CN113110377B - Small fault detection method for sampling mechanical arm closed-loop control system - Google Patents

Small fault detection method for sampling mechanical arm closed-loop control system Download PDF

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CN113110377B
CN113110377B CN202110331788.4A CN202110331788A CN113110377B CN 113110377 B CN113110377 B CN 113110377B CN 202110331788 A CN202110331788 A CN 202110331788A CN 113110377 B CN113110377 B CN 113110377B
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fault
mechanical arm
neural network
residual error
controller
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CN113110377A (en
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王敏
刘雅梅
曾宇鹏
戴诗陆
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Foshan Newhinken Intelligent Technology Co ltd
South China University of Technology SCUT
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South China University of Technology SCUT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
    • G05B23/0262—Confirmation of fault detection, e.g. extra checks to confirm that a failure has indeed occurred
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/24—Pc safety
    • G05B2219/24065—Real time diagnostics

Abstract

The invention discloses a small fault detection method of a sampling mechanical arm closed-loop control system, which comprises the following steps: designing a self-adaptive neural network controller of the discrete time mechanical arm; constructing a dynamic estimator to approximate the unknown dynamics of the system; calculating a system dynamic residual error caused by a fault and a residual error compensated by a controller, and further obtaining an enhanced total measurable fault residual error; calculating a weighted recursive absolute fault residual accumulated value; designing a fault detection decision scheme, comparing a fault residual accumulated value obtained by real-time calculation with a self-adaptive threshold, and if a certain moment exists and the fault residual accumulated value is larger than the self-adaptive threshold, judging that the mechanical arm has a fault at the moment; the fault detection scheme provided by the invention ensures that the quick detection of the fault is realized after the mechanical arm system breaks down, solves the problems of frequent fault change and low fault diagnosis speed through a weighted recursion absolute residual accumulation mechanism, and ensures the safety and the rapidity of the fault detection system.

Description

Small fault detection method for sampling mechanical arm closed-loop control system
Technical Field
The invention relates to the technical field of robot fault detection, in particular to a small fault detection method of a sampling mechanical arm closed-loop control system.
Background
Fault detection is an important problem in modern engineering systems, which have received much attention so far, where the requirements for safety and reliability are increasing and the main goal of fault detection is to identify the occurrence of system faults during real-time operation. Timely and accurate fault diagnosis is critical to the reliable and efficient operation of many engineering systems, especially those critical to safety, such as aircraft engines, chemical processes, industrial robots, power networks, and the like.
Minor faults generally refer to those faults that are less than the system uncertainty (e.g., unmodeled dynamics or interference/noise), which generally occur at an early stage before the larger fault occurs. Early detection of minor faults helps to avoid major faults and catastrophic consequences, and helps to minimize maintenance activities and costs. However, in non-linear uncertain systems, minor faults are difficult to detect because they may be hidden in unmodeled system dynamics. In addition, detecting faults from real-time closed-loop control is also a challenging problem. This is because the effects of a fault are typically compensated for by the controller and are difficult to detect. Closed loop control systems are generally robust to external faults, and the controller can compensate for the effects of the fault, thereby maintaining tracking and regulation performance. This is particularly true when the magnitude of the fault is relatively small, so that only little fault information is available for fault diagnosis. In view of this, how to effectively process the fault information supplemented by the controller from the real-time closed-loop control system, and how to quickly and accurately perform fault diagnosis is a challenge problem to be solved urgently.
Disclosure of Invention
In order to overcome the defects and shortcomings in the prior art, the invention provides a small fault detection method of a sampling mechanical arm closed-loop control system, and provides a dynamic estimation method based on deterministic learning aiming at the problem that small faults are difficult to detect in a nonlinear uncertain system, so that the uncertain dynamics of the system can be effectively and accurately modeled, and the estimation of fault information is realized; aiming at the problem that the closed-loop system is difficult to detect faults due to the compensation effect of the controller, a total measurable fault residual error detection scheme based on controller compensation is designed, the compensation effect of the controller on fault information can be eliminated, the enhancement of the detectable fault information is realized, and the rapid detection of the faults is ensured; meanwhile, on the basis, the problems of frequent fault change and low fault diagnosis speed are solved by designing a weighted recursion absolute residual error accumulation mechanism, and the safety and the rapidity of a fault detection system are guaranteed.
The invention also provides a small fault detection system of the sampling mechanical arm closed-loop control system.
A third object of the present invention is to provide a storage medium.
It is a fourth object of the invention to provide a computing device.
In order to achieve the purpose, the invention adopts the following technical scheme:
a small fault detection method of a sampling mechanical arm closed-loop control system comprises the following steps:
establishing a mechanical arm dynamic model and an expected regression trajectory model based on data sampling, and designing a self-adaptive neural network controller;
constructing a dynamic estimator to approximate the unknown dynamics of the system;
calculating the total measurable fault residual of the system;
total measurable fault residual phie(k) Calculated by the following formula:
φe(k)＝φf(k)-φu(k)
φf(k) for fault dynamic residuals, i.e. system dynamic residuals caused by faults:
Figure BDA0002996379360000021
φu(k) residual error compensated for the controller, i.e. the effect of the controller on the compensation of system faults:
Figure BDA0002996379360000022
wherein k is the operation time of the sampling mechanical arm system, k-1 represents the previous operation time of the sampling mechanical arm system, h (X (k), u (k)) represents the actual system dynamic state affected by small disturbance, X (k) represents the system state, u (k) is a system self-adaptive controller, and u (k) is a system self-adaptive controller0(k) Represents the controller in the normal mode of operation,
Figure BDA0002996379360000031
representing a weight constant matrix of a neural network for approximating unknown dynamics of the system, S (X (k), u (k)) being a vector[XT(k),uT(k)]TIs an input gaussian radial basis function vector;
calculating a weighted recursive absolute fault residual accumulated value;
designing a weighted recursive absolute fault residual error accumulation mechanism to calculate a fault residual error accumulation value e (k) in real time:
Figure BDA0002996379360000032
wherein, TaKT, K is positive integer, T is system sampling period, b is the parameter of treating the design, satisfies 0 < b < 1, when the mechanical arm is operated under normal mode, total measurable trouble residual error phie(k) Satisfies the following conditions:
Figure BDA0002996379360000033
ε＝[ε1,...,εn]Tis an approximation error of unknown dynamics of the system and satisfies | | | Epsilon | | | luminance∞＜ε*The controller compensates the residual error to satisfy | | phiu||∞＜εu *，
Figure BDA0002996379360000034
Is the upper bound value of the system disturbance, | |. the non-woven phosphor∞An infinite norm representing a vector;
designing a fault detection decision scheme:
designing adaptive thresholds
Figure BDA0002996379360000035
Figure BDA0002996379360000036
A fault detection decision scheme: the fault residual error accumulated value e (k) obtained by real-time calculation is compared with an adaptive threshold value
Figure BDA0002996379360000037
Comparing, if there is a certain time kdSo that
Figure BDA0002996379360000038
If true, it is determined at kdThe mechanical arm breaks down at all times.
As a preferred technical solution, the data sampling-based mechanical arm dynamics model is expressed as:
Figure BDA0002996379360000039
wherein, TsFor a sampling interval, the sampling time point is kTs，X(k)＝[x1(k),x2(k)]T，x1(k)＝[x1,1(k),x1,2(k),…,x1,n(k)]T、x2(k)＝[x2,1(k),x2,2(k),…,x2,n(k)]TRespectively the angular displacement and angular velocity of the joint of the mechanical arm, n corresponds to the number of joints of the mechanical arm, u (k) is control torque, f0(X (k)) and g0(X (k)) is a system unknown nonlinear function, g0(X(k))＝TsM(x1(k))-1，f0(X(k))＝x2(k)+TsM(x1(k))-1[-Vm(x1(k),x2(k))x2(k)-G(x1(k))]，M(x1(k) Is an inertia matrix of the robot arm, Vm(x1(k),x2(k) Is a centripetal force matrix, G (x)1(k) Is a gravity term, M (x)1(k)),Vm(x1(k),x2(k)),G(x1(k) Are unknown, d (k) is a bounded perturbation;
the system dynamics in the case of a fault are as follows:
Figure BDA0002996379360000041
wherein f isf(X(k))，gf(X (k)) represents the unknown nonlinear function of the fault system.
As a preferred technical solution, the expected regression trajectory model is expressed as:
Figure BDA0002996379360000042
wherein x isd(k)＝[xd1(k),xd2(k)]T，xd1(k) Is a desired reference trajectory, x, of the angular position of the jointd2(k) Is the desired reference trajectory of the angular velocity of the joint, f (x)d1(k),xd2(k) ) is a given continuous function.
As a preferred technical solution, the designing of the adaptive neural network controller is specifically represented as:
Figure BDA0002996379360000043
the weight updating rule of the neural network is given by the following formula:
Figure BDA0002996379360000044
wherein the content of the first and second substances,
Figure BDA0002996379360000045
is an estimate of the weight of the ideal neural network, Sa(Z (k)) is a Gaussian radial basis function vector having as input vector Z (k), where [ x [, ]1 T(k),x2 T(k),xd1 T(k+2)]TFor the input of the neural network, Γ is the gain term of the weight update rate of the neural network, and z (k) ═ x1(k)-xd1(k) Is the tracking error between the angular position of the mechanical arm and the reference trajectory.
As a preferred technical solution, the configuration dynamics estimator approximates system unknown dynamics, and the dynamics estimator is represented as:
Figure BDA0002996379360000051
wherein the content of the first and second substances,
Figure BDA0002996379360000052
is x2(k) Is estimated, a ═ diag { a ═ d1,...,anIs a design parameter, satisfies 0 < | aiI < 1, i ═ 1,.. n
Figure BDA0002996379360000053
Represents an adaptive neural network for learning unknown dynamics of the system,
Figure BDA0002996379360000054
an estimate of the weights of the ideal neural network is represented,
Figure BDA0002996379360000055
an input vector which is a radial basis function S (X (k), u (k));
the weight updating rule of the neural network is given by the following formula:
Figure BDA0002996379360000056
wherein the content of the first and second substances,
Figure BDA0002996379360000057
C＝diag{c1,...,cnis a design constant satisfying 0 < ci＜2,i＝1,...,n；
After the NN weight estimates converge, a constant neural network is used
Figure BDA0002996379360000058
The approximation system is unaware of dynamics, i.e.:
Figure BDA0002996379360000059
wherein the content of the first and second substances,
Figure BDA00029963793600000510
is a weight of an adaptive neural network
Figure BDA00029963793600000511
A converged constant matrix, [ K ]1,K1+K2+1]Is composed of
Figure BDA00029963793600000512
Time period of stable convergence, [ epsilon ]1,...,εn]TTo approximate the error, satisfy | | | Epsilon | | | luminance∞＜ε*；
For system unknown dynamics f in normal mode0(X(k))+g0(X(k))u0(k) Can be locally and accurately approximated by a constant neural network
Figure BDA00029963793600000513
The realization method comprises the following steps:
Figure BDA00029963793600000514
wherein the content of the first and second substances,
Figure BDA00029963793600000515
Figure BDA00029963793600000516
Figure BDA00029963793600000517
is the adaptive neural network weight in the normal mode
Figure BDA00029963793600000518
The constant matrix of the convergence is then determined,
Figure BDA00029963793600000519
{kl|kl＝l,l+2,l+4,···,l+2n,···},[ka,kb]is composed of
Figure BDA0002996379360000061
Period of stable convergence,. epsilon0＝[ε01,...,ε0n]TTo approximate the error, satisfy | | ε0||∞＜ε0 *。
In order to achieve the second object, the invention adopts the following technical scheme:
a minor fault detection system of a sampling mechanical arm closed-loop control system comprises: the system comprises a model construction module, a self-adaptive neural network controller construction module, a dynamic estimator construction module, a total measurable fault residual error calculation module, an absolute fault residual error accumulated value calculation module and a fault detection decision construction module;
the model construction module is used for establishing a mechanical arm dynamics model and an expected regression trajectory model based on data sampling;
the self-adaptive neural network controller constructing module is used for constructing a self-adaptive neural network controller;
the dynamic estimator building module is used for building a dynamic estimator to approximate unknown dynamic of a system;
the total measurable fault residual error calculation module is used for calculating the total measurable fault residual error of the system;
the absolute fault residual accumulated value calculating module is used for calculating a weighted recursion absolute fault residual accumulated value;
the fault detection decision building module is used for building a weighted recursion absolute fault residual error accumulation mechanism to calculate a fault residual error accumulation value in real time, and the fault residual error accumulation value e (k) obtained by real-time calculation and a set self-adaptive threshold value
Figure BDA0002996379360000062
Comparing, if there is a certain time kdSo that
Figure BDA0002996379360000063
If true, it is determined at kdThe mechanical arm breaks down at all times.
As a preferred technical solution, the total measurable fault residual calculation module is used for calculating a total measurable fault residual of the system, and is specifically represented as:
φe(k)＝φf(k)-φu(k)
Figure BDA0002996379360000064
Figure BDA0002996379360000065
wherein phi isf(k) For fault dynamic residual, phiu(k) Residual errors compensated for by the controller, k is the operating time of the sampled arm system, k-1 represents the previous operating time of the sampled arm system, h (X (k), u (k)) represents the actual system dynamics affected by small disturbances, X (k) represents the system state, u (k) is a system adaptive controller, u (k)0(k) Represents the controller in the normal mode of operation,
Figure BDA0002996379360000071
representing a weight constant matrix of the neural network for approximating the unknown dynamics of the system, S (X (k), u (k)) being a vector [ X [, (k) ]T(k),uT(k)]TIs the input gaussian radial basis function vector.
As a preferred technical solution, the absolute fault residual accumulated value calculating module is configured to calculate a weighted recursive absolute fault residual accumulated value, and is specifically represented as:
Figure BDA0002996379360000072
the adaptive threshold value
Figure BDA0002996379360000073
Expressed as:
Figure BDA0002996379360000074
wherein, TaKT, K is positive integer, T is system sampling period, b is the parameter of treating the design, satisfies 0 < b < 1, when the mechanical arm is operated under normal mode, total measurable trouble residual error phie(k) Satisfies the following conditions:
Figure BDA0002996379360000075
ε＝[ε1,...,εn]Tis an approximation error of unknown dynamics of the system and satisfies | | | Epsilon | | | luminance∞＜ε*The controller compensates the residual error to satisfy | | phiu||∞＜εu *，
Figure BDA0002996379360000076
For the upper bound of system disturbances, | | | - ∞ represents the infinite norm of the vector.
In order to achieve the third object, the invention adopts the following technical scheme:
a storage medium stores a program that, when executed by a processor, implements the glitch detection method of the sampling manipulator closed-loop control system described above.
In order to achieve the fourth object, the invention adopts the following technical scheme:
a computing device comprising a processor and a memory for storing a processor-executable program, the processor, when executing the program stored in the memory, implementing a glitch detection method as described above for a sampling manipulator closed-loop control system.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the invention provides a dynamic estimation method based on deterministic learning, which can effectively and accurately model the uncertain dynamics of a system, solve the problem that small faults are submerged in the unknown dynamics of the system and achieve the technical effect of separating small fault items from the unknown dynamics of the system;
(2) the invention adopts a total fault information residual error detection scheme based on controller compensation, increases the detectable fault information, solves the technical problem that small faults are difficult to detect, and improves the rapidity of fault detection.
(3) The invention adopts a weighted recursion absolute fault accumulation mechanism, solves the technical problem of symbol constraint of a fault function, accelerates fault residual accumulation, reduces a detection threshold value and shortens detection time.
Drawings
FIG. 1 is a flowchart illustrating the overall control of the small failure detection system of the robot arm of the present invention;
FIG. 2 is a graph showing the variation of the tracking error of the robot arm according to the present invention;
FIG. 3 is a constant neural network during normal operation of the robot arm of the present invention
Figure BDA0002996379360000081
For system unknown dynamics f0(X(k))+g0(x (k)) u (k) approximation effect map;
FIG. 4 shows the residual phi compensated by the manipulator controller according to the present inventionu(k) A graph of variation of (d);
FIG. 5 shows the dynamic residual phi of the fault according to the present inventionf(k) Residual error phi from total measurable fault of systeme(k) A graph of variation of (d);
FIG. 6 shows the fault residual error cumulative value e (k) and the adaptive threshold value of the robot arm in the operation process of the present invention
Figure BDA0002996379360000082
Graph of the variation of (c).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
As shown in fig. 1, the present embodiment provides a minor fault detection method for a closed-loop control system of a sampling mechanical arm, including the following steps:
s1: establishing a discrete-time single-connecting-rod rigid mechanical arm dynamic model based on sampling data, which is specifically represented as follows:
Figure BDA0002996379360000091
where k represents the operating time of the sampled discrete arm system, TsRepresenting a sampling interval of time having a sampling time point kTs，X(k)＝[x1(k),x2(k)]T；x1(k) And x2(k) The angular displacement of the mechanical arm joint and the angular velocity u (k) of the joint are respectively control torque f0(X (k)) and g0(X (k)) is a system unknown nonlinear function, g0(X(k))＝TsM(x1(k))-1，f0(X(k))＝x2(k)+TsM(x1(k))-1[-Vm(x1(k),x2(k))x2(k)-G(x1(k))]，M(x1(k) Is an inertia matrix of the robot arm, Vm(x1(k),x2(k) Is a centripetal force matrix, G (x)1(k) Is a gravity term, M (x)1(k)),Vm(x1(k),x2(k)),G(x1(k) Are unknown, d (k) is a bounded small perturbation.
The relevant parameters of the single-link rigid mechanical arm system selected in the embodiment are respectively as follows: sampling time Ts＝0.05s，M(x1(k))＝l2m，Vm(x1(k),x2(k))＝2，G(x1(k))＝lmgcos(x1(k) Link length l is 0.25m, link mass m is 1kg, and gravitational acceleration g is 9.8m/s2System disturbance d (k) 0.04cos (2k) sin (x)1(k) Upper bound value of system disturbance)
Figure BDA0002996379360000092
The system dynamics in the case of a fault are as follows:
Figure BDA0002996379360000093
wherein f isf(X(k))，gf(X (k)) representsThe barrier system does not know the nonlinear function. In the present embodiment, f is setf(X(k))＝1.01f0(X(k))，gf(X(k))＝1.03g0(X(k))。
The expected regression trajectory of the rigid mechanical arm is as follows:
Figure BDA0002996379360000101
wherein x isd1(k) Is a desired reference trajectory, x, of the angular position of the jointd2(k) Is the desired reference trajectory of the angular velocity of the joint, f (x)d1(k),xd2(k) ) is a given continuous function. The desired periodic trajectory selected in this example is: x is the number ofd1(k)＝0.5sin(0.01πk)。
Designing an adaptive neural network controller:
Figure BDA0002996379360000102
the weight updating rule of the neural network is given by the following formula:
Figure BDA0002996379360000103
wherein the content of the first and second substances,
Figure BDA0002996379360000104
is an estimate of the weight of the ideal neural network, Sa(Z (k)) is a Gaussian radial basis function vector having as input vector Z (k), where [ x [, ]1(k),x2(k),xd1(k+2)]TIs the input of the neural network, z (k) ═ x1(k)-xd1(k) For the tracking error between the angular position of the mechanical arm and the reference track, Γ is a gain term of the weight update rate of the neural network, and in this example, Γ is selected to be 0.18.
S2: the configuration dynamics estimator estimates the system unknown dynamics:
Figure BDA0002996379360000105
wherein the content of the first and second substances,
Figure BDA0002996379360000106
is x2(k) Is determined by the estimated value of (c),
Figure BDA0002996379360000107
is an adaptive neural network used to learn the unknown dynamics of the system,
Figure BDA0002996379360000108
is an estimated value of the weight of the ideal neural network,
Figure BDA0002996379360000109
an input vector of the radial basis function S (x (k), u (k)), where a is a design parameter, is selected to be 0.5 in this embodiment.
The weight updating rule of the neural network is given by the following formula:
Figure BDA00029963793600001010
wherein the content of the first and second substances,
Figure BDA00029963793600001011
c is a design constant, c ═ diag { c1,...,cnIs a design constant satisfying 0 < ci< 2, i ═ 1. In this example, c is selectedi＝0.5，i＝1,...,n。
After the NN weight estimates converge, a constant neural network is used
Figure BDA0002996379360000111
The approximation system is unaware of dynamics, i.e.:
Figure BDA0002996379360000112
wherein the content of the first and second substances,
Figure BDA0002996379360000113
is a weight of an adaptive neural network
Figure BDA0002996379360000114
A converged constant matrix, [ K ]1,K1+K2+1]Is composed of
Figure BDA0002996379360000115
In the stable convergence time period, epsilon is an approximation error and satisfies that epsilon is less than epsilon*。
For system unknown dynamics f in normal mode0(X(k))+g0(X(k))u0(k) Can be locally and accurately approximated by a constant neural network
Figure BDA0002996379360000116
The realization method comprises the following steps:
Figure BDA0002996379360000117
wherein the content of the first and second substances,
Figure BDA0002996379360000118
Figure BDA0002996379360000119
Figure BDA00029963793600001110
is the adaptive neural network weight in the normal mode
Figure BDA00029963793600001111
The constant matrix of the convergence is then determined,
Figure BDA00029963793600001112
{kl|kl＝l,l+2,l+4,···,l+2n,···},[ka,kb]is composed of
Figure BDA00029963793600001113
Period of stable convergence,. epsilon0To approximate the error, satisfy | ∈0|＜ε0 *。
S3: calculating the total measurable fault residual of the system;
total measurable fault residual phie(k) Can be calculated by the following formula:
φe(k)＝φf(k)-φu(k)
φf(k) for fault dynamic residuals, i.e. system dynamic residuals caused by faults:
Figure BDA00029963793600001114
φu(k) residual error compensated for the controller, i.e. the effect of the controller on the compensation of system faults:
Figure BDA00029963793600001115
wherein k is the current operation time of the sampling mechanical arm system, k-1 represents the previous operation time of the sampling mechanical arm system, h (X (k), u (k)) is the actual system dynamic state affected by small disturbance, X (k) is the system state, u (k) is the system self-adaptive controller, u (k)0(k) Represents the controller in the normal mode of operation,
Figure BDA00029963793600001116
is a weight constant matrix for approximating the neural network of the unknown dynamics of the system, and S (X (k), u (k)) is a vector [ X [, (k) ]T(k),uT(k)]TIs the input gaussian radial basis function vector.
S4: calculating a weighted recursive absolute fault residual accumulated value:
Figure BDA0002996379360000121
wherein, TaKT, K is a positive integer, T is a system sampling period,b is a parameter to be designed, b is more than 0 and less than 1, and when the mechanical arm operates in a normal mode, the total measurable fault residual phie(k) Satisfies the following conditions:
Figure BDA0002996379360000122
ε＝[ε1,...,εn]Tis an approximation error of unknown dynamics of the system and satisfies | | | Epsilon | | | luminance∞＜ε*The controller compensates the residual error to satisfy | | phiu||∞＜εu *，
Figure BDA0002996379360000123
Is the upper bound value of the system disturbance, | |. the non-woven phosphor∞Representing an infinite norm of the vector. . In this example ε*+εu *＝0.01，
Figure BDA0002996379360000124
T200, design K1, and b 0.995.
S5: designing a fault detection decision scheme:
designing adaptive thresholds
Figure BDA0002996379360000125
Figure BDA0002996379360000126
The fault detection decision scheme is characterized in that a fault residual error accumulated value e (k) obtained by real-time calculation and an adaptive threshold value are used
Figure BDA0002996379360000127
Comparing, if there is a certain time kdSo that
Figure BDA0002996379360000128
If true, it is determined at kdThe mechanical arm breaks down at all times.
In this example, x1And x2Is x1(0)＝0.1，x2(0)＝0.1；The central points of the neural network of the adaptive controller are uniformly distributed in [ -1.5,1.5 [ -1.5 [ ]]×[-1.5,1.5]×[-1.5,1.5]Upper, width is eta1＝[0.375,0.375,0.375]TThe number of nodes is 1331; the central points of the neural network of the dynamic estimator are uniformly distributed in [ -1,1 [ -1 [ ]]×[-1,1]×[1,4]Upper, width is eta2＝[0.25,0.25,0.375]TThe number of nodes is 1331.
As shown in fig. 2, the tracking trajectory of the angular displacement of the joint of the mechanical arm and the desired angular displacement is obtained, as can be seen. When the system normally operates, the tracking performance is good, the angular displacement tracking error converges to a small neighborhood of zero, and when k is 400000, the system breaks down, and the tracking error slightly fluctuates. As shown in FIG. 3, a constant neural network is obtained
Figure BDA0002996379360000131
For system unknown dynamics f0(X(k))+g0(x (k)) u (k) and it can be seen that the constructed dynamics estimator can accurately approximate the system unknown dynamics. As shown in fig. 4, the residual phi compensated by the controller is obtainedu(k) Of the change curve of (1), under normal conditions of phiu(k) Maintained in a small neighborhood around zero, and phi after failureu(k) And increases rapidly. As shown in FIG. 5, the dynamic residual phi of the fault of the present embodiment is obtainedf(k) Residual error phi from total measurable fault of systeme(k) The change curve shows that after the compensation effect of the controller is eliminated, the fault residual error information can be detected to be phif(k) Increase to phie(k) And the fault residual error accumulation speed is accelerated. As shown in FIG. 6, the fault residual error accumulated value e (k) and the adaptive threshold value of the mechanical arm operation process are obtained
Figure BDA0002996379360000132
The change curve of (2). It can be seen that the residual cumulative value e (k) increases rapidly after a fault, at kdA fault is detected in step 400029.
Example 2
A minor fault detection system of a sampling mechanical arm closed-loop control system comprises: the system comprises a model construction module, a self-adaptive neural network controller construction module, a dynamic estimator construction module, a total measurable fault residual error calculation module, an absolute fault residual error accumulated value calculation module and a fault detection decision construction module;
in this embodiment, the model construction module is configured to establish a mechanical arm dynamics model and an expected regression trajectory model based on data sampling;
in this embodiment, the adaptive neural network controller constructing module is configured to construct an adaptive neural network controller;
in this embodiment, the dynamic estimator building module is configured to build a dynamic estimator approximating the unknown dynamics of the system;
in this embodiment, the total measurable fault residual error calculation module is used for calculating a total measurable fault residual error of the system;
in this embodiment, the absolute fault residual accumulated value calculating module is configured to calculate a weighted recursive absolute fault residual accumulated value;
in this embodiment, the fault detection decision building module is configured to build a weighted recursive absolute fault residual accumulation mechanism to calculate a fault residual accumulation value in real time, and compare the fault residual accumulation value e (k) obtained through real-time calculation with a set adaptive threshold
Figure BDA0002996379360000141
Comparing, if there is a certain time kdSo that
Figure BDA0002996379360000142
If true, it is determined at kdThe mechanical arm breaks down at all times.
In this embodiment, the total measurable fault residual calculation module is used for calculating a total measurable fault residual of the system, and is specifically represented as:
φe(k)＝φf(k)-φu(k)
Figure BDA0002996379360000143
Figure BDA0002996379360000144
wherein phi isf(k) For fault dynamic residual, phiu(k) Residual errors compensated for by the controller, k is the operating time of the sampled arm system, k-1 represents the previous operating time of the sampled arm system, h (X (k), u (k)) represents the actual system dynamics affected by small disturbances, X (k) represents the system state, u (k) is a system adaptive controller, u (k)0(k) Represents the controller in the normal mode of operation,
Figure BDA0002996379360000145
representing a weight constant matrix of the neural network for approximating the unknown dynamics of the system, S (X (k), u (k)) being a vector [ X [, (k) ]T(k),uT(k)]TIs the input gaussian radial basis function vector.
In this embodiment, the absolute fault residual accumulated value calculating module is configured to calculate a weighted recursive absolute fault residual accumulated value, which is specifically represented as:
Figure BDA0002996379360000146
in this embodiment, the adaptive threshold is used
Figure BDA0002996379360000147
Expressed as:
Figure BDA0002996379360000148
wherein, TaKT, K is positive integer, T is system sampling period, b is the parameter of treating the design, satisfies 0 < b < 1, when the mechanical arm is operated under normal mode, total measurable trouble residual error phie(k) Satisfies the following conditions:
Figure BDA0002996379360000151
ε＝[ε1,...,εn]Tis an approximation error of unknown dynamics of the system and satisfies | | | Epsilon | | | luminance∞＜ε*The controller compensates the residual error to satisfy | | phiu||∞＜εu *D is the upper bound of system disturbance, | |. the luminance | |∞Representing an infinite norm of the vector.
Example 3
This embodiment provides a storage medium, which may be a storage medium such as a ROM, a RAM, a magnetic disk, or an optical disk, and the storage medium stores one or more programs, and when the programs are executed by a processor, the method for detecting minor faults of the sampling mechanical arm closed-loop control system according to embodiment 1 is implemented.
Example 4
The embodiment provides a computing device, which may be a desktop computer, a notebook computer, a smart phone, a PDA handheld terminal, a tablet computer, or other terminal devices with a display function, where the computing device includes a processor and a memory, where the memory stores one or more programs, and when the processor executes the programs stored in the memory, the method for detecting minor faults of the sampling mechanical arm closed-loop control system in embodiment 1 is implemented.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (8)

1. A small fault detection method of a sampling mechanical arm closed-loop control system is characterized by comprising the following steps:
establishing a mechanical arm dynamic model and an expected regression trajectory model based on data sampling, and designing a self-adaptive neural network controller;
constructing a dynamic estimator to approximate the unknown dynamics of the system;
calculating the total measurable fault residual of the system;
total measurable fault residual phie(k) Calculated by the following formula:
φe(k)＝φf(k)-φu(k)
φf(k) for fault dynamic residuals, i.e. system dynamic residuals caused by faults:
Figure FDA0003470893770000011
φu(k) residual error compensated for the controller, i.e. the effect of the controller on the compensation of system faults:
Figure FDA0003470893770000012
wherein k is the operation time of the sampling mechanical arm system, k-1 represents the previous operation time of the sampling mechanical arm system, h (X (k), u (k)) represents the actual system dynamic state affected by small disturbance, X (k) represents the system state, u (k) is a system self-adaptive controller, and u (k) is a system self-adaptive controller0(k) Represents the controller in the normal mode of operation,
Figure FDA0003470893770000013
representing a weight constant matrix of the neural network for approximating the unknown dynamics of the system, S (X (k), u (k)) being a vector [ X [, (k) ]T(k),uT(k)]TIs an input gaussian radial basis function vector;
calculating a weighted recursive absolute fault residual accumulated value;
designing a weighted recursive absolute fault residual error accumulation mechanism to calculate a fault residual error accumulation value e (k) in real time:
Figure FDA0003470893770000014
wherein, TaKT, K is positive integer, T is system sampling period, b is the parameter of treating the design, satisfies 0 < b < 1, when the mechanical arm is operated under normal mode, total measurable trouble residual error phie(k) Satisfies the following conditions:
Figure FDA0003470893770000021
ε＝[ε1,...,εn]Tis an approximation error of unknown dynamics of the system and satisfies | | | Epsilon | | | luminance∞＜ε*The controller compensates the residual error to satisfy | | phiu||∞＜εu *，
Figure FDA0003470893770000022
Is the upper bound value of the system disturbance, | |. the non-woven phosphor∞An infinite norm representing a vector;
designing a fault detection decision scheme:
designing adaptive thresholds
Figure FDA0003470893770000023
Figure FDA0003470893770000024
A fault detection decision scheme: the fault residual error accumulated value e (k) obtained by real-time calculation is compared with an adaptive threshold value
Figure FDA0003470893770000025
Comparing, if there is a certain time kdSo that
Figure FDA0003470893770000026
If true, it is determined at kdThe mechanical arm breaks down at all times.
2. The method for minor fault detection of a sampling mechanical arm closed-loop control system according to claim 1, wherein the mechanical arm dynamic model based on data sampling is represented as:
Figure FDA0003470893770000027
wherein, TsFor a sampling interval, the sampling time point is kTs，X(k)＝[x1(k),x2(k)]T，x1(k)＝[x1,1(k),x1,2(k),…,x1,n(k)]T、x2(k)＝[x2,1(k),x2,2(k),…,x2,n(k)]TRespectively the angular displacement and angular velocity of the joint of the mechanical arm, n corresponds to the number of joints of the mechanical arm, u (k) is control torque, f0(X (k)) and g0(X (k)) is a system unknown nonlinear function, g0(X(k))＝TsM(x1(k))-1，f0(X(k))＝x2(k)+TsM(x1(k))-1[-Vm(x1(k),x2(k))x2(k)-G(x1(k))]，M(x1(k) Is an inertia matrix of the robot arm, Vm(x1(k),x2(k) Is a centripetal force matrix, G (x)1(k) Is a gravity term, M (x)1(k)),Vm(x1(k),x2(k)),G(x1(k) Are unknown, d (k) is a bounded perturbation;
the system dynamics in the case of a fault are as follows:
Figure FDA0003470893770000028
wherein f isf(X(k))，gf(X (k)) represents the unknown nonlinear function of the fault system.
3. The method of claim 1, wherein the expected regression trajectory model is expressed as:
Figure FDA0003470893770000031
wherein x isd(k)＝[xd1(k),xd2(k)]T，xd1(k) As the position of the joint angleDesired reference track, xd2(k) Is the desired reference trajectory of the angular velocity of the joint, f (x)d1(k),xd2(k) ) is a given continuous function.
4. The method for minor fault detection of a sampling mechanical arm closed-loop control system as claimed in claim 1, wherein the designing of the adaptive neural network controller is specifically represented as:
Figure FDA0003470893770000032
the weight updating rule of the neural network is given by the following formula:
Figure FDA0003470893770000033
wherein the content of the first and second substances,
Figure FDA0003470893770000034
is an estimate of the weight of the ideal neural network, Sa(Z (k)) is a Gaussian radial basis function vector having as input vector Z (k), where [ x [, ]1 T(k),x2 T(k),xd1 T(k+2)]TFor the input of the neural network, Γ is the gain term of the weight update rate of the neural network, and z (k) ═ x1(k)-xd1(k) Is the tracking error between the angular position of the mechanical arm and the reference trajectory.
5. The method of claim 1, wherein the formation dynamics estimator approximates system unknown dynamics, the dynamics estimator represented as:
Figure FDA0003470893770000035
wherein the content of the first and second substances,
Figure FDA0003470893770000036
is x2(k) Is estimated, a ═ diag { a ═ d1,...,anIs a design parameter, satisfies 0 < | aiI < 1, i ═ 1,.. n
Figure FDA0003470893770000037
Represents an adaptive neural network for learning unknown dynamics of the system,
Figure FDA0003470893770000038
an estimate of the weights of the ideal neural network is represented,
Figure FDA0003470893770000039
an input vector which is a radial basis function S (X (k), u (k));
the weight updating rule of the neural network is given by the following formula:
Figure FDA0003470893770000041
wherein the content of the first and second substances,
Figure FDA0003470893770000042
C＝diag{c1,...,cnis a design constant satisfying 0 < ci＜2,i＝1,...,n；
After the NN weight estimates converge, a constant neural network is used
Figure FDA0003470893770000043
The approximation system is unaware of dynamics, i.e.:
Figure FDA0003470893770000044
wherein the content of the first and second substances,
Figure FDA0003470893770000045
is a weight of an adaptive neural network
Figure FDA0003470893770000046
A converged constant matrix, [ K ]1,K1+K2+1]Is composed of
Figure FDA0003470893770000047
Time period of stable convergence, [ epsilon ]1,...,εn]TTo approximate the error, satisfy | | | Epsilon | | | luminance∞＜ε*；
For system unknown dynamics f in normal mode0(X(k))+g0(X(k))u0(k) Can be locally and accurately approximated by a constant neural network
Figure FDA0003470893770000048
The realization method comprises the following steps:
Figure FDA0003470893770000049
wherein the content of the first and second substances,
Figure FDA00034708937700000410
is the adaptive neural network weight in the normal mode
Figure FDA00034708937700000411
The constant matrix of the convergence is then determined,
Figure FDA00034708937700000412
{kl|kl＝l,l+2,l+4,···,l+2n,···},[ka,kb]is composed of
Figure FDA00034708937700000413
Period of stable convergence,. epsilon0＝[ε01,...,ε0n]TTo approximate the error, satisfy | | ε0||∞＜ε0 *。
6. A minor fault detection system of a sampling mechanical arm closed-loop control system is characterized by comprising: the system comprises a model construction module, a self-adaptive neural network controller construction module, a dynamic estimator construction module, a total measurable fault residual error calculation module, an absolute fault residual error accumulated value calculation module and a fault detection decision construction module;
the model construction module is used for establishing a mechanical arm dynamics model and an expected regression trajectory model based on data sampling;
the self-adaptive neural network controller constructing module is used for constructing a self-adaptive neural network controller;
the dynamic estimator building module is used for building a dynamic estimator to approximate unknown dynamic of a system;
the total measurable fault residual error calculation module is used for calculating the total measurable fault residual error of the system;
the total measurable fault residual error calculation module is used for calculating the total measurable fault residual error of the system, and is specifically represented as follows:
φe(k)＝φf(k)-φu(k)
Figure FDA0003470893770000051
Figure FDA0003470893770000052
wherein phi isf(k) For fault dynamic residual, phiu(k) Residual errors compensated for by the controller, k is the operating time of the sampled arm system, k-1 represents the previous operating time of the sampled arm system, h (X (k), u (k)) represents the actual system dynamics affected by small disturbances, X (k) represents the system state, u (k) is a system adaptive controller, u (k)0(k) Represents the controller in the normal mode of operation,
Figure FDA0003470893770000053
representing a weight constant matrix of the neural network for approximating the unknown dynamics of the system, S (X (k), u (k)) being a vector [ X [, (k) ]T(k),uT(k)]TIs an input gaussian radial basis function vector;
the absolute fault residual accumulated value calculating module is used for calculating a weighted recursion absolute fault residual accumulated value;
the absolute fault residual accumulated value calculating module is used for calculating a weighted recursive absolute fault residual accumulated value, and is specifically represented as:
Figure FDA0003470893770000054
the adaptive threshold value
Figure FDA0003470893770000055
Expressed as:
Figure FDA0003470893770000056
wherein, TaKT, K is positive integer, T is system sampling period, b is the parameter of treating the design, satisfies 0 < b < 1, when the mechanical arm is operated under normal mode, total measurable trouble residual error phie(k) Satisfies the following conditions:
Figure FDA0003470893770000061
ε＝[ε1,...,εn]Tis an approximation error of unknown dynamics of the system and satisfies | | | Epsilon | | | luminance∞＜ε*The controller compensates the residual error to satisfy | | phiu||∞＜εu *，
Figure FDA0003470893770000062
Is the upper bound value of the system disturbance, | |. the non-woven phosphor∞An infinite norm representing a vector;
the fault detection decision building module is used for building a weighted recursion absolute fault residual error accumulation mechanism to calculate a fault residual error accumulation value in real time, and the fault residual error accumulation value e (k) obtained by real-time calculation and a set self-adaptive threshold value
Figure FDA0003470893770000063
Comparing, if there is a certain time kdSo that
Figure FDA0003470893770000064
If true, it is determined at kdThe mechanical arm breaks down at all times.
7. A storage medium storing a program, wherein the program when executed by a processor implements a glitch detection method of a sampling manipulator closed-loop control system of any one of claims 1-5.
8. A computing device comprising a processor and a memory for storing a program executable by the processor, wherein the processor, when executing the program stored by the memory, implements a glitch detection method for a sampling manipulator closed-loop control system as claimed in any one of claims 1 to 5.
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