: 1) in the receiving-transmitting devices or far to the economic links; 2) in radio when evaluating noise immunity of schemes (algorithms) signal processing in modelling systems; 3) in Metrology for measurement of characteristics of the atmosphere, etc.

To solve the problem of detecting anomalous measurements currently used theory of statistical decisions using parametric methods that require a priori information about the distribution of the measured process and its parameters (mathematical expectation, variance, correlation functions, and some others). For effective detection and elimination of abnormal measurements, it is necessary to know the statistical characteristics of normal and abnormal components of the noise.

The use of nonparametric statistics in the methods and algorithms validation of the results of the measurement assumes that the functional form of the distributions of noise components of a priori unknown. When using non-parametric statistics a priori information is for reference only differences between the competing hypotheses, the distribution covered by one or another hypothesis, not specified.

There is a method of detecting anomalous measurements using U-statistics [Marchuk VI Primary processing of measurement results with a limited amount of the a priori information.
Edited by Rumyantsev KE.. Taganrog. TGTU. 2003, 160 C.]. Applies only if the sample is N independent measurements of a random process y_{k}distributed by the normal law.

The characteristics of the method-analogue, coinciding with the characteristics of the proposed technical solution, the following: sampling the signal at a time, storing the digital signal, calculation of the standard deviation, the detection of abnormal measurements.

The disadvantages of the known method and device implements are:

- this method is used only for stationary processes;

- requires a priori information about the mathematical expectation, standard deviation and distribution law of the random process y_{k}.

Barriers to achieving the desired technical result are as follows:

in most cases, a priori information about the functional form of the distribution, as well as the mathematical expectation and standard deviation are limited.

The structural scheme of the device that implements the method is similar, comprises a generator of clock pulses, the switch, the first and second registers, the adder, the computing unit standard deviation, comparing the device, the setting unit level of significance.

Famous pic is b detection of anomalous measurements by the method of splitting into intervals [Perevertkin S.M. and other on-Board telemetry equipment spacecraft. - M.: Mashinostroenie, 1977. 208 S.], where the elimination of a single anomalous dimension of the measurement results is performed using the approximation of the unknown distribution of the noise only in the region of large positive values of the argument (the right tail of the density distribution), it is assumed that the distribution of noise refers to the exponential type. For the approximation of the right-wing "tails" unknown distribution functions F(y) of exponential type uses the expression

where α_{1}u_{1}τ, respectively, the extreme intensity function, the characteristic largest value and an additional parameter, determined from experimental data; n_{1}is the sample size.

To estimate these values, corresponding to the unknown distribution of the noise, according to the method of moments using the reference noise channel, m_{1}once the fetch is made of n_{1}independent members (total N=m_{1}n_{1}). In each of the m_{1}private samples are allocated the maximum largest members of y_{k}where k=1, ...,

m_{1}and calculated the average maximum membersand their dispersion D_{1}on the basis of which is determined evaluation

where C=0,5772 - Euler constant.

The full sample of N members again divided into m_{2}samples with n_{2}members (N=

m_{2}n_{2}, m_{2}>m_{1}). In each of the m_{2}samples are allocated the maximum amount of members in_{k}where k=1, ..., m_{2}and determinedD_{2},,complying with the new split full original sample. According to the procedure of detection is determined by the parameter

On a priori value of false alarm probability of α is determined by the value of the critical threshold

The characteristics of the method-analogue, coinciding with the characteristics of the proposed technical solution, the following: sampling the signal at a time, storing the digital signal, the allocation of time segments, splitting the original implementation on the intervals, the detection of abnormal measurements.

The disadvantages of the known method and device, it implements are:

the discovery procedure is not effective in the treatment group of anomalous measurements;

the presence of anomalous dimensions makes the sample is inhomogeneous, which leads to errors in the determination of the parameters of the distribution law;

a well - known method is applicable only in the case of processing donochnyj anomalous dimensions,
if the amplitude does not exceed two times the average value of y_{k};

Barriers to achieving the desired technical result are as follows:

- the heterogeneity of the sample leads to errors in the determination of the parameters of the distribution law, which is a consequence of the presence in the sample of anomalous measurements;

- the known method does not allow to detect anomalous group of measurement;

the algorithm for determining the threshold P and parameters,based on the selection and processing of only the highest members of private samples, which increases the influence of anomalous measurements on the estimation of parameters.

The structural scheme of the device that implements the method is similar, comprises a generator of clock pulses, the switch, the first and second registers, the adder comparing device, the computing unit threshold, the block partitioning.

Known digital smoothing device with advanced detection and elimination of abnormal measurements Pat. No. 2010325. The block detection and elimination of abnormal measurements provides obtaining the absolute value of the difference |Δ_{k}| between the current k-th reference input signal y_{k}and the value of the smoothed output signalthe comparison circuit provides a comparison signal score is based magnitude of the difference |Δ_{
k}| ID valid values of Δ and gate generates an output characteristic is exceeded.

In the smoothing device is implemented following the smoothing algorithm:

where the value of m_{k}and m_{k-1}defined as the present value of the input signal relative to its average value, respectively, for the k-th and (k-1)-th moments of the current time is equal to

The value of Δ is valid strobe shows the deviation of the input signal, N_{with}- the value of the division factor.

When checking the condition |Δ_{k}| (6), which is the condition for the absence of errors, the transition occurs on the branch of computing. If no errors are not met, then the calculated value of m_{k}it is considered wrong and instead for the formation of the current smoothed value is the previous correct value of m_{k-1}. Such a replacement due to the monotonicity of the original smoothed signal does not lead to its distortion. If after this the next step of smoothing the absence occurs, the error is classified as a fixed anomalous dimension. Failure to comply with the conditions of absence of errors is a sign of failure.

The characteristics of the method-analogue, coinciding with the characteristics of the proposed technical solution, followed by the s: discretization signal over time, storing digital signal, the selection of the smoothed signal, detection and elimination of abnormal measurements.

The disadvantages of the known method and device implements are:

the discovery procedure is ineffective in the treatment group of anomalous measurements;

- requires a priori knowledge of the possible values of Δ gate.

Barriers to achieving the desired technical result are as follows:

because this method allows to detect only a single anomalous dimension, the detection efficiency is a group of abnormal measurements will be low;

- the value of Δ is set depending on the class of input signals and the scope of application of the smoothing device.

The structural scheme of the device that implements the algorithm, contains the first adder, the counter counts, the first and second decoders, the first and the second element And the element OR trigger block set division ratio of the first register and the second adder, the second register, the third decoder, the counter anomalous dimensions, the unit selection module, the comparison circuit, the third element And the clock.

Closest to the invention is a device for the detection and elimination of abnormal values Pat. No. 2301445.

The considered device-a prototype of which involves: 1) memorizing the input realization of y_{
1}, y_{2}, ..., y_{n}; 2) splitting the input realization at intervals ∇_{j}random numbers having a uniform distribution law; 3) the condition that the intervals include not less than l values of the initial implementation, if the condition is not met, then the newly generated random number partitioning; 4) the presence on each interval ∇_{j},input realization estimates of the coefficients of the approximating polynomial a+bt+ct^{2}using the method of least squares; 5) finding the difference Δ_{k}between the evaluation values of the approximating function S_{k}and the original implementation of the results of measurements y_{k}; 6) on each interval ∇_{j}estimation of standard deviationand set thresholdwhere 0<A≤3; 7) on each interval ∇_{j}for the differencing process checks the condition S_{k}+ε_{j}<y_{k}<S_{k}-ε_{j}, 8) if the condition specified in paragraph 7, y_{k}receives one penalty value of 1; 9) repeat the procedures in paragraphs 1-8 To time with the accumulation of penalty values; 10) fined for all values of the original implementation is determined by the average value of fines; 11) the times at which the total number of fines exceeds the average of the value,
are defined as abnormal.; 12) individual and group anomalous measurements are corrected by linear interpolation carried out on two points, the corresponding values obtained measurement to the anomalous dimension (group of anomalous dimensions) and after the anomalous dimension (group of anomalous dimensions).

Device for detecting and removing anomalous dimension contains the buffer unit, the storage unit of the measurement results, the switches, the unit is split into intervals, the random number generator block elimination communication values, the power ranking, register storing a sample of random numbers, the block approximation, the subtraction unit, a storage unit residues, the evaluation unit evaluation of standard deviation, the power factor setting unit multiplied by the coefficient setting block threshold, the comparator, the storage register of fines, arithmetic summing device unit address of anomalous measurements, the delay unit, a storage register, a clock.

The disadvantages of the known devices of the prototype are:

- error in the estimation of standard deviation to determine the threshold value of fines for each interval;

- priori information about the value of the coefficient A.

Barriers to achieving the desired order is the result are as follows:

- evaluation of standard deviation values of the entire interval partitioning;

the dependence of the coefficient a from the values of probability of false alarm.

The aim of the invention is the detection and elimination of anomalous dimensions in the original discrete implementation of the results of measurements at a fixed probability of false alarm.

The proposed device comes from having a single discrete implementation

y_{1}, y_{2}, ..., y_{n}measurement results obtained at equidistant points in time t_{1}, t_{2}, ..., t_{n}where y(t_{k})=y_{k},.

A simplified mathematical model of the measurement results is described by the expression (1).

The essence of the proposed device consists of dividing the original discrete implementation of the results of measurements y_{k}at intervals ∇_{j},random length and approximation on each of them by a polynomial of the second degree, where p is the number of intervals.

Multiple splitting into intervals ∇_{j}and approximation of their value measurements allow us to multiply the evaluation of a single realization of the measurement results. On each interval ∇_{j}is the approximation of values of the measurement results by a polynomial of second degree by the method of least isih squares and calculates a difference Δ_{
k}between the evaluation values of the approximating function S_{k}and the original implementation of the results of measurements y_{k}.

To estimate standard deviationon each interval

Δ_{j}the result is a set of ranked values and discarded two extreme values of this range in order to reduce the error of the estimate standard deviation.

Then on each interval set thresholdand the value of the coefficient a is determined from the equation: A(α)=7,1α^{2}-7α+2,6 [Tokarev, S. a Study of the effectiveness of the adaptive method for the detection of abnormal values when the multiplicative noise component (article). - Proceedings of the Russian scientific and technical society of radio engineering, electronics and communication them. Popov Central Museum of communications. "Digital signal processing and its applications". Vol. IX-2, Moscow, 2007, s-389], where α is a priori specified probability of false alarm.

The threshold is exceeded, a differential process fined each interval of the partition, i.e. if

then y_{k}receives one penalty is equal to 1. The above procedure of determining fines is repeated for each of the replicated estimates of the baseline implementation. When this happens nakoplenie the values of fines for items in the original implementation if the condition (8),
i.e:

where- the number of penalty values.

At the end of processing fined for all values of the original implementation is determined by the average value of the fines. The samples in which the total number of fines exceeds the average value will be determined as abnormal.

Individual and group anomalous measurements are corrected by linear interpolation carried out on two points, the corresponding values of the obtained measurements to the anomalous dimension (group of anomalous dimensions) and after the anomalous dimension (group of anomalous dimensions).

Device for the detection and elimination of abnormal measurements at a fixed value of false alarm probability (figure 1) contains the block storage measurements 1, the inlet of which is an information input device, the output of which is connected to the inputs of switches 2.n, to the control inputs of which are connected to the output of the block is split at intervals of 3, which contains the random number generator 21, which are distributed on a uniform law, the output of which is connected to the input of the block address associated values 22, the output of which is connected to the input of block ranking 23, the output of which is connected to the input of the register storing the sample of random numbers 24, whose output is an information output the Loka split at intervals of 3, to the outputs of the switches 2.n connected to the inputs of blocks approximation 3.n, the outputs are connected to first inputs of blocks subtraction 4.n, to the second inputs of which are connected to the output of the storage unit measurements 1, the outputs of blocks subtraction 4.n connected to the inputs of the storage units are residues 5.n the outputs are connected to the inputs of blocks of ranking values on the intervals 6.n, the outputs of which are connected to the inputs of the blocks get truncated samples 7.n the outputs are connected to the inputs of blocks calculate estimates of standard deviation 8.n, the outputs of which are connected to the inputs of multiplier units 9.n, to the second inputs of which are connected to the output of register storage coefficient 14, input of which is connected to the output of the unit for determining the coefficient of 13, to the input of which is connected to the output of the setting unit probability of false alarm 12, the outputs of the multiplier units 9n are connected to first inputs of Comparators 10.n, to the second inputs of which are connected the outputs of the storage units are residues 5.n, the outputs of the Comparators 10.n connected to the inputs of blocks storing fines 11.n the outputs are connected to inputs of the arithmetic summing device 15, the first output of which is connected to the first input of the comparator 17, and a second output connected to the input of the unit for computing the threshold 16, the output of which is connected to the second input of the comparator 17, the output of Kotor is connected to th the input of the storage register of fines 18, the output of which is connected to the first input of the block correct anomalous dimension 19, to the second input of which is connected to the output of the delay unit 26, an input connected to the output of the storage unit measurements 1, the output of block elimination of the anomalous dimension 19 is connected to the input of storage register 20, whose output is an information output device. Synchronous operation of the device is provided by clock 25.

Device for the detection and elimination of abnormal measurements at a fixed value of false alarm probability is as follows. The original discrete implementation of the results of measurements of physical quantities in each of the n channels is divided into m intervals with random numbers. On each of the m intervals is the approximation of the original discrete realization of a polynomial of second degree whose coefficients are determined by using the method of least squares. Therefore, determined by the n estimates of the original discrete implementation for each of the m intervals. In each of the n channels are defined residues, by subtracting estimates of approximating polynomials of the original discrete implementation for each of the m intervals. Then on each interval partitioning result is a set of ranked values and m is determined estimates of standard deviation for the chopped samples in each of the n channels. Then determined by the detection threshold anomalous dimensions by multiplying the values of the estimated standard deviation by a coefficient whose value is determined according to a priori specified false alarm probability for each interval of m. The values of the residuals obtained for each of the m intervals, are compared with the threshold detection of anomalous dimensions. When exceeding the values of the residues of a certain threshold, the reference sample has one penalty value. For value received fines of n channels is the arithmetic mean separately for each sample. Therefore, determined by the net value of fines for each of the samples of the original discrete implementation. The resulting values obtained fines is determined by the average value of penalty values. In the original discrete implementation abnormal are those samples whose volume received fines, higher than the average. Individual and group anomalous measurements are corrected by linear interpolation carried out on two points, the corresponding values of the obtained measurements to the anomalous dimension (group of anomalous dimensions) and after the anomalous dimension (group of anomalous dimensions). Thus, the anomalous dimensions are excluded from the original discrete R is ment, and the processed data is fed to the output device.

This method of detecting anomalous measurements is as follows. In the storage unit measurements 1 is written to the original discrete implementation of the results of measurements of physical quantities. The block is split at intervals of 3 generates a ranked sequence of random numbers distributed according to the uniform law eliminated the "bundles", which are consecutively supplied to the switches 2.n. The obtained intervals in blocks approximation 3.n is the approximation of the original discrete realization of a polynomial of the 2nd degree by the method of least squares. In blocks subtraction 4.n are the remains by subtracting estimates of approximating polynomial of the original discrete implementation, written in the storage unit measurements 1. Value balances recorded in the storage units of the residues 5.n. In blocks 6.n on each interval the result is a set of ranked values, which are received in blocks get truncated samples 7.n, where discarded the first and last values of each of the ranked list. Next, in blocks 8.n on truncated samples are calculated estimates of standard deviation of residuals. On each interval of the partition m, the values of standard deviation obtained for truncated samples, cleverly which are stated on the coefficient blocks the multiplication 9.n. The coefficient value stored in the register 14, which is defined in the block definition of the coefficient of 13, and is set in the setting unit probability of false alarm 12. The obtained thresholds are received at the inputs of Comparators 10.n, on a second input which receives data on the balances of the storage blocks of residues 5.n. The obtained thresholds detection of anomalous measurements are compared with values of residues. If the balance value exceeds the threshold value, the reference gets a penalty value that is recorded in the storage units of fines 11.n. The data from the storage blocks of fines 11.n in each of the n channels are routed to the inputs of the arithmetic summing device 15, which is the arithmetic average of the penalties for each of the samples, and the formation of the result data obtained fines. In the computing unit threshold 16 is determined by the average size of the penalty among result values fines. The comparator 17 compares the value of penalties, with their average value. The number of samples where the value of the fines received exceeds the threshold, are considered abnormal and are recorded in the storage register of fines 18. Further rooms with anomalous values of the storage register of fines 18 and the values of the original discrete implementation of the block 1 through the delay unit 26 receives the inputs of block elimination anomie is lnyh measurements 19, where individual and group anomalous measurements are corrected by linear interpolation carried out on two points, the corresponding values of the obtained measurements to the anomalous dimension (group of anomalous dimensions) and after the anomalous dimension (group of anomalous dimensions). Thus, the anomalous dimensions are excluded from the original discrete implementation, and the processed data is fed to the storage register 20, the output of which data is fed to the output device.

Device for the detection and elimination of abnormal measurements at a fixed value of false alarm probability, containing a block of storage of the measurement results, the entrance of which is an information input of the n channels, each of which consists of a switch, to the control inputs of which are connected to the output of the block is split into intervals, which contains the generator of random numbers distributed according to the uniform law, the output of which is connected to the input of the block address associated values, the output of which is connected to the input unit of ranking, the output of which is connected to the input of the register storing the sample of random numbers, whose output is an information output unit split into intervals, to the outputs switches connected to the inputs of blocks approximation, the outputs of which are connected to the input of the m blocks subtraction, to the second inputs of which are connected to the output of the storage unit of the measurement results, the outputs of blocks subtraction is connected to the inputs of the storage blocks of residues, the outputs of blocks calculate estimates of standard deviation are connected to the inputs of multiplier units, to the second inputs of which are connected to the output of register storage coefficient, the output of block multiplication connected with the first inputs of the Comparators, to the second inputs of which are connected the outputs of the storage blocks of residues, the outputs of the Comparators are connected to the inputs of the storage units of fines, the outputs of which are connected with inputs arithmetically summing device, the output of which is connected to the first input of the comparator and the input of the computing unit threshold, the output of which is connected to the second input of the comparator the output of the comparator is connected to the input of the storage register of fines, the output of which is connected to the first input of the correct anomalous dimension, to the second input of which is connected to the output of the delay unit, the input of which is connected to the output of the storage unit of the measurement results, the output of block elimination of the anomalous dimension is connected to the input of the storage register whose output is an information output device, characterized in that each of n channels inputted blocks ranking values on intervals whose inputs are connected to outputs b the shackles storage residues, the outputs of blocks of ranking values on the intervals connected to the inputs of the blocks receiving the truncated sample, the outputs are connected to the inputs of blocks calculate estimates of standard deviation, to the inputs of register storage coefficient is connected to the output of the power factor determination, to the input of which is connected to the output of the setting unit probability of false alarm, the timing device is provided with clock pulses.

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