CN114217595B - X-type rudder AUV fault detection method based on interval observer - Google Patents
X-type rudder AUV fault detection method based on interval observer Download PDFInfo
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Abstract
The invention provides an interval observer-based X-shaped rudder AUV fault detection method, which is used for researching the problem that each parameter in an underwater robot dynamics model has a larger modeling error, and an RBF neural network is used for carrying out online identification on the system modeling error, and whether the system fails or not is judged directly through residual signals output by the interval observer and an actual system.
Description
Technical Field
The invention relates to the technical field of underwater robot fault diagnosis, in particular to an underwater robot fault detection method with larger modeling errors of various parameters in a dynamic model due to the influence of factors such as external environment and the like.
Background
The underwater robot has wider application in a complex marine environment, and in the integral structure of the X-shaped rudder underwater robot, the X-shaped rudder is a key execution mechanism for realizing normal navigation of the X-shaped rudder underwater robot, and the navigation safety of the underwater robot can be seriously threatened by the fault of the X-shaped rudder underwater robot. Therefore, in order to improve the reliability and safety of the navigation of the X-shaped rudder underwater robot, the research on the fault detection method of the X-shaped rudder of the underwater robot has very important significance.
At present, in the field of fault diagnosis of underwater robots, domestic and foreign scholars mainly take the research of the output loss of an underwater robot propeller and the faults of a sensor as main materials, and at present, as the number of serial products of the X-shaped rudder underwater robot is relatively small, the research related to the faults of the X-shaped rudder underwater robot is not yet mature.
The current application of the fault detection method based on the observer needs to be based on the premise of establishing an accurate system analysis model, and the established model must be capable of reflecting the mechanism of system fault occurrence. However, in practice, due to the influence of various uncertain factors outside, it is difficult to obtain an accurate system analysis model, and the method for establishing the accurate analysis model of the nonlinear system and the practical application thereof need to be studied in depth. However, in practical engineering application, detecting and accurately estimating the faults of the system often takes time and effort, and at this time, interval estimation of the faults shows application value. And the fact that various parameters in a dynamic model obtained through model identification have large deviation from reality due to the influence of factors such as environment is considered. Based on the above-mentioned problems, a fault detection method based on a neural network interval observer is proposed in this patent.
Disclosure of Invention
The invention aims to provide an X-shaped rudder underwater robot fault detection method based on a neural network interval observer. The invention can ensure that whether the X-shaped rudder fails or not can be accurately detected even if the underwater robot system is influenced by factors such as external environment and the like and has larger modeling error in the dynamic model.
The purpose of the invention is realized in the following way: the method comprises the following steps:
step one: the method comprises the steps of combining an X-shaped rudder underwater robot dynamics model, carrying out linear transformation on state quantity, and introducing system model modeling error uncertainty into the model;
step two: combining the result of the step one, designing an observer of the fault detection zone of the X-shaped rudder underwater robot;
step three: and (3) combining the result of the step two, and verifying the stability of the designed interval observation system according to the Lyapunov theory.
The invention also includes such structural features:
1. the first step specifically comprises: the deflection values of four rudder blades of the X-shaped rudder underwater robot are sequentially recorded as: [ delta ] 1 δ 2 δ 3 δ 4 ] T The thrust and moment distribution relation of the X-shaped rudder and the propeller is as follows:
wherein X is T Is the thrust of the propeller; x is X M Torque generated for the propeller; u is the navigation speed of the underwater robot in the x direction; delta * Rudder angle for the first rudder turn; x is X ** ，Is a hydrodynamic parameter related to the first rudder blade; definition: x= [ x ] 1 ,x 2 ] T ，x 1 ＝η，x 2 ＝J(η)v
The method for transforming the X-shaped rudder underwater robot dynamics model into a state space equation comprises the following steps:
wherein:k is a damage degree distribution matrix of rudder blades;wherein K is more than or equal to 0 and less than or equal to 1; e (E) a Is a fault distribution matrix of rudder blades; t is a propeller thrust matrix; f (f) a (t) is a rudder blade fault function; />Wherein d (t) is external interference;
modeling uncertainty in an X-rudder underwater robot system is expressed in the following form:
wherein,representing theoretical values of corresponding variables in the underwater robot system model; m is M η ，C η ，D η ，g η Representing actual values of corresponding variables in the underwater robot system model; ΔM η ，ΔC η ，ΔD η ，Δg η Representing uncertainty of corresponding variables in the underwater robot system model;
for the faults of the X-shaped rudder underwater robot actuator, let u '=u+deltau, wherein u is the designed control quantity, u' is the actual control quantity, and deltau is the system uncertainty caused by the faults and the like; the uncertainty of the system model of the X-shaped rudder underwater robot is expressed as:
then there are:
2. the second step specifically comprises: through analysis and research on modeling errors of the system model in the first step, a neural network interval observer is designed as follows:
wherein:is the RBF neural network output value used for estimating the uncertainty term delta of the system; the uncertain term delta of the system model is identified on line by adopting an RBF neural network, and the specific expression of the RBF neural network is given as follows:
wherein,the difference between the output of the upper (lower) boundary of the interval observer and the actual system output; w epsilon R 6×k A weight matrix between an implicit layer and an output layer of the RBF neural network; m and sigma are respectively a center vector and a width parameter in the radial basis function of the RBF neural network;
model uncertainty delta has optimal approximation valueCan be expressed as:
wherein: w (W) * To obtain optimal value through RBF neural networkCorresponding parameters of time W, wherein the upper bound of the optimal weight satisfies the condition of W F ≤W M ，W M Is constant, ε is the optimal value +.>Between the system uncertainty term deltaAnd it satisfies:
after the model uncertainty term delta is approximated on line through the RBF neural network, the estimated value of the obtained model uncertainty is as follows:
its uncertainty error equationCan be represented by the following formula:
the hidden layer output error is defined as:
the method can obtain:
weight evaluation error in mediumIts interference term w can be expressed as:
defining states and output errors in case no failure of the X-rudder occurs:
thereby obtaining an error dynamic system:
from the definition of the interval observer, it can be obtained: e, e + (t)≥0，e - (t)≥0，
The following network weight adaptive law is designed:
wherein: f (F) i ＝F i T ＞0,k i And (2) representing the network weight adaptive rate parameters of the upper-bound observer and the lower-bound observer respectively.
3. The third step specifically comprises: defining a Lyapunov function:
wherein: p=p T >0 is satisfied (A-L) T A matrix of p+p (a-L) = -Q conditions; q is an arbitrary positive definite matrix;
the derivation of the above is available:
the error dynamic system formula and the network weight self-adaptive law are brought into the above formula to obtain:
wherein:
the simplified process is as follows:
wherein: gamma ray 1 ＝k 1 F 1 ，α 1 ＝W M +c 1 /γ 1 ；
Can obtain the derivative of the guaranteed VThe conditions for the semi-negative are as follows:
the lower boundary interval observer guarantees the derivative of VThe conditions for the semi-negative are:
at the spherical radius r + 、r - Derivatives other thanAll are negative, the state estimation error of the established neural network interval observer is +.>Is->Ultimately being consistently bounded.
Compared with the prior art, the invention has the beneficial effects that: the existing observer-based fault detection method needs to set a proper threshold according to the generated residual signal, and analyze and evaluate the state of the system. However, various uncontrollable factors often exist in the actual running process of the system, so that the problem of missing report and false report of fault information of an observer can be caused by the wrong selection of the threshold value in the fault detection process of the system, and therefore, how to select a proper threshold value interval is always difficult to study currently; in the research of the fault diagnosis method, the fault detection of the motion state of the observed system can be realized by judging whether the actual output of the observed system is in the estimated interval output by the constructed upper-bound observer and lower-bound observer. Compared with the traditional fault detection method, the interval observer does not need to design an additional threshold value, and the residual signal can be used as a direct judgment basis for judging whether the system fault occurs or not. The method is simpler and more visual, is convenient to design, can be directly applied to fault decision, and solves the problem that the threshold value of the traditional observer is difficult to select in the fault detection method.
Drawings
FIG. 1 is a flow chart of the present patent failure detection scheme.
Fig. 2 is a graph showing the results of the speed profile of the present invention patent in the absence of faults.
Fig. 3 is a speed profile result in the case of a rudder blade damage failure of the present invention patent.
Fig. 4 shows the speed profile results in the case of a stuck rudder blade failure according to the present invention.
Fig. 5 is a speed profile result in the case of failure of the rudder blade of the present invention.
Fig. 6 is a speed profile result in the case of a rudder blade constant deviation fault of the present invention patent.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
Fig. 1 is a flowchart of the fault detection process of the inter-underwater robot observer of the present invention. Referring to fig. 1, the specific implementation steps of the method for detecting the failure of the underwater robot based on the neural network interval observer are as follows:
step (1): the method comprises the steps of combining an underwater robot dynamics model, carrying out linear transformation on state quantity, and introducing system model modeling error uncertainty into the model;
conventional underwater robot dynamics models can be generally described in the form of:
wherein eta is the attitude vector of the underwater robot under a fixed coordinate system, eta epsilon R 6×1 The method comprises the steps of carrying out a first treatment on the surface of the v is the linear velocity and angular velocity vector of the underwater robot in the hull coordinate system, v ε R 6×1 The method comprises the steps of carrying out a first treatment on the surface of the M is mass and inertia matrix, M epsilon R 6×6 The method comprises the steps of carrying out a first treatment on the surface of the C (v) is the Coriolis force matrix and the centripetal force matrix, C (v) E R 6×6 The method comprises the steps of carrying out a first treatment on the surface of the D (v) is a fluid resistance matrix, D (v) εR 6×6 The method comprises the steps of carrying out a first treatment on the surface of the g (eta) is a matrix of restoring force and moment, g (eta) epsilon R 6×1 The method comprises the steps of carrying out a first treatment on the surface of the τ is acting force and moment, τ ε R 6×1 。
The deflection values of four rudder blades of the X-shaped rudder underwater robot are sequentially recorded as: [ delta ] 1 δ 2 δ 3 δ 4 ] T The thrust and torque distribution relationship of the X-rudder and the propeller is as follows:
wherein X is T Is the thrust of the propeller; x is X M Torque generated for the propeller; u is the navigation speed of the underwater robot in the x direction; delta * Rudder angle for the first rudder turn; x is X ** ，The hydrodynamic parameters related to the rudder blade of the first embodiment are related to the length of the hull and the shape and area of the rudder.
The following definitions are made:
x＝[x 1 ,x 2 ] T (4)
wherein x is 1 ＝η，x 2 ＝J(η)v。
The X-shaped rudder underwater robot dynamics model is transformed into a form of a state space equation, and can be expressed as follows:
wherein:
F(x 1 ,x 2 ,t)＝J(x 1 )M -1 (x 1 )J T (x 1 )[-J -T (x 1 )C(x 1 ,x 2 )J -1 (x 1 )x 2 -J -T (x 1 )D(x 1 ,x 2 )J -1 (x 1 )x 2 -J -T (x 1 )g(x 1 )]
u(t)＝δ(t)
k is a damage degree distribution matrix of rudder blades; wherein K is more than or equal to 0 and less than or equal to 1;
E a is a fault distribution matrix of rudder blades;
t is a propeller thrust matrix;
f a (t) is a rudder blade fault function;
wherein d (t) is the external disturbance.
Because the motion of the X-shaped rudder underwater robot has the characteristics of strong nonlinearity and strong coupling, the characteristic causes great uncertainty of each parameter in the established underwater robot motion model; meanwhile, factors such as unknown disturbance in the external environment can also cause certain influence on the underwater robot motion system model. The modeling error existing in the system model is used as an uncertainty item of the system, and the system with model uncertainty is described.
Modeling uncertainty in an X-rudder underwater robot system is expressed in the following form:
wherein,
representing theoretical values of corresponding variables in the underwater robot system model;
M η ，C η ，D η ，g η representing actual values of corresponding variables in the underwater robot system model;
ΔM η ，ΔC η ，ΔD η ，Δg η representing the uncertainty of the corresponding variable in the model of the underwater robot system.
For the faults of the X-shaped rudder underwater robot actuator, let u '=u+deltau, wherein u is the designed control quantity, u' is the actual control quantity, and deltau is the system uncertainty caused by the faults and the like; according to equation (6), the X-rudder underwater robot system model uncertainty can be expressed as:
then equation (6) can be rewritten as:
in summary, the dynamics model of the X-rudder underwater robot constructed based on the model identification method has great uncertainty in actual work, and the existence of these factors can directly affect the motion control of the underwater robot system. Therefore, the method takes the influence factors as unified uncertainty, researches the method for estimating the influence factors on line, and takes the obtained estimated value of the uncertainty of the system as an uncertainty item in the interval observer, so that the observation performance of the designed neural network interval observer can be further improved.
Step (2): combining the result of the step (1), designing a neural network fault detection interval observer of the rudder fault of the X-shaped rudder underwater robot;
the analysis and research on the modeling error of the system model in the step (1) can be known: if the uncertain item of the underwater robot system is not identified, a great difference exists between the established observer model and the actual system, so the patent aims at the problem and designs a neural network interval observer as follows:
wherein:
is the RBF neural network output value used to estimate the system uncertainty term delta.
In the patent, an uncertain term delta of a system model is identified on line by adopting an RBF neural network, and the specific expression of the RBF neural network is given as follows:
wherein,the difference between the output of the upper (lower) boundary of the interval observer and the actual system output; w epsilon R 6×k A weight matrix between an implicit layer and an output layer of the RBF neural network; m and sigma are the center vector and width parameters, respectively, in the radial basis function of the RBF neural network.
Theoretically, there is an optimal approximation of the model uncertainty ΔCan be expressed as:
W * to obtain optimal value through RBF neural networkCorresponding parameters of time W, wherein the upper bound of the optimal weight satisfies the condition of W F ≤W M ，W M Is constant, ε is the optimal value +.>And system uncertainty term deltaApproximation error between, and which satisfies: />
After the model uncertainty term delta is approximated on line through the RBF neural network, the estimated value of the obtained model uncertainty is as follows:
its uncertainty error equationCan be represented by the following formula:
the hidden layer output error is defined as:
combining formula (13) with formula (14) is obtainable:
weight evaluation error in mediumIts interference term w can be expressed as:
when no failure occurs in the X-rudder, the state and the output error are defined according to the formulas (8), (9) and (13):
thereby obtaining an error dynamic system:
from the definition of the interval observer, it can be obtained: e, e + (t)≥0，e - (t)≥0，
The following network weight adaptive law is designed:
wherein:
F i ＝F i T ＞0,k i and (2) representing the network weight adaptive rate parameters of the upper-bound observer and the lower-bound observer respectively.
Step (3): and (3) combining the result of the step (2), and verifying the stability of the designed neural network fault detection interval observation system according to the Lyapunov theory.
The Lyapunov function is defined as follows:
wherein:
P＝P T >0 is satisfied (A-L) T A matrix of p+p (a-L) = -Q conditions;
q is an arbitrary positive definite matrix.
Deriving the formula (20) can be obtained:
the error dynamic system formula (18) and the network weight self-adaptive law formula (19) can be obtained by the following formula:
wherein:
the simplification of formula (22) can be obtained:
wherein:
γ 1 ＝k 1 F 1 ，
α 1 ＝W M +c 1 /γ 1 。
can obtain the derivative of the guaranteed VThe conditions for the semi-negative are as follows:
similarly, the lower inter-zone observer guarantees the derivative of VThe conditions for the semi-negative are:
since the above parameters are all bounded terms, this means that the radius of the sphere is r + 、r - Derivatives other thanAre all negative, so that the state estimation error of the neural network interval observer established by the method can be ensured>Is->Ultimately being consistently bounded.
(4) Application case
The invention discloses an X-shaped rudder underwater robot fault detection method based on a neural network interval observer, which is designed for verifying the effectiveness of the method, and comprises the following steps of:
1) Under the condition of verification of no fault, the neural network interval observer in the patent can effectively estimate the speed curve of the X-shaped rudder underwater robot;
2) When t=15s, rudder blade damage, rudder blade locking, rudder blade failure and rudder blade constant deviation faults are respectively designed for the rudder 1 of the X-shaped rudder of the underwater robot, and the validity of the neural network fault detection interval observer designed by the patent is verified.
In the simulation experiment verification process, the initial state, external interference and the like of the X-shaped rudder underwater robot are the same.
The results obtained by using the Matlab/Simulink simulation platform are shown in FIGS. 2-6, respectively.
According to the simulation result of fig. 2, when the X-rudder underwater robot has no fault, the actual output speed of the system is between two estimated values of the section observer, which proves that the designed section observer can effectively track and estimate the system.
According to the simulation results of fig. 3 to 6, when the X-type rudder underwater robot has no fault, the actual output speed of the system is between two estimated values of the section observer at all times, but when t=15s, the actual output of the system part speed exceeds the section range of the section observer due to the rudder blade fault of the rudder 1, which proves that the designed neural network section observer can effectively detect the fault of the system.
In summary, the invention researches the problem that each parameter in the dynamics model of the underwater robot has larger modeling error, uses RBF neural network to perform online identification on the modeling error of the system, directly judges whether the system has faults or not through the residual signals output by the interval observer and the actual system, and is suitable for the field of fault diagnosis of the underwater robot.
Claims (3)
1. The X-shaped rudder AUV fault detection method based on the interval observer is characterized by comprising the following steps of:
step one: the method comprises the steps of combining an X-shaped rudder underwater robot dynamics model, carrying out linear transformation on state quantity, and introducing system model modeling error uncertainty into the model;
step two: combining the result of the step one, designing an observer of the fault detection zone of the X-shaped rudder underwater robot; through analysis and research on modeling errors of the system model in the first step, a neural network interval observer is designed as follows:
wherein:is the RBF neural network output value used for estimating the uncertainty term delta of the system; the uncertain term delta of the system model is identified on line by adopting an RBF neural network, and the specific expression of the RBF neural network is given as follows:
wherein,the difference value between the output of the upper or lower boundary of the interval observer and the output of the actual system; w epsilon R 6×k A weight matrix between an implicit layer and an output layer of the RBF neural network; m and sigma are respectively a center vector and a width parameter in the radial basis function of the RBF neural network;
model uncertainty delta has optimal approximation valueCan be expressed as:
wherein: w (W) * To obtain optimal value through RBF neural networkCorresponding parameters of time W, wherein the upper bound of the optimal weight satisfies the condition of W F ≤W M ，W M Is constant, ε is the optimal value +.>Approximation error with the system uncertainty term Δ, and it satisfies:
after the model uncertainty term delta is approximated on line through the RBF neural network, the estimated value of the obtained model uncertainty is as follows:
its uncertainty error equationCan be represented by the following formula:
the hidden layer output error is defined as:
the method can obtain:
weight evaluation error in mediumIts interference term w can be expressed as:
defining states and output errors in case no failure of the X-rudder occurs:
e + ＝x + -x,
thereby obtaining an error dynamic system:
from the definition of the interval observer, it can be obtained: e, e + (t)≥0，e - (t)≥0，
The following network weight adaptive law is designed:
wherein: f (F) i ＝F i T ＞0,k i The network weight self-adaptive rate parameters of the upper-bound observer and the lower-bound observer are respectively represented by more than 0, i=1 and 2;
step three: and (3) combining the result of the step two, and verifying the stability of the designed interval observation system according to the Lyapunov theory.
2. The method for detecting an fault of an X-rudder AUV based on an interval observer according to claim 1, wherein the first step specifically comprises: the deflection values of four rudder blades of the X-shaped rudder underwater robot are sequentially recorded as: [ delta ] 1 δ 2 δ 3 δ 4 ] T The thrust and moment distribution relation of the X-shaped rudder and the propeller is as follows:
wherein X is T Is the thrust of the propeller; x is X M Torque generated for the propeller; u is the navigation speed of the underwater robot in the x direction; delta * Rudder angle for the first rudder turn; x is X ** ，Is a hydrodynamic parameter related to the first rudder blade; definition: x= [ x ] 1 ,x 2 ] T ，x 1 ＝η，x 2 ＝J(η)v
The method for transforming the X-shaped rudder underwater robot dynamics model into a state space equation comprises the following steps:
wherein:k is a damage degree distribution matrix of rudder blades; wherein K is more than or equal to 0 and less than or equal to 1; e (E) a Is a fault distribution matrix of rudder blades; t is a propeller thrust matrix; f (f) a (t) is a rudder blade fault function; />Wherein d (t) is external interference;
modeling uncertainty in an X-rudder underwater robot system is expressed in the following form:
wherein,representing theoretical values of corresponding variables in the underwater robot system model; m is M η ，C η ，D η ，g η Representing actual values of corresponding variables in the underwater robot system model; ΔM η ，ΔC η ，ΔD η ，Δg η Representing uncertainty of corresponding variables in the underwater robot system model;
for the faults of the X-shaped rudder underwater robot actuator, let u '=u+deltau, wherein u is the designed control quantity, u' is the actual control quantity, and deltau is the system uncertainty caused by the fault reasons; the uncertainty of the system model of the X-shaped rudder underwater robot is expressed as:
then there are:
3. the method for detecting the fault of the AUV of the X-type rudder based on the interval observer according to claim 1, wherein the third step specifically comprises the following steps: defining a Lyapunov function:
wherein: p=p T >0 is satisfied (A-L) T A matrix of p+p (a-L) = -Q conditions; q is an arbitrary positive definite matrix;
the derivation of the above is available:
the error dynamic system formula and the network weight self-adaptive law are brought into the above formula to obtain:
wherein:
the simplified process is as follows:
wherein: gamma ray 1 ＝k 1 F 1 ，α 1 ＝W M +c 1 /γ 1 ；
Can obtain the derivative of the guaranteed VThe conditions for the semi-negative are as follows:
the lower boundary interval observer guarantees the derivative of VThe conditions for the semi-negative are:
at the spherical radius r + 、r - Derivatives other thanAll are negative, the state estimation error of the established neural network interval observer is +.>Is->Ultimately being consistently bounded.
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