[go: up one dir, main page]

CN114063456A - Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm - Google Patents

Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm Download PDF

Info

Publication number
CN114063456A
CN114063456A CN202111350431.7A CN202111350431A CN114063456A CN 114063456 A CN114063456 A CN 114063456A CN 202111350431 A CN202111350431 A CN 202111350431A CN 114063456 A CN114063456 A CN 114063456A
Authority
CN
China
Prior art keywords
fault
vector
state
value
early warning
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202111350431.7A
Other languages
Chinese (zh)
Other versions
CN114063456B (en
Inventor
王振华
张文瀚
沈毅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology Shenzhen
Original Assignee
Harbin Institute of Technology Shenzhen
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology Shenzhen filed Critical Harbin Institute of Technology Shenzhen
Priority to CN202111350431.7A priority Critical patent/CN114063456B/en
Publication of CN114063456A publication Critical patent/CN114063456A/en
Application granted granted Critical
Publication of CN114063456B publication Critical patent/CN114063456B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Testing And Monitoring For Control Systems (AREA)

Abstract

本发明公开了一种利用自回归模型和卡尔曼滤波算法的故障预测与预警方法，所述方法包括如下步骤：一、建立故障自回归退化模型的状态方程与测量方程；二、计算状态向量预测值

Figure DDA0003355663040000011
三、计算系统状态协方差矩阵的预测值P(k|k‑1)；四、计算滤波增益系数K(k)；五、计算系统状态协方差矩阵的估计值P(k)；六、计算状态向量估计值
Figure DDA0003355663040000012
七、计算测量向量的预测值
Figure DDA0003355663040000013
到
Figure DDA0003355663040000014
八、计算测量向量预测值的上边界
Figure DDA0003355663040000015
到
Figure DDA0003355663040000016
和下边界y(k)到y(k+m)；九、确定故障预警结果；十、每个k时刻重复二～九，迭代实现故障预测和预警。该方法能够在控制系统发生故障之前给出可靠的预警信号，有效保障系统的安全性及稳健性，其原理清晰，算法简单，易于实际工程实现。

Figure 202111350431

The invention discloses a fault prediction and early warning method using an autoregressive model and a Kalman filter algorithm. The method includes the following steps: 1. Establishing the state equation and measurement equation of the fault autoregressive degradation model; 2. Calculating the state vector prediction value

Figure DDA0003355663040000011
3. Calculate the predicted value P(k|k-1) of the system state covariance matrix; 4. Calculate the filter gain coefficient K(k); 5. Calculate the estimated value P(k) of the system state covariance matrix; 6. Calculate State vector estimate
Figure DDA0003355663040000012
7. Calculate the predicted value of the measurement vector
Figure DDA0003355663040000013
arrive
Figure DDA0003355663040000014
8. Calculate the upper bound of the predicted value of the measurement vector
Figure DDA0003355663040000015
arrive
Figure DDA0003355663040000016
and the lower boundary y (k) to y (k+m); 9. Determine the fault early warning result; 10. Repeat 2 to 9 at each k time to iteratively realize fault prediction and early warning. The method can give a reliable early warning signal before the failure of the control system, and effectively guarantee the safety and robustness of the system. The principle is clear, the algorithm is simple, and it is easy to implement in practical engineering.

Figure 202111350431

Description

Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm
Technical Field
The invention relates to a fault early warning method of a control system, in particular to a method for predicting and early warning faults of the control system by using an autoregressive model and a Kalman filtering algorithm.
Background
Modern control systems are becoming more and more complex and, accordingly, the safety and reliability of the control systems are of particular importance. However, various failures occurring when an actual system is operated may reduce the reliability thereof and even destroy the stability of the system, thereby causing a serious safety accident. Therefore, in order to improve the safety and reliability of the control system, it is necessary to diagnose a fault and take countermeasures in time to minimize damage to the system caused by the fault. Generally speaking, what has more impact on control system safety is the existence within it of various graceful faults caused by performance degradation of system components. In the initial stage of the gradual fault, the amplitude is small, so that the performance of the control system cannot be seriously influenced, but the fault amplitude is gradually increased along with the continuous accumulation of the time dimension, so that the threat to the safety and the reliability of the system is higher. In particular, when the gradual fault progresses to a system component performance failure threshold, the safety and stability of the whole control system are seriously threatened. Therefore, the model of the degradation process is established aiming at the slowly-varying fault of the control system, the future fault development trend of the control system is predicted, and the fault early warning is timely made before the performance failure, so that the method has important significance for improving the reliability and the safety of the control system.
According to relevant published documents at home and abroad, the current fault prediction and early warning algorithms are mostly based on fuzzy network or deep learning technology to carry out fault degradation modeling and prediction, the requirements on the data volume of faults and the calculated amount of model training are high, and the application range is limited. Meanwhile, most of the existing methods need to train the fault model offline in advance, model parameters cannot be updated and adjusted online in real time, and an accurate fault prediction result is difficult to provide, so that the reliability of fault early warning is influenced to a certain extent.
Since the use of fuzzy networks or deep learning techniques for fault degradation modeling and prediction requires a high amount of computation, such algorithms are only suitable for control systems with a simple structure and a small number of components. In the face of the development trend that the modern control system structure is increasingly complex and the number of the components is increasing, the fault prediction and early warning algorithms cannot meet the requirement of high-efficiency accurate fault early warning performance, and the modern control system urgently needs a fault early warning algorithm which is good in applicability, small in calculated amount and reliable in performance.
Disclosure of Invention
The invention aims to provide a fault prediction and early warning method by utilizing an autoregressive model and a Kalman filtering algorithm, which can give out a reliable early warning signal before a control system fails, effectively ensures the safety and the robustness of the system, has clear principle and simple algorithm and is easy to realize in actual engineering.
The purpose of the invention is realized by the following technical scheme:
a fault prediction and early warning method using an autoregressive model and a Kalman filtering algorithm comprises the following steps:
step one, establishing a state equation and a measurement equation of a fault autoregressive degradation model:
Figure BDA0003355663020000021
wherein x (k) and x (k-1) are state vectors of the system at the time k and k-1, respectively; a (k-1) is a one-step transition matrix of the degradation model state; w (k-1) is a disturbance vector of the system; c is a measurement matrix; v (k) is the measured noise vector of the system; y (k) is a measurement vector;
step two, calculating the predicted value of the state vector
Figure BDA0003355663020000031
Figure BDA0003355663020000032
In the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000033
is an estimated value of the state vector at the moment k-1;
step three, calculating a predicted value P (k | k-1) of the covariance matrix of the system state:
P(k|k-1)＝A(k-1)P(k-1)A(k-1)T+Q；
in the formula, P (k-1) is an estimated value of a covariance matrix of system errors at the k-1 moment; q is a system noise covariance matrix;
step four, calculating a filter gain coefficient K (k):
K(k)＝P(k|k-1)CT/(CP(k|k-1)CT+R)；
in the formula, R is a covariance matrix of a measurement noise vector;
step five, calculating an estimated value P (k) of the covariance matrix of the system state:
P(k)＝P(k|k-1)-K(k)CP(k|k-1)；
wherein, P (k) is the estimated value of the state covariance matrix at the time k;
sixthly, calculating the state vector estimated value
Figure BDA0003355663020000034
Figure BDA0003355663020000035
In the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000036
is an estimated value of the state vector at the moment k;
step seven, calculating the predicted value of the measurement vector
Figure BDA0003355663020000037
To
Figure BDA0003355663020000038
Figure BDA0003355663020000039
In the formula (I), the compound is shown in the specification,
Figure BDA00033556630200000310
to
Figure BDA00033556630200000311
Measuring the predicted value of the vector at the moment from k to k + m;
Figure BDA00033556630200000312
as an estimate of the state vector at time k
Figure BDA00033556630200000313
The ith element of (1); n is the order used by the fault autoregressive degradation model; m is the step length of predicting the fault from the current moment to the back;
step eight, calculating the upper boundary of the predicted value of the measurement vector
Figure BDA0003355663020000041
To
Figure BDA0003355663020000042
And a lower boundaryy(k) Toy(k+m)：
Figure BDA0003355663020000043
In the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000044
to
Figure BDA0003355663020000045
Measuring the upper boundary of the vector predicted value for the time from k to k + m;y(k) toy(k + m) is the lower boundary of the measurement vector prediction value at the moment from k to k + m;
step nine, determining a fault early warning result:
Figure BDA0003355663020000046
and isy(k+j)≤ythAnd is
Figure BDA0003355663020000047
In the formula, ythA set fault detection threshold;
if all j enable the above formula to be satisfied when j is taken from 0 to m, the failure is not predicted at the moment k;
if j is taken from 0 to m, and if one j exists so that the above expression is not satisfied, the fact that the fault is predicted at the moment k is shown, and the predicted future fault occurrence moment is k + j*；
And step ten, repeating the step two to the step nine at each moment k, and iteratively realizing fault prediction and early warning.
The invention provides a fault early warning method by using an autoregressive model and a Kalman filtering algorithm, which can predict the future change value of a fault according to the degradation characteristic of the fault and effectively early warn the fault on the basis, and has the advantages and beneficial effects that:
(1) an autoregressive model is adopted to describe the degradation process of the fault, the model is simple in form and wide in description range, and the fault early warning method is good in applicability;
(2) the Kalman filtering algorithm is used for updating the model parameters on line in real time, the parameter estimation precision is high, the on-line operation calculated amount is small, and the realization of an actual hardware platform is easy;
(3) the fault early warning signal is given through a fault predicted value and upper and lower boundaries thereof, so that the reliability of an early warning result is ensured, and the safety of a control system is further improved.
Drawings
FIG. 1 is a flow chart of a fault prediction and early warning method using an autoregressive model and a Kalman filtering algorithm in accordance with the present invention.
Fig. 2 shows the result of slowly varying fault data of the dc motor.
Fig. 3 shows the motor creep fault prediction and early warning result when k is 180.
Fig. 4 shows the prediction and early warning result of the creep fault of the motor when k is 185.
Fig. 5 shows the motor creep failure prediction and early warning result when k is 190.
Fig. 6 shows the motor creep failure prediction and warning result when k is 195.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a fault prediction and early warning method by using an autoregressive model and a Kalman filtering algorithm, which comprises the following steps:
step one, establishing a state equation and a measurement equation of a fault autoregressive degradation model, wherein the formulas are as follows:
Figure BDA0003355663020000051
wherein x (k) and x (k-1) are state vectors of the system at the time k and k-1, respectively; a (k-1) is a one-step transition matrix of the degradation model state; w (k-1) is a disturbance vector of the system; c is a measurement matrix; v (k) is the measured noise vector of the system; y (k) is a measurement vector.
Step two, calculating the predicted value of the state vector
Figure BDA0003355663020000061
The formula is as follows:
Figure BDA0003355663020000062
in the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000063
is an estimate of the state vector at time k-1.
Step three, calculating a predicted value P (k | k-1) of the covariance matrix of the system state, wherein the formula is as follows:
P(k|k-1)＝A(k-1)P(k-1)A(k-1)T+Q (3)；
in the formula, P (k-1) is an estimated value of a covariance matrix of system errors at the k-1 moment; q is a system noise covariance matrix.
Step four, calculating a filter gain coefficient K (k), wherein the formula is as follows:
K(k)＝P(k|k-1)CT/(CP(k|k-1)CT+R) (4)；
where R is a covariance matrix of the measured noise vector.
Step five, calculating an estimated value P (k) of the covariance matrix of the system state, wherein the formula is as follows:
P(k)＝P(k|k-1)-K(k)CP(k|k-1) (5)；
where p (k) is an estimated value of the state covariance matrix at time k.
Sixthly, calculating the state vector estimated value
Figure BDA0003355663020000064
The formula is as follows:
Figure BDA0003355663020000065
in the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000066
is an estimate of the state vector at time k.
Step seven, calculating the predicted value of the measurement vector
Figure BDA0003355663020000067
To
Figure BDA0003355663020000068
The formula is as follows:
Figure BDA0003355663020000069
in the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000071
to
Figure BDA0003355663020000072
Measuring the predicted value of the vector at the moment from k to k + m;
Figure BDA0003355663020000073
as an estimate of the state vector at time k
Figure BDA0003355663020000074
The ith element of (1); n is the order used by the fault autoregressive degradation model; and m is the step length of predicting the fault from the current moment to the back.
Step eight, calculating the upper boundary of the predicted value of the measurement vector
Figure BDA0003355663020000075
To
Figure BDA0003355663020000076
And a lower boundaryy(k) Toy(k + m), the formula is as follows:
Figure BDA0003355663020000077
in the formula (I), the compound is shown in the specification,
Figure BDA0003355663020000078
to
Figure BDA0003355663020000079
Measuring the upper boundary of the vector predicted value for the time from k to k + m;y(k) toyAnd (k + m) is the lower boundary of the measurement vector prediction value from k to k + m.
Step nine, determining a fault early warning result, wherein the fault early warning strategy is as follows:
if a pair j takes m from 0, all j cause the following to hold:
Figure BDA00033556630200000710
and isy(k+j)≤ythAnd is
Figure BDA00033556630200000711
It means that no failure is predicted at time k.
If j is taken from 0 to m, and if there is one j and expression (9) does not hold, it means that a failure is predicted at time k, and the predicted future failure time is k + j*Wherein, ythIs a set fault detection threshold.
And step ten, repeating the step two to the step nine at each moment k, and iteratively realizing fault prediction and early warning.
Preferably, in step one, the system state vector is given by equation (10):
x＝[f c1 c2 …cn]T (10)；
wherein f is a fault value of the engineering system, obtained by measurement, c1、c1、…、cnCoefficients of an autoregressive model; the measured value y is f; the matrices A (k-1) and C are given by equation (11) and equation (12), respectively:
Figure BDA0003355663020000081
C＝[1 0 0 … 0] (12)。
preferably, in step two, the iterative calculation is started from k ═ n +1, and the state vector estimation values at the first n +1 time instants are respectively given by formula (13) and formula (14):
Figure BDA0003355663020000082
Figure BDA0003355663020000083
preferably, in step seven, the predicted value of the vector is measured
Figure BDA0003355663020000084
To
Figure BDA0003355663020000085
Determined by iterative calculation through an autoregressive model method, wherein autoregressive model parameters are state vector estimated values
Figure BDA0003355663020000086
Figure BDA0003355663020000086
2 nd to n +1 th elements.
Preferably, in step eight, the upper bound of the vector predictor is measured
Figure BDA0003355663020000087
To
Figure BDA0003355663020000088
And a lower boundaryy(k) Toy(k + m) is determined by the 3 sigma interval of kalman filtering,
Figure BDA0003355663020000089
is composed of
Figure BDA00033556630200000810
Standard deviation of (2).
Preferably, in step nine, the fault early warning result is jointly determined by measuring the magnitude relation between the vector predicted value and the upper and lower boundaries thereof and the fault detection threshold value.
In summary, the invention first describes the dynamic degradation process of the fault by using an autoregressive model; updating the model parameters on line in real time by using a Kalman filtering algorithm, thereby realizing the prediction of the fault value and the upper and lower bounds thereof at the future moment; and finally, combining the failure prediction result with the set failure threshold value to realize effective early warning of the failure. According to the method, the fault degradation dynamic is described by using the autoregressive model, the model is simple in form and good in application, and the application range of the algorithm is widened; the method updates the model parameters on line in real time by using Kalman filtering, and has the advantages of high parameter estimation precision, simple algorithm, clear principle and convenient actual hardware realization; the algorithm gives out a fault early warning signal by utilizing the fault predicted value and the upper and lower boundaries thereof, and the reliability of the early warning result is ensured.
Examples of the applications
The following describes an application process of the fault prediction and early warning method using an autoregressive model and a kalman filter algorithm by using an example of a dc motor. Considering that the performance of the direct current motor is gradually degraded along with the increase of the running time, so that the temperature of the motor under the normal running condition is continuously increased, the difference value between the temperature of the motor under the normal running condition and the nominal temperature can be used as an indication signal of the gradual fault of the direct current motor, and the gradual fault data result shown in fig. 2 can be drawn through the collected temperature data of the motor under the normal running condition.
In the fault prediction algorithm simulation, the step length of predicting the fault from the current time is set to be m-20, the order of a fault autoregressive degradation model is set to be n-20, and an output matrix C of the degradation model is set to be [ 100 … 0 ]]. The fault detection threshold is selected as ythInitial value of Kalman Filter Algorithm 3.8
Figure BDA0003355663020000091
Is selected as
Figure BDA0003355663020000092
Initial value of state
Figure BDA0003355663020000093
Is selected as p (k) 10-4In+1，In+1An n +1 dimensional identity matrix; the covariance matrix of the perturbation w (k) and the noise v (k) is Q10-4In+1And R is 10-4. Given simulation parameters and measurement based mitigationThe failure prediction simulation results shown in fig. 3-6 can be obtained by changing the failure data.
As can be seen from the simulation results in fig. 3-6, when k is 180 and k is 185, the actual creep fault data of the dc motor does not exceed the given fault detection threshold, and the designed method also does not give a fault warning signal. When k is 190 and k is 195, the actual slow-varying fault data of the direct current motor exceeds a given fault detection threshold, and the method can quickly and accurately predict the fault and give an early warning signal, so that the effectiveness of the method is verified.

Claims (7)

1. A fault prediction and early warning method using an autoregressive model and a Kalman filtering algorithm is characterized by comprising the following steps:
step one, establishing a state equation and a measurement equation of a fault autoregressive degradation model:
Figure FDA0003355663010000011
wherein x (k) and x (k-1) are state vectors of the system at the time k and k-1, respectively; a (k-1) is a one-step transition matrix of the degradation model state; w (k-1) is a disturbance vector of the system; c is a measurement matrix; v (k) is the measured noise vector of the system; y (k) is a measurement vector;
step two, calculating the predicted value of the state vector
Figure FDA0003355663010000012
Figure FDA0003355663010000013
In the formula (I), the compound is shown in the specification,
Figure FDA0003355663010000014
is an estimated value of the state vector at the moment k-1;
step three, calculating a predicted value P (k | k-1) of the covariance matrix of the system state:
P(k|k-1)＝A(k-1)P(k-1)A(k-1)T+Q；
in the formula, P (k-1) is an estimated value of a covariance matrix of system errors at the k-1 moment; q is a system noise covariance matrix;
step four, calculating a filter gain coefficient K (k):
K(k)＝P(k|k-1)CT/(CP(k|k-1)CT+R)；
in the formula, R is a covariance matrix of a measurement noise vector;
step five, calculating an estimated value P (k) of the covariance matrix of the system state:
P(k)＝P(k|k-1)-K(k)CP(k|k-1)；
wherein, P (k) is the estimated value of the state covariance matrix at the time k;
sixthly, calculating the state vector estimated value
Figure FDA0003355663010000015
Figure FDA0003355663010000021
In the formula (I), the compound is shown in the specification,
Figure FDA0003355663010000022
is an estimated value of the state vector at the moment k;
step seven, calculating the predicted value of the measurement vector
Figure FDA0003355663010000023
To
Figure FDA0003355663010000024
Figure FDA0003355663010000025
In the formula，
Figure FDA0003355663010000026
To
Figure FDA0003355663010000027
Measuring the predicted value of the vector at the moment from k to k + m;
Figure FDA0003355663010000028
as an estimate of the state vector at time k
Figure FDA0003355663010000029
The ith element of (1); n is the order used by the fault autoregressive degradation model; m is the step length of predicting the fault from the current moment to the back;
step eight, calculating the upper boundary of the predicted value of the measurement vector
Figure FDA00033556630100000210
To
Figure FDA00033556630100000211
And a lower boundaryy(k) Toy(k+m)：
Figure FDA00033556630100000212
In the formula (I), the compound is shown in the specification,
Figure FDA00033556630100000213
to
Figure FDA00033556630100000214
Measuring the upper boundary of the vector predicted value for the time from k to k + m;y(k) toy(k + m) is the lower boundary of the measurement vector prediction value at the moment from k to k + m;
step nine, determining a fault early warning result:
Figure FDA00033556630100000215
and isy(k+j)≤ythAnd is
Figure FDA00033556630100000216
In the formula, ythA set fault detection threshold;
if all j enable the above formula to be satisfied when j is taken from 0 to m, the failure is not predicted at the moment k;
if j is taken from 0 to m, and if one j exists so that the above expression is not satisfied, the fact that the fault is predicted at the moment k is shown, and the predicted future fault occurrence moment is k + j*；
And step ten, repeating the step two to the step nine at each moment k, and iteratively realizing fault prediction and early warning.
2. The method for predicting and warning faults by using the autoregressive model and the Kalman filtering algorithm as claimed in claim 1, wherein in the step one, the state vector of the system is given by the following formula:
x＝[f c1 c2 … cn]T；
wherein f is a fault value of the engineering system, c1、c1、…、cnAre coefficients of an autoregressive model.
3. The method for predicting and warning faults using an autoregressive model and a kalman filter algorithm according to claim 1, wherein in the first step, the matrix a (k-1) is given by the following formula:
Figure FDA0003355663010000031
wherein f is a fault value of the engineering system.
4. The method for predicting and warning faults by using the autoregressive model and the Kalman filtering algorithm according to claim 1, wherein in the step one, C is respectively given by the following formulas:
C＝[1 0 0 … 0]。
5. the method for predicting and warning faults by using the autoregressive model and the kalman filter algorithm as claimed in claim 1, wherein in the second step, the iterative computation is started from k to n +1, and the state vector estimation value at the first n +1 moments is given by the following formula:
Figure FDA0003355663010000041
Figure FDA0003355663010000042
6. the method for predicting and warning faults by using an autoregressive model and a Kalman filtering algorithm as claimed in claim 1, wherein in the seventh step, the predicted value of the measurement vector
Figure FDA0003355663010000043
To
Figure FDA0003355663010000044
Determined by iterative calculation through an autoregressive model method, wherein autoregressive model parameters are state vector estimated values
Figure FDA0003355663010000045
2 nd to n +1 th elements.
7. The method of claim 1, wherein in step eight, an upper bound of vector predictors is measured
Figure FDA0003355663010000046
To
Figure FDA0003355663010000047
And a lower boundaryy(k) Toy(k + m) is determined by the 3 sigma interval of kalman filtering,
Figure FDA0003355663010000048
is composed of
Figure FDA0003355663010000049
Standard deviation of (2).
CN202111350431.7A 2021-11-15 2021-11-15 Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm Active CN114063456B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111350431.7A CN114063456B (en) 2021-11-15 2021-11-15 Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111350431.7A CN114063456B (en) 2021-11-15 2021-11-15 Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm

Publications (2)

Publication Number Publication Date
CN114063456A true CN114063456A (en) 2022-02-18
CN114063456B CN114063456B (en) 2023-06-02

Family

ID=80272295

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111350431.7A Active CN114063456B (en) 2021-11-15 2021-11-15 Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm

Country Status (1)

Country Link
CN (1) CN114063456B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115220345A (en) * 2022-07-15 2022-10-21 国网江苏省电力有限公司 Gas turbine state monitoring method based on multivariate state autoregression and Kalman filtering

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4812995A (en) * 1987-05-19 1989-03-14 Girgis Adly A Adaptive Kalman Filtering in fault classification
US5210704A (en) * 1990-10-02 1993-05-11 Technology International Incorporated System for prognosis and diagnostics of failure and wearout monitoring and for prediction of life expectancy of helicopter gearboxes and other rotating equipment
WO1997049977A1 (en) * 1996-06-24 1997-12-31 Arcelik A.S. Model-based fault detection system for electric motors
US20050114023A1 (en) * 2003-11-26 2005-05-26 Williamson Walton R. Fault-tolerant system, apparatus and method
CN101859146A (en) * 2010-07-16 2010-10-13 哈尔滨工业大学 A Satellite Fault Prediction Method Based on Predictive Filtering and Empirical Mode Decomposition
CN108845495A (en) * 2018-04-03 2018-11-20 南通大学 Intermittent fault diagnosis and Active Fault-tolerant Control Method based on the double-deck Kalman filter
CN109508475A (en) * 2018-10-17 2019-03-22 北京航空航天大学 One kind being based on the modified failure active predicting method of multidimensional Kalman filtering
CN110647721A (en) * 2018-06-27 2020-01-03 北京自动化控制设备研究所 A Multivariate Information Fusion Fault Detection Optimization Method
CN112949026A (en) * 2021-01-19 2021-06-11 中国人民解放军火箭军工程大学 Age and state dependence considered degradation equipment residual life prediction method

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4812995A (en) * 1987-05-19 1989-03-14 Girgis Adly A Adaptive Kalman Filtering in fault classification
US5210704A (en) * 1990-10-02 1993-05-11 Technology International Incorporated System for prognosis and diagnostics of failure and wearout monitoring and for prediction of life expectancy of helicopter gearboxes and other rotating equipment
WO1997049977A1 (en) * 1996-06-24 1997-12-31 Arcelik A.S. Model-based fault detection system for electric motors
US20050114023A1 (en) * 2003-11-26 2005-05-26 Williamson Walton R. Fault-tolerant system, apparatus and method
CN101859146A (en) * 2010-07-16 2010-10-13 哈尔滨工业大学 A Satellite Fault Prediction Method Based on Predictive Filtering and Empirical Mode Decomposition
CN108845495A (en) * 2018-04-03 2018-11-20 南通大学 Intermittent fault diagnosis and Active Fault-tolerant Control Method based on the double-deck Kalman filter
CN110647721A (en) * 2018-06-27 2020-01-03 北京自动化控制设备研究所 A Multivariate Information Fusion Fault Detection Optimization Method
CN109508475A (en) * 2018-10-17 2019-03-22 北京航空航天大学 One kind being based on the modified failure active predicting method of multidimensional Kalman filtering
CN112949026A (en) * 2021-01-19 2021-06-11 中国人民解放军火箭军工程大学 Age and state dependence considered degradation equipment residual life prediction method

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115220345A (en) * 2022-07-15 2022-10-21 国网江苏省电力有限公司 Gas turbine state monitoring method based on multivariate state autoregression and Kalman filtering
CN115220345B (en) * 2022-07-15 2025-07-15 国网江苏省电力有限公司 A gas turbine state monitoring method based on multivariate state autoregression and Kalman filtering

Also Published As

Publication number Publication date
CN114063456B (en) 2023-06-02

Similar Documents

Publication Publication Date Title
CN110298455B (en) Mechanical equipment fault intelligent early warning method based on multivariate estimation prediction
CN107941537B (en) A method for evaluating the health status of mechanical equipment
CN104850889B (en) Airplane rotation actuator drive unit adaptive fault detection, isolation and confidences assessment method
CN111628501B (en) AC/DC large power grid transient voltage stability assessment method and system
KR101021801B1 (en) Control Plane Driver Failure Diagnosis of Unmanned Aerial Vehicle Using Adaptive Unknown Input Observer
CN114564000B (en) Active fault tolerance method and system based on intelligent aircraft actuator fault diagnosis
CN113242209B (en) A Generalized Accumulation and Detection Method for False Data Injection Attacks in Smart Grid
CN115407662B (en) Robust fault detection method based on expansion fault detection observer and member collection estimation
KR20150142763A (en) Apparatus for predicting and controlling commutation failure of high voltage direct current system
CN111538316B (en) Performance-based fault diagnosis method and system for actuating mechanism of closed-loop control system
CN114063456A (en) Fault prediction and early warning method using autoregressive model and Kalman filtering algorithm
CN112504357A (en) Dynamic analysis method and system for river channel flow capacity
CN107239622B (en) Aircraft lock mechanism component wear degradation and function degradation competition failure analysis method
CN1472674A (en) Dynamic Adaptive Alarm Method of Equipment State Based on Probabilistic Model
CN112531736A (en) Wide-area damping controller design method for suppressing inter-area oscillation of power system
CN108108552A (en) Load based on failure mechanism damage accumulation model carries on a shoulder pole behavior modeling and emulation mode altogether
CN109324591B (en) Device and method for fault diagnosis of stochastic hybrid system based on robust estimator
EP3712430A1 (en) Detecting wind turbine performance change
CN119472315B (en) Data-driven train fault-tolerant tracking control method
CN115358294A (en) Micro fault detection method for high-speed train traction system
CN114036506A (en) A method for detecting and defending false data injection attacks based on LM-BP neural network
CN116203848B (en) An integrated drive method for aircraft elevator fault perception and protection
CN114254555A (en) Deep learning-based counteraction wheel fault detection and health assessment system and method
Ibaraki et al. H/sub/spl infin//optimization of Luenberger state observers and its application to fault detection filter design
CN108759860A (en) A kind of inertia device Life Calculating Methods and system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant