A fault diagnosis method based on state set separation and set-valued observer

Abstract

The application provides a fault diagnosis method based on state set separation and set value observer, which is suitable for discrete linear constant LTI systems. The method establishes a state space model containing bounded random disturbance and measurement noise, determines observer gain and system input for passive and active fault diagnosis, respectively. Using these parameters, state estimation sets and residual sets are constructed, and fault diagnosis is performed by analyzing the relationship between residual signals and sets. When a fault is detected, the state estimation set at the previous time is used as the initial value to further analyze and identify the fault type. This method is particularly suitable for systems with significant noise influence, and through innovative parameter optimization and state set separation strategy, it improves the accuracy and application range of fault diagnosis, and is suitable for passive and active fault diagnosis scenarios.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fault diagnosis, in particular to a fault diagnosis method based on state set separation and set-valued observer. BACKGROUND

[0002] With the progress of aviation, aerospace, industry, electronic communication, robot and other fields, the complexity, integration and automation level of the system are increasing, at the same time, the possibility of faults and risks occurring inside the system is also increasing. If these faults cannot be handled in time, the system may develop from a fault state to a failure state, which will cause the performance of the system to decline, and even cause serious personnel casualties and property losses. Therefore, the fault diagnosis technology with high reliability and real-time performance has very important significance for industrial application scenarios that require high safety and reliability.

[0003] The methods currently used in fault diagnosis technology mainly focus on model-based fault diagnosis methods and data-driven fault diagnosis methods. The diagnosis effect of the data-driven fault diagnosis method highly depends on the quantity and quality of historical data, and has weak self-adaptive ability. The model-based fault diagnosis method has more explicit physical meaning, but due to the existence of uncertainties such as disturbances and noises in the actual system, the method cannot obtain the accurate model of the real system in the actual modeling process. At the same time, the diagnosis performance of the model-based fault diagnosis method is highly dependent on the mathematical model of the diagnosis object, so this kind of method must be able to handle the influence of disturbances, noises and modeling errors on fault diagnosis. This technology is called robust fault diagnosis. In recent years, with the development of set theory, probability theory and numerical optimization technology, the model-based robust fault diagnosis technology has developed a new paradigm, which enables this kind of technology to obtain reliable fault diagnosis thresholds in real time under the premise of tolerating disturbances and noises, so it has very broad application prospects in many industrial production links.

[0004] The model-based robust fault diagnosis scheme can be further divided into passive fault diagnosis (PFD) and active fault diagnosis (AFD). Compared with the former, the latter not only accepts the input and output information of the system, but also further designs the system input to stimulate the system to obtain more information for diagnosis target, so the design is more complex. However, under the premise of ensuring robustness, the latter has higher sensitivity than the former, especially in the diagnosis of early faults, small faults and other faults, so it is foreseeable that it will have broader application potential and prospects.

[0005] The existing model-based robust fault diagnosis technology mainly falls into two categories: one is a random method, which treats the disturbance and noise as random variables, that is, assumes that the disturbance and noise obey a known probability distribution, such as a Gaussian distribution. Representative methods include fault diagnosis technologies based on Kalman filter, extended Kalman filter, and unscented Kalman filter. The relative influence of the disturbance and noise under the probability distribution on the system fault is considered by considering the probability distribution of the uncertainty such as disturbance and noise. The advantage of this scheme is high sensitivity. It is difficult to obtain the accurate probability distribution of the disturbance and noise, and the error of the probability distribution causes the fault diagnosis result to be unreliable: the existing random fault diagnosis scheme based on the assumption that the distribution of the disturbance and noise is known needs to know the accurate probability distribution information of the disturbance and noise. However, in actual engineering, especially in some large and complex systems, due to testing difficulties or cost limitations, it is often difficult to obtain enough high-quality experimental samples to establish the accurate probability distribution of certain parameters. Moreover, even a slight deviation of the distribution parameters from the true value can cause a large deviation in the reliability of the fault diagnosis conclusion. Therefore, in the case of error between the actual distribution and the theoretical distribution, false alarm or missed detection of faults will occur, which greatly reduces the reliability of the technology.

[0006] Another type of fault diagnosis scheme is the bounded method. Although the probability distribution of the uncertainty such as disturbance and noise cannot be accurately obtained, its upper and lower bounds are relatively easy to obtain. Representative methods include set theory unknown input observer, set observer, and set member filter. In practice, it is often easier and more reliable to obtain the upper and lower bounds of the disturbance and noise than to obtain their accurate probability distribution. For example, in the processing of uncertainty caused by friction, it is difficult to obtain the probability distribution of the friction coefficient due to the complexity of the lubrication environment. However, according to existing experience, the interval of the friction coefficient is easy to obtain. The advantage of this scheme is that it does not require prior information about the distribution of the disturbance and noise, and has a wider range of applications. High conservatism problem: the existing fault diagnosis scheme with unknown but bounded disturbance and noise distribution has high conservatism, which leads to high missed detection rate. For example, the fault diagnosis method based on the set theory unknown input observer has high conservatism when the system is mainly affected by measurement noise, and the set observer has high conservatism when the system is mainly affected by random disturbance.

[0007] It should be noted that the information disclosed in the above background section is only for understanding the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0008] The main purpose of the present application is to solve the problems existing in the above background technology, and to provide a fault diagnosis method based on state set separation and set observer.

[0009] To achieve the above object, the present application adopts the following technical solutions:

[0010] A fault diagnosis method based on state set separation and set-valued observer, comprising:

[0011] S1: Establishing a state space model of a discrete linear constant LTI system to be diagnosed with bounded random disturbance and measurement noise, which is used to describe the dynamic behavior of the system under normal and fault states;

[0012] S2: According to the state space model, determining the undetermined parameters of the set-valued observer; wherein for passive fault diagnosis, determining the observer gain; for active fault diagnosis, determining the observer gain and system input, which is designed to facilitate the fault diagnosis process;

[0013] S3: According to the determined parameters of the set-valued observer, establishing the dynamic equation of the state estimation set and the residual set for the healthy mode of the discrete LTI system, wherein the state estimation set is used to represent the possible state range of the system, and the residual set is used to detect the deviation between the system state and the model prediction;

[0014] S4: According to the established state estimation set and residual set, making a fault diagnosis decision by analyzing the relationship between the residual signal and the residual set to determine whether the system has a fault;

[0015] S5: When it is determined that there is a fault, using the state estimation set at the previous fault detection time as the initial value of the state estimation set of other possible fault modes at that time, and then using the determined set-valued observer parameters to establish the state estimation set of other modes to further analyze and identify the fault type;

[0016] S6: According to the established state estimation set of other modes, by comparing the relationship between the residual signal and the residual set of other modes, excluding the modes that do not match, until the only matched fault mode is finally determined, and the fault diagnosis is completed.

[0017] Further:

[0018] In step S1, an equation describing the evolution of the state of the system over time is constructed, which includes the current state of the system, control input, actuator fault influence and random disturbance; an equation describing the relationship between the output of the system and the state of the system is constructed, which also considers the noise influence in the measurement process; the dynamic of the system is described by a parameter matrix; a diagonal matrix is used to represent the multi-dimensional multiplicative fault of the actuator, wherein the elements of the diagonal matrix represent the health state of each actuator.

[0019] Random disturbances and measurement noises of the system are considered as bounded, and a set of centrally symmetric polytopes is used to describe the range of the disturbances and noises; the properties of the set of centrally symmetric polytopes, including the invariance under linear transformation and the rules of set operations such as Minkowski sum, are used to handle the uncertainties in the system dynamics.

[0020] The dynamic equations of the set-valued observer are constructed using the system input vector, output vector and the to-be-determined observer parameters to dynamically update the state and output estimation sets to reflect the estimated state and output of the system at the current time; interval matrices are used to represent different fault modes to ensure that the inclusion relationship of the state vector and the output vector at consecutive times is maintained when the system operates in a specific mode.

[0021] In step S2, the design steps for the to-be-determined parameters of the set-valued observer are as follows: constructing an optimization problem based on state set separation to determine the observer gain composition And Constructing an optimization problem based on the minimum size of the state estimation set to determine the free variable Determining the observer gain; if it is active fault diagnosis, constructing an optimization problem based on the maximum distance of the state estimation set center to determine the system input.

[0022] The design of passive fault diagnosis includes: defining the output consistent state set, which contains all the system states mapped within the given output set; in the case of bounded noise energy, using unbounded centrally symmetric polytopes to describe the output consistent state set to handle the unbounded set problem caused by the irreversible output matrix; establishing a fault diagnosis criterion to determine whether the system is in a specific fault mode by detecting whether the system output belongs to the predicted output set; from the perspective of state set, establishing a fault diagnosis criterion equivalent to the system output set to detect whether the system state is consistent with the predicted state set.

[0023] By designing to separate two different state estimation sets of the same mode from each other, the accuracy of fault diagnosis is improved; the state error set is defined to quantify the difference between the two state estimation sets; the observer gain is optimized to maximize the repulsive tendency of the origin with respect to the state error set, thereby improving the accuracy of fault diagnosis; the maximum-minimum optimization problem is converted into a maximization problem, and solved by mathematical methods such as Lagrange duality to determine the observer gain; the free parameter is designed to minimize the size of the state estimation set to improve the efficiency of fault diagnosis.

[0024] The design of the active fault diagnosis includes: after the observer gain is determined, the system input is actively designed to promote the fault diagnosis process; the input is designed to make the state estimation set centers in different modes as far away as possible to facilitate the rapid differentiation of different system modes; an optimization problem is constructed, and the target is to maximize the distance between the state estimation set centers in different modes to facilitate accurate diagnosis of the fault; the system input is determined by solving the optimization problem, so that the actual output signal can quickly and accurately reflect the mode in which the system is located.

[0025] A computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the fault diagnosis method based on state set separation and set-valued observer.

[0026] A computer program product includes a computer program, and the computer program is executed by a processor to implement the fault diagnosis method based on state set separation and set-valued observer.

[0027] The present application has the following beneficial effects:

[0028] The present application provides a fault diagnosis method based on set-valued observer from a new perspective of promoting state set separation, which can effectively solve the problem that the active fault diagnosis method based on set theory needs to determine the system input before designing the observer gain. The fault diagnosis method based on the fault diagnosis design framework of the present application can have application space in passive fault diagnosis and active fault diagnosis. The fault diagnosis method of the present application shows better fault diagnosis performance, especially for systems mainly affected by noise.

[0029] Other beneficial effects of the embodiments of the present application will be further described below. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a flowchart of the fault diagnosis method based on set-valued observer in the embodiments of the present application.

[0031] Figure 2 is a flowchart of the fault diagnosis method based on set-valued observer in the embodiments of the present application.

[0032] Fig. 3(a) and Fig. 3(b) are actual application diagrams of the fault diagnosis of the embodiments of the present application, in which the system fails at k=10.

[0033] Figure 4 is a residual set visualization diagram of a system using set theory and unknown input observer in the embodiments of the present application at k=0 to k=12.

[0034] Figure 5is a visualized schematic diagram of the output estimation set and the actual output signal when the embodiment of the present application detects a fault at k = 12.

[0035] Figure 6 is a visualized schematic diagram of the output estimation set and the actual output signal when the embodiment of the present application separates a fault at k = 13. DETAILED DESCRIPTION

[0036] The embodiments of the present application are described in detail below. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present application and its applications.

[0037] The present application proposes a fault diagnosis method based on state set separation and set-valued observer, which is suitable for discrete linear time-invariant (LTI) systems. The method establishes a state space model containing bounded random disturbance and measurement noise, determines the observer gain and system input for passive and active fault diagnosis, respectively. Using these parameters, the state estimation set and residual set are constructed, and fault diagnosis is performed by analyzing the relationship between the residual signal and the set. When a fault is detected, the state estimation set at the previous time is used as the initial value to further analyze and identify the fault type. This method is particularly suitable for systems with significant noise influence. Through innovative parameter optimization and state set separation strategy, the accuracy and application range of fault diagnosis are improved, and it is suitable for passive and active fault diagnosis scenarios.

[0038] Referring to Figure 1 , the embodiment of the present application provides a fault diagnosis method based on state set separation and set-valued observer, comprising:

[0039] S1: Establish a state space model of a discrete linear time-invariant (LTI) system to be diagnosed with bounded random disturbance and measurement noise, which is used to describe the dynamic behavior of the system under normal and fault conditions;

[0040] S2: Determine the undetermined parameters of the set-valued observer according to the state space model; wherein for passive fault diagnosis, determine the observer gain; for active fault diagnosis, determine the observer gain and system input, which is designed to facilitate the fault diagnosis process;

[0041] S3: According to the determined parameters of the set-valued observer, establish the dynamic equation of the state estimation set and the residual set for the healthy mode of the discrete LTI system, wherein the state estimation set is used to represent the possible state range of the system, and the residual set is used to detect the deviation between the system state and the model prediction;

[0042] S4: According to the established state estimation set and the residual set, a fault diagnosis decision is made by analyzing the relationship between the residual signal and the residual set to determine whether there is a fault in the system;

[0043] S5: When it is determined that there is a fault, the state estimation set of the previous time before fault detection is used as the initial value of the state estimation set of other possible fault modes at that time, and then the state estimation set of other modes is established using the determined set-valued observer parameters to further analyze and identify the fault type;

[0044] S6: According to the established state estimation set of other modes, the relationship between the residual signal and the residual set of other modes is compared to exclude the unmatched modes until the only matched fault mode is finally determined, and the fault diagnosis is completed.

[0045] In some embodiments, in step S1, an equation describing the evolution of the state of the system over time is constructed, which includes the current state of the system, control input, actuator fault influence and random disturbance; an equation describing the relationship between the output of the system and the state of the system is constructed, which takes into account the noise influence in the measurement process; the system dynamics are described by a parameter matrix; a diagonal matrix is used to represent the multi-dimensional multiplicative fault of the actuator, wherein the elements of the diagonal matrix represent the health status of each actuator.

[0046] In some embodiments, the random disturbance of the system and the measurement noise are considered to be bounded, and a central symmetric polyhedron set is used to describe the value range of the disturbance and noise; the properties of the central symmetric polyhedron set, including the preservation under linear transformation and the set operation rules such as Minkowski sum, are used to handle the uncertainty in the system dynamics. The dynamic equation of the set-valued observer is constructed using the system input vector, output vector and the to-be-determined observer parameters to dynamically update the state and output estimation set to reflect the estimated state and output of the system at the current time; an interval matrix is used to represent different fault modes to ensure that the inclusion relationship of the state vector and the output vector at consecutive times is maintained when the system is running in a certain mode.

[0047] Referring to Figure 2 In some embodiments, in step S2, the design steps for the to-be-determined parameters of the set-valued observer are as follows: an optimization problem based on state estimation set separation is constructed to determine the observer gain composition and An optimization problem based on the minimum size of the state estimation set is constructed to determine the free variable The observer gain is determined; if it is active fault diagnosis, an optimization problem based on the maximum distance of the center of the state estimation set is constructed to determine the system input; if it is passive fault diagnosis, the determined observer gain and free variable are directly used for state estimation without additional optimization of the system input.

[0048] In some embodiments, the design of the passive fault diagnosis includes: defining an output consensus set, which contains all the system states mapped within a given output set; using unbounded central symmetric polyhedron to describe the output consensus set in the case of bounded noise energy, to deal with the unbounded set problem caused by irreversible output matrix; establishing a fault diagnosis criterion to determine whether the system is in a specific fault mode by detecting whether the system output belongs to the predicted output set; from the perspective of state set, establishing a fault diagnosis criterion equivalent to the system output set to detect whether the system state is consistent with the predicted state set.

[0049] Further, by designing two different state estimation sets of the same mode to be separated from each other, the fault diagnosis is facilitated; defining a state error set to quantify the difference between the two state estimation sets; optimizing the observer gain to maximize the repulsive tendency of the origin with respect to the state error set, thereby improving the accuracy of fault diagnosis; converting the maximum-minimum optimization problem into a maximum problem and solving it by mathematical methods such as Lagrange duality to determine the observer gain; designing a free parameter to minimize the size of the state estimation set to improve the efficiency of fault diagnosis.

[0050] In some embodiments, the design of the active fault diagnosis includes: after determining the observer gain, actively designing the system input to facilitate the fault diagnosis process; designing the input to make the centers of the state estimation sets under different modes as far away as possible to facilitate the rapid differentiation of different system modes; constructing an optimization problem whose goal is to maximize the distance between the centers of the state estimation sets under different modes to facilitate accurate diagnosis of faults; by solving the optimization problem, the system input is determined so that the actual output signal can quickly and accurately reflect the mode in which the system is in.

[0051] The present application proposes an innovative fault diagnosis method based on state set separation and set-valued observer, which effectively improves the detection ability of system faults. Compared with the prior art, the present application promotes the separation of state sets, optimizes the design of observer parameters, especially in the determination of observer gain, making the fault diagnosis process more sensitive and accurate. In addition, the present application also expands the application range of repulsive tendency, by defining the repulsive tendency of a point to an unbounded centrally symmetric polyhedron, improving the processing ability of system dynamics uncertainty, which is particularly important in dealing with disturbances and noises in complex systems. The fault diagnosis method of the present application is not only suitable for passive fault diagnosis, but also for active fault diagnosis, so that it can perform outstanding performance in different diagnosis scenarios. Especially in systems with greater noise influence, the present application shows better diagnostic performance than existing methods, which can significantly reduce the false alarm rate and false alarm rate, thereby improving the reliability and safety of the system. Through this comprehensive method, the present application provides strong technical support for the high safety and reliability requirements in industrial applications.

[0052] The following further describes the algorithm examples and experimental verification of the specific embodiments of the present application.

[0053] Referring to Figure 1 A fault diagnosis method based on state set separation and set-valued observer, comprising the following steps:

[0054] S1: Establishing a state space model of a discrete linear constant system to be diagnosed with bounded random disturbance and measurement noise;

[0055] S2: Determining the undetermined parameters of the set-valued observer according to the state space model of the system to be diagnosed (determining the observer gain for passive fault diagnosis; determining the observer gain and system input for active fault diagnosis);

[0056] S3: Using the set-valued observer to establish the dynamic equation of the state estimation set and the residual set for the healthy mode of the discrete LTI system;

[0057] S4: Making a fault diagnosis decision according to the relationship between the residual signal and the residual set;

[0058] S5: After detecting a fault, using the state estimation set at the time before the fault is detected as the state estimation set of other possible fault modes at that time, and using the set-valued observer to establish the state estimation set of other modes;

[0059] S6: Excluding the mismatched modes according to the relationship between the residual signal and the residual set of other modes, until only one mode is left, i.e. completing fault diagnosis.

[0060] Referring to Figure 2In some embodiments, the step of designing the pending parameters of the set-valued observer in step S2 is as follows:

[0061] S21: Constructing an optimization problem based on state set separation determination and

[0062] S22: Constructing an optimization problem based on state estimation set size minimization to determine free variables

[0063] S23: Determining the observer gain;

[0064] S24: If active fault diagnosis, construct an optimization problem based on the maximum distance of the state estimation set center to determine the system input.

[0065] System modeling

[0066] Taking a mechanical arm as an example, the dynamics modeling of an n-degree-of-freedom mechanical arm is as follows:

[0067]

[0068] where, respectively represent the joint position, joint velocity and joint acceleration. represents the inertia matrix, represents the centrifugal force and Coriolis force, is the gravity term, is the control torque. It can be represented as:

[0069]

[0070] Design new state variables and the input vector u = τ, discretize the above equation, and consider the random disturbance ω of the system, to get the discrete-time state equation

[0071]

[0072] where, Δt represents the sampling time.

[0073] The fault of the mechanical arm actuator is modeled as a multiplicative fault

[0074]

[0075] where, τ i , respectively represent the actual torque of the i-th joint and the calculated nominal torque. g i represents the multiplicative fault loss coefficient.

[0076] The above mechanical arm actuator multiplicative fault model conforms to a general linear discrete time-invariant system affected by a multi-dimensional multiplicative actuator fault.

[0077] Consider a linear discrete time-invariant system affected by a multi-dimensional multiplicative actuator fault in the following form:

[0078] x k+1 =Ax k +BGu k +Eω k ,

[0079] y k =Cx k +Fη k , (1)

[0080] wherein, and are parameter matrices of the system, and the parameter matrix (A, C) is detectable. is an input of the system at the kth moment, is an output of the system at the kth moment, is a state of the system at the kth moment, is a random disturbance suffered by the system at the kth moment, is measurement noise of the system at the kth moment. is a diagonal matrix, used for characterizing a multi-dimensional multiplicative actuator fault, 0≤g i <1, and G is a unit matrix I when all actuators are healthy.

[0081] In the embodiment of the present application, the random disturbance and the measurement noise are considered to have a bounded value, and a central symmetric polyhedron set is used to characterize, respectively, and It should be noted that the central symmetric polyhedron has the following two properties:

[0082] (1) KZ1 = <Kg1, KH1>,

[0083] (2)

[0084] wherein, Z1 = <g1, H1> and Z2 = <g2, H2> are central symmetric polyhedron sets, K represents a linear transformation matrix with a corresponding dimension, and the operator is a Minkowski sum, and the Minkowski sum of the set X and Y is defined as

[0085] Further, the input vector u k and the output vector y k, the set-valued observer is constructed as follows:

[0086]

[0087] where, L k i is the observer parameter to be determined, and is the state and output estimation set at time k+1.

[0088] is the interval matrix used to model the fault range of the ith sensor. When the system is running in the ith mode, if the state vector satisfies at time k, it can be guaranteed that the inclusion relationship and holds at time k+1.

[0089] The above central symmetric polytope can be unfolded to obtain the unfolded form of the center and the generating matrix of the state estimation set and the output estimation set:

[0090]

[0091] Passive fault diagnosis design

[0092] The output consistent state set at time k is defined as:

[0093]

[0094] where, In the case of bounded noise energy, if the output matrix C is non-invertible, the output consistent set will be an unbounded set, and an unbounded set cannot be described by a central symmetric polytope. Further, the present application uses an unbounded central symmetric polytope to describe the central symmetric unbounded set. The unbounded central symmetric polytope is defined as follows:

[0095]

[0096] where, g is the center, H is the bounded generating matrix, and H ∞ is the unbounded generating matrix. The unbounded central symmetric polytope can be simply denoted as:

[0097] Z = <g, H, H ∞ >.

[0098] According to the definition in (4), the output consistent state set at time k can be represented by an unbounded central symmetric polytope as:

[0099]

[0100] The criterion for fault diagnosis is to check whether the following equation holds:

[0101]

[0102] When (6) is violated, it means that the system is not in the ith mode, then this mode can be excluded from the candidate modes. Fault diagnosis is achieved when and only when there is only one mode left. For the fault diagnosis criterion (6), combined with the definition of the output consistent state set, we can get the fault diagnosis criterion equivalent to (6) from the perspective of state sets:

[0103]

[0104] When the output consistent state set at time k is used as the state estimation set at time k, the state set that each direction of the set-valued observer (2) can reach with the least conservatism is obtained when the observer gain is 0.

[0105] Inspired by (7), if the state estimation sets for the same mode are separated from each other, it can be sufficient to show that the system is not running in this mode. Therefore, fault diagnosis can be promoted by promoting the separation of two different state estimation sets for the same mode. Two state estimation sets for the same mode are designed as follows:

[0106]

[0107] At time k, the actual fault matrix and the disturbance are G i ∈G i and If the actual value is known, a more accurate state estimation set can be obtained, so (8) can be rewritten as:

[0108]

[0109] Define the state error set as:

[0110]

[0111] From the perspective of sets, it is easy to understand that the separation between two sets is equivalent to excluding the origin from the Minkowski sum of the two sets. For example, if you want to separate and An equivalent method is to exclude the origin from Based on this intuitive finding, the observer gain will be optimized by promoting the exclusion of the origin from

[0112] Since the output consistent state set at time k is ​is an unbounded set, is also an unbounded set, while the previous measures of the separation tendency of a set are based on bounded sets. In order to measure the separation degree between unbounded sets, the concept of the repulsion tendency is further extended to unbounded central-symmetrical polyhedrons. Based on this extension, the repulsion tendency of the origin with respect to is given by

[0113]

[0114] where

[0115] By maximizing the repulsion tendency of the origin with respect to , the optimization problem of the observer gain that promotes fault diagnosis is given by

[0116]

[0117] where is the optimal value of the optimization problem (11).

[0118] The optimization problem (12) is a max-min optimization problem, which is very difficult to solve directly. In order to solve this optimization problem more efficiently, the inner optimization problem of the optimization problem (12) is first solved by Lagrange duality. The dual problem of the inner optimization problem is a maximization problem, and the inner optimization problem is a linear problem, whose Lagrange duality is strong duality, and the duality gap is 0. Therefore, the max-min optimization problem (12) can be the same as the optimal value of a maximization problem. After duality, the multiplication of two optimization variables appears in the maximization problem. By variable substitution, a linear optimization problem is obtained:

[0119]

[0120] The relationship between the optimal solution of the optimization problem (12) and the optimal solution of the optimization problem (13) is given by

[0121]

[0122] where is an arbitrary matrix, and are determined by the optimal solution of the optimization problem (13):

[0123]

[0124] It can be seen that It is a freely designable variable. Generally, a smaller size of the state estimation set is beneficial for fault diagnosis. In this embodiment of the invention, the Frobenius norm is used to measure the state estimation set. Size: For a set of centrally symmetric polyhedra Z1 =<g1,H1> Its Frobenius norm size is defined as The operator ||·|| F This represents the Frobenius norm. For further design of free parameters... By reducing the size of the state estimation set, the following optimization problem can be established:

[0125]

[0126] The analytical solution to optimization problem (15) is:

[0127]

[0128] in,

[0129] Active fault diagnosis design

[0130] After obtaining the observer gain, the active fault diagnosis method further designs the system input to further facilitate fault diagnosis. The design principle of the input is to make the state estimates of each mode set... The centers are far apart from each other, so that the actual output signal can be included in only one output estimation set as soon as possible. The corresponding optimization problem is:

[0131]

[0132] in, The result is obtained by substituting the observer gain determined during the passive fault diagnosis design process into the set-valued observer iteration formula (3). The input signal obtained by solving the optimization problem (17) can further promote the realization of fault diagnosis.

[0133] Validity verification

[0134] To verify the effectiveness of the method described in the embodiments of the present invention, consider that system (1) has the following parameters:

[0135]

[0136] The initial state of the system is x0 = [0,0,0,0]. T The initial state estimation set is random perturbation set Measurement noise set The input constraint set is U = <0, 5I²>. The actuator fault interval matrix is ​​set as follows:

[0137]

[0138] Assume that the first actuator fault occurs at k = 10 (i.e. the first actuator fault is injected into the system at k = 10), the fault matrix is:

[0139]

[0140] According to the method of the embodiment of the present application, the effectiveness of passive fault diagnosis is verified first, and the given constant input is u = [-0.4, -0.2] T . For the convenience of description, define and are the projections of the residual set corresponding to the i-th mode on the first and second dimensional components respectively, and is the residual signal corresponding to the i-th mode. In Fig. 3(a), the healthy mode residual component signal exceeds the upper bound of the healthy mode residual set projection, so it can be judged that the set-valued observer of the healthy state detects that the system has occurred a fault at k = 12 on the first dimensional component. And in Fig. 3(a), the second fault mode residual component signal exceeds the upper bound of the second fault mode residual set projection, so it can be judged that the second fault mode is separated at k = 13 on the first dimensional component (i.e. it is judged that the system does not occur the second fault mode). At this time, there is only one candidate mode left, so the fault occurs in the first fault mode is diagnosed, thereby proving the effectiveness of the embodiment of the present application. Fig. 3(b) shows the residual component signals of the healthy mode and the two fault modes on the second dimensional component with time, and their relationship with the respective residual set projections. Figure 4 The residual set visualization of the system using set theory and unknown input observer is shown from k = 0 to k = 12. Figure 5 The healthy mode output estimation set and the actual output signal when the system is detected to have occurred a fault at k = 12 are shown. Figure 6 The first and second mode output estimation sets and the actual output signal when the fault mode is separated at k = 13 are shown.

[0141] Compared with the prior art, the main advantages of the present application are embodied in the following aspects:

[0142] Compared with the existing fault diagnosis method based on the set value observer, the application promotes the fault diagnosis from the perspective of state estimation set, is a fault diagnosis technical scheme based on the set value observer and the output consistent state set from the perspective of state estimation set separation. Compared with the existing fault diagnosis method based on the set value observer, the application promotes the fault diagnosis from the perspective of state estimation set, is a fault diagnosis technical scheme based on the set value observer and the output consistent state set from the perspective of state estimation set separation. Compared with the existing fault diagnosis method based on the set value observer, the application promotes the fault diagnosis from the perspective of state estimation set, is a fault diagnosis technical scheme based on the set value observer and the output consistent state set from the perspective of state estimation set separation.

[0143] The embodiment of the application further provides a storage medium for storing a computer program, which is executed to perform at least the method described above.

[0144] The embodiment of the application further provides a control device, comprising a processor and a storage medium for storing a computer program; wherein the processor is used to execute the computer program to perform at least the method described above.

[0145] The embodiment of the application further provides a processor, which executes a computer program to perform at least the method described above.

[0146] The storage medium can be implemented by any type of non-volatile storage device or combination thereof. The non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a ferromagnetic random access memory (FRAM), a flash memory, a magnetic surface memory, an optical disc, or a compact disc read-only memory (CD-ROM). The magnetic surface memory can be a disk memory or a tape memory. The storage medium described in the embodiment of the application is intended to include but is not limited to these and any other suitable type of memory.

[0147] In several embodiments provided by the present application, it should be understood that the disclosed system and method can be implemented in other manners. The described device embodiments are merely illustrative, for example, the division of the units is only a logical function division, and there can be another division manner in actual implementation, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed coupling, or direct coupling or communication connection between the components can be indirect coupling or communication connection through some interfaces, devices or units, and can be electrical, mechanical or other forms.

[0148] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, that is, can be located in one place, or can be distributed on a plurality of network units; some or all of the units can be selected according to actual needs to achieve the purpose of the embodiment.

[0149] In addition, each functional unit in each embodiment of the present application can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be realized in the form of hardware or in the form of hardware plus software functional unit.

[0150] Those skilled in the art can understand that all or part of the steps of the above-mentioned method embodiments can be completed by program instruction related hardware, and the foregoing program can be stored in a computer readable storage medium, and the program executes the steps including the above-mentioned method embodiments when executed; and the foregoing storage medium includes: mobile storage device, read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk and various storage medium capable of storing program codes.

[0151] Alternatively, the integrated unit of the present application, if implemented in the form of a software function module and sold or used as an independent product, can also be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present application can be embodied in the form of a software product, and the computer software product is stored in a storage medium, and includes several instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the methods described in the embodiments of the present application. The foregoing storage medium includes: mobile storage device, ROM, RAM, magnetic disk or optical disk, and various storage medium capable of storing program codes.

[0152] The methods disclosed in the several method embodiments of the present application can be combined arbitrarily without conflict to obtain new method embodiments.

[0153] The features disclosed in the several product embodiments of the present application can be combined arbitrarily without conflict to obtain new product embodiments.

[0154] The features disclosed in the several method or device embodiments of the present application can be combined arbitrarily without conflict to obtain new method embodiments or device embodiments.

[0155] The above is a further detailed description of the present application in combination with specific preferred embodiments, and the specific implementation of the present application should not be limited to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of equivalent substitutions or obvious modifications can be made, and the performance or use is the same, which should be regarded as belonging to the protection scope of the present application.

Claims

1. A fault diagnosis method based on state set separation and set-valued observer, characterized in that, Comprising: S1: establishing a state-space model of a discrete linear time-invariant (LTI) system to be diagnosed with bounded random disturbances and measurement noises, which is used to describe the dynamic behavior of the system in normal and fault conditions; S2: determining the parameters of a set-valued observer according to the state-space model; wherein, for passive fault diagnosis, the observer gain is determined; for active fault diagnosis, the observer gain and system input are determined, which are designed to facilitate the fault diagnosis process; S3: establishing the dynamic equations of state estimation sets and residual sets for the healthy mode of the discrete LTI system according to the determined parameters of the set-valued observer, wherein the state estimation sets are used to represent the possible state range of the system, and the residual sets are used to detect the deviation between the system state and the model prediction; S4: making a fault diagnosis decision to determine whether the system has a fault by analyzing the relationship between the residual signal and the residual sets according to the established state estimation sets and residual sets; S5: when it is determined that there is a fault, using the state estimation set at the previous fault detection time as the initial value of the state estimation set of other possible fault modes at that time, and then establishing the state estimation sets of other modes using the determined parameters of the set-valued observer to further analyze and identify the fault type; S6: according to the established state estimation sets of other modes, excluding the modes that do not match by comparing the relationship between the residual signal and the residual sets of other modes, until the only matching fault mode is finally determined, and the fault diagnosis is completed.

2. The fault diagnosis method based on state set separation and collective observer according to claim 1, characterized in that, In step S1, an equation describing the evolution of the system state over time is constructed, which includes the current state of the system, the control input, the effect of actuator faults, and random disturbances; an equation describing the relationship between the system output and the system state is constructed, which takes into account the noise effect in the measurement process; the system dynamics are described by a parameter matrix; a diagonal matrix is used to represent the multi-dimensional multiplicative faults of the actuators, wherein the elements of the diagonal matrix represent the health status of each actuator.

3. The fault diagnosis method based on state set separation and collective observer according to claim 2, characterized in that, The random disturbances and measurement noises of the system are considered to be bounded, and a central symmetric polyhedron set is used to describe the value range of the disturbances and noises; the properties of the central symmetric polyhedron set, including the preservation under linear transformation and the set operation rules such as Minkowski sum, are used to handle the uncertainties in the system dynamics.

4. The fault diagnosis method based on the state set separation and collective observer according to claim 2 or 3, characterized in that, The dynamic equations of the set-valued observer are constructed using the system input vector, the output vector, and the to-be-determined observer parameters to dynamically update the state and output estimation sets to reflect the estimated state and output of the system at the current time; An interval matrix is used to represent different fault modes to ensure that the inclusion relationship of the state vector and the output vector at consecutive times is maintained when the system is running in the corresponding fault mode.

5. The fault diagnosis method based on a set-separation and set-valued observer of state sets according to any one of claims 1 to 3, characterized in that, In step S2, the design step of the pending parameters of the set-valued observer is as follows: constructing an optimization problem based on state set separation to determine the observer gain composition and ; constructing an optimization problem based on the minimum size of the state estimation set to determine the free variable ; determining the observer gain; if it is active fault diagnosis, constructing an optimization problem based on the maximum distance of the state estimation set center to determine the system input, and if it is passive fault diagnosis, directly using the determined observer gain and free variable to perform state estimation.

6. The fault diagnosis method based on a set-separation and set-valued observer of state sets according to any one of claims 1 to 3, characterized in that, The design of the passive fault diagnosis includes: defining an output consistent state set, which contains all the system states mapped within a given output set; using unbounded central symmetric polyhedron to describe the output consistent state set in the case of bounded noise energy, to deal with the unbounded set problem caused by irreversible output matrix; establishing a fault diagnosis criterion to determine whether the system is in the corresponding fault mode by detecting whether the system output belongs to the predicted output set; from the perspective of state set, establishing a fault diagnosis criterion equivalent to the system output set to detect whether the system state is consistent with the predicted state set.

7. The fault diagnosis method based on the state set separation and collective observer according to claim 6, characterized in that, The design of the passive fault diagnosis includes: defining an output consistent state set, which contains all the system states mapped within a given output set; using unbounded central symmetric polyhedron to describe the output consistent state set in the case of bounded noise energy, to deal with the unbounded set problem caused by irreversible output matrix; establishing a fault diagnosis criterion to determine whether the system is in the corresponding fault mode by detecting whether the system output belongs to the predicted output set; from the perspective of state set, establishing a fault diagnosis criterion equivalent to the system output set to detect whether the system state is consistent with the predicted state set. The design of the passive fault diagnosis includes: defining an output consistent state set, which contains all the system states mapped within a given output set; using unbounded central symmetric polyhedron to describe the output consistent state set in the case of bounded noise energy, to deal with the unbounded set problem caused by irreversible output matrix; establishing a fault diagnosis criterion to determine whether the system is in the corresponding fault mode by detecting whether the system output belongs to the predicted output set; from the perspective of state set, establishing a fault diagnosis criterion equivalent to the system output set to detect whether the system state is consistent with the predicted state set.

8. The fault diagnosis method based on a set-separation and set-valued observer of the state set according to any one of claims 1 to 3, characterized in that, The design of the passive fault diagnosis includes: defining an output consistent state set, which contains all the system states mapped within a given output set; using unbounded central symmetric polyhedron to describe the output consistent state set in the case of bounded noise energy, to deal with the unbounded set problem caused by irreversible output matrix; establishing a fault diagnosis criterion to determine whether the system is in the corresponding fault mode by detecting whether the system output belongs to the predicted output set; from the perspective of state set, establishing a fault diagnosis criterion equivalent to the system output set to detect whether the system state is consistent with the predicted state set.

9. A computer readable storage medium storing a computer program, characterized in that, The computer program is executed by the processor to realize the fault diagnosis method based on state set separation and set-valued observer according to any one of claims 1-8.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the fault diagnosis method based on state set separation and set-valued observer according to any one of claims 1-8.

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