CN109241640A - A kind of multiple faults partition method of the Mechatronic Systems based on BG-LFT model - Google Patents

Abstract

The invention discloses a kind of multiple faults partition methods of Mechatronic Systems based on BG-LFT model, comprising: models to non-linear Mechatronic Systems, obtains the Bond Graph Model of non-linear Mechatronic Systems；In the way of linear fraction transformation, BG-LFT model is established, and goes out according to BG-LFT model inference the expression formula of the analytical redundancy relation ARR of system, then be respectively partially separated the nominal section of parameters in system and uncertainty；The BG-LFT model is that para-linkage graph model carries out obtained model after linear fraction transformation；The analytical redundancy relation ARR of system is analyzed, multiple faults isolation matrix is obtained；Breakdown judge is carried out to system using multiple faults isolated algorithm, obtains fault element information.The present invention solves the problems, such as multiple faults in system while Fault Isolation when occurring, and significantly improves the isolability of failure in the simultaneous situation of multiple faults.

Description

A Multi-Fault Isolation Method for Electromechanical Systems Based on BG-LFT Model

technical field

The invention relates to the field of multi-fault isolation diagnosis of a system, in particular to a multi-fault isolation method of an electromechanical system based on a BG-LFT model.

Background technique

In recent years, electromechanical systems have been widely used in modern production and life, and with the development and progress of science and technology, the structure has become more and more complex. Therefore, it is necessary to study the fault diagnosis of electromechanical systems. Because the faults of electromechanical systems are of various types and sources, it is difficult to detect and isolate them. Moreover, because most electromechanical systems contain nonlinearity and parameter uncertainty, they have higher requirements for fault diagnosis.

At present, there are in-depth research on fault diagnosis methods at home and abroad. The fault diagnosis system of modern electromechanical devices requires sensitive fault diagnosis, and the traditional fault diagnosis methods have gradually failed to meet the requirements.

Among them, fault isolation is an important link in fault diagnosis, and its main task is to isolate the real faulty components after the system detects a fault. The traditional fault isolation method based on the fault characteristic matrix is not high on component fault isolation, and most of them are only suitable for the occurrence of a single fault. The fault isolation method can no longer meet the fault isolation requirements when multiple faults occur simultaneously.

SUMMARY OF THE INVENTION

In order to overcome the above-mentioned defects in the prior art, the present invention provides a multi-fault isolation method for an electromechanical system based on the BG-LFT model, which solves the problem of fault isolation when multiple faults occur simultaneously in the system. This significantly improves the isolation of faults.

To achieve the above object, the present invention adopts the following technical solutions, including:

A multi-fault isolation method of electromechanical system based on BG-LFT model, comprising the following steps:

S1, modeling the nonlinear electromechanical system to obtain the bond graph model of the nonlinear electromechanical system;

S2, establish a BG-LFT model according to the method of linear fractional transformation, and derive the expression of the analytical redundancy relation ARR of the system according to the BG-LFT model, and then respectively calculate the nominal part and uncertainty of each parameter in the system Partial separation; the BG-LFT model is the model obtained after carrying out the linear fractional transformation to the bond graph model;

S3, analyze the analytical redundancy relation ARR of the system to obtain a multi-fault isolation matrix, and judge whether the parameters in the analytical redundancy relation ARR of the system are isolating according to the multi-fault isolation matrix;

S4, using a multi-fault isolation algorithm to perform fault judgment on the parameters with isolation to obtain faulty component information.

In step S1, the bond graph model of the nonlinear electromechanical system includes: a motor, a transmission shaft, a deceleration mechanism, and a load; the power flow direction of the bond graph model of the nonlinear electromechanical system is from the motor to the drive shaft, from the motor to the drive shaft. The transmission shaft points to the reduction mechanism, and the reduction mechanism points to the load.

In step S2, the following steps are included:

S21, the expression of the analytical redundancy relation ARR of the system derived according to the BG-LFT model is shown in formula (1):

Among them, the superscript L indicates that the model has added linear fractional transformation; the subscript m indicates the mth parameter in the bond graph model, m=1,2,3...,n; represents the isolation feature of the mth parameter in the bond graph model, and the isolation feature is obtained by calculating the sensor signal in the bond graph; represents the mth parameter in the bond graph model The parameter item of , the mth parameter contains both the nominal part θ _m and the uncertainty part Δθ _m ;

S22, the nominal part and the uncertainty part of each parameter in the analytical redundancy relation ARR of the system are separated, and the expression of the analytical redundancy relation ARR of the separated system is shown in formula (2):

S23, extracting the analytical redundancy relation ARR of the separated system, and extracting the part Np in which the parameters in the analytical redundancy relation ARR only contain the nominal part, and the parameters in the analytical redundancy relation ARR only contain the uncertain part The part Up of , the expression of the analytical redundancy relation ARR of the extracted system is shown in formula (3):

In step S3, a multi-fault isolation matrix is obtained according to the structural characteristics of the unseparated analytical redundancy relation ARR of the system, and the isolation of parameters in the analytical redundancy relation ARR is obtained; wherein, the rows of the multi-fault isolation matrix represent parameters, and the columns represent the parameters. Isolation characteristics; 1 in the multi-fault isolation matrix means that the parameters of the row are sensitive to the fault characteristics of the column, 0 in the multi-fault isolation matrix means that the parameters of the row are not sensitive to the fault characteristics of the column, and each parameter is in its The values under the corresponding isolation characteristics are all 1; if the isolation characteristics of a parameter are unique among all isolation characteristics, that is, except for the isolation characteristics of this parameter, this parameter is not sensitive to the other isolation characteristics, and multi-fault isolation If the value of this parameter row in the matrix is all 0 under the other isolation feature columns, the parameter can be isolated.

In step S4, if the residual error of a certain analytical redundancy relationship ARR of the system is higher than the residual error threshold, the multi-fault isolation algorithm is used to perform fault judgment on the parameters that can be isolated in the analytical redundancy relationship ARR, and obtain: Fault element information, namely fault parameters; the multi-fault isolation algorithm is:

S41, define the number i of faulty components in the system, i=1, 2, . . . , n, n represents the number of all components in the system, that is, the number of all parameters in the analytical redundancy relationship ARR of the system;

S42, determine the fault set F _i when the number of fault elements is i, and the fault set F _i contains subsets, and each subset f _j in the fault set Fi contains _i elements, That is, the number of elements in the fault set f _j is i, indicating that the fault of the system is caused by this i element in the set f _j ;

S43, starting from i=1 and ending with i=n, successively calculate each subset f _j in the fault set F _i , Obtain each element r _j in the set R _j , and correspondingly obtain the value of each element c _j in the set Con _j according to each element r _j in the set R _j , if an element r _j in the set R _j If the fluctuation of the corresponding data is small, then the element c _j in the corresponding set Con _j =1; if the fluctuation of an element r _j in the fluctuation set R _j is large, then the element c _{j in the corresponding set Con j =} 0 ; The small fluctuation means that the fluctuation is only within 10% of the fluctuation of the system under normal conditions, otherwise, the fluctuation is large; if the value of an element c _j in the set Con _j is 1, it means that the fault in the system is composed of a subset of Generated by the elements in f _j , the fault element of the system is the subset represented by the element in f _j , and the number of fault elements of the system is the number of elements in the subset f _j ;

Among them, the calculation method of each element r _j in the set R _j is:

If i=1, start from j=1 to Finish,

If i≠1, start from j=1 to At the end, define e _k as the kth element in the subset f _j , k=1, 2, ..., i; define intermediate variables M _k , N _k , and define the initial values of the intermediate variables M _k , N _k , N _k =N′ _k − ₁ /M _k ; r _j =N _k .

The advantages of the present invention are:

(1) The BG-LFT model adopted by the present invention takes into account the fluctuation of parameters, and uses the concept of linear fractional transformation to describe the uncertain part of the parameters separately under the framework of the bond graph, which is closer to the real system.

(2) The traditional fault isolation method is based on the fault characteristic matrix, and its isolation method is not high in isolation of component faults, and usually can only deal with the occurrence of a single fault, while the multi-fault isolation method proposed by the present invention is based on multiple faults. The isolation matrix analyzes the isolation of all parameters in the analytical redundancy relationship ARR of the system, effectively handles the situation of multiple faults, and improves the isolation capability of faulty components through the analysis of isolation characteristics.

(3) The present invention performs fault isolation analysis on the analytic redundancy relationship ARR of a single system, which reduces the amount of calculation; when multiple ARRs are triggered at the same time, multiple fault isolation analysis is performed on the multiple ARRs, and the judgment result is more accurate. Reliable.

Description of drawings

FIG. 1 is an overall flow chart of the present invention.

FIG. 2 is a BG-LFT model of the electromechanical system of the present invention.

Fig. 3(1) is the experimental result diagram of r _js under the single fault condition of the present invention.

FIG. 3(2) is a graph of the experimental result of r _fs under the single fault condition of the present invention.

FIG. 3(3) is a graph of the experimental result of r _K under the single fault condition of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

As shown in Figure 1, a multi-fault isolation algorithm for electromechanical systems based on the BG-LFT model includes the following steps:

S1, modeling the nonlinear electromechanical system to obtain the bond graph model of the nonlinear electromechanical system;

S2, establish a BG-LFT model according to the method of linear fractional transformation, and derive the expression of the analytical redundancy relation ARR of the system according to the BG-LFT model, and then respectively calculate the nominal part and uncertainty of each parameter in the system Partial separation; the BG-LFT model is the model obtained after carrying out the linear fractional transformation to the bond graph model;

S3, analyze the analytical redundancy relation ARR of the system to obtain a multi-fault isolation matrix, and judge whether the parameters in the analytical redundancy relation ARR of the system are isolating according to the multi-fault isolation matrix;

S4, using a multi-fault isolation algorithm to perform fault judgment on the parameters with isolation, obtain fault element information, and isolate the fault.

In step S1, the bond graph model of the nonlinear electromechanical system includes: a motor, a transmission shaft, a deceleration mechanism, and a load; the power flow direction of the bond graph model of the nonlinear electromechanical system is from the motor to the drive shaft, from the motor to the drive shaft. The transmission shaft points to the reduction mechanism, and the reduction mechanism points to the load.

In step S2, the following steps are included:

S21, the expression of the analytical redundancy relation ARR of the system derived according to the bond graph model is shown in the following formula:

Among them, the superscript L indicates that the model has added linear fractional transformation; the subscript m indicates the mth parameter in the bond graph model, m=1,2,3...,n; represents the isolation feature of the mth parameter in the bond graph model, and the isolation feature is obtained by calculating the sensor signal in the bond graph; represents the mth parameter in the bond graph model The parameter item of , the mth parameter contains both the nominal part θ _m and the uncertainty part Δθ _m ;

S22, the nominal part and the uncertainty part of each parameter in the analytical redundancy relation ARR of the system are separated, and the expression of the analytical redundancy relation ARR of the system after separation is shown in the following formula:

S23, extracting the analytical redundancy relation ARR of the separated system, and extracting the part Np in which the parameters in the analytical redundancy relation ARR only contain the nominal part, and the parameters in the analytical redundancy relation ARR only contain the uncertain part For the part of Up, the expression of the analytical redundancy relation ARR of the extracted system is shown in the following formula:

As shown in FIG. 2 , in this embodiment, the analytical redundancy relation ARR of the system is derived according to the bond graph model of the electromechanical system, including the analytical redundancy relation ARR _LFT1 and the analytical redundancy relation ARR _LFT2 , and the expressions are as follows:

In the formula, J _m , f _m , and K in ARR _LFT1 are the component parameters of the analytical redundancy relationship ARR _LFT1 in the system, representing the moment of inertia of the motor, the viscous friction coefficient of the mechanical part of the motor, and the stiffness of the transmission shaft; in ARR _LFT1 of are the isolation characteristics of component parameters J _s , f _s , and K, respectively; U is the input control voltage.

J _s , f _s , and K in ARR _LFT2 are the component parameters of the analytical redundancy relationship ARR _LFT2 in the system, representing the moment of inertia of the load, the viscous friction coefficient of the load part, and the stiffness of the transmission shaft, _respectively ; are the isolation characteristics of component parameters J _s , f _s , and K, respectively; K in ARR _LFT1 and K in ARR _LFT2 are one component parameter, and the corresponding isolation characteristics are also consistent.

Wherein, the isolation feature is obtained by calculating the sensor signal in the bond graph model, and the isolation feature of the component can be obtained by the following formula:

In the formula, the subscript m represents the mth parameter in the bond graph model, m=1,2,3...,n; represents the isolation feature of the mth parameter in the bond graph model; A parameter term representing the mth parameter θ _m in the bond graph model.

In step S3, a multi-fault isolation matrix is obtained according to the structural characteristics of the analytical redundancy relationship, and the isolation of parameters in each analytical redundancy relationship is obtained, wherein the analytical redundancy relationship used to obtain the multi-fault isolation matrix is not yet separated. The analytic redundancy relationship of ARR _LFT1 and ARR _LFT1 are analytic redundancy relationships without separation of nominal part and uncertainty part;

In this embodiment, the multi-fault isolation matrix of ARR _LFT1 is obtained, and the multi-fault isolation matrix of ARR _LFT1 is shown in the following table:

In this embodiment, the multi-fault isolation matrix of ARR _LFT2 is obtained, and the multi-fault isolation matrix of ARR _LFT2 is shown in the following table:

Among them, the rows of the multi-fault isolation matrix represent parameters, and the columns represent the isolation characteristics, that is, the parameters corresponding to each row in the multi-fault isolation matrix are consistent, and the isolation characteristics corresponding to each column are consistent; 1 in the multi-fault isolation matrix Indicates that the parameters of this row are sensitive to the fault characteristics of this column, 0 in the multi-fault isolation matrix means that the parameters of this row are not sensitive to the fault characteristics of this column, and the value of each parameter under its corresponding isolation characteristics is 1 ; If the isolation characteristic of a parameter is unique among all isolation characteristics, the parameter is insensitive to other isolation characteristics except the isolation characteristic of this parameter, and the row of this parameter in the multi-fault isolation matrix is under the column of other isolation characteristics The value of is 0, the parameter is isolated.

In step S4, if the residual error of a certain analytical redundancy relationship ARR of the system is higher than the residual error threshold, a multi-fault isolation algorithm is used to perform fault judgment on the parameters that can be isolated in the analytical redundancy relationship ARR, and the fault is obtained. Component information, that is, fault parameters; the determination of the residual threshold value is different according to the difference of the diagnosis object and the application environment. Specifically, the residual error threshold value is determined by testing according to the diagnosis object and the application environment.

The multiple fault isolation algorithm is:

S41, define the number i of faulty components in the system, i=1, 2, . . . , n, n represents the number of all components in the system, that is, the number of all parameters in the analytical redundancy relationship ARR of the system;

S42, determine the fault set F _i when the number of fault elements is i, and the fault set F _i contains subsets, and each subset f _j in the fault set Fi contains _i elements, That is, the number of elements in the fault set f _j is i, indicating that the fault of the system is caused by this i element in the set f _j ;

S43, starting from i=1 and ending with i=n, successively calculate each subset f _j in the fault set F _i , Obtain each element r _j in the set R _j , and correspondingly obtain the value of each element c _j in the set Con _j according to each element r _j in the set R _j , if an element r _j in the set R _j If the fluctuation of the corresponding data is small, then the element c _j in the corresponding set Con _j =1; if the fluctuation of an element r _j in the fluctuation set R _j is large, then the element c _{j in the corresponding set Con j =} 0 ; The small fluctuation means that the fluctuation is only within 10% of the fluctuation of the system under normal conditions, otherwise, the fluctuation is large; if the value of a certain element c _j in the set Con _j is 1, it means a fault in the system Generated by the subset being the elements in f _j , the fault element of the system is the element represented by the element in f _j , and the number of fault elements of the system is the number of elements in the subset f _j ;

Among them, the calculation method of each element r _j in the set R _j is:

If i=1, start from j=1 to Finish,

If i≠1, start from j=1 to At the end, define e _k as the kth element in the subset f _j , k=1, 2, ..., i; define intermediate variables M _k , N _k , and define the initial values of the intermediate variables M _k , N _k , N _k =N′ _k − ₁ /M _k ; r _j =N _k .

Specifically, the multi-fault isolation algorithm is mainly divided into two parts, the main program and the judgment program. When the residual error of an ARR is higher than the residual error threshold, the main program starts to run. If there are n components in this ARR, from 1 to n Determine the number of faults. Suppose that a component fails, call the subroutine fault judgment program to judge, check the returned set Con _j , the number of elements in Con _j is equal to the number of sub-sets in the fault set Fi _, and correspond one-to-one. If the sum of all elements c _j in the set Con _j is 1, the corresponding element in f is faulty, and the main program jumps out and ends; if the sum of all the elements c _j in the set Con _j is 0, it is assumed that two components fail The subroutine is called cyclically until all elements fail. The subroutine judges the sub-set f _j in the fault set Fi, if the fault is caused by the element in _{f j, the element c j in the} corresponding position in the set Con _j is set to 1, otherwise it is set to 0.

The pseudocode of the multiple fault isolation algorithm is shown below:

If the residual error of the ARR _LFT2 of the system is higher than the residual error threshold, as shown in Fig. 3(1), (2), (3), it is the fluctuation of r _Js , r _fs , and _rk under the single fault condition, respectively, because The fluctuation of r _fs is small, so it can be judged that the fault parameter of the system is f _s .

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the present invention. within the scope of protection.

Claims (5)

1. A BG-LFT model-based multi-fault isolation method for an electromechanical system is characterized by comprising the following steps of:

s1, modeling the nonlinear electromechanical system to obtain a bonding diagram model of the nonlinear electromechanical system;

s2, establishing a BG-LFT model according to a linear fractional transformation mode, deducing an expression of an analytic redundancy relation ARR of the system according to the BG-LFT model, and separating a nominal part and an uncertain part of each parameter in the system respectively; the BG-LFT model is a model obtained by performing linear fractional transformation on a bonding diagram model;

s3, analyzing the analytic redundancy relation ARR of the system to obtain a multi-fault isolation matrix, and judging whether the parameters in the analytic redundancy relation ARR of the system have isolability or not according to the multi-fault isolation matrix;

and S4, carrying out fault judgment on the isolated parameters by using a multi-fault isolation algorithm to obtain fault element information.

2. The BG-LFT model-based multi-fault isolation method for an electromechanical system according to claim 1, wherein in step S1, the bond map model of the nonlinear electromechanical system comprises: the device comprises a motor, a transmission shaft, a speed reducing mechanism and a load; the power flow direction of the bonding diagram model of the nonlinear electromechanical system is sequentially from the motor to the transmission shaft, from the transmission shaft to the speed reducing mechanism and from the speed reducing mechanism to the load.

3. The BG-LFT model-based multi-fault isolation method for an electromechanical system according to claim 1, wherein the step S2 comprises the following steps:

s21, the expression of the analytic redundancy relation ARR of the system deduced according to the BG-LFT model is shown as the formula (1):

wherein, the superscript L represents that the model adds linear fractional transformation; the subscript m denotes the mth parameter in the bond map model, m being 1,2,3 …, n;the isolation characteristic represents the mth parameter in the bonding diagram model, and is obtained by calculating the sensor signal in the bonding diagram;representing the m-th parameter in the bond map modelItem of parameter (m), m-th parameterContaining both the nominal part theta_mAnd contains an uncertainty portion Δ θ_m；

S22, separating the nominal part and the uncertainty part of each parameter in the analytical redundancy relationship ARR of the system, wherein the expression of the analytical redundancy relationship ARR of the separated system is shown in formula (2):

s23, extracting the analytical redundancy relationship ARR of the separated system, and extracting a part Np where the parameter in the analytical redundancy relationship ARR only contains the nominal part and a part Up where the parameter in the analytical redundancy relationship ARR only contains the uncertainty part, where the expression of the analytical redundancy relationship ARR of the extracted system is shown in formula (3):

4. the BG-LFT model-based multi-fault isolation method for an electromechanical system according to claim 3, wherein in step S3, a multi-fault isolation matrix is obtained according to structural characteristics of an unseparated Analytical Redundancy Relationship (ARR) of the system, so as to obtain isolability of parameters in the Analytical Redundancy Relationship (ARR); wherein, the rows of the multi-fault isolation matrix represent parameters, and the columns represent isolation characteristics; 1 in the multi-fault isolation matrix indicates that the parameters of the row are sensitive to the fault characteristics of the column, 0 in the multi-fault isolation matrix indicates that the parameters of the row are insensitive to the fault characteristics of the column, and the value of each parameter under the corresponding isolation characteristic is 1; if the isolation characteristic of a certain parameter has uniqueness in all the isolation characteristics, namely the parameter is not sensitive to other isolation characteristics except the isolation characteristic of the parameter, and the values of the parameter row of the multi-fault isolation matrix under the other isolation characteristic columns are 0, the parameter has isolability.

5. The BG-LFT model based multi-fault isolation method of an electromechanical system according to claim 4, wherein in step S4, if a residual error of an Analytic Redundancy Relationship (ARR) of the system is higher than a residual error threshold, a multi-fault isolation algorithm is used to perform fault judgment on isolatable parameters in the Analytic Redundancy Relationship (ARR) to obtain fault element information, i.e. information of fault parameters; the multi-fault isolation algorithm is as follows:

s41, defining the number i of the failed components in the system, where i is 1,2, …, n, n represents the number of all the components in the system, that is, the number of all the parameters in the analytic redundancy relationship ARR of the system;

s42, determining a fault set F under the condition that the number of the fault elements is i_iSet of faults F_iTherein containA subset of the fault sets, and a fault set F_iEach subset f of_jWherein each of the I elements is provided with an i element,i.e. set of faults f_jThe number of the middle elements is i, and the fault of the system is represented by the set f_jThe i elements in (a);

s43, starting from i ═ 1 to i ═ n, for the failure set F in turn_iEach subset f of_jThe calculation is carried out in such a way that,to obtain a set R_jEach element r in (1)_jAnd according to the set R_jEach element r in (1)_jCorresponding to get the set Con_jEach element c of_jIf set R_jA certain element r in (1)_jIs small, the corresponding set Con is_jElement c in (1)_j1 is ═ 1; if the fluctuation is set R_jA certain element r in (1)_jIf the fluctuation of (c) is large, the corresponding set Con_jElement c in (1)_j0; the fluctuation is small, namely the fluctuation is only within 10% of the fluctuation under the normal condition of the system, and otherwise, the fluctuation is large; if set Con_jA certain element c_jA value of 1 indicates that the fault in the system is grouped by subset into f_jIs generated, the faulty element of the system is for the subset, is f_jAnd the number of faulty elements of the system is for the subset to be f_jThe number of middle elements;

wherein the set R_jEach element r in (1)_jThe calculation method is as follows:

if i is 1, starting from j 1 toAnd the process is finished, so that the process is finished,

if i ≠ 1, starting from j ≠ 1End, define e_kAs a subset f_jK is 1,2, …, i; defining intermediate variables M_k，N_kAnd to the intermediate variable M_k，N_kIs defined in the initial value of (a),N_k＝N′_k-1/M_k；r_j＝N_k。