CN114115185B - Fault detection threshold value calculation method based on interval operation - Google Patents

Fault detection threshold value calculation method based on interval operation Download PDF

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CN114115185B
CN114115185B CN202111350425.1A CN202111350425A CN114115185B CN 114115185 B CN114115185 B CN 114115185B CN 202111350425 A CN202111350425 A CN 202111350425A CN 114115185 B CN114115185 B CN 114115185B
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error
interval
residual
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CN114115185A (en
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王振华
马有道
沈毅
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Harbin Institute of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/20—Pc systems
    • G05B2219/24—Pc safety
    • G05B2219/24065—Real time diagnostics
    • 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
    • Y04S10/52—Outage or fault management, e.g. fault detection or location

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Abstract

The invention discloses a fault detection threshold value calculation method based on interval operation, which comprises the following steps: describing the range of initial state estimation errors, disturbance vectors and measurement noise uncertainty by using a vector interval; step two, deriving a vector interval in which a state estimation error is positioned when no fault exists by utilizing an error dynamic equation and the property of interval operation; step three: and calculating a vector interval in which the residual error is positioned when no fault exists according to the relation between the residual error and the state estimation error as a threshold value. According to the method, dynamic thresholds for fault detection can be automatically generated according to the initial state estimation error, the disturbance vector and the measuring noise range, the thresholds of all components of residual errors in the fault-free state can be accurately calculated, and the purpose of fault detection of a given system is achieved by utilizing the thresholds.

Description

Fault detection threshold value calculation method based on interval operation
Technical Field
The invention belongs to the field of fault detection, relates to a fault detection threshold calculation method, and in particular relates to a fault detection threshold calculation method based on interval operation.
Background
In actual industrial production, serious damage is often caused by faults of systems such as instruments and equipment. The fault generated by the system can be timely detected, and the fault is a direction of important attention in the field of fault diagnosis. Fault detection methods currently in wide use include model-based methods, data-based methods, and experience-based methods. The fault detection method based on the model requires that the system model is known, and has low influence on the main view, high accuracy of detection results and low requirement on the actual measured data quantity, so that the fault detection method is paid attention to. Among the model-based fault detection methods, observer-based fault detection is the most commonly used method. The basic idea of observer-based fault detection is to estimate the system output signal without faults by using the observer, and then compare the output estimated value with the actual output to obtain a residual signal capable of reflecting the faults. In an ideal case, if the residual is not zero, this indicates a failure. However, since the system model is affected by the uncertainty of the state, the process disturbance and the measurement noise at the initial time, the residual error is not zero when there is no fault, and thus a threshold value needs to be set to distinguish the influence of the fault from the uncertainty. In the fault detection process, the design of the threshold is very important: setting the threshold too large increases the false alarm rate, and setting the threshold too small increases the false alarm rate. Therefore, how to evaluate the effect of uncertainty on the residual and set a reasonable threshold is an important element of fault detection. However, there is currently little research effort in threshold design. Traditional threshold design methods rely primarily on the experience of the designer.
Describing uncertainty with vector intervals is a description method used to represent uncertainty boundaries. By means ofRespectively representing n-dimension and m x n-dimension European space, the endpoint vector of a given vector interval +.>And and (2)>The vector interval is defined as:
where the index i represents the i-th component of the corresponding vector.
For vectors in the vector intervalEndpoint->x is the upper and lower boundaries of the vector x, and satisfies the following interval operation properties:
wherein A is + ＝max(A,0)，A - ＝A + -A。
Disclosure of Invention
In order to solve the problem that the existing fault detection threshold design depends on experience of a designer, the invention provides a system and an effective fault detection threshold calculation method based on interval operation.
The invention aims at realizing the following technical scheme:
a fault detection threshold value calculation method based on interval operation comprises the following steps:
step one, describing the range of initial state estimation errors, disturbance vectors and measurement noise uncertainty by using vector intervals, wherein the method comprises the following specific steps of:
for a linear continuous time invariant system as follows:
in the method, in the process of the invention,the state vector, the measurement vector, the disturbance vector and the measurement noise vector of the system at the moment t are respectively, n x 、n y 、n w 、n v Dimensions of x (t), y (t), w (t), v (t), A, B, C, D, respectively 1 、D 2 Is a constant matrix with proper dimension;
the range of initial state estimation errors, disturbance vectors, measurement noise uncertainty is described by vector intervals:
where e (0) is the initial state estimation error, e(0) The upper and lower boundaries of the known initial state estimation error are respectively, w (t) is the disturbance vector at the moment t,/-> wThe upper and lower boundaries of the known disturbance vector, v (t) is the measurement noise at time t,/respectively> vThe upper and lower boundaries of the known measurement noise, respectively.
Step two, deriving a vector interval in which the state estimation error is positioned when no fault exists by utilizing an error dynamic equation and the property of interval operation, wherein:
the error dynamic equation is:
in the method, in the process of the invention,is the state estimation error at time t, +.>Is the gain matrix of the fault detection observer.
The vector interval where the state estimation error is located when there is no fault is:
in the method, in the process of the invention, e(t) is the upper and lower boundaries of the state estimation error e (t) at the time t respectively:
in the method, in the process of the invention,respectively t time->Upper and lower boundaries of (2):
step three: calculating a vector interval in which the residual error is positioned when no fault exists as a threshold according to the relation between the residual error and the state estimation error, wherein the vector interval in which the residual error is positioned when no fault exists is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device, r(t) is the upper and lower boundaries of the t-moment residual vector r (t):
the threshold value of each component of the residual isAndr(t) the range of the interval enclosed by the corresponding components, namely:
wherein r is imax (t)、r imin (t) the upper and lower boundaries of the ith component of the residual vector at time t, r i (t) are respectively-> rThe ith component of (t).
Compared with the prior art, the invention has the following advantages:
1. the threshold value calculation method provided by the invention is a dynamic threshold value obtained by describing the uncertainty range by using the vector interval, and has the advantages of simple form and easy calculation. When the prior conditions such as disturbance vector, measurement noise and the like are changed, the range of the disturbance vector can be described in real time by using a vector interval, and meanwhile, the range of state estimation errors and residual errors involved in the calculation process is given in the form of the vector interval.
2. The error general solution obtained by deduction according to the state estimation error is related to the initial time state of the system, so that the residual error threshold obtained according to the invention considers the influence of the initial state on the system.
3. In the process of solving the residual error threshold, the range of each component of the residual error vector is given according to the definition of the vector interval, and the range is used as the fault detection threshold of each component of the residual error. Compared with the traditional threshold value based on the residual norm, the threshold value obtained by the method has higher practicability in fault detection.
Drawings
FIG. 1 is a flow chart of a method for calculating a fault detection threshold based on interval operation;
FIG. 2 is a relationship between actual residuals and designed thresholds for no failure;
FIG. 3 shows the relationship between the actual residual error and the designed threshold value after the fault signal is applied.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a fault detection threshold value calculation method based on interval operation. And then designing a residual error generator based on an observer, obtaining a dynamic equation of the state estimation error through a system equation and an observer equation, obtaining a general solution of the state estimation error based on the dynamic equation of the state estimation error, and obtaining a vector interval in which the state estimation error is positioned in real time by combining the related property of interval operation. And then the relation between the residual error and the error is obtained by defining the residual error, and the range of the residual error without faults is obtained, and the range of each component of the residual error without faults can be obtained according to the definition of the vector interval and used as the threshold value of residual error evaluation in fault diagnosis. As shown in fig. 1, the specific steps are as follows:
step one, describing the range of uncertainty such as initial state estimation error, disturbance vector, measurement noise and the like by using a vector interval.
For a linear continuous time invariant system as follows:
in the method, in the process of the invention,the state vector, the measurement vector, the disturbance vector and the measurement noise vector of the system at the moment t are respectively, n x 、n y 、n w 、n v Dimensions of x (t), y (t), w (t), v (t), A, B, C, D, respectively 1 、D 2 Is a constant matrix with suitable dimensions.
The range of uncertainty of initial state estimation errors, disturbance vectors, measurement noise and the like is described by using vector intervals:
where e (0) is the initial state estimation error, e(0) The upper and lower boundaries of the known initial state estimation error are respectively, w (t) is the disturbance vector at the moment t,/-> wThe upper and lower boundaries of the known disturbance vector, v (t) is the measurement noise at time t,/respectively> vThe upper and lower boundaries of the known measurement noise, respectively.
And step two, deriving a vector interval in which the state estimation error is positioned when no fault exists by utilizing the error dynamic equation and the property of interval operation.
Assume that an observer-based residual generator has been designed to:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the state estimation vector at time t, +.>Is the residual vector at time t, for detecting malfunctions->Is the gain matrix of the fault detection observer. In the present invention, it is assumed that L is a constant matrix that has been designed. In order to obtain the threshold value for fault detection, the range of the residual r (t) in the absence of faults needs to be calculated, for which the following state estimation errors are defined:
and (3) taking the difference between the steps (4) and (5) to obtain an error dynamic equation:
based on (7), a general solution of the error dynamics can be obtained:
for the integral term in (8):
the method comprises the following steps:
a kind of electronic device with high-pressure air-conditioning system:
ζ(0)＝0 (11)。
based on the nature of the interval operation, one can obtainThe vector interval in which:
in the method, in the process of the invention,respectively t time->Upper and lower boundaries of (2):
and then carrying out interval operation on the state estimation error (6) to obtain a vector interval in which the state estimation error at the moment t is positioned:
in the method, in the process of the invention, e(t) is the upper and lower boundaries of the state estimation error e (t) at the time t respectively:
step three: and calculating a vector interval in which the residual error is positioned when no fault exists according to the relation between the residual error and the state estimation error as a threshold value.
The definition of the residual is available from (5):
through step two we can obtain an expression of the state estimation error. By using the relation between the residual error and the state estimation error given in (15), the threshold range of the residual error r (t) can be obtained by using the section operation property, and the threshold value of fault diagnosis can be performed by the threshold value.
The vector interval in which the residual error is located can be obtained by the property of interval operation:
in the method, in the process of the invention, r(t) is the upper and lower boundaries of the t-moment residual vector r (t):
as can be seen from the definition of the vector interval, the range of the i element of the residual error described in (17) is the range of the interval surrounded by the i element of the endpoint vector, namely:
wherein r is imax (t)、r imin (t) are respectively tThe upper and lower boundaries of the i-th component of the temporal residual vector, r i (t) are respectively-> rThe ith component of (t).
The range of each component of the residual obtained according to (19) is the fault detection threshold of each component of the residual designed by the invention.
Examples:
the linear continuous time-invariant system model is given as:
where u (t) =1.5 sin (3 t), matrix parameters:
further, assume that the initial state estimation error and the interference noise satisfy:
[-2-1-2] T ≤e(0)≤[212] T ；
-0.2≤w(t)≤0.2；
-0.1≤v(t)≤0.1。
executing the first step: describing an initial state estimation error and an interference noise range by using a vector interval:
wherein:
executing the second step: for a linear continuous time invariant system design like the residual generator of (5), to stabilize the observer, the observer gain is chosen here:
a dynamic equation based on the residual generator of the observer and the state estimation error can be derived and a general solution of the state estimation error can be derived. The vector interval where the state estimation error is located in no fault can be obtained in real time by utilizing the property of interval operation.
Executing the third step: and obtaining a vector section in which the residual error is positioned when no fault exists by utilizing the relation between the residual error and the state estimation error, and taking the range of each component of the obtained residual error as a fault detection threshold value of each component of the residual error.
The threshold range for fault detection residual evaluation obtained by the present invention is shown in fig. 2. Wherein the solid line represents the actual residual error of the system, and the broken line represents the fault detection threshold value of each component of the residual error obtained by the invention. It can be found that the actual residual component does not exceed the designed threshold range in the absence of faults. To verify that the designed threshold has the ability to detect faults, actuator faults are added:
wherein:
the fault detection result shown in fig. 3 is obtained, and it can be seen from the graph that the actual residual error of the system after 5s exceeds the designed threshold range, and the system can be detected to be faulty after 5 s.
Conclusion of this example: the invention is used for carrying out residual threshold calculation on the given linear continuous time-invariant system, thereby realizing the fault detection of the given system. The invention uses vector interval to describe the range of uncertainty such as initial state estimation error and interference noise, and for the general solution of state estimation error, uses the property of interval operation to deduce the vector interval where state estimation error is located at all time, and then uses the relation between system residual error and state estimation error to obtain the vector interval where residual error is located when no fault, and uses the definition of vector interval to obtain the boundary of each variable of residual error at any time when no fault is located and uses the boundary as the threshold range of fault detection. In order to detect the fault detection capability, a fault signal is manually added, and the fault which can be detected by the residual error threshold value obtained according to the invention is found to be smaller. The threshold value obtained according to the invention is a dynamic threshold value which changes along with time, so that the fault of the system can be accurately detected, and meanwhile, the method for describing the uncertainty by using the vector interval is simple and convenient to calculate and easy to implement. The method can accurately obtain the threshold value of the residual error signal of the system, achieves the aim of fault detection based on the model, and is a reliable residual error evaluation threshold value calculation method.

Claims (1)

1. The fault detection threshold value calculation method based on interval operation is characterized by comprising the following steps:
step one, describing the range of initial state estimation errors, disturbance vectors and measurement noise uncertainty by using vector intervals, wherein the method comprises the following specific steps of:
for a linear continuous time invariant system as follows:
in the method, in the process of the invention,the state vector, the measurement vector and the disturbance direction of the system at the moment t are respectivelyQuantity and measurement noise vector, n x 、n y 、n w 、n v Dimensions of x (t), y (t), w (t), v (t), A, B, C, D, respectively 1 、D 2 Is a constant matrix;
the range of initial state estimation errors, disturbance vectors, measurement noise uncertainty is described by vector intervals:
where e (0) is the initial state estimation error, e(0) The upper and lower boundaries of the known initial state estimation error are respectively, w (t) is the disturbance vector at the moment t,/-> wThe upper and lower boundaries of the known disturbance vector, v (t) is the measurement noise at time t,/respectively> vUpper and lower boundaries of known measurement noise, respectively;
step two, deriving a vector interval in which the state estimation error is positioned when no fault exists by utilizing an error dynamic equation and the property of interval operation, wherein:
the error dynamic equation is:
in the method, in the process of the invention,is the state estimation error at time t, +.>Is the gain matrix of the fault detection observer;
the vector interval where the state estimation error is located when there is no fault is:
in the method, in the process of the invention, e(t) is the upper and lower boundaries of the state estimation error e (t) at the time t respectively;
ethe expressions of (t) are respectively:
in the method, in the process of the invention,respectively t time->Upper and lower boundaries of (2);
the expressions of (2) are respectively:
step three: calculating a vector interval in which the residual error is positioned when no fault exists as a threshold according to the relation between the residual error and the state estimation error, wherein:
the vector interval where the residual error is located when no fault exists is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device, r(t) is the upper and lower boundaries of the residual vector r (t) at the moment t, and the threshold value of each component of the residual is +.>Andr(t) the range of the interval enclosed by the corresponding components, namely:
in the method, in the process of the invention,upper and lower boundaries of the ith component of the residual vector at time t,/respectively> r i (t) are respectively-> rThe ith component of (t);
rthe expressions of (t) are respectively:
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