Estimation Methods of Actuator Faults based on Bayesian Learning

Abstract

The present disclosure discloses a estimation methods of actuator faults based on bayesian learning, and belongs to the technical field of system detection. According to the present disclosure, an actuator fault is modeled based on a random walking model, and a joint posterior probability distribution of a system state variable and the actuator fault is represented using two mutually independent hypothesis distributions based on a variational Bayesian theory; a system state variable and an actuator fault of a system at a moment k are predicted at a moment k−1; and a predicted system state variable and a predicted actuator fault are iteratively updated at the moment k according to the Bayesian theory to output an estimated value of the system state variable at the moment k as well as a variance of the estimated value and an estimated value of the actuator fault at the moment k as well as a variance of the estimated value. In the present disclosure, by fully using a structure that Bayesian learning is applied to online estimation and decoupling the system state variable of mutually coupled variables and the actuator fault, an actuator fault estimation method for a random system is provided, and can estimate an actuator fault of the random system.

Claims

1. An estimation method of actuator faults based on bayesian learning, comprising the following steps: step (1): modeling an actuator fault as follows based on a random walking model:
f.sub.k=f.sub.k-1+w.sub.k.sup.f (formula 1), where f.sub.k is a potential actuator fault at a moment k, f.sub.k-1 is a potential actuator fault at a moment k−1, w.sub.k.sup.f is a process noise, and k is a time sequence; step (2): representing a joint posterior probability distribution p(x.sub.k, f.sub.k|y.sub.1:k) of a system state variable x.sub.k and the actuator fault f.sub.k using two mutually independent hypothesis distributions q(x.sub.k|y.sub.1:k) and q(f.sub.k|y.sub.1:k) based on a variational Bayesian theory, namely:
p(x.sub.k,f.sub.k|y.sub.1:k)=q(x.sub.k|y.sub.1:k)q(f.sub.k|y.sub.1:k) (formula 2), and approximating the joint posterior probability distribution of the system state variable x.sub.k and the actuator fault f.sub.k at the moment k−1 as follows:
q(x.sub.k-1|y.sub.1:k-1)=N({circumflex over (x)}.sub.k-1,P.sub.k-1) (formula 3), and
q(f.sub.k-1|y.sub.1:k-1)=N({circumflex over (f)}.sub.k-1,Δ.sub.k-1) (formula 4), where y.sub.1:k={y.sub.1, y.sub.2, . . . , y.sub.k} represents a collection of observation signals from a moment 1 to the moment k, {circumflex over (x)}.sub.k-1 represents an estimated value of the system state variable at the moment k−1, P.sub.k-1 is a variance of {circumflex over (x)}.sub.k-1, {circumflex over (f)}.sub.k-1 is an estimated value of the actuator fault at the moment k−1, and Δ.sub.k-1 is a variance of {circumflex over (f)}.sub.k-1; step (3): predicting, at the moment k−1, a system state variable and an actuator fault at the moment k, and iteratively updating, at the moment k, a predicted system state variable and a variance and a predicted actuator fault and a variance according to the Bayesian theory to output an estimated value {circumflex over (x)}.sub.k of the system state variable x.sub.k at the moment k and a variance P.sub.k of the estimated value and to output an estimated value {circumflex over (f)}.sub.k of the actuator fault f.sub.k at the moment k and a variance Δ.sub.k thereof; step (4): judging whether k=.sub.step is satisfied, if YES, ending the method, otherwise k=k+1, and skipping to step (2), step being the maximum time length; and step (5): if the estimated value of the actuator factor is 0, determining that no actuator fault occurs, and if the estimated value of the actuator fault is deviated from 0, determining that an actuator fault occurs, and overhauling a system.

2. The estimation method according to claim 1, wherein, in the step (3), predicted values at the moment k−1 are used as initial values for iterative updating at the moment k, namely {circumflex over (x)}.sub.k.sup.i=0={circumflex over (x)}.sub.k.sup.−, P.sub.k.sup.i=0=P.sub.k.sup.−, {circumflex over (f)}.sub.k.sup.i=0={circumflex over (f)}.sub.k.sup.−, and Δ.sub.k.sup.i=0=Δ.sub.k.sup.−, where i represents an iteration step count, and the maximum iteration step count thereof is set to N; {circumflex over (x)}.sub.k.sup.− is a predicted value of the system state variable at the moment k; P.sub.k.sup.− is a predicted variance of the system state variable at the moment k; {circumflex over (f)}.sub.k.sup.− is a predicted value of the actuator fault at the moment k; Δ.sub.k.sup.− is a predicted variance of the actuator fault at the moment k; Θ=τI, and I is a unit matrix; and τ∈(0,1] is an adjustable parameter.

3. The estimation method according to claim 1, wherein, in the step (3), the system state variable and the variance at the moment k are predicted at the moment k−1 according to a dynamic model equation of an automatic control system where an actuator is located, as shown in formula (5):
{circumflex over (x)}.sub.k.sup.−=A{circumflex over (x)}.sub.k-1+Bu.sub.k-1+{circumflex over (f)}.sub.k-1 (formula 5), and
P.sub.k.sup.−=AP.sub.k-1A.sup.T+Δk.sub.k-1+BQ.sub.kB.sup.T (formula 6), where {circumflex over (x)}.sub.k.sup.− is a predicted value of the system state variable at the moment k, P.sub.k.sup.− is a predicted variance of the system state variable at the moment k, {circumflex over (x)}.sub.k-1 is the estimated value of the system state variable at the moment k−1, {circumflex over (f)}.sub.k-1 is the estimated value of the actuator fault at the moment k−1, u.sub.k-1 is a controller output of the automatic control system where the actuator is located, P.sub.k-1 is the variance of {circumflex over (x)}.sub.k-1, Δ.sub.k-1 is the variance of {circumflex over (f)}.sub.k-1, Q.sub.k is a variance of the process noise, A is a state transition matrix, and B is a controller input matrix.

4. The estimation method according to claim 3, wherein the iteratively updating the predicted system state variable and variance at the moment k according to the Bayesian theory comprises the following steps:
{circumflex over (x)}.sub.k.sup.i={circumflex over (x)}.sub.k.sup.−+{circumflex over (f)}.sub.k.sup.i-1+K(y.sub.k−C({circumflex over (x)}.sub.k.sup.−+{circumflex over (f)}.sub.k.sup.i-1)) (formula 7),
P.sub.k.sup.i=P.sub.k.sup.−−KCP.sub.k.sup.− (formula 8), and
K=P.sub.k.sup.−C.sup.T(CP.sub.k.sup.−C.sup.T+R.sub.k).sup.−1 (formula 9), where {circumflex over (x)}.sub.k.sup.i is an estimated value of the system state variable obtained by an i-th iteration at the moment k; {circumflex over (x)}.sub.k.sup.− is the predicted value of the system state variable at the moment k; {circumflex over (f)}.sub.k.sup.i-1 is an estimated value of the actuator fault obtained by an i−1-th iteration; i represents an iteration step count, and the maximum iteration step count thereof is set to N; K is a filter gain in the automatic control system where the actuator is located; y.sub.k is an observed value of the system state variable at the moment; C is an observation matrix of the system state variable; P.sub.k.sup.i is a variance of the system state variable obtained by the i-th iteration at the moment k; P.sub.k.sup.− is the predicted variance of the system state variable at the moment k; and R.sub.k is a variance of an observation noise.

5. The estimation method according to claim 4, wherein, in the step (3), the estimated value {circumflex over (x)}.sub.k of the system state variable x.sub.k at the moment k and the variance P.sub.k thereof are output as follows:
{circumflex over (x)}.sub.k={circumflex over (x)}.sub.k.sup.i (formula 10), and
P.sub.k=P.sub.k.sup.i (formula 11), where {circumflex over (x)}.sub.k is the estimated value of the system state variable at the moment k, and P.sub.k is the variance of {circumflex over (x)}.sub.k.

6. The estimation method according to claim 1, wherein, in the step (3), the actuator fault and the variance at the moment k are predicted at the moment k−1 according to a dynamic actuator fault equation as shown in formula (1):
{circumflex over (f)}.sub.k.sup.−=τ{circumflex over (f)}.sub.k-1 (formula 12), and
Δ.sub.k.sup.−=ΘΔ.sub.k-1Θ.sup.T (formula 13), where {circumflex over (f)}.sub.k.sup.− is the predicted value of the actuator fault at the moment k; Δ.sub.k.sup.− is the predicted variance of the actuator fault at the moment k; {circumflex over (f)}.sub.k-1 is the estimated value of the actuator fault at the moment k−1; Δ.sub.k-1 is the variance of {circumflex over (f)}.sub.k-1; Θ=τI, and I is a unit matrix; and τ∈(0,1] is an adjustable parameter.

7. The estimation method according to claim 6, wherein the iteratively updating the predicted actuator fault and variance at the moment k according to the Bayesian theory comprises the following steps:
{circumflex over (f)}.sub.k.sup.i={circumflex over (f)}.sub.k.sup.−+Δ.sub.k.sup.−(Δ.sub.k.sup.−+P.sub.k.sup.−).sup.−1({circumflex over (x)}.sub.k.sup.i−A{circumflex over (x)}.sub.k-1−{circumflex over (f)}.sub.k.sup.−) (formula 14), and
Δ.sub.k.sup.i=Δ.sub.k.sup.−−Δ.sub.k.sup.−(Δ.sub.k.sup.−+P.sub.k.sup.−).sup.−1Δ.sub.k.sup.− (formula 15), where {circumflex over (f)}.sub.k.sup.i is an estimated value of the actuator fault obtained by the i-th iteration at the moment k, {circumflex over (f)}.sub.k.sup.− is the predicted value of the actuator fault at the moment k, Δ.sub.k.sup.− is the predicted variance of the actuator fault at the moment k, P.sub.k.sup.− the predicted variance of the system state variable at the moment k, {circumflex over (x)}.sub.k.sup.i is the estimated value of the system state variable obtained by the i-th iteration at the moment k, {circumflex over (x)}.sub.k-1 is the estimated value of the system state variable at the moment k−1, and Δ.sub.k.sup.i is a variance of the actuator fault obtained by the i-th iteration at the moment k.

8. The estimation method according to claim 7, wherein, in the step (3), the estimated value f.sub.k of the actuator fault at the moment k and the variance Δ.sub.k thereof are output as follows:
f.sub.k={circumflex over (f)}.sub.k.sup.i (formula 16), and
Δ.sub.k=Δ.sub.k.sup.i (formula 17).

9. The estimation method according to claim 1, further comprising: establishing a dynamic state model and a dynamic observation model of an open-loop control loop comprising the actuator fault, and preprocessing obtained observation data using a 3δ criterion, the preprocessing comprising eliminating a singular value.

10. The estimation method according to claim 1, wherein the system is a one-degree-of-freedom torque system, the actuator is a motor in the one-degree-of-freedom torque system, a fault estimation of the actuator is a fault estimation of the motor, and the actuator fault comprises: inter-turn or interphase short circuit of a stator winding of the motor, bar breaking of a rotor, eccentricity of a rotor shaft, and generation of an additional signal caused by a phenomenon that uniformity of an electromagnetic field in an air gap is damaged.

Description

BRIEF DESCRIPTION OF FIGURES

[0030] FIG. 1 is an open-loop structure diagram of an automatic control system where an actuator is located;

[0031] FIG. 2 is a flowchart of an actuator fault estimation method according to Example 1;

[0032] FIG. 3 is a structural schematic diagram of a torque system according to Example 2;

[0033] FIG. 4 is a flow block diagram of application of a method of the present disclosure to a one-degree-of-freedom torque system according to Example 2;

[0034] FIG. 5A is an estimation effect diagram of a fault signal of a first fault square wave according to Example 2;

[0035] FIG. 5B is an estimation effect diagram of a fault signal of a second fault square wave according to Example 2;

[0036] FIG. 6A is an estimation effect diagram of a fault signal of a first trigonometric wave according to Example 2; and

[0037] FIG. 6B is an estimation effect diagram of a fault signal of a second trigonometric wave according to Example 2.

DETAILED DESCRIPTION

[0038] The present disclosure will be further described below with reference to the drawings and specific examples to ensure that those skilled in the art can understand and implement the present disclosure better. However, the listed examples are not intended to limit the present disclosure.

Example 1

[0039] The present example discloses a estimation methods of actuator faults based on bayesian learning. The method is introduced below with application to a navigation positioning system as an example. As shown in FIG. 1, a state model and an observation model are created for a navigation control loop including an actuator:

x.sub.k=Ax.sub.k-1+Bu.sub.k-1+f.sub.k+w.sub.k-1 (formula 18), and

y.sub.k=Cx.sub.k+ν.sub.k (formula 19).

[0040] where x.sub.k=[x.sub.k,1,{dot over (x)}.sub.k,1] is a system state variable, x.sub.k,1 and {dot over (x)}.sub.k,1 representing a displacement and a speed respectively; y.sub.k is a noisy observation signal, and in a navigation positioning system, y.sub.k is a displacement obtained through a sensor; u.sub.k-1 is a controller output, and in the navigation positioning system, the controller output u.sub.k-1 is an acceleration; f.sub.k is a potential actuator fault; w.sub.k-1 is a process white noise, and w.sub.k-1˜N(0,Q.sub.k) follows a Gaussian distribution; Q.sub.k is a known variance of the process noise w.sub.k-1; k is a time sequence; R.sub.k is a variance of an observation noise ν.sub.k; A is a state transition matrix; B is a controller input matrix; C is an observation matrix of a state; ν.sub.k is the observation noise, and ν.sub.k˜N(O,R.sub.k) follows a Gaussian distribution; N(0,Q.sub.k.sup.f) is a Gaussian distribution of which a mean value is 0 and a variance is Q.sub.k.sup.f; and N(0,R.sub.k) is a Gaussian distribution of which a mean value is 0 and a variance is R.sub.k.

[0041] Since a dimension of the state of a controlled object is relatively high, and the number of sensors that are mounted is limited, a dimension of the observation signal is usually lower than the dimension of the system state variable. In addition, since industrial data records usually include much exceptional data, a 3δ criterion is used to perform singular value elimination and data cleaning on obtained data. Here, the 3δ criterion is that information within three times of a standard deviation is valid information and information beyond three times of the standard deviation is a singular value.

[0042] Specifically, as shown in FIG. 2, the estimation method specifically includes the following steps.

[0043] In step 1, since time when an actuator fault occurs, a value assigned when the actuator fault occurs, a duration, and a subsequent dynamic condition are all unknown and needed by subsequent steps, the actuator fault is dynamically modeled at first based on a random walking model, as shown in formula (1):

f.sub.k=f.sub.k-1+w.sub.k.sup.f (formula 1),

[0044] where f.sub.k is a potential actuator fault at a moment k; f.sub.k-1 is a potential actuator fault at a moment k−1; w.sub.k.sup.f is a white noise following a Gaussian distribution w.sub.k.sup.f˜N(0,Q.sub.k.sup.f), and Q.sub.k.sup.f is a known noise variance; k is a time sequence; and N(0,Q.sub.k.sup.f) is a Gaussian distribution of which a mean value is 0 and a variance is Q.sub.k.sup.f.

[0045] In step 2, related parameters are initialized.

[0046] Since an algorithm uses a recursive structure, the related parameters need to be initialized at the moment k=0. Correspondingly, a maximum time length step is given, a maximum iteration step count is set to N, an initial value of a system state variable is {circumflex over (x)}.sub.0, a corresponding initial variance is P.sub.0, an initial value of an estimated value of the actuator fault is {circumflex over (f)}.sub.0=0, and a fault variance is Δ=0.

[0047] In step 3, approximate estimation is performed on a joint posterior probability distribution of the system state variable and the actuator fault.

[0048] The joint posterior probability distribution p(x.sub.k, f.sub.k|y.sub.1:k) of the system state variable and the actuator fault are represented using two mutually independent hypothesis distributions q(x.sub.k|y.sub.1:k) and q(f.sub.k|y.sub.1:k) based on a variational Bayesian theory, namely:

p(x.sub.k,f.sub.k|y.sub.1:k)=q(x.sub.k|y.sub.1:k)q(f.sub.k|y.sub.1:k) (formula 2), and

[0049] the joint posterior probability distribution of the system state variable and the actuator fault are approximated at a moment k−1 as follows:

q(x.sub.k-1|y.sub.1:k-1)=N({circumflex over (x)}.sub.k-1,P.sub.k-1) (formula 3), and

q(f.sub.k-1|y.sub.1:k-1)=N({circumflex over (f)}.sub.k-1,Δ.sub.k-1) (formula 4),

[0050] where y.sub.1:k={y.sub.1, y.sub.2, . . . , y.sub.k} represents a collection of observation signals from a moment 1 to the moment k, x.sub.k is a system state variable at the moment k, {circumflex over (x)}.sub.k-1 represents an estimated value of the system state variable at the moment k−1, P.sub.k-1 is a variance of {circumflex over (x)}.sub.k-1, {circumflex over (f)}.sub.k-1 is an estimated value of the actuator fault at the moment k−1, and Δ.sub.k-1 is a variance of {circumflex over (f)}.sub.k-1.

[0051] In step 4, the system state variable and the actuator fault at the moment k are predicted at the moment k−1.

[0052] First, the system state variable and the variance at the moment k are predicted at the moment k−1 according to a state model equation, i.e., formula (18), of an open-loop control loop where an actuator is located:

{circumflex over (x)}.sub.k.sup.−=A{circumflex over (x)}.sub.k-1+Bu.sub.k-1+{circumflex over (f)}.sub.k-1 (formula 5), and

P.sub.k.sup.−=AP.sub.k-1A.sup.T+Δk.sub.k-1+BQ.sub.kB.sup.T (formula 6),

[0053] where {circumflex over (x)}.sub.k.sup.− is a predicted value of the system state variable at the moment k, P.sub.k.sup.− is a predicted variance of the system state variable at the moment k, {circumflex over (x)}.sub.k-1 is an estimated value of the system state variable at the moment k−1, {circumflex over (f)}.sub.k-1 is an estimated value of the actuator fault at the moment k−1, u.sub.k-1 is a controller output of an automatic control system, P.sub.k-1 is a variance of {circumflex over (x)}.sub.k-1, Δ.sub.k-1 is a variance of {circumflex over (f)}.sub.k-1, Q.sub.k is a known variance of the process noise, A is a state transition matrix, and B is a controller input matrix.

[0054] Second, the actuator fault and the variance at the moment k are predicted at the moment k−1 according to a dynamic actuator fault equation, i.e., formula (1):

{circumflex over (f)}.sub.k.sup.−=τ{circumflex over (f)}.sub.k-1 (formula 12), and

Δ.sub.k.sup.−=ΘΔ.sub.k-1Θ.sup.T (formula 13),

[0055] where {circumflex over (f)}.sub.k.sup.− is the predicted value of the actuator fault at the moment k; Δ.sub.k.sup.− is the predicted variance of the actuator fault at the moment k; {circumflex over (f)}.sub.k-1 is the estimated value of the actuator fault at the moment k−1; Δ.sub.k-1 is the variance of {circumflex over (f)}.sub.k-1; Θ=τI, and I is a unit matrix; and τ∈(0, 1] is an adjustable parameter. If τ∈(0, 1] approaches to 1, the estimated value of the fault will be smooth, but a response speed is low. If τ∈(0,1] approaches to 0, the response speed will be fast, but the randomness is high.

[0056] In step 5, initialization is performed for iterative updating.

[0057] The predicted values at the moment k−1 are used as initial values for iterative updating at the moment k, namely {circumflex over (x)}.sub.k.sup.i=0={circumflex over (x)}.sub.k.sup.−, P.sub.k.sup.i=0=P.sub.k.sup.−, {circumflex over (f)}.sub.k.sup.i=0={circumflex over (f)}.sub.k.sup.−, and Δ.sub.k.sup.i=0=Δ.sub.k.sup.−. Here, i represents an iteration step count, and the maximum iteration step count is set to N.

[0058] In step 6, the predicted system state variable and actuator fault are iteratively updated according to the Bayesian theory.

[0059] First, the predicted system state variable and variance at the moment k are iteratively updated according to the Bayesian theory, specifically including the following steps:

{circumflex over (x)}.sub.k.sup.i={circumflex over (x)}.sub.k.sup.−+{circumflex over (f)}.sub.k.sup.i-1+K(y.sub.k−C({circumflex over (x)}.sub.k.sup.−+{circumflex over (f)}.sub.k.sup.i-1)) (formula 7),

P.sub.k.sup.i=P.sub.k.sup.−−KCP.sub.k.sup.− (formula 8), and

K=P.sub.k.sup.−C.sup.T(CP.sub.k.sup.−C.sup.T+R.sub.k).sup.−1 (formula 9),

[0060] where {circumflex over (x)}.sub.k.sup.i is an estimated value of the system state variable obtained by an i-th iteration at the moment k; {circumflex over (x)}.sub.k.sup.− is the predicted value of the system state variable at the moment k; {circumflex over (f)}.sub.k.sup.i-1 is an estimated value of the actuator fault obtained by an i−1-th iteration at the moment k; i represents the iteration step count, and the maximum iteration step count thereof is set to N; K is a filter gain in the automatic control system; y.sub.k is an observed value of the system state variable at the moment k; C is an observation matrix of the system state variable; P.sub.k.sup.i is a variance of the system state variable obtained by the i-th iteration at the moment k; P.sub.k.sup.− is the predicted variance of the system state variable at the moment k; and R.sub.k is a variance of an observation noise.

[0061] Second, the predicted actuator fault and variance at the moment k are iteratively updated according to the Bayesian theory, specifically including the following steps:

{circumflex over (f)}.sub.k.sup.i={circumflex over (f)}.sub.k.sup.−+Δ.sub.k.sup.−(Δ.sub.k.sup.−+P.sub.k.sup.−).sup.−1({circumflex over (x)}.sub.k.sup.i−A{circumflex over (x)}.sub.k-1−{circumflex over (f)}.sub.k.sup.−) (formula 14), and

Δ.sub.k.sup.i=Δ.sub.k.sup.−−Δ.sub.k.sup.−(Δ.sub.k.sup.−+P.sub.k.sup.−).sup.−1Δ.sub.k.sup.− (formula 15),

[0062] where {circumflex over (f)}.sub.k.sup.i is an estimated value of the actuator fault obtained by the i-th iteration at the moment k, Δ.sub.k.sup.− is the predicted variance of the actuator fault at the moment k, P.sub.k.sup.− is the predicted variance of the system state variable at the moment k, {circumflex over (x)}.sub.k.sup.i is the estimated value of the system state variable obtained by the i-th iteration at the moment k, {circumflex over (x)}.sub.k-1 is the estimated value of the system state variable at the moment k−1, {circumflex over (f)}.sub.k.sup.− is the predicted value of the actuator fault at the moment k, Δ.sub.k.sup.i is a variance of the actuator fault obtained by the i-th iteration at the moment k, and Δ.sub.k.sup.− is the predicted variance of the actuator fault at the moment k.

[0063] In step 7, whether i=N is satisfied is judged, if YES, the next step is executed, otherwise, i=i+1, and a skip to first in step 6 is made.

[0064] In step 8, the estimated value of the system state variable at the moment k and the variance of the estimated value are output:

{circumflex over (x)}.sub.k={circumflex over (x)}.sub.k.sup.i (formula 10), and

P.sub.k=P.sub.k.sup.i (formula 11),

[0065] where {circumflex over (x)}.sub.k is the estimated value of the system state variable at the moment k, and P.sub.k is the variance of {circumflex over (x)}.sub.k.

[0066] In step 9, the actuator fault f.sub.k at the moment k and the variance Δ.sub.k thereof are output:

f.sub.k={circumflex over (f)}.sub.k.sup.i (formula 16), and

Δ.sub.k=Δ.sub.k.sup.i (formula 17).

[0067] In step 10, whether k=.sub.step is satisfied is judged, if YES, the method is ended, otherwise k=k+1, and a skip to step 2 is made, where step is the maximum time length.

[0068] In step 11, if the estimated value of the actuator factor is 0, it is determined that no actuator fault occurs, and if the estimated value of the actuator fault is deviated from 0, it is determined that the actuator fault occurs.

Example 2

[0069] In the present example, the estimation method in Example 1 is used to perform fault estimation on a controlled object, i.e., a motor in a one-degree-of-freedom torque system. Multiple torque modules may be connected based on the torque system to form a multi-degree-of-freedom torque system, which can simulate a flexible coupling effect between an actuating mechanism and a load in a complex industrial process, or some applications or equipment with torsional compliances and flexible joints, such as mechanical structures like a high-gear-ratio harmonic transmission and a light transmission shaft. The one-degree-of-freedom torque system is formed by coupling a rotary torque module and a rotary basic servo unit, the rotary servo unit is on one side, and the direct current motor is horizontally connected with an output shaft, and can drive a torsional load through a flexible coupling. FIG. 3 shows the structural schematic diagram of the torque system.

[0070] In practical uses, the motor in the torque system is a main device that drives the load, i.e., an actuator of the torque system. An electromagnetic relationship in the motor is very complex. Besides, continuous high-speed running and the influence of electrical, mechanical and environmental running conditions, etc., may easily cause the phenomena of winding loosening, insulation deterioration, bearing abrasion, intensified vibration, high temperature overheating, etc., to further cause various faults, such as inter-turn or interphase short circuit of a stator winding of the motor, bar breaking of a rotor, eccentricity of a rotor shaft, the phenomenon that the uniformity of an electromagnetic field in an air gap is damaged, and the phenomenon that a magnetic potential of the air gap is non-uniform due to existence of a high-order harmonic in a current of the stator winding. Therefore, describing, analyzing and estimating an actuator fault is an effective method for ensuring the system performance.

[0071] The torque system is modeled. A system state variable is x.sub.k=[x.sub.n,1,x.sub.n,2,{dot over (x)}.sub.n,1,{dot over (x)}.sub.n,2], where x.sub.n,1 and x.sub.n,2 represent angular positions of a rigid load and a tortional load respectively. In addition, the two variables are measured by a coder to form an observation signal y.sub.k. A control signal u.sub.k is a voltage signal applied to the motor. A potential actuator fault f.sub.k is simulated by a random walking model. Matrices A, B and C in a state space model are obtained respectively as follows:

[00001] $A = [\begin{matrix} 0.9 7 8 & 0.0 2 2 & 0.0 0 9 6 & 7.2 814 \times 10^{- 5} \\ 0.0 8 7 8 & 0.9122 & 2.9161 \times 10^{4} & 0.0 0 9 4 \\ - 4.2 5 7 8 & 4.2 5 7 8 & 0.9122 & 0.0 214 \\ 17.012 & - 17.012 & 0.085 8 & 0.8 4 3 6 \end{matrix}], B = [\begin{matrix} 0.0 2 2 3 \\ 3.3 7 44 \times 10^{- 4} \\ 4.3 913 \\ 0.1335 \end{matrix}], and$ $C = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{matrix}] .$

[0072] Moreover, a variance of a process noise and a variance of an observation noise are respectively as follows:

[00002] $Q_{k} = [\begin{matrix} 0.0 01 & 0 & 0 & 0 \\ 0 & 0.0 01 & 0 & 0 \\ 0 & 0 & 0.0 01 & 0 \\ 0 & 0 & 0 & 0.0 01 \end{matrix}], and$ $R_{k} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] .$

[0073] The whole implementation process lasts for 10 s, sampling time is 0.01 s, and totally 1,000 sample data points are collected. A starting point of the whole implementation case is as follows:

[00003] $x_{0} = [\begin{matrix} 0 \\ 0 \\ 0 \\ 0 \end{matrix}], and P_{0} = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] .$

[0074] An iteration step count is N=2, and an adjustable parameter is τ=0.9. A noise variance introduced to the random walking model for the fault is:

[00004] $Q_{k}^{f} = [\begin{matrix} 0.01 & 0 & 0 & 0 \\ 0 & 0.01 & 0 & 0 \\ 0 & 0 & 0.01 & 0 \\ 0 & 0 & 0 & 0.01 \end{matrix}] .$

[0075] FIG. 4 shows a flow block diagram of application of the present disclosure to the one-degree-of-freedom torque system. FIG. 5A, FIG. 5B, FIG. 6A, and FIG. 6B show implementation effects of the method of the present disclosure in the one-degree-of-freedom torque system. FIG. 5A and FIG. 5B show estimation effects of two types of square actuator faults in the present disclosure. FIG. 6A and FIG. 6B show estimation effects of trigonometric actuator faults in the present disclosure. It can be seen from the implementation effect diagrams that, when an amplitude of an estimated value of an actuator fault is not 0, it indicates that a fault occurs to the motor in the torque system, and time when the fault occurs can be rapidly determined accordingly. In addition, comparison with an actuator fault curve in simulation shows that a fault can be detected immediately when the fault occurs, and an amplitude of a fault signal can be obtained relatively accurately, to thereby implement accurate estimation of the fault of the motor.

[0076] The method proposed in the present disclosure is applied to the fields of motion control systems represented by a three-degree-of-freedom helicopter system, process control systems represented by a continuous stirred tank reactor, etc.

[0077] The above examples are only preferred examples listed for completely describing the present disclosure and not intended to limit the scope of protection of the present disclosure. Equivalent replacements or transformations made by those skilled in the art based on the present disclosure fall within the scope of protection of the present disclosure. The scope of protection of the present disclosure is defined by the claims.

Estimation Methods of Actuator Faults based on Bayesian Learning

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G06N7/01

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G05B23/0254

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G05B13/048

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G05B23/024

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G06F18/24155

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International classification

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G05B23/02

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G06K9/62

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G06N7/00

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Abstract

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