CN114217595B - X-type rudder AUV fault detection method based on interval observer - Google Patents

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

A fault detection method for X-type rudder AUV based on interval observer

Technical field

The patent of this invention relates to the field of underwater robot fault diagnosis technology, and in particular to an underwater robot fault detection method that causes large modeling errors in various parameters in the dynamic model due to the influence of external environment and other factors.

Background technique

Underwater robots are widely used in complex marine environments. In the overall structure of the X-rudder underwater robot, the X-rudder is the key actuator to achieve normal navigation of the X-rudder underwater robot. Its failure may be serious. Threaten the navigation safety of underwater robots. Therefore, in order to improve the reliability and safety of the X-rudder underwater robot's navigation, it is of great significance to study the fault detection method of the X-rudder of the underwater robot.

At present, in the field of underwater robot fault diagnosis, domestic and foreign scholars mainly focus on the research on underwater robot propeller output loss and sensor failure. At this stage, due to the relatively small number of X-type rudder underwater robot series products, This leads to the fact that there is no relatively mature theory in the research related to its failure.

The application of current observer-based fault detection methods requires the establishment of an accurate system analytical model, and the established model must be able to reflect the mechanism of system failure. However, in fact, due to the influence of various external uncertain factors, it is difficult to obtain an accurate analytical model of the system. In-depth research is needed on the establishment methods and practical applications of accurate analytical models of nonlinear systems. However, in actual engineering applications, detecting and accurately estimating system faults is often time-consuming and labor-intensive. At this time, interval estimation of faults shows its application value. Moreover, it is considered that due to the influence of environmental and other factors, there is a large deviation between the parameters in the dynamic model obtained through model identification and the actual situation. Based on the above problems, a fault detection method based on neural network interval observer is proposed in this patent.

Contents of the invention

The purpose of the patent of this invention is to provide a fault detection method for an X-type rudder underwater robot based on a neural network interval observer. The patented invention can ensure that even when the underwater robot system is affected by factors such as the external environment, resulting in large modeling errors in its dynamic model, it can still accurately detect whether the X-shaped rudder is faulty.

The purpose of the present invention is achieved in this way: the steps are as follows:

Step 1: Combined with the X-rudder underwater robot dynamics model, linearly transform the state quantity, and introduce system model modeling error uncertainty into the model;

Step 2: Combined with the results of Step 1, design the fault detection interval observer for the X-type rudder underwater robot;

Step 3: Combined with the results of Step 2, verify the stability of the designed interval observation system based on Lyapunov theory.

The present invention also includes the following structural features:

1. Step 1 specifically includes: recording the deflection values of the four rudder blades of the X-type rudder underwater robot in sequence as: [δ ₁ δ ₂ δ ₃ δ ₄ ] ^T , the thrust and moment distribution relationship between the X-type rudder and the propeller for:

Among _{them, X T is} the _thrust of _the propeller; is the hydrodynamic parameter related to the *th rudder blade; definition: x=[x ₁ ,x ₂ ] ^T , x ₁ =η, x ₂ =J(η)v

The X-rudder underwater robot dynamic model is transformed into a state space equation in the form:

in: K is the damage degree distribution matrix of the rudder blade; where 0≤K≤1; E _a is the fault distribution matrix of the rudder blade; T is the propeller thrust matrix; f _a (t) is the rudder blade failure function;/> Among them, d(t) is external interference;

The modeling uncertainty in the X-rudder underwater robot system is expressed in the following form:

in, Represents the theoretical values of the corresponding variables in the underwater robot system model; M _η , C _η , D _η , and g _η represent the actual values of the corresponding variables in the underwater robot system model; ΔM _η , ΔC _η , ΔD _η , and Δg _η represent water The uncertainty of the corresponding variables in the robot system model;

For the X-type rudder underwater robot actuator failure, let u′=u+Δu, where u is the designed control quantity, u′ is the actual control quantity, and Δu is the system uncertainty caused by the fault and other reasons; let the X-type rudder The uncertainty of the underwater robot system model is expressed as:

Then there are:

2. Step 2 specifically includes: through the analysis and research on the modeling error of the system model in step 1, design the neural network interval observer as shown below:

in: is the output value of the RBF neural network used to estimate the system uncertainty term Δ; the RBF neural network is used to identify the uncertainty term Δ of the system model online. The specific expression of the given RBF neural network is:

in, is the difference between the output of the upper bound (lower bound) of the interval observer and the actual system output; W∈R ^6×k is the weight matrix between the hidden layer and the output layer of the RBF neural network; m and σ are the RBF neural network respectively. The center vector and width parameters in the radial basis function;

Model uncertainty Δ has an optimal approximation value It can be expressed as:

Among them: W ^* is the optimal value obtained through RBF neural network is the corresponding parameter of W, where the upper bound of the optimal weight satisfies: ||W|| _F ≤ _{W M} , W _M is a constant value, and ε is the optimal value/> The approximation error between and the system uncertainty term Δ, and it satisfies:

After online approximation of the model uncertainty term Δ through the RBF neural network, the estimated value of the model uncertainty is:

Its uncertainty error equation It can be expressed by the following formula:

Define the hidden layer output error as:

Available:

The weight evaluation error in the formula Its interference term w can be expressed as:

Define the status and output error when no fault occurs in the X-type rudder:

This leads to the error dynamic system:

According to the definition of interval observer, we can get: e ⁺ (t) ≥ 0, e ^- (t) ≥ 0,

Design the following network weight adaptive law:

Among them: _Fi = _Fi ^T > 0, k _i > 0, i = 1, 2, representing the network weight adaptation rate parameters of the upper bound observer and the lower bound observer respectively.

3. Step three specifically includes: defining the Lyapunov function:

Among them: P=P ^T >0 is a matrix that satisfies the condition of (AL) ^T P+P(AL)=-Q; Q is any positive definite matrix;

Derivating the above equation we can get:

By incorporating the error dynamic system formula and network weight adaptive law into the above formula, we can get:

in:

After simplification we get:

Among them: γ ₁ =k ₁ F ₁ , α ₁ =W _M +c ₁ /γ ₁ ;

It is possible to obtain the derivative that guarantees V The conditions for seminegative definiteness are as follows:

The lower bound interval observer guarantees the derivative of V The conditions for seminegative definiteness are:

Derivatives outside the spherical radius r ⁺ , r ^- are all negative definite, the state estimation error of the established neural network interval observer/> and/> Ultimately it is uniformly bounded.

Compared with the existing technology, the beneficial effect of the present invention is that the existing observer-based fault detection method needs to set an appropriate threshold based on the generated residual signal to analyze and evaluate the status of the system. However, there are often various uncontrollable factors in the actual operation of the system. As a result, in the process of fault detection of the system, the wrong selection of the threshold will lead to the omission of fault information and false alarms in the observer. Therefore, how to choose The appropriate threshold interval has always been a difficulty in current research; and since the interval observer can give the upper and lower bounds of the system state estimate, in the study of fault diagnosis methods, it can be judged whether the actual output of the observed system is within the constructed upper bound The observer and the lower bound observer output are within the estimated interval, thereby achieving fault detection of the motion state of the observed system. Compared with traditional fault detection methods, the interval observer does not need to design additional thresholds, and its residual signal can be used as a direct basis for judging whether a system fault occurs or not. This method is simpler and more intuitive, and is convenient to design. It can be directly applied to fault decision-making and overcomes the difficulty of threshold selection in fault detection methods of traditional observers.

Description of the drawings

Figure 1 is a flow chart of the patented fault detection solution of the present invention.

Figure 2 shows the speed curve results of the patent of the invention under no fault condition.

Figure 3 is the speed curve result of the rudder blade damage failure of the patent of the present invention.

Figure 4 is the speed curve result when the rudder blade stuck in the patented invention fails.

Figure 5 is the speed curve result when the rudder blade of the invention patent fails.

Figure 6 shows the speed curve results of the rudder blade patented by the present invention under constant deviation failure.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 is a flow chart of the fault detection process of the underwater robot interval observer patented by the present invention. Combined with Figure 1, the specific implementation steps of an underwater robot fault detection method based on a neural network interval observer are as follows:

Step (1): Combined with the underwater robot dynamics model, linearly transform the state quantity, and introduce system model modeling error uncertainty into the model;

A conventional underwater robot dynamics model can generally be described in the following form:

Among them, eta is the attitude vector of the underwater robot in the fixed coordinate system, eta∈R ^6×1 ; v is the linear velocity and angular velocity vector of the underwater robot in the hull coordinate system, v∈R ^6×1 ; M is Mass and inertia matrix, M∈R ^6×6 ; C(v) is the Coriolis force matrix and centripetal force matrix, C(v)∈R ^6×6 ; D(v) is the fluid resistance matrix, D(v)∈R ^6×6 ; g(η) is the restoring force and moment matrix, g(η)∈R ^6×1 ; τ is the action force and moment, τ∈R ^6×1 .

The deflection values of the four rudder blades of the X-type rudder underwater robot are recorded in sequence as: [δ ₁ δ ₂ δ ₃ δ ₄ ] ^T . The thrust and moment distribution relationship between the X-type rudder and the propeller is as follows:

Among _{them, X T is} the _thrust of _the propeller; is the hydrodynamic parameter related to the first rudder blade, and its value is related to the length of the hull, the shape and area of the rudder.

The following definitions are made below:

x＝[x ₁ ,x ₂ ] ^T (4)

Among them, x ₁ =η, x ₂ =J(η)v.

The X-rudder underwater robot dynamic model is transformed into the form of a state space equation, which can be expressed as:

in:

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 the damage degree distribution matrix of the rudder blade; where 0≤K≤1;

E _a is the fault distribution matrix of the rudder blade;

T is the propeller thrust matrix;

f _a (t) is the rudder blade failure function;

Among them, d(t) is external interference.

Since the motion of the X-rudder underwater robot has strong nonlinearity and strong coupling, this characteristic leads to great uncertainty in the parameters of the established underwater robot motion model; at the same time, unknown factors in the external environment Factors such as disturbances will also have a certain impact on the underwater robot motion system model. This patent uses the modeling error existing in the system model as the uncertainty term of the system to describe the system with model uncertainty.

The modeling uncertainty in the X-rudder underwater robot system is expressed in the following form:

in,

Represents the theoretical value of the corresponding variable in the underwater robot system model;

M _η , C _η , D _η , g _η represent the actual values of the corresponding variables in the underwater robot system model;

ΔM _η , ΔC _η , ΔD _η , Δg _η represent the uncertainties of the corresponding variables in the underwater robot system model.

For the X-type rudder underwater robot actuator failure, let u′=u+Δu, where u is the designed control quantity, u′ is the actual control quantity, and Δu is the system uncertainty caused by faults and other reasons; according to Equation (6 ), the uncertainty of the X-rudder underwater robot system model can be expressed as:

Then equation (6) can be rewritten as:

In summary, the X-rudder underwater robot dynamic model constructed based on the model identification method has great uncertainties in actual work. The existence of these factors will directly affect the motion control of the underwater robot system. Therefore, this patent treats these influencing factors as unified uncertainties, studies methods for online estimation, and uses the obtained estimated value of system uncertainty as the uncertainty term in the interval observer, which can further improve the design Observation performance of neural network interval observer.

Step (2): Combined with the results of step (1), design a neural network fault detection interval observer for the rudder failure of the X-type rudder underwater robot;

Through the analysis and research on the modeling errors of the system model in step (1), it can be known that if the uncertainty terms of the underwater robot system are not identified, there will be a gap between the established observer model and the actual system. There is a big difference, so this patent aims at this problem and designs a neural network interval observer as shown below:

in:

is the RBF neural network output value used to estimate the system uncertainty term Δ.

In this patent, RBF neural network is used to identify the uncertainty term Δ of the system model online. The specific expression of the given RBF neural network is:

in, is the difference between the output of the upper bound (lower bound) of the interval observer and the actual system output; W∈R ^6×k is the weight matrix between the hidden layer and the output layer of the RBF neural network; m and σ are the RBF neural network respectively. Center vector and width parameters in radial basis functions.

Theoretically, there is an optimal approximation value for model uncertainty Δ It can be expressed as:

W ^* is the optimal value obtained through RBF neural network is the corresponding parameter of W, where the upper bound of the optimal weight satisfies: ||W|| _F ≤ _{W M} , W _M is a constant value, and ε is the optimal value/> The approximation error between the system uncertainty term Δ and it satisfies:/>

After online approximation of the model uncertainty term Δ through the RBF neural network, the estimated value of the model uncertainty is:

Its uncertainty error equation It can be expressed by the following formula:

Define the hidden layer output error as:

Combining equation (13) with equation (14) we can get:

The weight evaluation error in the formula Its interference term w can be expressed as:

When no fault occurs in the X-type rudder, the state and output error are defined according to equation (8), equation (9) and equation (13):

This leads to the error dynamic system:

According to the definition of interval observer, we can get: e ⁺ (t) ≥ 0, e ^- (t) ≥ 0,

Design the following network weight adaptive law:

in:

_Fi = _Fi ^T > 0, k _i > 0, i = 1, 2, respectively represent the network weight adaptation rate parameters of the upper bound observer and the lower bound observer.

Step (3): Combined with the results of step (2), verify the stability of the designed neural network fault detection interval observation system according to Lyapunov theory.

Define the Lyapunov function of the following form:

in:

P=P ^T >0 is a matrix that satisfies the condition of (AL) ^T P+P(AL)=-Q;

Q is any positive definite matrix.

By deriving equation (20), we can get:

Putting the error dynamic system equation (18) and the network weight adaptive law (19) into the above equation, we can get:

in:

Simplifying equation (22) we can get:

in:

γ ₁ = k ₁ F ₁ ,

α ₁ =W _M +c ₁ /γ ₁ .

It is possible to obtain the derivative that guarantees V The conditions for seminegative definiteness are as follows:

In the same way, the lower bound interval observer guarantees the derivative of V The conditions for seminegative definiteness are:

Since the above parameters are all bounded terms, this means that the derivatives outside the spherical radius r ⁺ and r ^- are all negative definite, so the state estimation error of the neural network interval observer established using the above method can be guaranteed/> and/> Ultimately it is uniformly bounded.

(4)Application cases

In order to verify the effectiveness of the X-type rudder underwater robot fault detection method based on the neural network interval observer designed by the patent of this invention, the following simulation experiment was designed:

1) Verify that under no fault conditions, the neural network interval observer in this patent can effectively estimate the speed curve of the X-type rudder underwater robot;

2) At t=15s, the rudder blade damage, rudder blade stuck, 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 to verify the neural network fault detection designed in this patent Validity of interval observers.

During the simulation experiment verification process, the initial state and external interference of the X-rudder underwater robot were the same.

The results obtained using the Matlab/Simulink simulation platform are shown in Figure 2-6.

According to the simulation results in Figure 2, when the X-rudder underwater robot is fault-free, the actual output speed of the system is always between the two estimated values of the interval observer, which proves that the designed interval observer can accurately predict the system. Perform effective tracking and estimation.

According to the simulation results in Figures 3 to 6, when the X-rudder underwater robot is fault-free, the actual output speed of the system is always between the two estimated values of the interval observer, but at t=15s, due to Rudder 1 had a rudder blade failure, causing the actual output of part of the system's speed to exceed the interval range of the interval observer, which proved that the designed neural network interval observer could effectively detect system faults.

In summary, the patent of this invention studies the problem of large modeling errors in various parameters in the underwater robot dynamics model. It uses RBF neural network to identify the system modeling errors online, and directly uses the interval observer to compare the results output by the actual system. The residual signal is used to determine whether the system is faulty. This method is suitable for the field of underwater robot fault diagnosis. It not only solves the problem of difficulty in selecting the fault threshold of traditional observers, but also has a higher sensitivity to faults, and therefore has a wider range of applications. Research and application value.

Claims (3)

1. An X-type rudder AUV fault detection method based on an interval observer, which is characterized in that the steps are as follows: Step 1: Combined with the X-rudder underwater robot dynamics model, linearly transform the state quantity, and introduce system model modeling error uncertainty into the model; Step 2: Combining the results of Step 1, design the fault detection interval observer for the X-type rudder underwater robot; through the analysis and research on the modeling error of the system model in Step 1, design the neural network interval observer as shown below Device: in: is the output value of the RBF neural network used to estimate the system uncertainty term Δ; the RBF neural network is used to identify the uncertainty term Δ of the system model online. The specific expression of the given RBF neural network is: in, is the difference between the output of the upper or lower bound of the interval observer and the actual system output; W∈R ^6×k is the weight matrix between the hidden layer and the output layer of the RBF neural network; m and σ are the paths of the RBF neural network respectively. The center vector and width parameters in the basis function; Model uncertainty Δ has an optimal approximation value It can be expressed as: Among them: W ^* is the optimal value obtained through RBF neural network is the corresponding parameter of W, where the upper bound of the optimal weight satisfies: ||W|| _F ≤ _{W M} , W _M is a constant value, and ε is the optimal value/> The approximation error between and the system uncertainty term Δ, and it satisfies: After online approximation of the model uncertainty term Δ through the RBF neural network, the estimated value of the model uncertainty is: Its uncertainty error equation It can be expressed by the following formula: Define the hidden layer output error as: Available: The weight evaluation error in the formula Its interference term w can be expressed as: Define the status and output error when no fault occurs in the X-type rudder: e ⁺ =x ⁺ -x, This gives us the error dynamic system: According to the definition of interval observer, we can get: e ⁺ (t) ≥ 0, e ^- (t) ≥ 0, Design the following network weight adaptive law: Among them: F _i = F _i ^T > 0, k _i > 0, i = 1, 2, representing the network weight adaptation rate parameters of the upper bound observer and the lower bound observer respectively; Step 3: Combined with the results of Step 2, verify the stability of the designed interval observation system based on Lyapunov theory. 2. An X-type rudder AUV fault detection method based on an interval observer according to claim 1, characterized in that step one specifically includes: recording the deflection values of the four rudder blades of the X-type rudder underwater robot in sequence. As: [δ ₁ δ ₂ δ ₃ δ ₄ ] ^T , the thrust and moment distribution relationship of the X-type rudder and propeller is: Among _{them, X T is} the _thrust of _the propeller; is the hydrodynamic parameter related to the *th rudder blade; definition: x=[x ₁ ,x ₂ ] ^T , x ₁ =η, x ₂ =J(η)v The X-rudder underwater robot dynamic model is transformed into a state space equation in the form: in: K is the damage degree distribution matrix of the rudder blade; where 0≤K≤1; E _a is the fault distribution matrix of the rudder blade; T is the propeller thrust matrix; f _a (t) is the rudder blade failure function;/> Among them, d(t) is external interference; The modeling uncertainty in the X-rudder underwater robot system is expressed in the following form: in, Represents the theoretical values of the corresponding variables in the underwater robot system model; M _η , C _η , D _η , and g _η represent the actual values of the corresponding variables in the underwater robot system model; ΔM _η , ΔC _η , ΔD _η , and Δg _η represent water The uncertainty of the corresponding variables in the robot system model; For the X-type rudder underwater robot actuator failure, let u′=u+Δu, where u is the designed control quantity, u′ is the actual control quantity, and Δu is the system uncertainty caused by the fault; The uncertainty of the lower robot system model is expressed as: Then there are: 3. An X-type rudder AUV fault detection method based on an interval observer according to claim 1, characterized in that step three specifically includes: defining the Lyapunov function: Among them: P=P ^T >0 is a matrix that satisfies the condition of (AL) ^T P+P(AL)=-Q; Q is any positive definite matrix; Derivating the above equation we can get: By incorporating the error dynamic system formula and network weight adaptive law into the above formula, we can get: in: After simplification we get: Among them: γ ₁ =k ₁ F ₁ , α ₁ =W _M +c ₁ /γ ₁ ; It is possible to obtain the derivative that guarantees V The conditions for seminegative definiteness are as follows: The lower bound interval observer guarantees the derivative of V The conditions for seminegative definiteness are: Derivatives outside the spherical radius r ⁺ , r ^- are all negative definite, the state estimation error of the established neural network interval observer/> and/> It is ultimately uniformly bounded.