Fast rate fault detection method for model-unknown multi-rate dynamic system

Abstract

The invention provides a fast rate fault detection method I of a multi-rate dynamic system with an unknown model, and belongs to the technical field of fault detection of digital-analog linkage. The problems that in a multi-rate sampling dynamic system with an unknown mechanism model, due to the fact that multi-rate data are not synchronous in the time dimension, future data dependence is prone to being generated by adopting a lifting technology, and consequently noncausality is caused, and fault detection delay is caused by a slow-rate diagnosis observer built according to existing data information are solved. According to the technical scheme, the method comprises the steps that a, an output stacking matrix is reconstructed; b, adopting a subspace identification method to solve an equivalent vector for a joint matrix formed by the input and reconstructed output stacked matrixes; c, generating a multi-dimensional residual diagnosis observer; and d, reconstructing a residual sequence generated by the fast rate and carrying out online fast rate residual evaluation. The method has the beneficial effects that the fault can be quickly and accurately detected, so that the fault diagnosis reliability of the system is improved.

Description

Technical Field

[0001] The invention relates to the technical field of fault detection of digital-analog linkage of a multi-rate sampling data system, and in particular to a fast rate fault detection method for a multi-rate dynamic system at a model position. Background Art

[0002] With the rapid expansion of the scale of industrial systems and the continuous improvement of the complexity of modern engineering systems, how to ensure the safety and reliability of their operation has become a key issue that needs to be solved urgently. Fault diagnosis technology can detect, locate and estimate faults in time when the system is running, providing a basis for effectively handling system faults or potential hidden dangers, thereby preventing system deterioration or catastrophic accidents. Therefore, fault diagnosis technology is regarded as a key technology to improve system safety, reliability and reduce accident risks, and has been widely studied by academia and industry in the past half century. On the other hand, in many large-scale complex engineering systems, due to the differences in subsystem or component functions and application requirements, sensors often sample various system parameters at different rates, and actuators also execute control commands at different rates, which is the so-called multi-rate sampling data system. Multi-rate sampling will lead to data asynchrony on the one hand, and will also change the nature of the system. Obviously, compared with conventional single-rate sampling systems, fault diagnosis of multi-rate sampling data systems is more challenging.

[0003] Although the existing machine learning and statistical methods for fault diagnosis are the mainstream of fault diagnosis in multi-rate sampling data systems, these methods only rely on data and have achieved good diagnostic results when applied to multi-rate static systems. However, for multi-rate dynamic systems with unknown models, these methods ignore the system dynamic characteristics implied in the data, so the fault diagnosis effect is greatly reduced. On the other hand, regarding the fault diagnosis of multi-rate dynamic systems, most of the current work assumes that the model parameters are known. However, due to the widespread existence of model uncertainty and parameter changes in industrial processes, it becomes extremely difficult to obtain an accurate system model, which greatly limits the effect and applicability of model-based methods in practical applications. In summary, the research on fast rate fault diagnosis of multi-rate dynamic systems with unknown models has important practical significance and application value, and a fast rate fault detection method for multi-rate dynamic systems with unknown models is proposed. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a fast-rate fault detection method for a multi-rate dynamic system with an unknown model. The method does not rely on the precise model parameters of the multi-rate sampling system. Even when the time dimension of the data is not synchronized or the system properties change due to multi-rate sampling, the method can still detect faults quickly and accurately, thereby improving the fault diagnosis reliability of the system.

[0005] The inventive concept of the present invention is:

[0006] The present invention provides a fast-rate fault detection method for a multi-rate dynamic system with an unknown model, which belongs to the technical field of fault detection of digital-analog linkage. It solves the problem of non-causality caused by the lack of synchronization of multi-rate data in the time dimension, the use of lifting technology that easily generates future data dependency, and the fault detection delay caused by a slow-rate diagnostic observer constructed based on existing data information in a dynamic system with multi-rate sampling and an unknown mechanism model. Its technical solution is: a. Reconstruct the output stacking matrix; b. Use the subspace identification method to solve the equivalent vector of the joint matrix composed of the input and reconstructed output stacking matrices; c. Generate a diagnostic observer for multi-dimensional residuals; d. Reconstruct the residual sequence generated by the fast rate and perform online fast-rate residual evaluation. The beneficial effects of the present invention are: quickly and accurately detect faults, thereby improving the fault diagnosis reliability of the system.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is specifically a fast rate fault detection method for a multi-rate dynamic system with an unknown model, comprising the following steps:

[0008] a. Use lifting technology to convert the asynchronously sampled input and output data in the dynamic system into data based on the same sampling base period, and then construct the input and output stacking matrix, and then calculate the weighted vector based on the heuristic algorithm to reconstruct the output stacking matrix;

[0009] b. In the framework of subspace identification, singular value decomposition and QR decomposition are performed on the joint matrix composed of the input and output stacked matrices to solve the equivalent vector, and the Luenberger observer parameter matrix is ​​determined based on the relationship between the equivalent vector and the diagnostic observer;

[0010] c. Design a post-filter with zero constraints to eliminate the dependency of the residual introduced by the lifting technology on future input and output data, obtain the Luenberger observer parameter matrix that satisfies the causal constraints, and further construct a multidimensional residual generator;

[0011] d. Perform QR decomposition on the joint matrix to calculate the covariance of the residual signal and the threshold at the same time. The residual signal generated in the base period is converted into a fast-rate residual signal through the inverse lifting technology. The fast-rate residual signal sequence is reconstructed and the fast-rate evaluation is performed on it. The threshold is combined to perform online fault detection logic judgment to achieve fast-rate fault detection.

[0012] Furthermore, in step a, the lifting technique is used to convert the asynchronously sampled input and output data in the dynamic system into data based on the same sampling base period, and then construct the input and output stacking matrix, as follows:

[0013] The input and output data in the multi-rate dynamic system are where u(k) is updated at a fast rate with a base period h, and the y of the i-th component of y(k) i The sampling period is H i =n i h,n i ∈Ν. Let M be n 1 ,…,n m The lowest common multiple of , then Mh is the common sampling period, Output y i The number of samples in a common period, is the total number of samples output in the common cycle. Applying the lifting technique to u(k) and y(k), the lifted data can be expressed as

[0014]

[0015] Among them, k s Represents the time index of updating data in the base period. Construct input and output stacking matrices for N sets of data, expressed as

[0016]

[0017] Where s represents the number of past levels.

[0018] The weight vector κ is calculated using the following heuristic algorithm:

[0019]

[0020] Among them, ι∈[1,s+1], 1 Q is a column vector whose elements are all 1, is the unit matrix. The output data y(k s ) is reconstructed as in Then the output stacking matrix becomes

[0021]

[0022] In the step b, under the subspace identification framework, singular value decomposition and QR decomposition are performed on the joint matrix composed of the input and output stacked matrices to solve the equivalent vector, and the Luenebrger observer is determined based on the relationship between the equivalent vector and the diagnostic observer, which is in the following form:

[0023] z(k s +1)=A z z(k s )+B z u(k s )+L z y(k s ),

[0024]

[0025] in, represents the observer state vector, represents the slow rate residual signal that does not satisfy the causal constraint, A z ,B z ,L z ,g,c z ,d z is the observation parameter matrix to be designed.

[0026] The joint matrix formed by the stacked matrices at the past s+1 time is expressed as right and Perform singular value decomposition

[0027]

[0028] in right Rearrange and perform QR decomposition:

[0029]

[0030] Get the equivalent vector: α n =Q y ((s+1)Qn,1:n+1), then the parameter matrix of the slow rate Q-dimensional diagnostic observer is

[0031]

[0032] in,

[0033]

[0034] Q u (1:η,sMl+1:(s+1)Ml)=Q y (1:η,s)κD u +Q y (1:η,sQ+2:(s+1)Q)ΞD u ,

[0035] η=(s+1)Qn,

[0036] Furthermore, in step c, a post-filter with zero constraints is designed to eliminate the dependency of the residual introduced by the lifting technology on future input and output data, and obtain a Luenberger observer that satisfies the causal constraints, which is in the form of:

[0037] z(ks +1)=A z z(k s )+B z u(k s )+L z y(k s ),

[0038] r(k s )=Gy(k s )-C z z(k s )-D z u(k s ),

[0039] in, represents the slow rate residual signal that satisfies the constraints.

[0040] Structural Satisfaction and The collection S L,j,p ={L,j,p}, where L represents the number of rows of the post-filter F, j and p represent matrices g and d respectively. z The number of columns of can be used to obtain the structure of the post-filter F, thereby obtaining the diagnostic observer parameters that satisfy the causal constraints:

[0041] G=Fg,C z =Fc z ,D z =Fd z ,A z , B z , L z Same as in step b.

[0042] Finally, in step d, and Construct a Hankle matrix and perform QR decomposition on it

[0043]

[0044] Combined with the result obtained in step b You can get:

[0045]

[0046] in, Represents the output stacked matrix The part related to noise.

[0047] For any The following relationship always holds:

[0048]

[0049] Thus, the residual signal r(k s ) is:

[0050]

[0051] The threshold is calculated as in, It represents the chi-square distribution value with M degrees of freedom and α confidence level.

[0052] The residual signal that satisfies the causal constraint generated in the base period is converted into a fast rate residual signal through the inverse lifting technique, and the fast rate residual signal is reconstructed and evaluated in real time in the form of

[0053]

[0054] Among them, r(Mk s +i-1) indicates the Mkth s +i-1 fast rate residual signals. Combined with the calculated threshold, online fast rate fault detection is performed, and the fault detection logic is described as follows:

[0055]

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1) In the case of an unknown multi-rate sampling dynamic system model, the present invention processes multi-rate data based on the lifting technology, effectively solving the problem of asynchronous sampling of multi-rate data;

[0058] 2) The present invention constructs a new output stacking matrix by introducing a weighted vector, solves the equivalent vector on this basis, and designs a Q-rate diagnostic observer. On this basis, a post-filter is designed, and by applying a zero constraint on the post-filter matrix in the residual generator, the non-causal constraint problem caused by the dependence of the residual on future input and output data caused by the application of the lifting technology is eliminated;

[0059] 3) The present invention introduces the inverse lifting technology to convert the residual signal that satisfies the causal constraint within the base period into a fast rate residual signal, and reconstructs the fast rate residual signal, thereby realizing fast rate fault detection and effectively reducing the fault detection delay problem;

[0060] 4) The present invention selects central air conditioning (HVAC) systems with high energy consumption and slow dynamics as experimental objects to verify the proposed method.

[0061] 5) The present invention first uses a lifting technique to convert multi-rate sampling data into data based on the same sampling base period, and introduces a weighted vector to process the boosted output data; then, under the subspace identification framework, the equivalent vector is solved to construct a diagnostic observer to generate a slow-rate multidimensional residual signal; subsequently, a post-filter is designed to solve the non-causal constraint problem between the residual signal and the input and output signals, and a corresponding diagnostic observer is formed to generate a slow-rate residual signal that satisfies the causal constraint; finally, the inverse lifting technique is used to convert the slow-rate residual signal that satisfies the causal constraint into a fast-rate residual signal and reconstruct it, thereby realizing fast-rate fault detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0063] Figure 1 A flowchart of the steps of a fast rate fault detection method for a multi-rate dynamic system with an unknown model provided by the present invention.

[0064] Figure 2 This is a diagram of a four-area building model according to an embodiment of the present invention.

[0065] Figure 3 This is a four-zone building HVAC system simulation environment built using the simulation software TRNSYS in the present invention.

[0066] FIG. 4( a ) is a PCA method fault detection diagram of a 10% stuck open position air valve in region A of an embodiment of the present invention;

[0067] FIG4( b ) is a slow rate fault detection diagram of the air valve of area A stuck at 10% of the open position according to an embodiment of the present invention;

[0068] FIG4( c ) is a 10% fast rate fault detection diagram of the air valve of area A stuck in the open position according to an embodiment of the present invention;

[0069] FIG. 5( a ) is a PCA method fault detection diagram of a damper in region A of an embodiment of the present invention being stuck at 30% of the open position;

[0070] FIG5( b ) is a fast rate fault detection diagram of a 30% air valve stuck in the open position in area A of an embodiment of the present invention;

[0071] FIG5(c) is a fast rate fault detection diagram of a 30% air valve stuck in the open position in area A according to an embodiment of the present invention.

[0072] FIG. 6( a ) is a PCA method fault detection diagram of a damper in region A of an embodiment of the present invention being stuck at 70% of the open position;

[0073] FIG6( b ) is a slow and fast rate fault detection diagram of the air valve of area A stuck at 70% of the open position according to an embodiment of the present invention;

[0074] FIG6( c ) is a fast rate fault detection diagram of 70% of the air valve stuck in the open position in area A of the embodiment of the present invention. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0076] Example 1

[0077] Reference Figure 1 Flowchart, this embodiment provides a fast rate fault detection method for a multi-rate dynamic system with an unknown model, comprising the following steps:

[0078] Step a: Use lifting technology to convert the asynchronously sampled input and output data of the dynamic system into data based on the same sampling base period, and then construct the input and output stacking matrix, as follows:

[0079] The input and output data in the multi-rate dynamic system are where u(k) is updated at a fast rate with a base period h, and the y of the i-th component of y(k) i The sampling period is H i =n i h,n i ∈Ν. Let M be n 1 ,…,n m The lowest common multiple of , then Mh is the common sampling period, Output y i The number of samples in a common period, is the total number of samples output in the common cycle. Applying the lifting technique to u(k) and y(k), the lifted data can be expressed as

[0080]

[0081] Among them, k s Represents the time index of updating data in the base period. Construct input and output stacking matrices for N sets of data, expressed as

[0082]

[0083] Where s represents the number of past levels.

[0084] The weight vector κ is calculated using the following heuristic algorithm:

[0085]

[0086] Among them, ι∈[1,s+1], 1 Q is a column vector whose elements are all 1, is the unit matrix. The output data y(k s ) is reconstructed as in Then the output stacking matrix becomes

[0087]

[0088] Step b: In the subspace identification framework, singular value decomposition and QR decomposition are performed on the joint matrix composed of the input and output stacked matrices to solve the equivalent vector. The Luenberger observer is determined based on the relationship between the equivalent vector and the diagnostic observer, which is in the following form:

[0089] z(k s +1)=A z z(k s )+B z u(k s )+L z y(k s ),

[0090]

[0091] in, represents the observer state vector, represents the slow rate residual signal that does not satisfy the causal constraint, A z ,B z ,L z ,g,c z ,d z is the observation parameter matrix to be designed.

[0092] The joint matrix formed by the stacked matrices at the past s+1 time is expressed as right and Perform singular value decomposition

[0093]

[0094] in right Rearrange and perform QR decomposition:

[0095]

[0096] Get the equivalent vector: αn =Q y ((s+1)Qn,1:n+1), then the parameter matrix of the slow rate Q-dimensional diagnostic observer is

[0097] in,

[0098]

[0099] Q u (1:η,sMl+1:(s+1)Ml)=Q y (1:η,s)κD u +Q y (1:η,sQ+2:(s+1)Q)ΞD u ,

[0100] η=(s+1)Qn,

[0101] Step c: Design the post-filter and impose zero constraints to eliminate the future data dependency introduced by the lifting technique and design a Luenebrger observer that satisfies the causal constraints in the form of:

[0102] z(k s +1)=A z z(k s )+B z u(k s )+L z y(k s ),

[0103] r(k s )=Gy(k s )-C z z(k s )-D z u(k s ),

[0104] Among them, r(k s ) represents the slow rate residual signal that satisfies the causal constraint.

[0105] Structural Satisfaction and The collection S L,j,p ={L,j,p}, where L represents the number of rows of the post-filter F, j and p represent matrices g and d respectively. z The number of columns of can be used to obtain the structure of the post-filter F, thereby obtaining the diagnostic observer parameters that satisfy the causal constraints:

[0106] G=Fg,C z =Fc z ,D z =Fdz ,A z , B z , L z Same as in step b.

[0107] Step d: Middle Pair and Construct a Hankle matrix and perform QR decomposition on it

[0108]

[0109] Combined with the result obtained in step b You can get:

[0110]

[0111] in, Represents the output stacked matrix The part related to noise.

[0112] For any The following relationship always holds:

[0113]

[0114] Thus, the residual signal r(k s ) is:

[0115]

[0116] The threshold is calculated as in, It represents the chi-square distribution value with M degrees of freedom and α confidence level.

[0117] The residual signal that satisfies the causal constraint in the base period is converted into a fast rate residual signal through the inverse lifting technique, and the fast rate residual signal is reconstructed for real-time evaluation, which is in the form of

[0118]

[0119] Among them, r(Mk s +i-1) indicates the Mkth s +i-1 fast rate residual signals. Combined with the calculated threshold, online fast rate fault detection is performed, and the fault detection logic is described as follows:

[0120]

[0121] In this embodiment, under the TRNSYS and MatlabR2018b environment, the experimental object is a four-zone central air conditioning (HVAC) with high energy consumption and slow changes, such as Figure 2 and3 As shown. This embodiment is used to verify the proposed method, aiming to detect the change of the air valve opening signal in the central air conditioning system. The air valve opening signal of each area is used as the input signal, the sampling period T = 10 minutes, and the air valve stuck fault of area A is selected, which is specifically manifested as the air valve is fixed at 10% of the open position when 200≤k≤500.

[0122] Select the temperature signal of each room as the output, and the sampling period of area A and B is T A , T B = 20 minutes, the sampling period of area C and D is T C , T D = 30 minutes. Since the sampling periods of input and output signals are inconsistent, the lifting technology is used to convert different sampling periods into common period sampling, which is expressed as MT. The calculation basis is as follows:

[0123]

[0124] Under a common base period, the number of samples for each output is as follows:

[0125]

[0126] The diagnostic observer that satisfies the causal constraints is as follows:

[0127] z(k s +1)=A z z(k s )+B z u(k s )+L z y(k s ),

[0128] r(k s )=Gy(k s )-C z z(k s )-D z u(k s ),

[0129] The specific dimensions and values ​​of the relevant parameter matrix are as follows:

[0130] κ=[0.1272 0.1272 0.1271 0.1272 0.1272 0.1272 0.1271 0.1272 0.9710.1272],

[0131]

[0132] Calculate the fast rate test statistic J(k) and threshold Jth =12.59(α=0.05).

[0133] Result description:

[0134] Figure 4(a) is a PCA fault detection effect diagram of the air valve stuck in the open position of area A at 10%, Figure 4(b) is a slow rate fault detection effect diagram, and Figure 4(c) is a fast rate fault detection effect diagram. It can be observed that the PCA method T in Figure 4(a) 2 The test statistic failed to identify the fault, and the SPE test statistic also failed to detect the fault in the interval 300≤k≤430; the detection effect of the slow rate detection method in Figure 4(b) is improved compared with the PCA method, but the slow rate detection method only detects the fault at k=210, and there is an obvious detection delay; compared with Figure 4(c), the designed fast rate detection method detects the fault at k=204, which can detect the fault quickly and accurately. Compared with the slow rate detection method, the detection effect is one base cycle earlier.

[0135] Example 2

[0136] The air valve stuck fault in area A is selected, which is specifically manifested as the air valve being fixed at 70% of the open position when 200≤k≤500.

[0137] Result description:

[0138] Figure 5(a) is the effect diagram of the PCA method for 10% of the air valves in area A stuck in the open position, Figure 5(b) is the effect diagram of the slow rate fault detection, and Figure 5(c) is the effect diagram of the proposed fast rate fault detection. As can be seen from Figure 5(a), the shortcomings of the PCA method are more prominent. Only the SPE test statistic detects the fault at a few moments, and the others fail to detect the fault; Figure 5(b) is the effect diagram of the slow rate fault detection. It can be seen that the delay phenomenon of the slow rate detection is more obvious. The fault is not detected until k=215. In this case, the fault detection rate and fault false alarm rate are 96.66% and 6.44% respectively; Figure 5(c) is the effect diagram of the fast rate fault detection. The fault is detected at k=204, which can quickly capture the dynamic characteristics of the system. Its detection rate and false alarm rate are 98.67% and 3.1% respectively, which is significantly better than the PCA method and the slow rate detection method.

[0139] Example 3

[0140] The air valve stuck fault in area A is selected, which is specifically manifested as the air valve being fixed at 90% of the open position when 200≤k≤500.

[0141] Result description:

[0142] Figure 6(a) is the effect diagram of the PCA method fault detection of 10% of the air valve stuck in the open position in area A, Figure 6(b) is the effect diagram of the slow rate fault detection, and Figure 6(c) is the effect diagram of the proposed fast rate fault detection. It can be seen that the proposed fast rate fault detection method quickly captures the dynamic characteristics of the system and detects the fault at k=210. Compared with the PCA detection method and the slow rate fault detection method, it shows a strong small fault detection ability.

[0143] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A fast rate fault detection method for a multi-rate dynamic system with an unknown model, characterized in that: The following steps are involved: a. Use lifting technology to convert the asynchronously sampled input and output data in the dynamic system into data based on the same sampling base period, and then construct the input and output stacking matrix, and then calculate the weighted vector based on the heuristic algorithm to reconstruct the output stacking matrix; b. In the framework of subspace identification, singular value decomposition and QR decomposition are performed on the joint matrix composed of the input and output stacked matrices to solve the equivalent vector, and the Luenberger observer parameter matrix is ​​determined based on the relationship between the equivalent vector and the diagnostic observer; c. Design a post-filter with zero constraints to eliminate the dependency of the residual introduced by the lifting technology on future input and output data, obtain the Luenberger observer parameter matrix that satisfies the causal constraints, and further construct a multidimensional residual generator; d. Perform QR decomposition on the joint matrix to calculate the covariance of the residual signal and the threshold at the same time. The residual signal that satisfies the causal constraint generated within the base period is converted into a fast-rate residual signal through the inverse lifting technology. The fast-rate residual signal sequence is reconstructed and the fast-rate evaluation is performed on it. The threshold is combined to perform online fault detection logic judgment to achieve fast-rate fault detection.

2. The fast rate fault detection method for a multi-rate dynamic system with unknown model according to claim 1, characterized in that: In step a, the lifting technique is used to convert the asynchronously sampled input and output data in the dynamic system into data based on the same sampling base period, and then construct the input and output stacking matrix, as follows: The input and output data in the multi-rate dynamic system are where u(k) is updated at a fast rate with a base period h, and the y of the i-th component of y(k) i The sampling period is H i =n i h,n i ∈Ν; let M be n1,…,n m The lowest common multiple of , then Mh is the common sampling period, Output y i The number of samples in a common period, is the total number of samples output in the common period. The lifting technique is applied to u(k) and y(k). The data after lifting is expressed as: Among them, k s Represents the time index of updating data in the base period, constructs input and output stacking matrices for N sets of data in the form of Among them, s represents the number of past levels; The weight vector κ is calculated using the following heuristic algorithm: Among them, ι∈[1,s+1], 1 Q is a column vector whose elements are all 1, As the unit matrix, the output data y(k s ) is reconstructed as in Then the output stacked matrix becomes 3. The fast rate fault detection method for a multi-rate dynamic system with unknown model according to claim 1, characterized in that: In the step b, under the subspace identification framework, singular value decomposition and QR decomposition are performed on the joint matrix composed of the input and output stacked matrices to solve the equivalent vector, and the Luenebrger observer is determined based on the relationship between the equivalent vector and the diagnostic observer, which is in the following form: z(k s +1)=A z z(k s )+B z u(k s )+L z y(k s ), in, represents the observer state vector, represents the slow rate residual signal that does not satisfy the causal constraint, A z ,B z ,L z ,g,c z ,d z is the observation parameter matrix to be designed; The joint matrix formed by the stacked matrices at the past s+1 time is expressed as right and Perform singular value decomposition in right Rearrange and perform QR decomposition: Get the equivalent vector: α n =Q y ((s+1)Qn,1:n+1), then the parameter matrix of the slow rate Q-dimensional diagnostic observer is in, Q u (1:η,sMl+1:(s+1)Ml)=Q y (1:η,s)κD u +Q y (1:η,sQ+2:(s+1)Q)ΞD u , 4. The fast rate fault detection method for a multi-rate dynamic system with unknown model according to claim 1, characterized in that: In step c, a post-filter with zero constraints is designed to eliminate the dependency of the residual introduced by the lifting technology on future input and output data, and obtain a Luenebrger observer that satisfies the causal constraints, which is in the form of: z(k s +1)=A z z(k s )+B z u(k s )+L z y(k s ), r(k s )=Gy(k s )-C z from(to s )-D z u(k s ), in, represents a slow rate residual signal satisfying the constraint; Structural Satisfaction and The collection S L,j,p ={L,j,p}, where L represents the number of rows of the post-filter F, j and p represent matrices g and d respectively. z The number of columns of the post-filter F is obtained, and thus the diagnostic observer parameters that satisfy the causal constraints are obtained: G=Fg,C z =Fc z ,D z =Fd z ,A z , B z , L z Same as in step b.

5. The fast rate fault detection method for a multi-rate dynamic system with unknown model according to claim 1, characterized in that: In step d, and Construct a Hankle matrix and perform QR decomposition on it Combined with the result obtained in step b get: in, represents the noise-related portion of the output stacking matrix; For any The following relationship always holds: The residual signal r(k s ) is: The threshold is calculated as in, It represents the chi-square distribution value with M degrees of freedom and α confidence level; The residual signal that satisfies the causal constraint generated in the base period is converted into a fast rate residual signal through the inverse lifting technique, and the fast rate residual signal is reconstructed and evaluated in real time in the form of Among them, r(Mk s +i-1) indicates the Mkth s +i-1 fast rate residual signals are combined with the calculated threshold to detect online fast rate faults. The fault detection logic is described as follows:

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