CN114647189B - Active fault diagnosis method, device and computer readable storage medium - Google Patents
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Abstract
The invention discloses an active fault diagnosis method, an active fault diagnosis device and a computer readable storage medium, wherein the method comprises the following steps: s1, establishing a dynamic equation in a system set form and a reference model according to a system model; s2, establishing an active fault diagnosis optimization problem capable of realizing output tracking control aiming at a single system mode; s3, converting the quadratic programming problem into a non-convex quadratic parameter programming problem, and searching an optimal solution by using a dichotomy; s4, designing input for active fault diagnosis and tracking control according to different stages of the system. On the basis of realizing fault diagnosis, the invention considers the system output tracking control at the same time, thereby realizing the reduction of the influence of the fault diagnosis on the performance of the system output tracking control.
Description
Technical Field
The present invention relates to the field of fault diagnosis technologies, and in particular, to an active fault diagnosis method, an active fault diagnosis device, and a computer readable storage medium.
Background
With the development of current industrial technology, control systems become more and more complex, and therefore some faults are unavoidable when the system is operated. In order to improve the safety and reliability of the system, fault diagnosis techniques are increasingly applied to various systems, and a large number of scholars are attracting their research. Since there is always some uncertainty in the actual system, such as modeling uncertainty, unknown disturbance and measurement noise, the fault diagnosis needs to have certain robustness, i.e. the influence of the system fault on the system can be detected in the presence of system uncertainty.
The current research methods of fault diagnosis mainly comprise two types of methods: random methods and deterministic methods. The random method mainly utilizes uncertainty of a random process and a probability theory modeling system; the deterministic method considers the system uncertainty factor bounded and models the system uncertainty using set theory. Within the framework of the deterministic method, fault diagnostics can also be divided into passive fault diagnostics PFD (passive fault diagnosis) and active fault diagnostics AFD (active fault diagnosis). The former uses the input and output information generated by the system itself to passively perform fault diagnosis, while the latter designs the input excitation system to generate more information for fault diagnosis. Because active fault diagnosis can utilize more system information, active fault diagnosis methods have lower conservation than passive fault diagnosis methods.
In the existing literature, a more mature active fault diagnosis method exists. For example, paper "Scott,J.K.,Findeisen,R.,Braatz,R.D.,&Raimondo,D.M.(2014).Input design for guaranteed fault diagnosis using zonotopes.Automatica,50(6),1580-1589." proposes an offline active fault diagnosis method to implement active fault diagnosis by offline designing an input sequence to achieve separation of output estimation sets. According to the method, the input sequence for realizing set separation is obtained by solving a mixed shaping quadratic programming MIQP (mixed integer quadratic programming) problem, and the calculation complexity is high. On the basis of the method, an online active fault diagnosis method is provided, all output estimation sets are separated step by online solving corresponding optimization problems, so that fault diagnosis is realized, and the calculation complexity is reduced. In addition to this, there are active fault diagnosis methods in which the input signal is designed in different ways to achieve fault diagnosis. However, the current active fault diagnosis method only considers realizing fault diagnosis, and ignores the system control performance, thus resulting in that the system control performance cannot be ensured during fault diagnosis.
In the prior art, the following disadvantages mainly exist:
1. The offline active fault diagnosis method based on the set needs to solve a MIQP problem offline, the calculation complexity increases exponentially with the increase of the shaping variable, and the offline characteristic cannot be combined with fault-tolerant control, so that the application range is limited.
2. The on-line active fault diagnosis method based on the set has the advantages that although the calculation complexity is reduced, the optimization target is complex and is not easy to combine with the control target, so that the combination of the control target and the control method is limited to a certain extent.
3. The existing active fault diagnosis method, whether an online method or an offline method only focuses on the fault diagnosis, is not combined with a control target, so that the output signal designed by the current method can only realize fault diagnosis, and the system output generates larger fluctuation during the fault diagnosis, thereby influencing the working performance of the system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an active fault diagnosis method, an active fault diagnosis device and a computer readable storage medium.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
An active fault diagnosis method comprises the following steps:
s1, establishing a dynamic equation in a system set form and a reference model according to a system model;
s2, establishing an active fault diagnosis optimization problem capable of realizing output tracking control aiming at a single system mode;
s3, converting the quadratic programming problem into a non-convex quadratic parameter programming problem, and searching an optimal solution by using a dichotomy;
s4, designing input for active fault diagnosis and tracking control according to different stages of the system.
In some embodiments, step S2 comprises: s2-1, establishing an active fault diagnosis optimization problem by utilizing an aggregate theory.
In some embodiments, step S2 further comprises: s2-2, establishing an output tracking control optimization problem according to tracking errors between the output collection center and the reference signals.
In some embodiments, step S2 further comprises: s2-3, combining the active fault diagnosis optimization target with the output tracking control optimization target.
In some embodiments, step S2-3 includes: active fault diagnosis is combined with output tracking control optimization targets for a single system modality.
In some embodiments, step S3 comprises: s3-1, converting the quadratic division planning problem into a non-convex quadratic parameter planning problem.
In some embodiments, step S3 further comprises: s3-2, converting the non-convex quadratic programming problem into a 0-1 integer programming problem by utilizing piecewise linear function approximation, and further solving.
In some embodiments, step S4 comprises:
s4-1, determining a control input design of a stage;
s4-2, inputting design and diagnosis strategies in an active fault diagnosis stage.
The invention also provides an active fault diagnosis device comprising a memory, a processor and a computer program stored in the memory and operable on the processor, characterized in that the processor implements the steps of any of the methods described above when executing the computer program.
The invention further provides a computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the steps of any of the methods described above.
Compared with the prior art, the invention has the beneficial effects that: the active fault diagnosis method, the active fault diagnosis device and the computer readable storage medium provided by the invention not only can realize fault diagnosis, but also can introduce the design of system output tracking control in the fault diagnosis stage so as to reduce the influence of the fault diagnosis on the system output tracking performance. Meanwhile, the invention adopts the active fault diagnosis idea, and can realize smooth fault-tolerant control after fault diagnosis is completed. Specifically, the present invention can realize:
1. after the system fails, performing online fault diagnosis to determine a fault mode of the system;
2. during fault diagnosis of the system, the influence of the fault diagnosis on the output tracking control performance of the system is reduced;
3. After fault diagnosis is completed, the system can smoothly realize fault-tolerant control.
Drawings
FIG. 1 is a flow chart of an active fault diagnosis method of an embodiment of the present invention;
FIG. 2 is a circuit diagram of a simulation example of an embodiment of the present invention;
FIGS. 3a, 3b, 3c and 3d are schematic diagrams of active fault diagnosis processes according to embodiments of the present invention;
FIGS. 4a and 4b are graphs of system output during active fault diagnosis of an embodiment of the present invention;
fig. 5a and 5b are schematic diagrams of health and fault residual sets according to embodiments of the present invention.
Detailed Description
The application will be further described with reference to the following drawings in conjunction with the preferred embodiments. It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other.
It should be noted that, in this embodiment, the terms of left, right, upper, lower, top, bottom, etc. are merely relative terms, or refer to the normal use state of the product, and should not be considered as limiting.
The active fault diagnosis method provided by the invention simultaneously considers the system output tracking control on the basis of realizing fault diagnosis, thereby reducing the influence of the fault diagnosis on the performance of the system output tracking control and enabling the system output to track the reference signal as much as possible during the fault diagnosis. Meanwhile, the invention adopts an online active fault diagnosis strategy, and fault-tolerant control can be smoothly realized after the system completes fault diagnosis. The innovative ideas of the embodiments of the present invention are embodied in:
1. the method for establishing the optimization target can simultaneously realize output tracking control and active fault diagnosis;
2. an adaptive weighted design algorithm for system inputs during fault diagnosis;
3. The whole working strategy of the active fault diagnosis method capable of realizing output tracking control.
As shown in fig. 1, the active fault diagnosis method according to the embodiment of the present invention includes the following steps:
s1: establishing a dynamic equation in a system set form and a reference model according to the system model;
consider a discrete linear time invariant system under the influence of actuator failure and disturbances as follows:
Wherein, AndThe system state, input, output, unknown disturbance and measurement error vector at time k, respectively. /(I) AndIs a system parameter matrix. /(I)Is a diagonal matrix and is used to describe a series of health or fault system modalities. Wherein G 0 is an identity matrix representing a healthy mode, i.e. G 0 =i; /(I)Represents the ith failure mode, the jth diagonal elementFaults occurring on the jth actuator are described. WhenIndicating complete failure of the jth actuator; whenIndicating a partial failure of the jth actuator.
Since the system disturbance and measurement error are unknown, it is assumed that ω k and η k are bounded and ω k∈W＝〈ωc,Hω>,ηk∈V＝<ηc,Hη is satisfied. It is also assumed that the system input u k is bounded and satisfies u k∈U＝〈uc,Hu. According to the system-bound assumption, for the ith system modality, the system's collective form dynamics equation is as follows:
Wherein the method comprises the steps of AndRepresenting the state and output estimate set, respectively, in the ith system modality. /(I)Represent minkoste sums. Based on the descriptive form of a centrosymmetric polyhedron, the kinetic equation (2) can be described in terms of a 'center-generator matrix':
where x c,i represents the state, y c,i represents the center of the output estimate set, AndThe generator matrix at time k is shown.The generator matrix at time k+1.
Establishing a corresponding reference model according to a system dynamics equation (1):
Wherein the method comprises the steps of AndRepresenting a reference input, a reference state and a reference output vector, respectively. Let's assume reference inputIs bounded and meets
S2: an active fault diagnosis optimization problem capable of realizing output tracking control is established aiming at a single system mode;
In order to make the active fault diagnosis optimization target consistent with the output tracking control optimization target, a corresponding optimization problem is established for a single system mode.
S2.1: establishing an active fault diagnosis optimization problem by utilizing an aggregate theory;
first, some basic principles of active fault diagnosis are introduced, and it is assumed that all system modes can be detected and separated in one step, that is, a fault of the system is detected at time k, and a fault mode of the system can be determined at time k+1. Thus all considered system modalities can be separated out in one step, the following conditions need to be met:
Wherein the method comprises the steps of AndOutput estimation sets corresponding to the ith and jth system modes at the moment k+1 are respectively represented, and are/isIs an empty set.
Based on the formula (5), the current mode of the system can be determined by judging the condition
Whether or not it is established. The current system modality is the only modality corresponding to the output estimation set that satisfies the condition (6). Thus, in order to achieve active fault diagnosis, the input u k needs to be designed to separate all output estimation sets.
However, in practical systems, it is difficult to design one input u k to separate all output estimation sets in one step, so it is necessary to design one output sequence to separate all output estimation sets in N steps. At present, the existing method converts an optimization problem of N-step separation into a one-step separation problem, however, the method needs to solve a shaping mixed quadratic programming problem offline, has high computational complexity, and is difficult to combine with tracking control. As can be seen from the formula (3), the input u k only affects the central change of the output estimation set, but does not affect the change of the shape and the volume of the output estimation set, and meanwhile, the volume and the shape of the output estimation set do not change greatly as time passes, so that the invention creates an active fault diagnosis optimization target by maximizing the distance between the centers of all the output estimation sets from the perspective of the centers of the output estimation set, and the mathematical expression is as follows:
Wherein the method comprises the steps of AndRespectively the centers of output estimation sets corresponding to the ith and jth system modes at the moment k+1,The number of system modes.
S2.2: establishing an output tracking control optimization problem according to the tracking error between the output collection center and the reference signal;
The invention realizes active fault diagnosis and simultaneously needs to ensure the output tracking control performance of the system. In order to establish the output tracking control optimization target, the invention utilizes the output estimation set CenterAnd reference outputThe square of the Euclidean distance between describes the performance of the system output tracking control, i.e.Since the system modalities cannot be determined during fault diagnosis, tracking control problems of all modalities need to be considered. Comprehensively considering all system modes, the optimization targets of the output tracking control are as follows:
Wherein the method comprises the steps of The reference output at time k+1.
S2.3: combining the active fault diagnosis optimization target with the output tracking control optimization target;
The optimization directions of formulas (7) and (8) are opposite as known from the active fault diagnosis and tracking control optimization target definition. If the distance between all output estimation set centers is maximized, the minimum tracking control optimization target cannot be ensured; in contrast, if the tracking error between all output estimation-set centers and the reference output is minimized, the maximization of the distance between all output estimation-set centers cannot be achieved. However, for a single system modality, the active fault diagnosis optimization objective is consistent with the output tracking control optimization objective. The invention thus first combines active fault diagnosis with output tracking control optimization objectives for a single system modality. For the mth system modality, its output tracking control optimization target is reconstructed as follows:
In combination with formulas (7) and (9), for the mth system modality, an optimization objective of active fault diagnosis and output tracking control is considered while constructing the following:
Wherein the method comprises the steps of Defining the moment k as the input for the mth system modality and e as an arbitrarily small positive number.
For ease of expression, two output errors are first definedAndThe following equations can be derived from equations (3) and (4):
Based on equation (12) it is then possible to obtain:
the optimization problem can be described as the following quadratic programming problem by taking equations (11) and (13) into (10):
Wherein,
S3: converting the quadratic programming problem (14) into a solution to the non-convex quadratic parameter programming problem, and searching for an optimal solution by using a dichotomy;
S3.1: converting the quadratic element programming problem (14) into a solution to the non-convex quadratic parameter programming problem;
To facilitate the description of the optimization problem solution, the symbolic expressions in the problem (14) are first simplified, the symbolic subscripts k and superscripts m in the omitted, and the optimization problem is re-described as:
Wherein the method comprises the steps of J 2(u)＝uTQ1u+Q2u+Q3 u is the system input. The problem can be converted into a quadratic parameter programming problem according to the following theorem.
Lemma 1: the following equation is defined:
Where λ is a parameter variable greater than 0.
Simultaneous commandU *＝u(λ* is the optimal solution to the optimization problem (16) if there is λ * +.0 so that pi (λ *) =0.
And (4) lemma 2: for the followingFunctionIs a continuously decreasing concave function.
According to the lemma 1, the optimization problem (14) can be solved by finding a λ * such that pi (λ *) =0. Therefore, the following quadratic programming problem needs to be considered first:
When the quadratic term And when the quadratic programming problem is a convex quadratic programming problem, the optimal solution can be obtained according to a convex optimization theory. However, it is not guaranteedThe constant holds, so solutions to the non-convex quadratic programming problem need to be considered.
S3.2: converting the non-convex quadratic programming problem into a 0-1 integer programming problem by utilizing a piecewise linear function approximation formula (18), and further solving the formula (18);
Since P 1-λQ1 is a real symmetric matrix, there is one orthogonal matrix D such that D T(P1-λQ1) d=Θ, where Respectively, the eigenvalues of the matrix Θ. Let z=du, then
F(z,λ)＝zTΘz+(P2-λQ2)D-1z+(P3-λQ3)。 (19)
Thus equation (18) can be converted into
Where z=du= < DU c,DHu >.
Assuming θ h(λ)≤0＜θh+1 (λ), the quadratic term in equation (19) can be re-described as:
Wherein the method comprises the steps of As a non-convex term, the present invention converts the non-convex optimization problem equation (20) into a convex problem by approximating the non-convex term with a piecewise linear function. For the ith component of z, the maximum and minimum values are defined as z i(m+1) and z i1, respectively, and the interval [ z i1,zi(m+1) ] is divided into m equal parts. By introducing a set of auxiliary variables γ ij (i=1, 2,..h, j=1, 2,..m+1) and 0-1 variables v ij (i=1, 2, h), equation (20) can be converted to a shaped quadratic programming problem as follows:
Obviously, there is some error in approximating the quadratic function with the piecewise linear function, i.e., there is an error between the optimal values of formulas (20) and (22). Assuming that the optimal solution of equation (22) is (v *,z*,γ*), let the optimal values of equations (20) and (22) be:
If (g *-f*)/f* is less than or equal to epsilon, then (v *,z*,γ*) is the epsilon-precision optimal solution of the optimization problem formula (20), otherwise, assuming that the ith component of z * is in the interval [ z is,zi(s+1) ], the new interval [ z is,zi(s+1) ] is utilized to solve the optimization problem formula (22) again until the optimal solution can meet (g *-f*)/f* is less than or equal to epsilon.
S3.3: finding lambda * by using a dichotomy to enable pi (lambda *) =0, and obtaining an optimal solution u * of the optimization problem formula (16);
According to lemma 2, the function pi (λ) decreases strictly, so only the upper and lower bounds λ u and λ l of λ need to be found to satisfy I.e. lambda * can be found by dichotomy so that pi (lambda *) =0. According to the definition of J 1 (u), forJ 1 (u) > 0 is assembled, so λ l =0 can be made. Because of
For the followingThe constant is established, so let the upper bound of lambda be
The procedure for the dichotomy is shown in Table 1.
TABLE 1 dichotomy algorithm
S4: according to different stages of the system, an input u k for active fault diagnosis and tracking control is designed;
The whole system operation process can be divided into two stages: a determination phase and an active fault diagnosis phase. The system mode of the determining stage is determined, and the system mode of the active fault diagnosis stage is unknown, so that main control targets of the two stages are different, and input design methods are different.
S4.1: determining a control input design of a stage;
Since the mode of the system is known in the determining stage, fault diagnosis is not needed in the stable stage, and only the output tracking control performance of the system is ensured. Assuming that the current mode of the system is in the mth system mode, at this time, the system input only needs to ensure that the error between the output estimation set center corresponding to the mth mode and the reference output is minimum, so that the control output design targets are as follows:
because the formula (24) is a convex quadratic programming problem, the formula (24) can be solved by using a convex optimization method. The optimal input is the optimal solution of the optimization problem formula (24).
S4.2: inputting design and diagnosis strategies in an active fault diagnosis stage;
In the active fault diagnosis stage, the system mode is unknown, so that the main control target of the stage is to realize active fault diagnosis and ensure the output control performance to a certain extent. To meet the control objective of this stage, it is first necessary to calculate the optimal control inputs for the individual system modalities according to step 3. However, at one moment only one input can be injected into the system, so that it is necessary to determine the final control input from the obtained plurality of optimal inputs. The invention obtains the final control input by using a weighted summation mode:
Wherein the method comprises the steps of Is a weight coefficient and satisfiesConsidering that the output of the system contains the modal information of the system, better control performance can be obtained by utilizing the self-adaptive design weight coefficient of the output information of the system. The adaptive weight coefficient is designed as follows:
It should be noted that at the initial time k f of the failure diagnosis, due to the system output The design of the weight coefficient using the formula (26) at this time loses practical significance without any system failure information, and therefore, the weight coefficient at the failure diagnosis initial time k f is specified to be designed as follows:
In the active fault diagnosis stage, an important control objective is to realize fault diagnosis, the input signal u k of the stage can be obtained by the method, u k is injected into the system to obtain the output y k+1 at the next moment, and the output y k+1 and the output estimation set are obtained according to the system The relation between the two can realize the on-line active fault diagnosis. In this stage, it is determined whether the condition (6) is satisfied at each moment, and if the output estimation set corresponding to the ith system mode does not satisfy the condition (6), it is indicated that the ith system mode is not the current system mode, and the system mode can be removed to reduce the calculation amount. Until only one output estimation set meets the condition (6), the fault diagnosis is completed, and the current mode of the system is the mode corresponding to the output estimation set.
After the fault diagnosis is completed, the system mode is determined again, so that the system enters the determining stage again, and the optimal control input of the system can be obtained through the step S4.2.
The overall fault diagnosis strategy is summarized in table 2.
TABLE 2 active fault diagnosis strategy for implementing output tracking control
In order to verify the effectiveness of the algorithm, the invention uses an electronic circuit example to design a simulation experiment. The electronic circuit diagram is shown in fig. 2. The system state is the capacitance voltage V C (t) and the inductance current i L (t), the system input is the two voltage sources V 1 (t) and V 2 (t), and the system input is the capacitance voltage and the resistor R 3. Furthermore, d (t) is the system perturbation, and a 1 and a 2 are the corresponding scaling coefficients, the matrix parameters of the kinetic equation in the form of the state space of the system are as follows:
Wherein the specific values of the parameters are R1＝5Ω,R2＝100Ω,R3＝1Ω,L＝0.8H,Cp＝5mF,Re＝R1+R2,a1＝1 and a 2 =2.
Introducing measurement uncertainty on the basis of the dynamic equation, and discretizing the system with sampling time of 0.1s to obtain the following dynamic equation:
xk+1＝Adxk+BdGiuk+Edωk,
yk＝Cdxk+Fdηk,
Wherein the method comprises the steps of
Four different fault modes are designed in the simulation example, namely:
the system disturbance constraint set W and the measurement noise set V are
Output constraint set is
The initial state of the system is x 0＝[0,0]T, and the reference input is
The system is assumed to be in the first failure mode when it fails. The whole working process of the system is as follows, from k=0 to k=14, the system is in a healthy mode, and only output tracking control of the system needs to be considered. At this stage, the system output may be obtained by solving equation (24). At time k=15, the system fails, and the system enters a failure diagnosis stage. At this stage, the input design is designed to achieve fault diagnosis while ensuring system output tracking control performance, and the input can be obtained in step S4.2. The whole fault diagnosis process is as shown in fig. 3a-3d, at time k=15, the system is faulty, at this time, all output estimation sets contain system output, the current mode of the system cannot be judged, the system output is obtained through step S4.2 and is injected into the system, all output estimation sets have a tendency of separation, and at time k=16, the output estimation sets are outputAndThe system output y 16 is not included, and the 0 th and 4 th system modes can be eliminated at this time; at time k=17,The system output y 17 is not included, at which point the 3 rd system modality may be excluded; at time k=18,Does not include the system output y 18 and onlyThe system output y 18 is included, and the system completes fault diagnosis at this time, and the 1 st system mode is the current system mode. In this process, as shown in fig. 4a and fig. 4b, the actual output of the system is in a healthy mode from k=0 to k=14, the actual output of the system can track the reference output, when k=15, the system fails, and the input design needs to simultaneously consider active fault diagnosis and output tracking control, at this time, the performance of the tracking control of the output of the system is affected to a certain extent, and after the fault diagnosis is completed, the mode of the system is determined to be the 1 st fault mode, and the system adjusts the control target, so that the output can re-track the reference signal.
In order to illustrate that the active fault diagnosis method can obtain a better output tracking effect during fault diagnosis, the result is shown in fig. 5a and 5b in comparison with an active fault diagnosis method that optimizes only an active fault diagnosis target. Wherein a solid line r 1 represents an error curve between the system output and the reference signal obtained by using the fault diagnosis method of the optimization target only; the dashed line r 2 represents the error curve between the system output and the reference signal obtained by the active fault diagnosis method proposed by the present invention. As can be seen from the figure, the active fault diagnosis method provided by the invention can effectively control the system output tracking control performance in the fault diagnosis stage, so that the system output tracking error is smaller. However, since this method needs to consider a plurality of optimization targets at the same time, the system needs a longer time to perform fault diagnosis.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several equivalent substitutions and obvious modifications can be made without departing from the spirit of the invention, and the same should be considered to be within the scope of the invention.
Claims (10)
1. An active fault diagnosis method is characterized by comprising the following steps:
s1, establishing a dynamic equation in a system set form and a reference model according to a system model;
Wherein, the kinetic equation of the system set form is as follows:
In the method, in the process of the invention, AndRepresenting the state and output estimation set in the ith system mode, respectively,Representing the minkoste sum,AndIs a system parameter matrix,Is a diagonal matrix, ω k∈W＝<ωc,Hω>,ηk∈V＝<ηc,Hη >,AndThe method comprises the steps of inputting at the moment k, unknown disturbance and measuring an error vector;
Wherein, the reference model is:
In the method, in the process of the invention, AndRepresenting a reference input, a reference state, and a reference output vector, respectively;
s2, establishing an active fault diagnosis optimization problem capable of realizing output tracking control aiming at a single system mode;
Wherein the optimization problem is described as the following quadratic element programming problem:
In the method, in the process of the invention,
X c,i represents a state; epsilon is an arbitrarily small positive number;
s3, converting the quadratic programming problem into a non-convex quadratic parameter programming problem, and searching an optimal solution by using a dichotomy;
The symbol expression in the problem (14) is simplified, the symbol subscript k and the superscript m in the formula are omitted, and the quadratic programming problem is converted into the solution of the quadratic programming problem:
wherein lambda is a parameter variable ,J1(u)＝uTP1u+P2u+P3+∈,J2(u)＝uTQ1u+Q2u+Q3,u greater than 0 as a system input;
When the quadratic term P 1-λQ1 is more than or equal to 0, the quadratic programming problem is a convex quadratic programming problem, and an optimal solution can be obtained according to a convex optimization theory; however, the constant establishment of P 1-λQ1 is not guaranteed, so that the solution of the non-convex quadratic programming problem needs to be considered;
s4, designing input for active fault diagnosis and tracking control according to different stages of the system.
2. The active fault diagnosis method according to claim 1, wherein step S2 includes:
S2-1, establishing an active fault diagnosis optimization problem by utilizing an aggregate theory.
3. The active fault diagnosis method according to claim 2, wherein step S2 further comprises:
S2-2, establishing an output tracking control optimization problem according to tracking errors between the output collection center and the reference signals.
4. The active fault diagnosis method according to claim 2, wherein step S2 further comprises:
S2-3, combining the active fault diagnosis optimization target with the output tracking control optimization target.
5. The active fault diagnosis method according to claim 4, wherein step S2-3 comprises: active fault diagnosis is combined with output tracking control optimization targets for a single system modality.
6. The active fault diagnosis method according to claim 1, wherein step S3 includes:
S3-1, converting the quadratic division planning problem into a non-convex quadratic parameter planning problem.
7. The active fault diagnosis method according to claim 6, wherein step S3 further comprises:
s3-2, converting the non-convex quadratic programming problem into a 0-1 integer programming problem by utilizing piecewise linear function approximation, and further solving.
8. The active fault diagnosis method according to claim 1, wherein step S4 includes:
s4-1, determining a control input design of a stage;
s4-2, inputting design and diagnosis strategies in an active fault diagnosis stage.
9. An active fault diagnosis device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1-8 when executing the computer program.
10. A computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the steps of the method according to any of claims 1-8.
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