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Method of searching for faulty module in discrete dynamic system

Method of searching for faulty module in discrete dynamic system
IPC classes for russian patent Method of searching for faulty module in discrete dynamic system (RU 2444774):
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FIELD: physics.

SUBSTANCE: unlike the existing method of searching for a faulty module in a continuous dynamic system, the reaction of a time-discrete system know to be properly functioning is recorded for discrete diagnosis cycles with pitch in control points; integral estimates of output signals are determined, for which at the moment of transmitting a test signal, discrete integration of signals is simultaneously initiated with pitch in each of the control points by transmitting signals to inputs of multiplier units, and a discrete exponential signal to second inputs of the multiplier units; output signals of the multiplier units are transmitted to inputs of the discrete integration units; integration is completed at the control instant; the obtained estimates are recorded; integral estimates of model signals are determined for each control point, for which a sample deviation of the parameter of the discrete transfer function is successively entered into each unit of the system and integral estimates of output signals of the system obtained as a result of integrating output signal estimates for each control point are found and each of the sample deviations is recorded; a defective module of the discrete system is determined by the minimum of the diagnostic feature.

EFFECT: possibility of searching for defects in a discrete dynamic system.

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The invention relates to the field of control and diagnostics of automatic control systems and their elements.

There is a method of diagnosing dynamic parts of control systems (Patent RF №2110828, MKI6G05B 23/02, 1998), based on the integration of the output signal of the block with a weight of e-αtwhere α is a real constant.

The disadvantage of this method is that its application for control of multiple units of a control system of an arbitrary structure leads to the necessity of integration of input and output signals of each of the controlled block.

The closest technical solution (prototype) is a way of finding a bad block in a dynamic system (a Positive decision from 12.07.2010, for a patent on the invention under the application №2009123999/08(033242), MKI6G05B 23/02, 2010).

The disadvantage of this method is that it enables the detection of defects only in a continuous dynamic system.

Technical problem on which this invention is directed, is the application of the method to search for defects in a discrete dynamical system with an arbitrary connection blocks.

This object is achieved in that pre-register response known good discrete-time system fj(t), j=1, 2, ..., k for N discrete the acts diagnosis t∈[1,N] with discrete spaced T sin the observation interval [0,Tk] (where Tk=Ts·N) in the k control points, and define the integral evaluation of the output signalsj=1, ..., k of the discrete system, which at the time of the test signal to the input of a discrete system with a nominal characteristics simultaneously begin the discrete integration of the control signals in increments of Tsseconds in each of the k control points with discrete weightsincrements of Tsseconds, whereby submitting to the first inputs of the k blocks the multiplication control signals on the second input units of the multiplication serves a discrete exponential signalincrements of Tsseconds, the output signals of the k blocks multiplication served on inputs k blocks of discrete integration step Tsseconds, discrete integration completed at time Ttoobtained by integrating the evaluation of the output signals Fj(α), j=1,...,k register, record the number m of the considered single defect blocks, define the integral evaluation signal models for each of the k control points obtained in the course of the trial deviations for m single defect blocks, which in turn in each block of discrete-time dynamical system is neither enter trial deviation parameter of the discrete transfer function and find the integral evaluation of the output signals of the system setting for discrete integral transformations α and the test signal x(t), the resulting discrete integration of the evaluation of the output signals for each of the k control points and each of the m test deviationsj=1, ..., k; i=1,..., m, register, determine the deviation of the integral of the estimated signals of the discrete model, the resulting trial variance parameters of different structural units ΔPji(α)=Pji(α)-Fj(α), j=1, ..., k; i=1, ..., m, define the normalized Delta values of the integral estimates of signals discrete model, the resulting trial variance for a single defect ratio

replace the system with a nominal characteristics controlled at the input of the system serves a similar test signal x(t), define the integral evaluation of the signals controlled discrete system for the k control points Fj(α), j=1, ..., k for parameter discrete integral transforms α, determine the deviation of the integral estimates of the signals controlled discrete system for the k control points from the nominal values ∆ Fj(α)=Fj(α)-Fj(α), j=1, ..., k, define the normalized Delta values of the integral estimates of the signals controlled discrete system of ratios

determine diagnostic characteristics from which otnosheniya

the minimum values of the diagnostic sign determines the ordinal number of the defective block.

The essence of the method consists in the following.

The method is based on the use of pilot deviations of the model parameters of discrete dynamic systems.

Using the vector interpretation of expression (3), we write it as follows

where φi(α is the angle between the normalized vector (a vector of unit length) of the variance of the integral estimates of signals discrete objectand the normalized vector (unit length) of the variance of the integral estimates of signals discrete modelthe resulting trial deviation of the i-th parameter of the respective structural unit.

Thus, the normalized diagnostic feature (3) represents the value of the square of the sine of an angle formed in the k-dimensional space (where k is the number of control points) of the normalized vectors of integral estimates test for deviation of the signals of the discrete model and the variance of the integral estimates of the discrete signals of the diagnostic object.

Trial deviation parameter of the corresponding structural unit that minimizes the value of the diagnostic sign (3), shows the defective unit. The region of possible values of the diagnostic characteristic lies in the interval [0, 1].

Thus, the proposed method of finding the defective block is to perform the following operations:

1. As a discrete dynamical system consider the system, for example with discrete zero-order interpolation, with sampling interval Ts, consisting of randomly connected dynamic blocks, number of single defects m blocks.

2. Pre-determine the testing time Tto≥TPPwhere TPPthe time transition of the discrete system. Transition time estimate for the nominal values of the parameters of the dynamic system.

3. Define the parameter integral transforms of the signals from the relation

4. Record the number of control points k.

5. Pre-determine the normalized vectorsvariance of the integral estimates of signals discrete model, the resulting trial deviations of the i-th block and defined above parameter integral transforms α, why do paragraphs 6-10.

6. Serves the test signal x(t) (unit step, linearly increasing, rectangular pulse and so on) to the input of the control system with the nominal essence and the ticks. Fundamental limitations on the type of input test the impact of proposed method does not.

7. Record the response of the system fj(t), j=1, 2, ..., k on the interval t∈[1,N] with discrete steps Tsseconds on the observation interval [0,Tk] (where Tk=Ts·N) in the k control points define discrete integral evaluation of the output signalsj=1, ..., k system. To do this, at the time of the test signal to the input of the control system with the nominal characteristics simultaneously begin the discrete integration of the control signals in increments of Tsseconds in each of the k control points with discrete weightsin discrete steps Tsseconds, wherefor which the control signals are served on the first inputs of the k blocks multiplication on the second input units of the multiplication serves a discrete exponential signal in increments of Tsseconds, the output signals of the k blocks multiplication served on inputs k blocks of discrete integration step Tsseconds, discrete integration completed at time Ttoobtained by discrete integration of the evaluation of the output signals Fj(α), j=1, ..., k register.

8. Define the integral evaluation of the signals of the discrete model d is I to each of the k control points, the resulting trial deviations of each of the m single defect blocks, which in turn, for each structural parameter block discrete dynamical system is administered trial deviation of this parameter discrete transfer function and perform paragraphs 6 and 7 for the same test signal x(t). The resulting discrete integration with a step of Tsseconds, the evaluation of the output signals for each of the k control points and each of the m test deviationsj=1,..., k; i=1, ..., m register.

9. Determine the deviation of the integral of the estimated signals of the discrete model, the resulting trial deviations of one structural unit ΔPji(α)=Pji(α)-Fj(α), j=1, ..., k; i=1, ..., m.

10. Define the normalized Delta values of the integral estimates of signals discrete model, the resulting trial deviations of one block according to the formula:

11. Replace the system with a nominal characteristics controlled. At the input of the system serves a similar test signal x(t).

12. Define the integral evaluation of the signals controlled discrete system for k checkpointj=1, ..., k, carrying out the operations described in paragraphs 6 and 7 in relation to con the controlled system.

13. Determine the deviation of the integral estimates of the signals controlled discrete system for the k control points from the nominal values ∆ Fj(α)=Fj(α)-Fj(α), j=1, ..., k.

14. Calculate the normalized values of the variance of the integral estimates of the signals controlled discrete system according to the formula:

15. Calculate the diagnostic signs of faulty structural unit according to formula (3).

16. The minimum values of the diagnostic sign determine the defective block.

Consider the implementation of the proposed method of finding the defect for discrete-time systems, block diagram of which is presented on the figure (see Fig. Block diagram of the diagnostic object).

Discrete transfer function block:

;;,

rated: K1=5; Z1=0.98; K2=0.09516; Q2=O.9048;3=0.0198; Q3=0.9802. When you search for a single structural defect in the form of deviation of the gain by 20% (k1=4) in the first link, when the flow speed of the test input signal of unit amplitude and the integral of the estimated signals for parameter α=0.5 and Tto=10, using three control points located at the outputs of blocks, use the I trial deviation to a value of 10%, the obtained values of diagnostic signs by the formula (3): J1=0; J2=03587; J3=0.1605. The analysis values of the diagnostic signs shows that the defect in the first structural unit of the controlled system is correct. It should be noted that the method is operable at larger values of the test deviations (10-40%). The limitation on the amount of trial deviation is the need to preserve the stability of models with a trial deviations.

Search single structural defects according to the proposed method as applied to discrete diagnostic object, represented in the figure, consists of the following operations:

1. Record the number of controlled single defects m=3.

2. By analyzing the graphs of the nominal transient characteristics determine the transition time of the system. For this example, the transition process is TPP=8 C. Record the time of control Tk≥TPP. For this example, Tk=10 S.

3. Define the parameter signal integrationFor this example, α=0.5.

4. Fixed reference point on the outputs of blocks: k=3.

5. Pre-find elements of vectors ΔPi(α) variance of the integral of the estimated signal model obtained in the course of the trial the deviations of all controlled single defects. The value trial variance is chosen equal to 10%.

6. Find the normalized vectorsvariance of the integral of the estimated signal model, the resulting trial variance of the corresponding parameters of all controlled single defects by the formula (1).

7. Replace the system with a nominal characteristics controlled, which entered the variance parameter of the first unit from the nominal 20%. At the input of the system serves a similar test signal x(t).

8. Determine the deviation of the integral of the estimated signals of the controlled system for the three control points from the nominal values ∆ Fj(α)=Fj(α)-Fj(α), j=1, 2, 3.

9. Calculate the normalized values of the variance of the integral of the estimated signals of the controlled systemby the formula (2).

10. Calculate the diagnostic signs of faulty units by the formula (3): J1=0; J2=0.3587; J3=0.1605, where J1indicates a defect in the first block, J2accordingly indicates a defect in the second, J3- defect in the third block.

11. The minimum values of the diagnostic sign determine the defect (in this case, the defect in the first structural unit).

Modeling processes to identify structural defects in other cases, his manifestation for this di the specific object of diagnosis for the same parameter integral transforms α and unit step input signal gives the following values of diagnostic features.

If there is a defect in the unit 2 (in the form of reducing the parameter k220%defect No. 2): J1=0.3557; J2=0; J3=0.6732.

If there is a defect in the unit 3 (in the form of reducing the parameter k320%defect No. 3): J1=0.1652; J2=0.668; J3=0.

The minimum value of the diagnostic sign in all cases correctly points to the defective block.

The way of finding a bad block in a discrete dynamic system, based on the fact that a fixed number m of dynamic elements included in the system, determine the testing time Tto≥TPPdetermine the parameter integral transforms of the signals from the relationuse a test signal on the interval t∈[0,TK]as the dynamic characteristics of the system using integral estimates for real values of α Laplace variable, fixed number of k control points in the system, record the reaction of the diagnostic object and the model, record the reaction of a known good system fj(t), j=1, 2,..., k on the interval t∈[0,TK] k control points that define the integral evaluation of the output signals Fj(α), j=1, ..., k system, which at the time of the test signal at the input of the system with nominal characteristics simultaneously start integration signal the fishery management system in each of the k control points with weights e -αtwhereby submitting to the first inputs of the k blocks the multiplication control signals on the second input units of the multiplication serves exponential signal e-αtthe output signals k blocks multiplication served on inputs k blocks of integration, integration completed at time Ttoobtained by integrating the evaluation of the output signals Fj(α), j=1, ..., k register, record the number of different trial variance of m, define the integral evaluation signal models for each of the k control points obtained in the course of the trial deviations blocks, which in turn, for each block of a dynamic system is administered trial deviation parameter transfer function and find the integral evaluation of the output signals of the system for the parameter α, and the test signal x(t), obtained by integrating the evaluation of the output signals for each of the k control points and pilot deviations of each of the m blocks of Pji(α), j=1, ..., k; i=1, ..., m register determine the deviation of the integral of the estimated signal model, the resulting trial deviations of the respective blocks Δji(α)=Rji(α)-FInom(α), j=1, ..., k; i=1, ..., m, define the normalized variance of the integral of the estimated signal model, gender is received in the trial deviations of the respective blocks from the relation replace the system with a nominal characteristics controlled at the input of the system serves a similar test signal x(t), define the integral evaluation of the signals of the controlled system for the k control points Fj(α), j=1, ..., k for the parameter α determines the deviation of the integral of the estimated signals of the controlled system for the k control points from the nominal values ∆ Fj(α)=Fj(α)-Fj(α), j=1, ..., k, define the normalized Delta values of the integral estimates of the signals of the controlled system from the relationdetermine the diagnostic signs of ratios, i=1, ..., m, the minimum diagnostic trait determines the defect, wherein the pre-recorded reaction known good discrete-time system fj(t), j=1, 2, ..., k for N discrete quanta diagnosis t∈[1, N] with discrete constant step Ts to the observation interval [0, Tk] (where Tk=Ts·N) in the k control points that define the integral evaluation of the output signals, j-1, ..., k of the discrete system, which at the time of the test signal to the input of a discrete system with a nominal characteristics simultaneously begin the discrete integration of the control signals in increments of Ts seconds in to the each of the k control points with discrete weights increments of Ts seconds, whereby submitting to the first inputs of the k blocks the multiplication control signals on the second input units of the multiplication serves a discrete exponential signalincrements of Ts seconds, the output signals of the k blocks multiplication served on inputs k blocks of discrete integration step Ts seconds, the discrete integration is complete at time Ttoobtained by integrating the evaluation of the output signals, j=1, ..., k register, define the integral evaluation signal models for each of the k control points obtained in the course of the trial deviations for m single defect blocks, which in turn in each block of discrete-time dynamical system is administered trial deviation parameter of the discrete transfer function and find the integral evaluation of the output signals of the system setting for discrete integral transformations α and the test signal x(t), the resulting discrete integration of the evaluation of the output signals for each of the k control points and each of the m test deviationsj=1, ..., k; i=1, ..., m register, the minimum diagnostic characteristic to determine a defective block of a discrete system.

 

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