RU2719747C1 - Method of searching for faulty unit in continuous dynamic system based on sensitivity function - Google Patents

Abstract

FIELD: physics.SUBSTANCE: invention relates to the diagnosis of automatic control systems. In the method of searching for a faulty unit in a continuous dynamic system, based on the sensitivity function, signs of integral estimates of output signals of the model are determined, which are obtained as a result of the structural function of sensitivity of each of the corresponding units. Elements of the deviation vector of integral estimates of output signals of the model, obtained as a result of a structural function of sensitivity and a vector of signs of deviations of integral estimates, are compared in pairs. Elements of inversion of sign vector of integral estimates of model output signals, obtained as a result of structural function of sensitivity and a vector of signs of deviations of integral estimates are matched. Binary diagnostic features are calculated, the unit value of which is used to define a structural unit with a defect.EFFECT: reduced hardware and software costs.1 cl, 1 dwg

Description

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

There is a method of searching for a faulty block in a continuous dynamic system based on the introduction of test deviations (Method for finding a faulty block in a continuous dynamic system based on the introduction of test deviations: Pat. 2676365 Russian Federation. IPC ⁷ G05B 23/02 (2006.01) / Shalobanov S.S. - No. 2018107521; claimed 02.28.2018; publ. 12.28.2018, Bull. No. 1).

The disadvantage of this method is that it uses the task of the values of the relative deviations of the parameters of the transfer functions for models with trial deviations.

The closest technical solution (prototype) is a method for finding a faulty unit in a continuous dynamic system based on a sensitivity function (Method for finding a faulty block in a continuous dynamic system based on a sensitivity function: Pat. 2680928 Russian Federation. IPC ⁷ G05B 23/02 (2006.01) / Shalobanov S.V., Shalobanov S.S. - No. 2018111888; claimed. 04/02/2018; publ. 02/28/2019, Bull. No. 7).

The disadvantage of this method is that it involves the use of complex diagnostic signs of a defect in the structural unit of the system.

The technical problem to which this invention is directed is to reduce hardware and software costs associated with the implementation of the calculation of normalized diagnostic signs of a defect.

, путем подачи на первые входы k блоков перемножения сигналов системы управления, на вторые входы блоков перемножения подают экспоненциальный сигнал е^-αt, выходные сигналы k блоков перемножения подают на входы k блоков интегрирования, интегрирование завершают в момент времени Т_к, полученные в результате интегрирования оценки выходных сигналов F_{j ном}(α), j=1, …, k регистрируют, фиксируют число m блоков системы, определяют интегральные оценки выходных сигналов модели для каждой из k контрольных точек и каждой из m моделей с функциями структурной чувствительности для каждого из m блоков динамической системы, для чего соединяют связью две модели: на вход первой модели подают тестовый сигнал x(t), выходом первой модели определяют вход контролируемого блока, соединяют выход первой модели со входом второй, входом второй модели становится выход контролируемого блока, находят интегральные оценки выходных сигналов системы для параметра α и входного сигнала x(t), полученные в результате интегрирования оценки выходных сигналов для каждой из k контрольных точек и каждой из m совмещенных моделей со структурной функцией чувствительности V_ji(α), j=1, …, k; i=1, …, m регистрируют, определяют знаки интегральных оценок выходных сигналов модели, полученные в результате структурной функции чувствительности каждого из соответствующих блоков sign(V_ji(α)), j=1, …, k; i=1, …, m, замещают систему с номинальными характеристиками контролируемой, на вход системы подают аналогичный входной сигнал x(t), определяют интегральные оценки сигналов контролируемой системы для k контрольных точек F_j(α), j=1, …, k для параметра интегрирования α, определяют отклонения интегральных оценок сигналов контролируемой системы для k контрольных точек от номинальных значений ΔF_j(α)=F_j(α)-F_{j ном}(α), j=1, …, k, определяют знаки отклонений интегральных оценок выходных сигналов контролируемой системы для k контрольных точек от номинальных значений sign(ΔF_j(α)), j=1, …, k, затем производят операцию попарного сравнения элементов вектора знаков интегральных оценок выходных сигналов модели, полученные в результате структурной функции чувствительности каждого из соответствующих блоков из соотношения sign(V_ji(α)), j=1, …, k; i=1, …, m и вектора знаков отклонений интегральных оценок sign(ΔF_j(α)), j=1, …, k по формуле:The problem is achieved by first registering the reaction of a known-good system ƒ _{j nom} (t), j = 1, ..., k on the interval t∈ [0, T _K ] at k control points, and determine the integral estimates of the output signals F _{j nom} (α), j = 1, ..., k of the system, for which, at the time of input of the input signal to the input of the system with nominal characteristics, the integration of the control system signals at each of k control points with weights e ^{-αt starts simultaneously}

, by applying the control system signals to the first inputs k of the multiplication blocks, the exponential signal e ^{-αt is} supplied to the second inputs of the multiplying blocks, the output signals of the multiplying blocks are fed to the inputs of the integration blocks k, the integration is completed at time T _to , obtained as a result of integration of the estimate the output signals F _{j nom} (α), j = 1, ..., k are recorded, the number m of system blocks is fixed, the integral estimates of the model output signals for each of k control points and each of m models with structural functions are determined sensitivity for each of the m blocks of the dynamic system, for which two models are connected: the test signal x (t) is fed to the input of the first model, the input of the controlled block is determined by the output of the first model, the output of the first model is connected to the input of the second, the output of the second model becomes the output of the controlled block, find the integrated estimates of the system output signals for the parameter α and the input signal x (t) obtained by integrating the estimates of the output signals for each of k control points and each of m combined firs sensitivity with structural function V _ji (α), j = 1, ..., k; i = 1, ..., m register, determine the signs of the integrated estimates of the output signals of the model, obtained as a result of the structural sensitivity function of each of the corresponding blocks sign (V _ji (α)), j = 1, ..., k; i = 1, ..., m, replace the system with the nominal characteristics of the controlled one, apply the same input signal x (t) to the input of the system, determine the integral estimates of the signals of the controlled system for k control points F _j (α), j = 1, ..., k for the integration parameter α, the deviations of the integral estimates of the signals of the controlled system for k control points from the nominal values ΔF _j (α) = F _j (α) -F _{j nom} (α), j = 1, ..., k are determined, the signs of the deviations of the integral estimates of the output signals of the controlled system for k control points from nominal s beginnings sign (ΔF _j (α)), j = 1, ..., k, then perform the operation of pairwise comparing the elements of the vector of signs of the integral estimates of the model output signals obtained as a result of the structural sensitivity function of each of the corresponding blocks from the relation sign (V _ji (α )), j = 1, ..., k; i = 1, ..., m and the vector of signs of deviations of the integral estimates sign (ΔF _j (α)), j = 1, ..., k according to the formula:

есть операция эквивалентности, то выражение (1) принимает значение 1 только в том случае, когда все элементы векторов sign(V_ji(α)), j=1, …, k. и sign(ΔF_j(α)), j=1, …, k для каждой контрольной точки попарно равны.Since the operation

is an equivalence operation, then expression (1) takes the value 1 only if all elements of the vectors sign (V _ji (α)), j = 1, ..., k. and sign (ΔF _j (α)), j = 1, ..., k for each control point are pairwise equal.

Then, the operation of pairwise comparing the elements of the inversion of the vector of the structural function of the sensitivity for the ith block inv (sign (V _ji (α))), j = 1, ..., k; i = 1, ..., m and the vector of signs of deviations of the integral estimates sing (ΔF _j (α)), j = 1, ..., k according to the formula:

есть операция эквивалентности, то выражение (2) принимает значение 1 только в том случае, когда все элементы векторов inv(sign(V_ji(α))), j=1, …, k. и sign(ΔF_j(α)), j=1, …, k для каждой контрольной точки попарно равны.Since the operation

is an equivalence operation, then expression (2) takes the value 1 only if all elements of the vectors inv (sign (V _ji (α))), j = 1, ..., k. and sign (ΔF _j (α)), j = 1, ..., k for each control point are pairwise equal.

Then produce the calculation of binary diagnostic features from the ratio:

The first term of formula (3) takes the value 1 if the signs of the deviations of the integral estimates of the output signals of the controlled system from the nominal values coincide with the elements of the vector of signs of the deviations of the integral estimates of the output signals of the model obtained as a result of the sensitivity function of different structural blocks, the second term of the formula (3) takes value 1, if the signs of deviations of the integrated estimates of the output signals of the controlled system from the nominal values coincide with the inverted elements of the vector of values These are deviations of the integral estimates of the model output signals obtained as a result of the sensitivity function of different structural blocks. The inversion of the vector of signs of deviations of the integrated estimates of the output signals of the model obtained as a result of the sensitivity function of different structural blocks takes into account the possibility of a defect in the same block both with a plus sign (for example, an increase in the value of a block parameter) and a minus sign (for example a decrease in the value of a block parameter )

The unit value of the binary diagnostic feature determines the structural unit with a defect.

Thus, the proposed method for searching for a structural defect is reduced to performing the following operations:

1. As a dynamic system, consider a system consisting of randomly connected dynamic blocks, with the number of blocks m considered.

2. Pre-determine the control time T _To ≥T _PP , where T _PP - the transition process of the system. The transient time is estimated for the nominal values of the parameters of the dynamic system.

.3. Determine the parameter of the integral signal conversion from the ratio

.

4. Fix the number of control points k.

5. Preliminarily determine the sign vectors of deviations of the integrated estimates of the output signals of the model sign (V _i (α)), i = 1, ..., m, obtained by integrating the sensitivity functions of the i-th block of each of m blocks for the nominal values of the parameters of the transfer functions of the blocks and the parameter α defined above, for which points 6-10 are performed.

6. The input signal x (t) (unit step, linearly increasing, rectangular pulse, etc.) is fed to the input of a control system with nominal characteristics. The proposed method does not provide fundamental restrictions on the type of input test exposure.

, для чего сигналы системы управления подают на первые входы к блоков перемножения, на вторые входы блоков перемножения подают экспоненциальный сигнал е^-αt, выходные сигналы k блоков перемножения подают на входы k блоков интегрирования, интегрирование завершают в момент времени Т_к, полученные в результате интегрирования оценки выходных сигналов F_{j ном}(α), j=1, …, k регистрируют.7. The reaction of the system ƒ _{j nom} (t), j = 1, ..., k on the interval t∈ [0, T _K ] at k control points is recorded and the integral estimates of the output signals F _{j nom} (α), j = 1, ..., k systems. For this, at the moment of supplying the input signal to the input of the control system with nominal characteristics, the integration of the output signals of the control system at each of k control points with weights e ^{-αt starts simultaneously}

why the control system signals are fed to the first inputs of the multiplication units, the exponential signal e ^{-αt is} supplied to the second inputs of the multiplying units, the output signals of the multiplying units are fed to the inputs of the integration blocks k, the integration is completed at time T _to , obtained as a result of integration estimates of the output signals F _{j nom} (α), j = 1, ..., k are recorded.

8. Integral estimates of the output signals of the sensitivity model for each of the k control points are determined, obtained as a result of using the structural sensitivity function of each of the m blocks, for which two models are connected in turn for each block of the dynamic system: a test signal x ( t), the output of the first model becomes the input of the controlled unit, connect the output of the first model with the input of the second, the input of the second model becomes the output of the controlled unit, and perform steps 6 and 7 for the same input signal x (t). Estimates of the output signals obtained as a result of integration for each of k control points and each of m combined models with the structure sensitivity function V _ji (α), j = 1, ..., k; i = 1, ..., m are recorded.

9. Determine the signs of the integrated estimates of the model output signals obtained as a result of using the structural sensitivity function by the formula

sign (V _ji (α)), j = 1, ..., k; i = 1, ..., m.

10. Substitute a system with controlled ratings. A similar input signal x (t) is supplied to the system input.

11. Determine the integral estimates of the output signals of the controlled system for k control points F _j (α), j = 1, ..., k, performing the operations described in paragraphs 6 and 7 in relation to the controlled system.

12. The deviations of the integrated estimates of the output signals of the controlled system for k control points from the nominal values ΔF _j (α) = F _j (α) -F _{j nom} (α), j = 1, ..., k are determined.

13. Determine the signs of deviations of the integrated estimates of the output signals of the controlled system for k control points from the nominal values of sign (ΔF _j (α)), j = 1, ..., k.

14. Perform the operation of pairwise comparison of the elements of the vector of signs of the integral estimates of the output signals of the model obtained as a result of the structural sensitivity of the i-th block of sign (V _ji (α)), j = 1, ..., k; i = 1, ..., m and the vector of signs of deviations of the integral estimates sign (ΔF _j (α)), j = 1, ..., k according to the formula:

15. Perform the operation of pairwise comparison of the inversion elements of the vector of signs of the integral estimates of the model output signals obtained as a result of the structural sensitivity function of the ith block inv (sign (V _ji- (α))), j = 1, ..., k; i = 1, ..., m and the vector of signs of deviations of the integral estimates sign (ΔF _j (α)), j = 1, ..., k according to the formula:

16. Binary diagnostic features are calculated from the ratio:

17. The unit value of the binary diagnostic feature determines the structural unit with a defect.

Consider the implementation of the proposed method for finding a defective block for a system whose structural diagram is shown in the figure (see. Fig. The structural diagram of the diagnostic object).

; блока 2:

; блока 3:

, номинальные значения параметров: Т₁=5 с; k₁=1; k₂=1; Т₂=1 с; k₃=1; Т₃=5 с. При поиске одиночного дефекта в виде отклонения постоянной времени Т₁=4 с (дефект №1) в первом блоке путем подачи ступенчатого тестового входного сигнала единичной амплитуды и интегральных преобразований сигналов для параметра α=0.5 и Т_к=10 с получены значения бинарных диагностических признаков наличия дефекта по формуле (3) при использовании трех контрольных точек (КТ1, КТ2 и КТ3), расположенных на выходах блоков. Дефект, вычисленный по формуле (3), дает следующие значения бинарных диагностических признаков: J₁=1;J₂=0;J₃=0.Transfer functions of block 1:

; block 2:

; block 3:

, nominal values of parameters: T ₁ = 5 s; k ₁ = 1; k ₂ = 1; T ₂ = 1 s; k ₃ = 1; T ₃ = 5 s. When searching for a single defect in the form of a deviation of the time constant T ₁ = 4 s (defect No. 1) in the first block by supplying a step test input signal of unit amplitude and integral signal transformations for the parameter α = 0.5 and T _to = 10 s, the values of binary diagnostic signs are obtained the presence of a defect according to formula (3) when using three control points (CT1, CT2 and CT3) located at the outputs of the blocks. The defect calculated by formula (3) gives the following values of binary diagnostic features: J ₁ = 1; J ₂ = 0; J ₃ = 0.

Simulation of the defect search processes in the second and third blocks for a given diagnostic object, with the same integration parameter α and with a single step input signal, gives the following values of binary pointers:

If there is a defect in block No. 2 (in the form of a decrease in the parameter T ₂ by 20%, defect No. 2): J ₁ = 0, J ₂ = 1; J ₃ = 0.

If there is a defect in block No. 3 (in the form of a decrease in the parameter T ₃ by 20%, defect No. 3): J ₁ = 0; J ₂ = 0; J ₃ = 1.

The single value of the binary diagnostic feature in all cases correctly determines the defective block.

Claims (5)

The method of searching for a faulty block in a continuous dynamic system based on the sensitivity function, based on the fact that the number of blocks m that are part of the system is fixed, the monitoring time T _K ≥T _{PP is} determined, where T _PP is the system transient time, the integral conversion parameter is determined signals from the ratio

, use a test signal on the interval t∈ [0, T _K ], use the integral signal estimates obtained for real values of the parameter α as the dynamic characteristics of the system, fix the number k of control points of the system, record the reaction of the diagnostic object and the reaction of a known-good system ƒ _{j nom} (t), j = 1, ..., k, on the interval t∈ [0, T _K ] at k control points, determine the integral estimates of the output signals F _{j nom} (α), j = 1, ..., k, of a working system , for which at the time of the test signal to the input of the system with nominal characteristics simultaneously begin integration of the output signals of the control system in each of the k control points with weights e ^-αt , where

, by supplying the control system output signals to the first inputs of the multiplication blocks, the exponential signal e ^{-t is} supplied to the second inputs of the multiplication blocks, the output signals of the multiplication blocks are fed to the inputs of the integration blocks k, the integration is completed at time T _k obtained by integration evaluation of the output signals _SG F _j (α), j = 1, ..., k, are recorded, the system is substituted with nominal characteristics of controlled, is fed to the input of the system a similar test signal x (t), define the integral estimates you -period signal controlled system for k checkpoint F _j (α), _j = 1, ..., k, for the parameter α, is determined deflection of integral estimates controlled system output signals for k of control points from the nominal values _{ΔF j (α) = F j} ( α) -F _{j nom} (α), j = 1, ..., k, determine the integral estimates of the model output signals for each of the k control points obtained by using the structural sensitivity function of each of the m blocks of a dynamic system, for which two models: test signal is input to the first model l x (t), the output of the first model becomes the input of the controlled unit, connect the output of the first model with the input of the second, the input of the second model becomes the output of the controlled unit, and find the integral estimates of the system output signals for parameter α and the input signal x (t) obtained in the result of integrating the estimates of the output signals for each of k control points and each of m combined models with the structural sensitivity function V _ji (α), j = 1, ..., k; i = 1, ..., m, register, calculate diagnostic signs of the presence of a defect, characterized in that they determine the signs of the integrated estimates of the model output signals obtained as a result of the structural sensitivity function of each of the corresponding blocks sign (V _ji (α)), j = 1 , ..., k; i = 1, ..., m, perform the operation of pairwise comparing the elements of the vector of the signs of the deviations of the integral estimates of the output signals of the model, obtained as a result of the structural sensitivity function of the i-th block sign (V _ji (α)), j = 1, ..., k; i = 1, ..., m, and the vector of signs of the deviations of the integral estimates by the formula

, perform the operation of pairwise comparison of the inversion elements of the vector of signs of the integral estimates of the model output signals obtained as a result of the sensitivity structure function of the ith block inv (sign (V _ji (α))), j = 1, ..., k; i = 1, ..., m, and the vector of signs of the deviation of the integral estimates by the formula

, calculate binary diagnostic features:

, a unit value of a binary diagnostic feature determines the structural block with a defect.

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