# Method of finding faulty units in discrete dynamic system

FIELD: information technology.

SUBSTANCE: reaction of a good, time-discrete system is recorded first; integral estimates of output signals of the discrete system are determined; the number of analysed single and multiple defects of units is recorded; integral estimates of signals of the model for each control point are determined; deviations of integral estimates of signals of the discrete model are determined; standardised values of deviations of integral estimates of signals of the discrete model are determined; the system with nominal characteristics is replaced with the controlled system; an analogue test signal is transmitted to the input of the system; integral estimates of signals of the controlled discrete signals are determined for control points for the discrete integral transformation parameter; deviations of the integral estimates of signals of the controlled discrete system are determined for control points from the nominal values; standardised values of deviations of integral estimates of signals of the controlled discrete system are determined from the ratio; diagnostic features are determined from the ratio; the index number of the single defect of the unit or a combination of defects of units is determined from the maximum value of the diagnostic feature.

EFFECT: broader functional capabilities of the method of finding one or several faulty units at once in a dynamic system with arbitrary connection thereof, and lower computational costs associated with use of a simpler diagnostic feature.

1 dwg

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

There is a method of searching for bad blocks in a dynamic system (a Positive decision on granting a patent for invention dated 19.12.2011 on application No. 2010148468, MKI^{6}G05B 23/02, 2011).

The disadvantage of this method is that it enables the detection of multiple defects only in a continuous dynamical system with a higher computational cost.

The closest technical solution (prototype) is a way of finding a defective block in the discrete dynamical system (a Positive decision on granting a patent for invention dated 21.09.2011 by application No. 2011101271/08(001575), MKI^{6}G05 23/02, 2011).

The disadvantage of this method is that it provides only single defects in a discrete dynamical system with a higher computational cost of determining the diagnostic indicator.

Technical problem on which this invention is directed, is to expand the functionality of the method for finding one or several bad blocks (multiple defects) in a discrete dynamical system with an arbitrary connection blocks, as well as reducing the computational costs associated with using less words is the main diagnostic character.

This object is achieved in that pre-register response known good discrete-time system f_{j}(t), j=1,2,...,k for N discrete quanta diagnosis t∈[1, N] with discrete constant step Ts to the observation interval [0,T_{k}] (where T_{k}=T_{s}·N) in the k control points, and 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 each of the k control points with discrete weightsincrements 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 T_{k}obtained by integrating the evaluation of the output signals F_{jo}(α), j=1,...,k register, record the number m of the considered single and multiple defects of blocks determined in agrilinae evaluation signal models for each of the k control points,
the resulting trial deviations for m single and multiple defects of blocks, which in turn in each block or combination of blocks of discrete dynamical systems impose 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 deviations, j=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 blocks or combinations of blocks, j=1,...,k; i=1,...,m, define the normalized Delta values of the integral estimates of signals discrete model, the resulting trial deviations for single and multiple defects of the 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 F_{j}(α), j=1,...,k for parameter discrete integral PR is the formation of α,
determine the deviation of the integral estimates of the signals controlled discrete system for the k control points from the nominal values, j=1,...,k, define the normalized Delta values of the integral estimates of the signals controlled discrete system of ratios

determine diagnostic characteristics of ratio

the maximum values of the diagnostic sign determines the ordinal number of a single defect block or a combination of defect blocks.

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 φ_{i}(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 modelobtained in the course of the trial deviation of the i - th parameter of the corresponding structural unit or combination of parameters of the structural blocks.

Thus the m standardized diagnostic feature (3) represents the value of the square of the cosine of the 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 or combination of units, maximizing the value of the diagnostic sign (3), indicates the presence of a defect block or combination of blocks. The region of possible values of the diagnostic characteristic lies in the interval [0,1].

Because the inventive method involves the calculation of a large number of diagnostic features, which is determined by the number of all considered combinations of blocks, even a minor reduction in computational cost when determining the sign by the formula (3) leads to a significant reduction in hardware or software costs for diagnosis. When replacing the diagnostic features in the prototype, indicating defects in their minimum values characteristicon the diagnostic features of the claimed method, pointing out the defects of their maximum valuesobtained savings on one visit is the calculation of one sign (formula (3) in the prototype and formula (3) in the present method).

Thus, the proposed method of finding the defective block or blocks of the discrete system consists of 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, with the number of single and multiple defects of blocks m.

2. Pre-determine the testing time T_{To}≥T_{PP}where T_{PP}the 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 or combination of blocks 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 a nominal characteristics. The principles of the territorial limitations on the type of input test the impact of proposed method does not.

7. Record the response of the system f_{j}(t), j=1,2,...,k on the interval t∈[1,N] with a discrete step Ts seconds, the observation interval [0, T_{k}] (where T_{k}=T_{s}·N) in the k control points define discrete integral evaluation of the output signals, j=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 Ts seconds in each of the k control points with discrete weightsa discrete step Ts seconds, wherewhat signals the control system serves to first inputs of the k blocks multiplication 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 T_{k}obtained by discrete integration of the evaluation of the output signals F_{j}(α), j=1,...,k register.

8. Define the integral evaluation of the signals of the discrete model for each of the k control points obtained in the course of the trial deviations of each of the m single and multiple defects b the shackles why alternately for each structural parameter block or combination of blocks of discrete-time 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 Ts seconds, the evaluation of the output signals for each of the k control points and each of the m test deviations, j=1,...,k; i=1,...,m register.

9. Determine the deviation of the integral of the estimated signals of the discrete model, the resulting trial variance parameters of one or several structural blocks**,**j=1,...,k; i=1,...,m.

10. Define the normalized Delta values of the integral estimates of signals discrete model, the resulting trial variance parameters of one or several units 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 checkpoint, j=1,...,k, carrying out the operations described in paragraphs 6 and 7 with respect to the controlled system.

13. Determine Aut deviation of the integral estimates of the signals controlled discrete system for the k control points from the nominal values 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 failed one or more defective structural units according to formula (3).

16. The maximum values of the diagnostic sign determine the defective block or blocks.

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

Discrete transfer function block:

;;,

rated: K_{1}=5; Z_{1}=0.98; K_{2}=0.09516; Q_{2}=0.9048;_{3}=0.0198; Q_{3}=0.9802. Define variants (m=7) pilot deviations in the form of reduction of the gain (k_{1},...,k_{3}each dynamic block and combinations of blocks 10%: k_{1}=4 (i=1; k_{2}=0.085644 (i=2); k_{3}=0.01782 (i=3); k_{1}=4 and k_{2}=0.085644 (i=4); k_{2}=0.085644 and k_{3}=0.01782 (i=5); k_{1}=4 and k_{3}=0.01782 (i=6); (k_{1}=4, k_{2}=0.085644 and k_{3}=0.01782 (i=7). When searching for multiple structural defect in the form of deviation of the gain by 20% (k_{1}=4, k_{2}=0.085644, k_{3}=0.01782) in the PE the PTO,
the second and third links, when applying speed test input signal of unit amplitude and the integral of the estimated signals for parameter α=0.5 and T_{k}=10, using three control points located at the outputs of blocks using a trial deviation to a value of 10%, the obtained values of diagnostic signs by the formula (3): J_{1}=0.3679; J_{2}=0.8047; J_{3}=0.2384; J_{4}=0.04742; J_{5}=0.1656; J_{6}=0.6125; J_{7}=0.9544. The analysis values of the diagnostic signs shows that multiple defect simultaneously in the first, second and third structural units 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 multiple structural defects according to the proposed method as applied to discrete diagnostic object, shown in the drawing, consists of the following operations:

1. Record the number of controlled single and multiple defects m=7.

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

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

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

5. Pre-find elements of vectors Δ_{i}(α) variance of the integral of the estimated signal model, the resulting trial deviations of all controlled single and multiple 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 and multiple defects by the formula (1).

7. Replace the system with a nominal characteristics controlled, which entered deviations of the first, second and third blocks 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, 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. Vices Aut diagnostic signs of faulty units by the formula (3): J_{
1}=0.3679; J_{2}=0.8047; J_{3}=0.2384; J_{4}=0.04742; J_{5}=0.1656; J_{6}=0.6125; J_{7}=0.9544, where J_{1}indicates a defect in the first block, J_{2}accordingly indicates a defect in the second, J_{3}indicates a defect in the third, J_{4}indicates defects in the first and second blocks, J_{5}- defects in the first and third blocks, J_{6}- defects in the second and third blocks, a J_{7}respectively defects in the first, second and third blocks.

11. The maximum values of the diagnostic sign determine the combination of multiple defect (in this case No. 7).

Modeling of processes of searching multiple defects in other cases, his manifestation for this diagnostic object with the same parameter integral transforms α and unit step input signal gives the following values of diagnostic features.

In the presence of defects in the blocks # 1 and # 3 (in the form of reduced parameters k_{1}and k_{3}20%multiple defect No. 5): J_{1}=0.29; J_{2}=0.5521; J_{3}=0.02254; J_{4}=0.01561; J_{5}=0.9897; J_{6}=0.2566; J_{7}=0.1511.

In the presence of defects in the blocks # 2 and # 3 (in the form of reduced parameters k_{2}and k_{3}20%defect No. 6): J_{1}=0.9265; J_{2}=0.8215; J_{3}=0.7527; J_{4}=0.1361; J_{5}=0.2113; J_{6}=0.9987; J_{7}=0.7978.

In the presence of defects in the blocks # 1 and # 2 (in the form of reduced the I parameter k_{
1}and k_{2}20%defect No. 4): J_{1}=0.3476; J_{2}=1.108e-0,05; J_{3}=0.5792; J_{4}=0.9994; J_{5}=0.04329; J_{6}=0.1783; J_{7}=0.0003697.

We show that this method is efficient for searching a single structural defects.

If there is a defect in the unit 3 (in the form of reducing the parameter k_{3}20%defect No. 3): J_{1}=0.8348; J_{2}=0.332; J_{3}=1; J_{4}=0.5549; J_{5}=0.002949; J_{6}=0.7836; J_{7}=0.4394.

If there is a defect in the unit 2 (in the form of reducing the parameter k_{2}20%defect No. 2): J_{1}=0.6443; J_{2}=1; J_{3}=0.3268; J_{4}=0.0009986; J_{5}=0.5067; J_{6}=0.788; J_{7}=0.8166.

If there is a defect in the unit 1 (in the form of reducing the parameter k_{1}20%defect No. 1): J_{1}=0.999; J_{2}=0.6413; J_{3}=0.8395; J_{4}=0.3335; J_{5}=0.2023; J_{6}=0.9339; J_{7}=0.5397.

The maximum value of the diagnostic sign in all cases correctly indicates bad blocks.

The way of finding bad blocks in a discrete dynamic system, based on the fact that record the number of dynamic elements in the system, determine the testing time T_{To}≥T_{PP}; use test signal on the interval t∈[0,T_{K}]as the dynamic characteristics of the system using integral estimates for real values of α Laplace variable, fixed number k of control that the EC system,
pre-register response known good discrete-time system f_{jo}(t), j=1,2,...,k for N discrete quanta diagnosis t∈[1,N] with discrete spaced T_{s}in the observation interval [0,T_{k}] (where T_{k}=T_{s}·N) in the k control points that 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 T_{s}seconds in each of the k control points with discrete weightsincrements of T_{s}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 T_{s}seconds, the output signals of the k blocks multiplication served on inputs k blocks of discrete integration step T_{s}seconds, discrete integration completed at time T_{k}obtained by integrating the evaluation of the output signalsj=1,...,k, register, define the integral evaluation signal models for each of the k control points, is received in the course of the trial deviations for m defect blocks,
why alternately for each defect 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 determine the deviation of the integral of the estimated signal model, the resulting trial deviations of the respective blocks, j=1,...,k; i=1,...,m, define the normalized variance of the integral of the estimated signal model, the resulting trial deviations blocks from the relationreplace 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 F_{j}(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, j=1,...,k, define the normalized Delta values the integration of the social assessments signals of the controlled system from the relation
wherein the fixed number m of test variance as the total number of single and multiple defects of blocks, the sample variance is injected alternately in each block for single defects or parameters of different combinations of blocks for multiple defects, determine the diagnostic signs of ratiosi=1,...,m, the maximum diagnostic indicator to determine the presence of single or multiple structural defect.

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