Fault diagnosis method based on state set separation and set value observer

Abstract

The invention provides a fault diagnosis method based on state set separation and a set value observer. The fault diagnosis method is suitable for a discrete linear steady LTI system. According to the method, a state space model containing bounded random disturbance and measurement noise is established, and observer gain and system input are respectively determined for passive and active fault diagnosis. And constructing a state estimation set and a residual set by using the parameters, and carrying out fault diagnosis by analyzing a relationship between a residual signal and the set. When a fault is detected, the state estimation set at the previous moment is used as an initial value, and the fault type is further analyzed and recognized. The method is especially suitable for a system with obvious noise influence, improves the accuracy and application range of fault diagnosis through an innovative parameter optimization and state set separation strategy, and is suitable for passive and active fault diagnosis scenes.

Description

Technical Field

[0001] The invention relates to a fault diagnosis technology, in particular to a fault diagnosis method based on state set separation and set-valued observer. Background Art

[0002] With the progress in aviation, aerospace, industry, electronic communications, robotics and other fields, the complexity, integration and automation of the system are increasing day by day. At the same time, the possibility of failure and risk in the system is also increasing. If these failures are not handled in time, the system may develop from a fault state to a failure state, causing the system performance to decline, and even causing significant casualties and property losses in severe cases. Therefore, fault diagnosis technology with high reliability and real-time performance is of great significance to industrial application scenarios that require high safety and reliability.

[0003] The methods currently used in fault diagnosis technology are mainly concentrated in model-based fault diagnosis methods and data-driven fault diagnosis methods. The diagnostic effect of data-driven fault diagnosis methods is highly dependent on the quantity and quality of historical data, and the adaptive ability is weak. The physical meaning of model-based fault diagnosis methods is clearer, but due to the existence of uncertainty factors such as disturbances and noise in the actual system, this method cannot obtain an accurate model of the real system in the actual modeling process. At the same time, the diagnostic performance of model-based fault diagnosis methods is highly dependent on the mathematical model of the diagnostic object. Therefore, this type of method must be able to handle the impact of disturbances, noise 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, model-based robust fault diagnosis technology has developed a new paradigm, which enables this technology to obtain reliable fault diagnosis thresholds in real time under the premise of tolerating disturbances and noise. Therefore, it has a very broad application prospect in many industrial production links.

[0004] Model-based robust fault diagnosis schemes can be further divided into passive fault diagnosis (PFD) and active fault diagnosis (AFD). Compared with the former, the latter, in addition to receiving the input and output information of the system, further designs the system input to stimulate the system to obtain more information for the diagnosis target, so the design is more complicated. However, under the premise of ensuring robustness, the latter has higher sensitivity than the former, especially for the diagnosis of early faults, minor faults, etc. It has significant advantages, so it can be foreseen that it will have broader application potential and prospects.

[0005] Existing model-based robust fault diagnosis techniques are mainly divided into two categories: one is the random method, which treats disturbances and noise as random variables, that is, it is assumed that disturbances and noise obey a known probability distribution, such as Gaussian distribution. Representative methods include fault diagnosis techniques based on Kalman filter, extended Kalman filter and unscented Kalman filter. By considering the probability distribution of uncertainties such as disturbances and noise, the relative influence of disturbances and noise under the distribution on system faults is considered. The advantage of this type of scheme is that it has high sensitivity. The accurate probability distribution of disturbances and noise is difficult to obtain, and the error in the probability distribution causes the problem of unreliable fault diagnosis results: the existing random fault diagnosis scheme based on the assumption that the distribution of disturbances and noise is known requires the accurate probability distribution information of disturbances and noise. However, in actual engineering, especially in some large and complex systems, it is usually difficult to obtain enough high-quality experimental samples to establish the accurate probability distribution of certain parameters due to testing difficulties or cost constraints. Moreover, even a small deviation between the distribution parameters and the true value may lead to a very large deviation in the reliability of the fault diagnosis conclusion. Therefore, when there is an error between the actual distribution and the theoretical distribution, it will cause false alarms or missed detections of faults, which greatly reduces the reliability of the technology.

[0006] Another type of fault diagnosis scheme is the bounded method. Although the probability distribution of uncertainties such as disturbances and noise cannot be accurately obtained, their upper and lower bounds are easier to obtain. Representative methods include set-theoretic unknown input observers, set-valued observers, and set membership filters. In practice, it is often easier and more reliable to obtain the upper and lower bounds of disturbances and noise than to obtain their accurate probability distributions. For example, in the treatment of uncertainty caused by friction, due to the complexity of the lubrication environment, it is difficult to obtain the probability distribution of the friction coefficient; however, based on existing experience, the interval in which the friction coefficient is located is easy to obtain. The advantage of this type of scheme is that there is no need to know the prior information of the disturbance and noise distribution in advance, and the application range is wider. High conservatism problem: The existing disturbance and noise distribution is unknown but bounded. The fault diagnosis scheme is highly conservative, which leads to a high missed detection rate. For example, the fault diagnosis method based on the set-theoretic unknown input observer is more conservative when the system is mainly affected by measurement noise, while the set-valued observer is more conservative when the system is mainly affected by random disturbances.

[0007] It should be noted that the information disclosed in the above background technology section is only used for understanding the background of the present application, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the invention

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

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

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

[0011] S1: Establish a state space model of the discrete linear time-invariant LTI system to be diagnosed with bounded random disturbances and measurement noise. The model is used to describe the dynamic behavior of the system under normal and fault conditions.

[0012] S2: Determine the unknown parameters of the 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 the system input are determined, and the system input is designed to facilitate the fault diagnosis process;

[0013] S3: According to the determined set-valued observer parameters, the dynamic equations of the state estimation set and the residual set are established for the healthy mode of the discrete LTI system, where 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: Based on the established state estimation set and residual set, a fault diagnosis decision is made 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 a fault exists, the state estimation set at the moment before the fault detection is used as the initial value of the state estimation set of other possible fault modes at that moment, 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;

[0016] S6: Based on the established state estimation set of other modes, by comparing the relationship between the residual signal and the residual set of other modes, the unmatched modes are eliminated until the only matching fault mode is finally determined to complete the fault diagnosis.

[0017] Further:

[0018] In step S1, an equation describing the evolution of the system state over time is constructed, which includes the current state of the system, control input, the impact of actuator failures, and random disturbances; an equation describing the relationship between the system output and the system state is constructed, which also takes into account the impact of noise during the measurement process; the system dynamics are described by a parameter matrix; and a diagonal matrix is ​​used to characterize the multidimensional multiplicative faults of the actuator, where the elements of the diagonal matrix represent the health status of each actuator.

[0019] The random perturbation and measurement noise of the system are considered to be bounded, and a set of centrosymmetric polyhedrons is used to describe the range of perturbation and noise. The properties of the set of centrosymmetric polyhedrons, including the conservation properties under linear transformations and set operation rules such as the Minkowski sum, are used to deal with the uncertainty in the system dynamics.

[0020] The dynamic equation of the set-valued observer is constructed using the system input vector, output vector and unknown observer parameters to dynamically update the state and output estimation sets to reflect the estimated state and output of the system at the current moment. The interval matrix is ​​used to characterize different fault modes to ensure that the inclusion relationship between the state vector and the output vector at continuous moments is maintained when the system operates in a specific mode.

[0021] In step S2, the design steps for the unknown parameters of the set-valued observer are as follows: Construct an optimization problem based on state set separation to determine the observer gain composition and Construct an optimization problem based on the minimum size of the state estimation set to determine the free variables Determine the observer gain; if it is active fault diagnosis, construct an optimization problem based on the maximum center distance of the state estimation set to determine the system input.

[0022] The design of the passive fault diagnosis includes: defining an output consistent state set, which contains all system states mapped within a given output set; when the noise energy is bounded, using an unbounded central symmetric polyhedron to describe the output consistent state set to deal with 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 the 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] Two different sets of state estimates of the same mode are separated by design to facilitate fault diagnosis; a set of state errors is defined to quantify the difference between the two sets of state estimates; the observer gain is optimized to maximize the repulsive tendency of the origin relative to the state error set, thereby improving the accuracy of fault diagnosis; the maximum-minimum optimization problem is transformed into a maximization problem and solved by mathematical methods such as Lagrangian duality to determine the observer gain; free parameters are designed to minimize the size of the state estimate set to improve the efficiency of fault diagnosis.

[0024] The design of active fault diagnosis includes: after the observer gain is determined, actively designing the system input to facilitate the fault diagnosis process; designing the input so that the centers of the state estimation sets under different modes are as far apart as possible to facilitate the rapid distinction of different system modes; constructing an optimization problem with the goal of maximizing the distance between the centers of the state estimation sets of different modes to facilitate accurate diagnosis of faults; determining the system input 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, wherein the computer program, when executed by a processor, implements the fault diagnosis method based on state set separation and set-valued observer.

[0026] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, the fault diagnosis method based on state set separation and set-valued observer is implemented.

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

[0028] The present invention provides a fault diagnosis method based on a set-valued observer from a new perspective of promoting the separation of state sets, which can effectively solve the problem that the previous active fault diagnosis method based on set theory needs to determine the system input before designing the observer gain. Through innovative design ideas and parameter optimization, the fault diagnosis method based on this fault diagnosis design framework can be applied in both passive fault diagnosis and active fault diagnosis. The fault diagnosis method of the present invention shows better fault diagnosis performance, especially for systems that are mainly affected by noise.

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

[0030] Figure 1 4 is a flow chart of a fault diagnosis method using a set-valued observer in an embodiment of the present invention.

[0031] Figure 2 It is a flow chart of determining set-valued observer parameters for facilitating fault diagnosis by utilizing separation trends between state estimation sets in an embodiment of the present invention.

[0032] FIG. 3( a ) and FIG. 3( b ) are schematic diagrams of actual application of fault diagnosis according to an embodiment of the present invention, wherein a fault occurs in the system when k=10.

[0033] Figure 4 It is a visualization diagram of residual sets of a system using set theory and an unknown input observer at the time k=0 to k=12 according to an embodiment of the present invention.

[0034] Figure 5It is a visualized schematic diagram of an output estimation set and an actual output signal when a fault is detected at time k=12 according to an embodiment of the present invention.

[0035] Figure 6 It is a visualized schematic diagram of an output estimation set and an actual output signal when a fault is separated at time k=13 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The following is a detailed description of the embodiments of the present invention. It should be emphasized that the following description is only exemplary and is not intended to limit the scope and application of the present invention.

[0037] The present invention proposes a fault diagnosis method based on state set separation and set-valued observer, which is applicable to discrete linear steady-state LTI systems. The method determines the observer gain and system input for passive and active fault diagnosis respectively by establishing a state space model containing bounded random disturbances and measurement noise. Using these parameters, the state estimation set and the 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 moment 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 strategies, the accuracy and application scope of fault diagnosis are improved, and it is also applicable to passive and active fault diagnosis scenarios.

[0038] See also Figure 1 The embodiment of the present invention 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 disturbances and measurement noise. This model is used to describe the dynamic behavior of the system under normal and fault conditions.

[0040] S2: Determine the unknown parameters of the 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 the system input are determined, and the system input is designed to facilitate the fault diagnosis process;

[0041] S3: According to the determined set-valued observer parameters, the dynamic equations of the state estimation set and the residual set are established for the healthy mode of the discrete LTI system, where 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: Based on the established state estimation set and residual set, a fault diagnosis decision is made by analyzing the relationship between the residual signal and the residual set to determine whether the system has a fault;

[0043] S5: When it is determined that a fault exists, the state estimation set at the moment before the fault detection is used as the initial value of the state estimation set of other possible fault modes at that moment, 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: Based on the established state estimation set of other modes, by comparing the relationship between the residual signal and the residual set of other modes, the unmatched modes are eliminated until the only matching fault mode is finally determined to complete the fault diagnosis.

[0045] In some embodiments, in step S1, an equation is constructed to describe the evolution of the system state over time, which includes the current state of the system, control input, the impact of actuator failures, and random disturbances; an equation is constructed to describe the relationship between the system output and the system state, which also takes into account the impact of noise during the measurement process; the system dynamics are described by a parameter matrix; and a diagonal matrix is ​​used to characterize the multidimensional multiplicative faults of the actuator, wherein the elements of the diagonal matrix represent the health status of each actuator.

[0046] In some embodiments, the random disturbance and measurement noise of the system are considered to be bounded, and a set of centrally symmetric polyhedrons is used to describe the range of disturbance and noise values; the properties of the set of centrally symmetric polyhedrons, including the preservation property under linear transformation and set operation rules such as Minkowski sum, are used to deal with 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 observer parameters to be determined to dynamically update the state and output estimation set to reflect the estimated state and output of the system at the current moment; the interval matrix is ​​used to characterize different fault modes to ensure that when the system operates in a specific mode, the inclusion relationship between the state vector and the output vector at continuous moments is maintained.

[0047] See also Figure 2 In some embodiments, in step S2, the design steps for the undetermined parameters of the set-valued observer are as follows: Construct an optimization problem based on state set separation to determine the observer gain composition and Construct an optimization problem based on the minimum size of the state estimation set to determine the free variables Determine the observer gain; if it is active fault diagnosis, construct an optimization problem based on the maximum center distance of the state estimation set to determine the system input; if it is passive fault diagnosis, directly use the determined observer gain and free variables to perform state estimation without additional optimization of the system input.

[0048] In some embodiments, the design of the passive fault diagnosis includes: defining an output consistent state set, which contains all system states mapped within a given output set; when the noise energy is bounded, using an unbounded central symmetric polyhedron to describe the output consistent state set to deal with 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 the 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] Furthermore, two different sets of state estimates of the same mode are separated from each other by design to facilitate fault diagnosis; a set of state errors is defined to quantify the difference between the two sets of state estimates; 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 transformed into a maximization problem and solved by mathematical methods such as Lagrangian duality to determine the observer gain; and free parameters are designed to minimize the size of the state estimation set to improve the efficiency of fault diagnosis.

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

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

[0052] The following further describes an algorithm example and experimental verification of a specific embodiment of the present invention.

[0053] See also Figure 1 , a fault diagnosis method based on state set separation and set-valued observer, comprising the following steps:

[0054] S1: Establish the state space model of the discrete linear time-invariant system to be diagnosed with bounded random disturbance and measurement noise;

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

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

[0057] S4: Make a fault diagnosis decision based on the relationship between the residual signal and the residual set;

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

[0059] S6: Eliminate unmatched modes based on the relationship between the residual signal and other modal residual sets until only one mode remains, thus completing the fault diagnosis.

[0060] See also Figure 2In some embodiments, the design steps of the undetermined parameters of the set-valued observer in step S2 are as follows:

[0061] S21: Constructing optimization problems based on state set separation and

[0062] S22: Construct an optimization problem based on the minimum size of the state estimation set to determine the free variables

[0063] S23: Determine observer gain;

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

[0065] System Modeling

[0066] Taking the robotic arm as an example, the dynamic modeling of the n-DOF robotic arm is carried out:

[0067]

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

[0069]

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

[0071]

[0072] in, Δt represents the sampling time.

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

[0074]

[0075] Among them, τ i , They represent the actual torque and the calculated nominal torque of the i-th joint respectively. i Represents the multiplicative failure loss coefficient.

[0076] The above-mentioned multiplicative fault model of the robot arm actuator conforms to the general linear discrete time-invariant system affected by multidimensional multiplicative actuator faults.

[0077] Consider a linear discrete time-invariant system of the following form subject to multidimensional multiplicative actuator failures:

[0078] x k+1 =Ax k +BGu k +Eω k ,

[0079] y k =Cx k +Fη k , (1)

[0080] in, and Both are parameter matrices of the system, and the parameter matrices (A, C) are detectable. is the input of the system at the kth moment, is the output of the system at the kth moment, is the state of the system at the kth moment, is the random disturbance suffered by the system at the kth moment, is the measurement noise of the system at the kth moment. is a diagonal matrix used to characterize multidimensional multiplicative actuator faults, When the i-th actuator fails, 0≤g i <1, when all actuators are healthy, G is the unit matrix and is recorded as I.

[0081] In the embodiment of the present invention, the random disturbance and the measurement noise are both considered to be bounded and are characterized by a set of centrally symmetric polyhedrons, which are respectively denoted as: and It should be noted that the central symmetric polyhedron has the following two properties:

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

[0083] (2)

[0084] Among them, Z1=<g1,H1> and Z2=<g2,H2> are all centrally symmetric polyhedrons, K represents a linear transformation matrix with corresponding dimensions, and the operator is the Minkowski sum, and the Minkowski sum of sets X and Y is defined as

[0085] Furthermore, using the input vector u in system (1) k With the output vector y k, construct a set-valued observer of the following form:

[0086]

[0087] in, L k i are the observer parameters whose parameters are to be determined, and is the set of state and output estimates at time k+1.

[0088] is the interval matrix used to model the fault range of the i-th sensor. When the system operates in the i-th mode, if the state vector satisfies at time k Then it can be guaranteed that the relation is included at time k+1 and Established.

[0089] Expanding the above central symmetric polyhedron can obtain the expanded form of the center and generation matrix of the state estimation set and output estimation set:

[0090]

[0091] Passive fault diagnosis design

[0092] Define the set of consistent output states at time k:

[0093]

[0094] in, In the case where the noise energy is bounded, if the output matrix C is irreversible, the output consistent set will be an unbounded set, and the unbounded set cannot be described by a centrosymmetric polyhedron. Further, the present invention uses an unbounded centrosymmetric polyhedron to describe the centrosymmetric unbounded set. is defined as follows:

[0095]

[0096] in, g is the center, H is the bounded generator matrix, H ∞ is an unbounded generating matrix. An unbounded central symmetric polyhedron can be simply written as:

[0097] Z= <g,H,H ∞ >.

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

[0099]

[0100] The criterion for fault diagnosis is to detect whether the following equation is true:

[0101]

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

[0103]

[0104] When the output consistent state set at time k is used as the state estimation set at time k, the state set with the minimum conservatism in all directions that can be achieved by the set-valued observer (2) 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 fully demonstrated that the system is not operating in this mode. Therefore, fault diagnosis is promoted by promoting the separation of two different state estimation sets for the same mode. The two state estimation sets for the same mode are designed as follows:

[0106]

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

[0108]

[0109] The state error set is defined 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. and An equivalent approach is to move the origin from Based on this intuitive finding, the observer gain will be eliminated by promoting the origin from Excluded from optimization.

[0112] Since the output consistent state set at time k It is an unbounded set when the output matrix C is not invertible. In this case, it is also an unbounded set. The previous methods for measuring the separation tendency of sets are based on bounded sets. In order to measure the degree of separation between unbounded sets, the concept of repulsive tendency is further extended to unbounded central symmetric polyhedrons. Based on this extension, we can get the value of the origin relative to The exclusion trend is:

[0113]

[0114] in

[0115] By maximizing the origin relative to The exclusion trend can be obtained by optimizing the observer gain to promote fault diagnosis as follows:

[0116]

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

[0118] The optimization problem (12) is a maximum-minimum optimization problem, and it is very difficult to solve it directly. In order to solve the optimization problem more efficiently, the inner optimization problem is first Lagrangian dualized, and the dual problem of the inner optimization problem is a maximization problem, which is better than the inner optimization problem being a linear problem. Its Lagrangian duality is a strong duality, and the duality gap is 0. Therefore, the maximum-minimum optimization problem (12) can be the same as the optimal value of a maximization problem. After the duality, two optimization variables are multiplied in the maximization problem. By variable substitution, a linear optimization problem is obtained:

[0119]

[0120] It can be obtained that the relationship between the optimal solution of the optimization problem (12) and the optimal solution of the optimization problem (13) is:

[0121]

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

[0123]

[0124] visible, is a free variable that can be designed. Generally speaking, a small size of the state estimation set is beneficial to fault diagnosis. In the embodiment of the present invention, the Frobenius norm is used to measure the state estimation set. Size: For the central symmetric polyhedron set Z1 =<g1,H1> , whose Frobenius norm dimension is defined as The operator ||·|| F represents the Frobenius norm. To further design the free parameters Reducing the size of the state estimate set, the following optimization problem can be formulated:

[0125]

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

[0127]

[0128] in,

[0129] Active fault diagnosis design

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

[0131]

[0132] in, It is obtained by substituting the observer gain determined in 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 embodiment of the present invention, consider that the 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:

[0137]

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

[0139]

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

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

[0142] Compared with the existing fault diagnosis method based on set-valued observer, the present invention proposes a method to promote fault diagnosis from the perspective of state estimation set, which is a fault diagnosis technical solution based on set-valued observer and output consistent state set to promote fault separation from the perspective of state estimation set separation. Compared with the existing repulsion trend based on centrosymmetric polyhedron, the present invention defines the repulsion trend from point to unbounded centrosymmetric polyhedron to describe the positional relationship between the point and the unbounded centrosymmetric polyhedron, and expands the range of set types to which the repulsion trend can be applied. Compared with the existing fault diagnosis method based on set-valued observer, the fault diagnosis effect achieved by the present invention shows a fault diagnosis performance superior to the existing methods on systems that are more affected by noise. Compared with the existing fault diagnosis method based on set-valued observer, the fault diagnosis method designed by the present invention can be applied to both passive fault diagnosis and active fault diagnosis.

[0143] An embodiment of the present invention further provides a storage medium for storing a computer program, which at least performs the above method when executed.

[0144] An embodiment of the present invention further provides a control device, comprising a processor and a storage medium for storing a computer program; wherein the processor is configured to execute at least the method described above when executing the computer program.

[0145] An embodiment of the present invention further provides a processor, wherein the processor executes a computer program and at least executes the method described above.

[0146] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. Among them, 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 magnetic random access memory (FRAM), 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 embodiments of the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0147] In the several embodiments provided by the present invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as: multiple units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the components shown or discussed can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be electrical, mechanical or other forms.

[0148] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units; some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0149] In addition, all functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately used as a unit, or two or more units may be integrated into one unit; the above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0150] Those skilled in the art can understand that: all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above method embodiments; and the aforementioned storage medium includes: mobile storage devices, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), disks or optical disks, etc. Various media that can store program codes.

[0151] Alternatively, if the above-mentioned integrated unit of the present invention is implemented in the form of a software function module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiment of the present invention can be essentially or partly reflected in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the methods described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as mobile storage devices, ROM, RAM, magnetic disks or optical disks.

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

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

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

[0155] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art of the present invention, several equivalent substitutions or obvious variations can be made without departing from the concept of the present invention, and the performance or use is the same, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A fault diagnosis method based on state set separation and set-valued observer, characterized in that: include: S1: Establish a state space model of the discrete linear time-invariant LTI system to be diagnosed with bounded random disturbance and measurement noise. The model is used to describe the dynamic behavior of the system under normal and fault conditions. S2: Determine the unknown parameters of the 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 the system input are determined, and the system input is designed to facilitate the fault diagnosis process; S3: According to the determined set-valued observer parameters, the dynamic equations of the state estimation set and the residual set are established for the healthy mode of the discrete LTI system, where 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; S4: Based on the established state estimation set and residual set, a fault diagnosis decision is made by analyzing the relationship between the residual signal and the residual set to determine whether the system has a fault; S5: When it is determined that a fault exists, the state estimation set at the moment before the fault detection is used as the initial value of the state estimation set of other possible fault modes at that moment, 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; S6: Based on the established state estimation set of other modes, by comparing the relationship between the residual signal and the residual set of other modes, the unmatched modes are eliminated until the only matching fault mode is finally determined to complete the fault diagnosis.

2. The fault diagnosis method based on state set separation and set-valued 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, control input, the impact of actuator failures, and random disturbances; an equation describing the relationship between the system output and the system state is constructed, which also takes into account the impact of noise during the measurement process; the system dynamics are described by a parameter matrix; and a diagonal matrix is ​​used to characterize the multidimensional multiplicative faults of the actuator, where the elements of the diagonal matrix represent the health status of each actuator.

3. The fault diagnosis method based on state set separation and set-valued observer according to claim 2, characterized in that: The random perturbation and measurement noise of the system are considered to be bounded, and a set of centrosymmetric polyhedrons is used to describe the range of perturbation and noise. The properties of the set of centrosymmetric polyhedrons, including the conservation properties under linear transformations and set operation rules such as the Minkowski sum, are used to deal with the uncertainty in the system dynamics.

4. The fault diagnosis method based on state set separation and set-valued observer according to claim 2 or 3, characterized in that: The dynamic equation of the set-valued observer is constructed using the system input vector, output vector and the observer parameters to be determined, so as to dynamically update the state and output estimation set to reflect the estimated state and output of the system at the current moment; The interval matrix is ​​used to characterize different fault modes to ensure that the inclusion relationship between the state vector and the output vector at continuous moments is maintained when the system operates in a specific mode.

5. The fault diagnosis method based on state set separation and set-valued observer according to any one of claims 1 to 4, characterized in that: In step S2, the design steps for the unknown parameters of the set-valued observer are as follows: Construct an optimization problem based on state set separation to determine the observer gain composition and Construct an optimization problem based on the minimum size of the state estimation set to determine the free variables Determine the observer gain; if it is active fault diagnosis, construct an optimization problem based on the maximum center distance of the state estimation set to determine the system input; if it is passive fault diagnosis, directly use the determined observer gain and free variables for state estimation.

6. The fault diagnosis method based on state set separation and set-valued observer according to any one of claims 1 to 5, characterized in that: The design of the passive fault diagnosis includes: defining an output consistent state set, which contains all system states mapped within a given output set; when the noise energy is bounded, using an unbounded central symmetric polyhedron to describe the output consistent state set to deal with 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 the 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 state set separation and set-valued observer according to claim 6, characterized in that: By designing two different state estimation sets of the same mode to be separated from each other, fault diagnosis is facilitated; a 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 relative to the state error set, thereby improving the accuracy of fault diagnosis; The maximum-minimum optimization problem is transformed into a maximization problem and solved by mathematical methods such as Lagrangian duality to determine the observer gain; free parameters are designed to minimize the size of the state estimation set to improve the efficiency of fault diagnosis.

8. The fault diagnosis method based on state set separation and set-valued observer according to any one of claims 1 to 7, characterized in that: The design of active fault diagnosis includes: after the observer gain is determined, actively designing the system input to facilitate the fault diagnosis process; designing the input so that the centers of the state estimation sets under different modes are as far apart as possible to facilitate the rapid distinction of different system modes; constructing an optimization problem with the goal of maximizing the distance between the centers of the state estimation sets of different modes to facilitate accurate diagnosis of faults; determining the system input by solving the optimization problem so that the actual output signal can quickly and accurately reflect the mode in which the system is located.

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

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

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