# Method of analyzing measurement signals from object under control (versions)

FIELD: measurement technology.

SUBSTANCE: method can be used for automatic estimation of state of distributed processes or objects of different physical nature. Measurement signal vector, i.e. noises disturbances and distortions with wide spectral range are formed additionally. After measurement information signals, calibration (control) signals or noise, disturbance or distortion signals are received the functional conversion of measurement signals is performed calculation of spectral characteristics of the signals. Measurement signals are transformed for any individual analyzed harmonic component of measurement signals.

EFFECT: improved precision of measurement.

2 cl, 11 dwg, 5 tbl

The method relates to the field of computing, namely to the section expert-analytical analysis of the various information and control, random and deterministic stationary and not stationary, diagnostic and other) signals, parameters and macroeconomic indicators received from the controlled process or object.

The known device, implement a method for processing of random signals, recorded on magnetic media, which consists in recording on magnetic media electrical signals of the random processes and calibration (control) signals, reproduction, spectral analysis and record the results of the analysis of the spectrograms, control acceptable level of distortion interference of the investigated random processes, and containing the power play, spectrum analyzer harmonic components of the measuring signals, the recording unit, the control unit and the power comparison [1-7].

Known methods of rejection of random signals, recorded on magnetic media [8], measuring information and calibration (control) signals, playback and analysis of the results in the form of spectrograms, control acceptable level of distortion interference of the investigated random signals, performing spectral analysis with a wide range of the of Ascot in the entire frequency range of the analyzed signal. The results of the analysis are compared with the characteristics of the spectrogram undistorted calibration control signal or the comparison vector spectral characteristics distorted by noise, interference and distortion measuring information and calibration (control) signals. By comparing the results of either method produces rejection distorted areas recording on magnetic media.

The General disadvantages of the known devices and methods are:

- subjectivity job priori thresholds, relative to which the exception (rejection) false (distorted noise) plots measuring signal;

- the performance and reliability of the measurement data is estimated on the restricted sample, the formation of which do not participate measuring signals, parameters, and performance;

- low reliability analysis measuring information and calibration (control) signals in the time and frequency domains;

- function analysis of the measuring signals is reduced only to the exclusion of distorted areas of stochastic processes in time and frequency domain, without solving the problems of support of decision making in conditions of uncertainty.

- limit the scope of application of the method only for the analysis of the distortion plots measuring signals, registered on magnetic media, without analysis parameters and indexes.

The closest in technical essence is a way of processing and analysis of measurement signals from the controlled object (options) [9], which consists in the operation of comparing the current vector amplitude-frequency characteristics of the calibration (control) and measurement information signal of the investigated random process, comparing the results of which implemented two possibilities for the analysis of measurement data:

1. If the modulus of the difference of the amplitude-frequency spectrum or the amplitude-frequency characteristics of the harmonic component of the measuring gauge control and information signals is greater than the specified relative error of calculation of the amplitude-frequency spectrum or the amplitude-frequency characteristics of the harmonic component in the analyzed frequency range or at a particular frequency analysis, obtained in this frequency range or within separate frequency information is excluded from further analysis.

2. Joint processing of amplitude-frequency characteristics measuring information and calibration (control) signals allows us to calculate confidence intervals and relative activities the major errors of the estimates of the amplitude-frequency spectrum and characteristics of measuring information signal. However, if the magnitude of the relative error obtained estimates of the amplitude-frequency spectrum of the measuring signal is greater than the specified relative error, obtained in this frequency range or within separate frequency information is also excluded from further analysis. With the determination of confidence intervals for the resulting amplitude-frequency characteristics of the measuring signal is solved their evaluation in probabilistic sense.

The main disadvantage of this method is:

- low accuracy of determination of the main parameters and indicators for measuring the information signal (amplitude-frequency spectrum and the characteristics of the spectral power density of the investigated random process);

- the operation of centering the original data relative to the arithmetic mean value of the implementation of the measuring information, the calibration control signal regardless of the frequency of the analyzed harmonic components of the investigated random process.

The aim of the invention is to improve the accuracy of the results of the calculation parameters and indicators in the processing and analysis of measurement information signals from a controlled process or object.

The goal in the first embodiment is achieved by the fact that additionally receive the measuring signal noise, interference and distortion with a wide range of frequencies with the controlled object and after receiving the measurement information signal, the calibration control signal or signal noise, interference and distortion directly before the calculation of the spectral characteristics of these signals produce the centering of the source data mentioned above, measurement signals for each of the analyzed harmonic component of the measuring information signal, the calibration control signal or signal noise, interference and distortion, relative to the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, the current values are calculated for each of the source data values of the measuring information signal, the calibration control signal or signal noise, interference and distortion by averaging the original data of these measuring signals on the averaging time interval, equal to the inverse value of the frequency of the analyzed harmonic component, and each value of the original data of the measurement information signal, the calibration control signal or signal is Ala noise noise and distortion correspond to the calculated current values of the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, and then produce the centering of the source data and measurement information signal, the calibration control signal or signal noise, interference and distortion relative to the corresponding functions of centering and perform an analysis of the measurement information signal, the calibration control signal or noise, interference and distortion by calculating the spectral characteristics of the measurement information signal, the calibration control signal or signal noise, interference and distortion, the comparison of the respective spectral characteristics of measuring information signal and calibration (control) signal or signal noise, interference and distortion, on the comparison of the record corresponding to the measurement information signal during the portion of time on the analyzed frequency range or at a particular frequency analysis in accordance with the dependence of the spectral characteristics of the measurement information signal and the calibration control signal or signal noise, interference and distortion as a function of time and frequency, and the upper limits of what this range is determined by the upper frequency measurement calibration (control) signal or noise signal, noise and distortion and, if the module of the difference between the spectral characteristics of the measurement calibration (control) signal or signal noise, interference and distortion and measurement information signal is greater than the specified relative error of calculation of the spectral characteristics of measuring information signal during the portion of time on the analyzed frequency range or at a particular frequency analysis, obtained on this part time, or range of frequencies or a single frequency measurement information is excluded from further analysis.

The goal in the second embodiment is achieved by the fact that additionally receive the measuring signal noise, interference and distortion with a wide range of frequencies with the controlled object and after receiving the measurement information signal, the calibration control signal or signal noise, interference and distortion, using as the spectral characteristics of the amplitude-frequency spectrum of these measuring signals directly before the calculation of the amplitude-frequency spectrum of the measuring signal, the calibration control signal or signal noise, interference and distortion produced by centering the source data mentioned above, the measuring signal p is each individual analyzed harmonic component of the measuring information signal, the calibration control signal or signal noise, interference and distortion relative to the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, the current values are calculated for each of the source data values of the measuring information signal, the calibration control signal or signal noise, interference and distortion by averaging the original data of these measuring signals on the averaging time interval, equal to the inverse value of the frequency of the analyzed harmonic component, and each value of the original data of the measurement information signal, the calibration control signal or signal noise, interference and distortion correspond the calculated current values of the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, and then produce a centering measuring information signal, the calibration control signal or signal noise, interference and distortion relative to the corresponding functions of centering and perform an analysis of the measurement information signal, the calibration control signal or signal noise, interference and distortion by calculating the amplitude and frequencies of the output characteristics of measuring information signal, the calibration control signal or signal noise, interference and distortion, the comparison of the respective amplitude-frequency characteristics measurement information signal and the calibration control signal or signal noise, interference and distortion, on the comparison of the record corresponding to the measurement information signal during the portion of time on the analyzed frequency range or at a particular frequency analysis in accordance with the dependence of the amplitude-frequency characteristics measurement information signal and the calibration control signal or signal noise, interference and distortion as a function of time or frequency, and the upper limit of this range is determined by the upper frequency measuring gauge (control signal or signal noise, interference and distortion, and, if the modulus of the difference of the amplitude-frequency characteristics measurement calibration (control) signal or signal noise, interference and distortion and measurement information signal is greater than the specified relative error of calculation of the amplitude-frequency characteristics measurement information signal during the portion of time on the analyzed frequency range or at a particular frequency analysis, obtained on this part time or in this frequency range, or at particular frequency measurement information is excluded from the further analysis process, the results of joint processing of amplitude-frequency characteristics measurement information signal and the calibration control signal or signal noise, interference and distortion calculate confidence intervals whose boundaries are determined by the current estimates of the corresponding amplitude-frequency characteristics measurement calibration (control) signal or signal noise, interference and distortion, and relative error of the obtained current estimates of the amplitude-frequency characteristics measurement information signal and, if the magnitude of the relative error obtained current estimates of the amplitude-frequency characteristics measurement information signal is greater than the specified relative error or, if the magnitude of the confidence limits of the measuring gauge (control) signal or signal noise, interference and distortion will be more current estimates of the amplitude-frequency characteristics measurement information signal, received on the analyzed portion of time in the analyzed frequency range or at a particular frequency measurement information is excluded from further analysis.

Compare the nutrient analysis of the prototype revealed in the proposed method, a new principle of analysis of measurement information signals of random processes using Fourier transform. The basis of the novelty of the proposed method is the centering of the source data and measurement information signals, the calibration control signal or signal noise, interference and distortion before the calculation of the parameters and indicators (spectral characteristics) of the measuring information of random processes at the same time on the same frequency bands or on the same single frequency analysis. The claimed method meets the criterion of "Novelty."

In practice, the conduct of specific test items and expert-analytical analysis of various stochastic processes meet strict requirements for the accuracy of the representation of the results of the analysis of measurement data of a random process, especially in cases when there is a need for analysis of causes of abnormal outcomes of the tests of the test object. The greatest attention is paid to the analysis of such measurement information signals and parameters as vibration, shock, acoustic random processes of nature, as well as macroeconomic parameters and indicators investigated in a wide frequency range. N is the most popular frequency characteristics, thus, from the whole range of parameters and indicators, random vibration, shock and acoustic processes, as well as macroeconomic parameters and indicators in the analysis of the results of development tests of the controlled object or process are the spectral characteristics of the measurement information signals of random processes (amplitude-frequency spectrum and power spectral density). It is the analysis of the spectral characteristics play a special role in the evaluation of acoustic, vibration state when conducting flight tests of the aircraft, especially when the unsuccessful outcome of the trials, the situational analysis of the behavior of macroeconomic parameters and indicators.

To understand the proposed method for the analysis of measurement data (signals, parameters, indicators) studied stochastic processes we introduce the concept of the information signal, measuring the information signal, the information of the calibration control signal, the measurement information of the calibration control signal and the measuring signal to noise, interference and distortion.

The information signal I_{x}(ω, t) we will agree to understand the signal, which is directly removed from the output of the sensor information that is installed on controlling the IOM object.

The signal I_{x}(ω, t) contains useful information about the state of the controlled object.

Under measuring information signal X(ω, t) we will agree to understand the signal receiving and recording station, directly on the system analysis of measurement data.

The information of the calibration control signal I_{y}(ω, t) we will agree to understand the signal, which is directly removed from the generator output of the reference sinusoidal signal, is installed on the test object.

Under the measurement information of the calibration control signal Y(ω, t) we will agree to understand the signal receiving and recording station, directly on the system analysis of measurement data.

Under the measuring signal to noise, interference and distortion S(ω, t) we will agree to understand the signal, which produces a distortion of the signals I_{x}(ω, t) and I_{y}(ω, t).

The nature of the signal S(ω, t) are the noise and interference introduced by the devices collect, transmit measurement signals from the controlled object (lethal machine) in the "ether", the noise introduced into the signal I_{x}(ω, t) and I_{y}(ω, t) by passing them over the air, and the noise and distortion introduced by the equipment for receiving, recording and processing. To obtain the signal is S(ω
, t) in a multi-channel radio systems, there is always the possibility to use an "empty" channel measurements, which is not transmitted telemetry information, i.e. not connected source of information. "Empty channel carries information only about the noise, interference, and distortion, which affect each of telemetry parameters multichannel radio system of the controlled object. When the selection of the reliable sections of the signal X(ω, t) for subsequent mathematical analysis of the problem arises qualitative and quantitative evaluation of the nature and intensity of the degree of distortion of this signal [1-7]. Distortion of the signals X(ω, t) and Y(ω, t) are by nature random and can be both stationary and non-stationary. For example, aging of equipment (airborne and ground) measurement, collection, acceptance, transformation and processing, as a rule, leads to distortion of signals I_{x}(ω, t) and I_{y}(ω, t), which are stationary.

Currently, the assessment of the degree of distortion of the signal X(ω, t) is performed on the basis of an assessment of the distortion of the signal Y(ω, t) with a priori known characteristics received from the controlled object simultaneously with the signals X(ω, t) [1-7]. In fact, the signal Y(ω, t) for each point in time and frequency and represents the vector sum of the data of the reference sinusoidal calibration control signal I_{
y}(ω, t) and the data signal S(ω, t), i.e.,

The essence of this approach is based on the analysis of the hardware characteristics (data, parameters) of the signal Y(ω, t), with identical properties distortions with respect to the signal X(ω, t). For example, in practice control the reliability of the telemetry data used individual service settings, including signals on-Board calibration levels of 0.50 and 100% scale telemetry, levels of markers of high and low frequency and frame counter.

In General, the signals X(ω, t) for each time point represent the vector sum of data for each time and frequency signals I_{x}(ω, t) and S(ω, t), i.e.,

In a multi-channel telemetric measurement systems for cyclic polling, for example, vibration sensors, the frequency of data transmission of vibration processes random nature of the controlled object is constant and is selected from the calculation of the maximum speed of their changes.

This cyclic polling frequency is chosen so that any periodic function that does not contain harmonic components with frequencies above some upper frequency is completely determined by a sequence of two values in one period of the top frequent is you.

For example, let the frequency range of the signal X(ω, t) for cyclic sampling frequency of 8 kHz is in the range from 0 to 2 kHz. Then one period of the signal Y(ω, t), for example, with a frequency of 1 kHz, accounting for 8 counts. At one period of the signal X(ω, t) with a frequency of 2 kHz have four starting with the ability to detect harmonic components of the signal S(ω, t) in the frequency range from 0 kHz to 4 kHz.

Analyzing the frequency spectrum of the signal Y(ω, t), the conclusion is that the whole spectrum of harmonic components of the signal from zero to the fundamental frequency belongs to the amplitude-frequency spectrum of the signal S(ω, t), except for a small frequency band around the main harmonic with a frequency of 1 kHz and in the vicinity of frequencies that are multiples of the fundamental frequency harmonics in the presence of nonlinear distortion sinusoidal signal Y(ω, t), i.e. in the vicinity of the frequencies 1 kHz, 2 kHz, 3 kHz and so This, in turn, leads to the conclusion that in fact the whole spectrum of harmonic components of the signal Y(ω, t) and the signal X(ω, t) overlaps the frequency range of the signal S(ω, t) (Figure 1).

Thus, when performing the fundamental conditions of theorem V.A. Kotelnikov the opportunity to analyze data not only measuring signal X(ω, t), but measuring with the persecuted noise noise and distortion S(ω, t) or measuring the calibration control signal Y(ω, t) subject to the limitations, which were discussed above.

In practice, the analysis of random processes in a wide range of frequencies for specific tests, for example, aircraft, vibration, shock, acoustic processes are referred to the so-called class of rapidly changing processes (BMP). The rationale for opportunities to improve the accuracy of results of the analysis of the measuring signals X(ω, t), in comparison with the prototype, consider the example of the analysis unreliable (hidden by noise, interference and distortion) plots of the signals X(ω, t) and Y(ω, t)observed by means of vibration parameters and resulting from the controlled object. As the source data of the measuring signal to noise, interference and distortion S(ω, t) we will use the measurement of the calibration control signal Y(ω, t) subject to the limitations discussed above, in its fundamental frequency and frequencies that are multiples of the fundamental frequency. Figure 2 presents a fragment of the plots of false information by a set of signals X(ω, t) and Y(ω, t) on paper, obtained with the help of specialized information processing systems "Spectr-JSC. Visually we can see that the plots of the signals X(ω, t) is Y(ω
, t) are "unreliable", as evidenced by the label inaccurate (black stripe) on paper (Figure 2). In table 1 the results of traditional amplitude-frequency data analysis section (slice) of the signal X(ω, t) (Figure 2). In the first, second and third columns of table 1 shows the results of the amplitude-frequency spectrum with a step of analyzing the frequency of 5 Hz plot the signal X(ω, t) with a duration of 0.2 sec with 694,8 seconds on 695,00 second, obtained using Fourier transform. Analysis of treatment results is to compare the obtained values of the estimates of the amplitude-frequency spectrum a priori, the calculated values of the estimates obtained in laboratory conditions in the analyzed frequencies (frequency components), which are the most dangerous from the point of view of the integrity and reliability of the controlled object without evaluating the accuracy of the results of the harmonic analysis [1-7]. Vector representation of the results of the analysis of the selected part of the signal X(ω, t) (BMP) is shown in Figure 3, which defined the direction and the amplitude of the kth frequency component of A_{x}(ω_{k}, t) with respect to the axes of the real ReA_{x}(ω_{k}, t) and imaginary ImA_{x}(ω_{k}, t) values in the analyzed frequency. In this module a_{x}(ω_{
, t) the vector of the k-th frequency component of the signal X(ω, t) in the analyzed frequency ωkis determined according to the following expression}

where ReA_{x}(ω_{k}, t) - cosine (real) and ImA_{x}(ω_{k}, t) - sine (imaginary) component of the signal X(ω, t). Component ImA_{x}(ω_{k}, t) of the signal X(ω, t) characterizes the phase angle shift of the spectral component in the analyzed frequency ω_{k}in relation to the spectral component at the frequency ω_{k}=0 for a given point in time. The presence of ImA_{x}(ω_{k}, t) due to the fact that the analyzed time interval is a redistribution of energy between frequency components of the signal spectrum X(ω, t). The phase angle shift α(ω_{k}vector_{x}(ω_{k}, t) with respect to an axis ReA_{x}(ω_{k}, t) is determined according to the following expression

While the analysis of the results of the processing on the selected time intervals of the signals X(ω, t), Y(ω, t) or S(ω, t) involves the following operations: decryption, centering and analysis using the Fourier transform in a given range and with a given step in the analysis of harmonic components (the analyzed frequencies), the measuring signal is in BMP [6, 7].

Using as input data the example above (Figure 2), we obtain the amplitude-frequency spectrum of the signal X(ω, t) using the data signal Y(ω, t) or S(ω, t) [8, 9]. Table 2 shows the results of the joint amplitude-frequency data analysis implausible plots of the signals X(ω, t), Y(ω, t) or S(ω, t). Similarly, according to expressions (3 and 4), are determined by the characteristics of the calibration control signal Y(ω, t) or signal noise, interference and distortion S(ω, t) - module a_{y;s}(ω_{k}, t) the vector of the k-th frequency component of the phase shift angle β(ω_{k}, t).

The magnitude of the projection of the vector A_{y;s}(ω_{k}, t) by a vector A_{x}(ω_{k}, t) is defined by the following expression

where A_{pr} ^{y;s}(ω_{k}, t) is the magnitude of the projection of the vector A_{y;s}(ω_{k}, t) by a vector A_{x}(ω_{k}, t) defines the confidence limits for the magnitude of the module A_{x}(ω_{k}t). Then the value of Ax(ω_{k}, t) can be represented by the following expression:

Vector representation of results of joint amplitude-frequency analysis of selected portions of the signals X(ω, t) and Y(ω, t) or S(ω, t) shown in figure 4, indicating e.g. the effect and value of the amplitude of the kth harmonic component of these signals A_{
x}(ω_{k}, t) and A_{y;s}(ω_{k}, t) with respect to the real axis ReA_{x}(ω_{k}, t), ReA_{y;s}(ω_{k}, t) and imaginary ImA_{x}(ω_{k}, t), ImA_{y;s}(ω_{k}, t) values in the analyzed frequency ω_{k}and their mutual arrangement. The analysis of the characteristics of the received amplitude-frequency spectrum (table 2) with regard to data analysis of signals Y(ω, t) or S(ω, t) gives the opportunity to make an examination of the reliability of the results of the analysis of the data signal X(ω, t), obtained in a traditional way. For example, you can draw conclusions about the reliability and accuracy of the obtained values of the amplitudes of those or other harmonic components of the investigated frequency range of the measurement information signal of the BMP on the considered time interval.

Traditionally, when conducting the analysis of random processes or their plots on the computer using the Fourier transform in order to conduct spectral analysis centering data analyzed stochastic processes and their plots are taken by a simple summation of their ordinates, by determining the arithmetic mean value and directly centering the data of a random process or area relative to the mean regardless of the frequencies of the analyzed harmonic components of the measuring signal X(ω , t) according to the following expressions:

where n is the number of measurements of the signal X(ω, t) of the investigated random process;

X_{i}(ω, t) - i-e the value of the measurement signal X(ω, t);

X_{c}(ω, t) is the average value of measurements of realization of the signal X(ω, t);

X_{C}(ω, t) - i-e centered value of the measurement signal X(ω, t).

For harmonic components listed above measurement signals with higher frequencies relative to the primary (first) of them, centering according to expressions (7) and (8) leads to deterioration of the accuracy of their performance when using the Fourier transform, which traditionally can be represented as the following expression

where a_{0}- constant component of the random process X(t) or its part;

a_{k}and b_{k}- sine and cosine coefficients of the k-th harmonic component of frequency ω_{k}the random process X(t) or its plot.

Centering measurements produce a relatively constant component and_{0}regardless of the frequency of the analyzed harmonic component by a simple subtraction of each dimension of the random process X(t) or its part of the permanent component.

When analog representation of the dimensions of the investigated random process X(t) or plot the sine and cosine components of the k-th harmonic with frequency ω_{k}are defined according to the expressions:

When discrete representation of measurements of a random process X(t) or plot the sine and cosine components of the k-th harmonic with frequency ©k are defined according to the expressions:

where X_{i}(t) - i-th dimension value of the random process X(t) or its part;

n - number of measurements of a random process X(t) or its part;

ω_{k}- k-th frequency value of k-th harmonic component of the random process X(t) or its plot.

The proposed method of analysis of the measuring data from the controlled object assumes the operation of centering the original measurements directly before the calculation of the sine and cosine components for each k-th harmonic amplitude-frequency spectrum of the measuring signal of the random process X(t) or its plot. Thus the Fourier transform of (9) can be written as follows:

where X_{k}(ω_{k}, t) - function of centering, from siteline which is centering measurement of a random process X(t), or its area,
which is a function of frequency ω_{k}and averaging time t_{k}.

This constant component and_{0}expression (9) becomes a function of X_{k}(ω_{k}, t) centering measurement of a random process X(t) or section for each k-th frequency component and is payable under the sign of the sum of the Fourier transforms (14), i.e. for each k-th harmonic component of frequency ω_{k}the measuring signal X(t) are computed individual functions of centering.

Under the function of centering the X_{k}(ω_{k}, t) is understood to be the function that depends on the frequency ω_{k}the analyzed harmonic component, the time averaging interval and type "window" averaging, the duration of which coincides with the duration of the averaging interval t_{k}=l/ω_{k}.

Under the "window" lets agree to same k-th averaging interval for the k-th harmonic component of frequency ω_{k}the random process X(t) or the time interval of analysis of macroeconomic parameters and indexes.

"Window" is for the set of measurements with different weight coefficients, distributed over time. Selection of the "window" is essential to center measurement of a random process X(t) or its plot. The physical essence of the centering this concludes the I is
for each of the analyzed harmonic component of frequency ω_{k}is determined by the k-th averaging interval and for each dimension of the investigational measuring signal X(t) random process calculates the arithmetic mean value for k, the interval calculated by the aggregate measurement of averaging interval. The calculation is carried out for each of the current values of the measuring signal of the random process X(t), or its area, i.e. the interval centering moves along a realization of a random process with a sampling increment dt data of the measuring signal. The choice of weights for the averaging interval is based on the fact that the farther the measurement is from the middle of the interval (window) averaging, the less its impact should be on the definition of the function of centering for the i-th dimension of the investigated measuring signal of a random process or its part. The distribution of the weights of the "window" of time may be linear, exponential, hyperbolic, etc. on Figure 5, as an example, shows a linear distribution of weight coefficients g(k) k-interval (window) averaging.

In this case, the weighting coefficients for each measurement interval ("window" averaging are defined as

where m=t_{k}/2 - number of measurements on the half-interval (window) averaging. Then, for each i-th dimension of the investigated measuring signal of a random process or its part calculates the average value in the interval ("window") averaging according to the following expression

where 2m is the number of dimensions of the investigated random process or parcel located in the interval ("window") averaging;

X_{k}(t) - dimension values that belong to the k-interval ("window") averaging, k=0,1,..., 2m;

X_{i;K}(t) - i-th average value of k, the interval ("window") averaging functions centering X_{k}(ω_{k}, t) for the i-th dimension of the investigated random process X(t) or its plot.

Centering each i-th dimension of the investigated random process X(t) or its part concerning the function of centering the X_{k}(ω_{k}, t) is a simple subtraction of the i-th dimension of the investigated random process X(t) or section k-mean value interval ("window") X_{i;k}(t) according to the following expression

where- centered i-th measurement of the test of the random process X(t) or its plot.

The obtained average mn is an increase on the interval ("window") averaging X_{
i;k}(t) snaps to the center of the interval ("window"), the center of which coincides with, for example, the first dimension of the investigated random process or its area, as shown in Fig.6, which leads to an increase in the real necessary amount of source data, measurement data capacity of the beginning and end of the analyzed stochastic process X(t) or its site an additional amount of data equal to half of the interval (window) centering.

To understand the capabilities of the proposed method of analysis we use the simplest form of the "window"when all the weights in the averaging interval is equal to (Fig.7). On Fig shows the initial and final position of the "window" with reference to its center to the first and last measurement of the test of the random process X(t) or its part for the main harmonics equal to 5 Hz. In this case, all the source data of the measuring signal of the random process X(t) or its plot, which belong to the interval ("window") of the averaging involved in the calculation of the arithmetic mean value for each i-th dimension of the investigated area of the BMP in its natural size (multiplication is performed on the unit). The determination of the actual characteristics of the function of centering X_{k}(ω_{k}t) plot measuring signal BMP consider the example of a site analysis of the signal is X(ω
, t) with a duration of 0.2 seconds with 694,8 seconds on 695,00 second, presented in figure 2 "movement" of the interval (window) averaging from left to right on the step size of the discretization of the measurement of time equal to dt=125 μs circular sampling rate 8 kHz, as shown in Fig.9.

Table 3 shows the function of centering the measuring gauge (control) signal Y(t) or its part for the harmonic components from 5 Hz to 45 Hz in 5 Hz increments BMP pr 30.i00. Table # 4 shows the function of centering the X_{k}(ω_{k}, t) of the measuring signal of the random process X(t) or its part for the harmonic components from 5 Hz to 45 Hz in 5 Hz increments BMP pr 23.i00, as shown in figure Figure 10. In the second columns of tables No. 3 and No. 4 are the average values of the received data functions centering of the measuring signal Y(t) and X(t). In table 4 the second column lists the functions of centering X_{k}(ω_{k}, t) for each of the harmonic components of the investigated area BMP pr 23.i00. The volume of data of each individual function of centering the X_{k}(ω_{k}, t) of the measuring signal Y(t) and X(t) corresponds to the amount of data of the investigated plots of these signals. In the third and fourth columns of tables No. 3 and No. 4 are the maximum and minimum values of the functions centering of the measuring signal Y(t) and X(t), respectively.
The data in table 4 show the dynamics of change in the function of centering the X_{k}(ω_{k}, t), and there is a significant spread between the minimum and maximum function values centering X_{k}(ω_{k}, t) for each of the analyzed harmonic component. The same holds true for the function of centering the measuring gauge (control) signal Y(t) in the analysis of data table No. 3. Analysis of the results shown in table 4, suggest that the function of centering the X_{k}(ω_{k}, t) is not constant and is a random function of its arguments, as shown in Figure 10. Table 5 shows the results of frequency analysis of the area of the measuring signal BMP pr 23.i00 duration 0.2 sec with 694,8 seconds on 695,00 second application of the proposed approach for performing the operation of centering. From the comparative analysis of the data given in tables # 2 and # 5, it is seen that the relative error of the results of the analysis decreases, thereby increasing the credibility of the analysis of a random process.

Figure 11 shows a block diagram of an apparatus for implementing the method.

The device comprises a block 1 of the signal reception unit 2 centering analyzer 3 spectrum, unit 4 registers the AI,
unit 5 comparison. The output of block 1 of the reception signals is connected to the input of block 2 of centering, the output of which is connected to the input of the analyzer 3 spectrum. The output of the analyzer 3 spectrum simultaneously connected to the first input unit 4 registration and input unit 5 comparison connected the output from the second input unit 4 registration. A device that implements the proposed method works as follows. Measuring information signals X(ω, t), Y(ω, t) or signal to noise, interference and distortion S(ω, t) are taken from the controlled object, if necessary, amplified by unit 1 of the reception signals received at the first input of block 2 of centering. On the other k-Tye unit 2 centering receives electrical signals proportional to the analyzed frequency components ω_{to}the analyzed measurement signals X(ω, t), Y(ω, t) or S(ω, t). From the output of block 2 is centered by measuring the signals X(ω, t), Y(ω, t) or S(ω, t) is fed to the input of the analyzer 3 spectrum and subjected to frequency analysis. The results of the spectrum analysis measurement information signals X(ω, t), Y(ω, t) or S(ω, t), obtained by calculating the amplitude-frequency characteristics of the random process from the output of the analyzer 3 spectrum, proceed respectively to the first input unit 4 registration and on a second input the block 5 comparison.
Unit 5 compares the amplitude-frequency characteristics of the signals X(ω, t), Y(ω, t) or S(ω, t) and a corresponding managing electrical signal at a certain time interval, which is supplied to the second input of block 4 of the Desk, where it received information is excluded from the further analysis process at some random interval of time, at a certain frequency range or at a particular frequency depending on the comparison result. The exceptional condition information determined by a particular value of the modulus of the difference of the amplitude-frequency characteristics of the above-mentioned measurement signals. If the module is the differencewill be greater than zero or more than a certain relative error in the range of the analyzed time-spans, the analyzed frequency range or single frequency signal X(ω, t), the output unit 5 compare to the second input unit 4 reception signal, which captures the plot of time domain, frequency range and analyzed the frequency (frequency component)on which information is excluded from further analysis.

The results of the experiment conducted in real conditions of full-scale testing of complex aircraft, confirm the accuracy obtained is of ibodov.

The proposed method of analysis of measurement data, implements a method of processing and estimation of stochastic processes and parameters and indicators, in General, allows you to:

1) to reduce the plots in the time and frequency domains with unreliable information, which significantly increases the utilization of expensive experimental information;

2) to improve the accuracy of the amplitude-frequency analysis of the measurement data of random processes, parameters and indicators;

3) to exclude using different types of control signals, based on the analysis of the BMP when conducting flight tests of aircraft required for checks of the results obtained temporal and spectral analysis on the reliability assessment of its accuracy;

4) to simplify the analysis of a random process through the use of data measuring signal noise, interference and distortion with a wide range of frequencies in a joint analysis with the measurement information signal;

5) to exclude the procedure set thresholds for making decisions about the reliability of the measurement information signals at the input of specialized processing systems and the analysis of random processes and limit the control of the reliability and accuracy of the final results, the hour is now analyze the output of a hardware-software systems analysis and processing of random variable processes;

6) to simplify the architecture of the specialized systems of data processing and analysis of random processes by eliminating the function of the input control their validity and to be limited to such systems only function "transparent" input measurement data of the studied stochastic processes with aircraft in the computer;

7) to achieve a significant reduction in the material and financial resources when using universal technical means for analyzing the measurement data of the studied stochastic processes;

8) allows to assess the dynamics of changes in predictive behavior of macroeconomic indicators of the country and the world economy;

9) to carry out comprehensive analysis of the current socio-economic situation (dynamic, structural, cluster, factor analysis), the analysis of the main socio-economic indicators of development actors in the country.

Table No. 1 | ||||

AMPLITUDE-FREQUENCY SPECTRUM of the rapidly changing PROCESS | ||||

Frequency analysis (Hz) | Assessment of congestion On the frequency Analysis of the BMP (m/s·) | The assessment phase of the frequency component of the BMP (rad.) | Confidence interval for estimating congestion on often is the analysis (m/s· C) | The relative error in the calculation of assessment overload BMP (%) |

1 | 2 | 3 | 4 | 5 |

5.00 | 1578.0930 | -1.5687 | 0.0000 | 0.0000 |

10.00 | 5584.6738 | -0.2235 | 0.0000 | 0.0000 |

15.00 | 12783.6855 | 1.4086 | 0.0000 | 0.0000 |

20.00 | 10209.2969 | -1.4532 | 0.0000 | 0.0000 |

25.00 | 1807.7573 | -0.9882 | 0.0000 | 0.0000 |

30.00 | 15078.3770 | 0.2624 | 0.0000 | 0.0000 |

35.00 | 33656.6875 | -0.7356 | 0.0000 | 0.0000 |

40.00 | 11086.4150 | 0.9873 | 0.0000 | 0.0000 |

45.00 | 9879.0654 | -0.7989 | 0.0000 | 0.0000 |

Conventional tillage plot BMP obtaining the amplitude-frequency spectrum for the time interval 594.800-595.000 file pr23.i00. The number of y on the interval BMP-1608. The value of the lower-level calibration K1=38.126167 and upper level K2=224.895233.

Table No. 2 | ||||

AMPLITUDE-FREQUENCY SPECTRUM of the rapidly changing PROCESS | ||||

Frequency analysis (Hz) | Assessment of congestion On the frequency Analysis of the BMP (m/s·) | The assessment phase of the frequency component of the BMP (rad.) | Confidence interval for estimating congestion on the frequency analysis (m/s·) | The relative error in the calculation of assessment overload BMP (%) |

1 | 2 | 3 | 4 | 5 |

5.00 | 1578.0930 | -1.5687 | 1216.1366 | 77.0637 |

10.00 | 5584.6738 | -0.2235 | 250.2629 | 4.4812 |

15.00 | 12783.6855 | 1.4086 | 2050.2485 | 16.0380 |

20.00 | 10209.2969 | -1.4532 | 615.9327 | 6.0331 |

25.00 | 1807.7573 | -0.9882 | 1146.0009 | 63.3933 |

30.00 | 15078.3770 | 0.2624 | 954.7341 | 6.3318 |

35.00 | 33656.6875 | -0.7356 | 4179.4834 | 12.4180 |

40.00 | 11086.4150 | 0.9873 | 2185.5984 | 197142 |

45.00 | 9879.0654 | -0.7989 | 3017.8687 | 30.5481 |

The results of the processing area of the BMP calculation of the relative error of the amplitude-frequency spectrum obtained by the time interval 594.800-595.000 files BMP pr23.i00 and control signal pr30.i00. The results obtained using the algorithm in patent No. 2160451 from 2000.

The number of ordinates at the site of treatment BMP-1608.

The number of ordinates at the site of processing of the control signal 1608. The value of the lower-level calibration K1=38.126167 and upper level K2=224.895233.

Table No. 3 | |||

FUNCTION CHARACTERISTICS CENTERING of the MEASURING CONTROL SIGNAL | |||

Frequency analysis (Hz) | The average value of the function of centering | The maximum value of the function of centering | The minimum value of the function of centering |

1 | 2 | 3 | 4 |

5.00 | -0.00621759 | 0.661684 | -0.671874 |

10.00 | -E-05 | 1.35062 | -1.40692 |

15.00 | 0.00390431 | 1.52603 | -1.23044 |

20.00 | 0.000922983 | 1.70654 | -1.67318 |

25.00 | -0.0097687 | 2.8035 | -2.89087 |

30.00 | -0.00897863 | 3.76904 | -3.4373 |

35.00 | -0.0114055 | 2.62547 | -2.35919 |

40.00 | -0.0105599 | 3.18818 | -3.06976 |

45.00 | -0.00271758 | 3.02716 | -3.21277 |

Function characteristics of centering on the time interval 594.800-595.000 control signal pr30.i00 obtained using the proposed method of centering the measuring data from the controlled object volume 1608 of the axis.

Table No. 4 | |||

FUNCTION CHARACTERISTICS CENTERING MEASURING INFORMATION SIGNAL rapidly changing PROCESS | |||

Frequency analysis (Hz) | The average value of the function of Centering | The maximum value of the function of centering | The minimum value of the Function of centering |

1 | 2 | 3 | 4 |

5.00 | -0.293823 | 1.30525 | -1.51426 |

10.00 | -0.081939 | 1.58834 | -1.51426 |

15.00 | -0.052608 | 2.52454 | -3.10684 |

20.00 | 0.0372908 | 3.08445 | -2.07528 |

25.00 | -0.0428925 | 2.39526 | -2.35377 |

30.00 | -0.0230508 | 2.48419 | -2.37412 |

35.00 | -0.00512051 | 2.74016 | -3.19541 |

40.00 | 0.00169974 | 3.72294 | -3.85946 |

45.00 | 0.00216886 | 3.51805 | -4.92045 |

Function characteristics of centering on the time interval 594.800-595.000 BMP pr23.i00 obtained using the proposed method of centering the measuring data from the controlled object volume 1608 of the axis.

Table No. 5 | ||||

AMPLITUDE-FREQUENCY SPECTRUM of the rapidly changing PROCESS | ||||

Frequency analysis (Hz) | Assessment of congestion On the frequency Analysis of the BMP (m/s·) | The assessment phase of the frequency component of the BMP (rad.) | Confidence interval for estimating congestion on the frequency analysis (m/s·) | The relative error in the calculation of the estimate p is regusci BMP (%) |

1 | 2 | 3 | 4 | 5 |

5.00 | 2470.5059 | 1.4798 | 5.2775 | 0.2136 |

10.00 | 9213.4258 | 0.7067 | 0.8673 | 0.0094 |

15.00 | 1589.8053 | -0.2773 | 0.3542 | 0.0223 |

20.00 | 7285.9785 | -1.4704 | 0.0556 | 0.0008 |

25.00 | 5282.8354 | 0.3012 | 0.0455 | 0.0009 |

30.00 | 6597.8496 | 0.3676 | 0.0957 | 0.0014 |

35.00 | 33087.0234 | -1.0747 | 0.2087 | 0.0006 |

40.00 | 5116.8613 | 0.5265 | 0.0815 | 0.0016 |

45.00 | 9164.8711 | -1.1292 | 0.2379 | 0.0026 |

The results of the processing area of the BMP calculation of the relative error of the amplitude-frequency spectrum obtained by the time interval 594.800-595.000 files BMP pr23.i00 and control signal RC. The results obtained using the proposed algorithm. The number of ordinates at the site of treatment BMP-1608. The number of ordinates to plot processing control signal is - 1608. The value of the lower-level calibration K1=38.126167 and upper level K2=224.895233.

Sources of information

1. Volner NF Hardware signal analysis. M: Soviet radio, 1977, p.132-135.

2. Mir GY Hardware characterization of random processes. M: Energy, 1967, s-409.

3. Gandt, Aperol. Measurement and analysis of random processes. Publishing house "Mir", 1974

4. Terent'ev V.N. A device for processing information with the control of reliability. Avts No. 802984. Bull. image. No. 5, 1981.

5. Terent'ev V.N. Device for controlling the reliability of the telemetry data. Avts No. 1035632. Bull. image. No. 30, 1987.

6. Terent'ev V.N. Device for analyzing information. Auth. St. No. 1081666. Bull. image. No. 11, 1984.

7. Terent'ev V.N. Device for analyzing information. Auth. St. No. 1191940. Bull. image. No. 42, 1985.

8. Omel'chenko V.V., Terent'ev V.N., Yashchenko CENTURIES the Way of rejection of random signals, recorded on magnetic media. RU # 95108707 A1. Bull. image. No. 4, 1997.

9. Omel'chenko V.V., Terent'ev V.N., Terent'ev A.V. Method of processing and analysis of measurement signals from the controlled object (options). The patent on the image. No. 2160451. Bull. No. 34, 2000

1. The method of analysis of the measuring signals from the controlled object, based on the fact that you get a measuring gauge (control) signal with a wide range of frequencies, representing the vector summational signal, fixed frequency and amplitude, and signal noise, interference and distortion, and measuring information signals, each of which represents the vector sum of the information signals and signal noise, interference and distortion, produce processing and analysis of the obtained measurement information signals and the control signal by calculating and comparing the spectral characteristics of these signals, characterized in that it further receive the measuring signal noise, interference and distortion with a wide range of frequencies with the controlled object, and after receiving the measurement information signal, the calibration control signal or signal noise, interference and distortion immediately before the calculation of spectral characteristics these signals produce the centering of the source data mentioned above, measurement signals for each of the analyzed harmonic component of the measuring information signal, the calibration control signal or signal noise, interference and distortion relative to the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, the current values are calculated for each of the source data values of the measuring information signal, the calibration is about control signal or noise signal, noise and distortion by averaging the original data of these measuring signals on the averaging time interval, equal to the inverse value of the frequency of the analyzed harmonic component, and each value of the original data of the measurement information signal, the calibration control signal or signal noise, interference and distortion correspond to the calculated current values of the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, and then produce the centering of the source data and measurement information signal, the calibration control signal or signal noise, interference and distortion relative to the corresponding functions of centering and perform an analysis of the measurement information signal, the calibration control signal or signal noise, interference and distortion by calculating the spectral characteristics of the measurement information signal, the calibration control signal or signal noise, interference and distortion, the comparison of the respective spectral characteristics of measuring information signal and the calibration control signal or signal noise, interference and distortion, the results of the comparison register corresponding measuring information si is cash on the analyzed portion of time in the analyzed frequency range or at a particular frequency analysis in accordance with the dependence of the spectral characteristics of the measurement information signal and the calibration control signal or signal noise, interference and distortion as a function of time and frequency, and the upper limit of this range is determined by the upper frequency measurement calibration (control) signal or signal noise, interference and distortion, and, if the module of the difference between the spectral characteristics of the measurement calibration (control) signal or signal noise, interference and distortion and measurement information signal is greater than the specified relative error of calculation of the spectral characteristics of measuring information signal during the portion of time on the analyzed frequency range or within separate frequency analysis, obtained on this part time, or range of frequencies or a single frequency measurement information is excluded from further analysis.

2. The method of analysis of the measuring signals from the controlled object, based on the fact that you get a measuring gauge (control) signal with a wide range of frequencies, representing the vector sum of the reference signal, fixed frequency and amplitude, and with whom drove noise noise and distortion measurement information signals, each of which represents the vector sum of the information signals and signal noise, interference and distortion, produce processing and analysis of the obtained measurement information signals and the control signal by calculating and comparing the spectral characteristics of these signals, characterized in that it further receive the measuring signal noise, interference and distortion with a wide range of frequencies with the controlled object and after receiving the measurement information signal, the calibration control signal or signal noise, interference and distortion, using as the spectral characteristics of the amplitude-frequency spectrum of these measurement signals, immediately before the calculation of the amplitude-frequency spectrum of the measurement information signal, the calibration control signal or signal noise, interference and distortion produced by centering the source data mentioned above, measurement signals for each of the analyzed harmonic component of the measuring information signal, the calibration control signal or signal noise, interference and distortion relative to the functions of centering the measuring information signal, the calibration control signal or signal the La noise interference and distortion, the current values are calculated for each of the source data values of the measuring information signal, the calibration control signal or signal noise, interference and distortion by averaging the original data of these measuring signals on the averaging time interval, equal to the inverse value of the frequency of the analyzed harmonic component, and each value of the original data of the measurement information signal, the calibration control signal or signal noise, interference and distortion correspond to the calculated current values of the functions of centering the measuring information signal, the calibration control signal or signal noise, interference and distortion, and then produce a centering measuring information signal calibration control signal or signal noise, interference and distortion relative to the corresponding functions of centering and perform an analysis of the measurement information signal, the calibration control signal or signal noise, interference and distortion by calculating the amplitude-frequency characteristics measurement information signal, the calibration control signal or signal noise, interference and distortion, the comparison of the respective amplitude-frequency characteristics measuring what's the information signal and the calibration control signal or noise signal, noise and distortion on the comparison of the record corresponding to the measurement information signal during the portion of time on the analyzed frequency range or at a particular frequency analysis in accordance with the dependence of the amplitude-frequency characteristics measurement information signal and the calibration control signal or signal noise, interference and distortion as a function of time or frequency, and the upper limit of this range is determined by the upper frequency measurement calibration (control) signal or signal noise, interference and distortion, and, if the modulus of the difference of the amplitude-frequency characteristics measurement calibration (control) signal or signal noise, interference and distortion and measuring the information signal is greater than the specified relative error of calculation of the amplitude-frequency characteristics measurement information signal during the portion of time on the analyzed frequency range or at a particular frequency analysis, obtained on this part time, or range of frequencies or a single frequency measurement information is excluded from the further analysis process, the results of joint processing of amplitude-frequency characteristics of the measuring information is ion signal and the control signal or the noise signal, noise and distortion calculate confidence intervals whose boundaries are determined by the current estimates of the corresponding amplitude-frequency characteristics measurement calibration (control) signal or signal noise, interference and distortion, and relative error of the obtained current estimates of the amplitude-frequency characteristics measurement information signal and, if the magnitude of the relative error obtained current estimates of the amplitude-frequency characteristics measurement information signal is greater than the specified relative error or if the magnitude of the confidence limits of the measuring gauge (control) signal or signal noise, interference and distortion will be more current estimates of the amplitude-frequency characteristics measurement information signal, received on the analyzed plot time on the analyzed frequency range or within separate frequency measurement information is excluded from further analysis.

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