A fast rate fault detection method for a model-unknown multi-rate dynamic system

Abstract

The application provides a fast-rate fault detection method for a model-unknown multi-rate dynamic system, and belongs to the technical field of fault detection of digital-hydraulic linkage. The application solves the problems of non-causality caused by the non-synchronization of multi-rate data in time dimension, the future data dependency caused by the adoption of promotion technology, and the fault detection delay caused by the slow-rate diagnostic observer constructed according to the existing data information in a model-unknown multi-rate sampled dynamic system. The technical scheme comprises the following steps: a. reconstructing an output stack matrix; b. solving equivalent vectors by adopting a subspace identification method on a joint matrix composed of the input and the reconstructed output stack matrix; c. generating a multi-dimensional residual diagnostic observer; and d. reconstructing a residual sequence generated at a fast rate and performing online fast-rate residual evaluation. The application has the beneficial effect of quickly and accurately detecting faults, thereby improving the fault diagnosis reliability of the system.

Description

Technical Field

[0001] This invention relates to the field of fault detection technology for multi-rate sampling data systems with digital-analog linkage, and specifically to a fast-rate fault detection method for multi-rate dynamic systems with model location. Background Technology

[0002] With the rapid expansion and increasing complexity of modern engineering systems, ensuring their safety and reliability has become a critical issue. Fault diagnosis technology can detect, locate, and estimate faults in a timely manner during system operation, providing a basis for effectively handling system failures or potential hazards, thereby preventing system deterioration or catastrophic accidents. Therefore, fault diagnosis technology is considered a key technology for improving system safety and reliability and reducing accident risks, and has been extensively studied by academia and industry over the past half-century. On the other hand, in many large-scale complex engineering systems, due to differences in the functions and application requirements of subsystems or components, sensors often sample various parameters of the system at different rates, and actuators also execute control commands at different rates, i.e., multi-rate sampling data systems. Multi-rate sampling leads to data asynchrony and also changes 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] While existing machine learning and statistical methods are currently the mainstream approaches for fault diagnosis in multi-rate sampled data systems, these methods rely solely on data. While they achieve good diagnostic results in multi-rate static systems, they neglect the implicit dynamic characteristics of the system within the data for multi-rate dynamic systems with unknown models, thus significantly reducing their diagnostic effectiveness. Furthermore, most current work on fault diagnosis for multi-rate dynamic systems assumes known model parameters. However, due to widespread model uncertainty and parameter variations in industrial processes, obtaining accurate system models is extremely difficult, which greatly limits the effectiveness and applicability of model-based methods in practical applications. In conclusion, research on fast-rate fault diagnosis for multi-rate dynamic systems with unknown models has significant practical implications and application value. Therefore, a fast-rate fault detection method for multi-rate dynamic systems with unknown models is proposed. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a fast-rate fault detection method for multi-rate dynamic systems with unknown models. This method does not rely on the precise model parameters of the multi-rate sampling system and can still quickly and accurately detect faults even when the data time dimension is asynchronous or the system properties change due to multi-rate sampling, thereby improving the reliability of fault diagnosis in the system.

[0005] The inventive concept of this invention is as follows: This invention provides a fast-rate fault detection method for multi-rate dynamic systems with unknown models, belonging to the field of fault detection technology in the field of analog-digital linkage. It solves the problems of non-causality caused by the asynchronous nature of multi-rate data in the time dimension and the potential for future data dependencies due to boosting techniques in dynamic systems with unknown mechanistic models, as well as the fault detection delay caused by slow-rate diagnostic observers constructed based on existing data. The technical solution is as follows: a. Reconstructing the output stacking matrix; b. Solving for equivalent vectors in the joint matrix composed of the input and reconstructed output stacking matrices using subspace identification; c. Generating a multi-dimensional residual diagnostic observer; d. Reconstructing the residual sequence generated by the fast rate and performing online fast-rate residual evaluation. The beneficial effect of this invention is that it can quickly and accurately detect faults, thereby improving the reliability of fault diagnosis in the system.

[0006] To achieve the above objectives, the technical solution adopted by this invention is specifically a method for detecting fast rate faults in a multi-rate dynamic system with an unknown model, comprising the following steps:

[0007] a. Using lifting techniques, the asynchronously sampled input and output data in a dynamic system are transformed into data based on the same sampling base period, thereby constructing an input and output stacking matrix, and then calculating a weighted vector based on a heuristic algorithm to reconstruct the output stacking matrix;

[0008] b. Under the subspace identification framework, singular value decomposition and QR decomposition are performed on the joint matrix composed of input and output stacked matrices to solve for equivalent vectors. Based on the relationship between the equivalent vectors and the diagnostic observer, the Luenberger observer parameter matrix is ​​determined.

[0009] c. Design a post-filter with zero constraints to eliminate the dependence of the residuals introduced by the lifting technique on future input and output data, obtain the Luenberger observer parameter matrix that satisfies the causal constraints, and further construct a multidimensional residual generator;

[0010] d. Perform QR decomposition on the joint matrix to calculate the covariance of the residual signal. Simultaneously, calculate the threshold. Use inverse boosting technology to convert the residual signal generated within the base period into a fast rate residual signal. Reconstruct the fast rate residual signal sequence and evaluate its fast rate. Combine the threshold with online fault detection logic to achieve fast rate fault detection.

[0011] Furthermore, in step a, the lifting technique is used to transform the asynchronously sampled input and output data in the dynamic system into data based on the same sampling base period, thereby constructing the input and output stacking matrix, as follows:

[0012] The input and output data in a multi-rate dynamic system are , ,in Updated at a fast rate with a base period h. The Each component The sampling period is Let M be... The least common multiple of , then For the common sampling period, For output The number of samples within the common period, This represents the total number of samples output within the common period. By applying enhancement techniques, the enhanced data can be represented as

[0013]

[0014] in, This represents the time index for updating data with the base period. Construct an input-output stacked matrix for N sets of data, represented as follows:

[0015]

[0016]

[0017] in, Indicates past level number.

[0018] The weighted vector is calculated using the following heuristic algorithm. :

[0019]

[0020] in, , , It is a column vector whose elements are all 1s. It is an identity matrix. The output data will be... The reconstruction of ,in Then the form of the output stacked matrix becomes

[0021]

[0022]

[0023] In step b, within 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 for equivalent vectors. Based on the relationship between the equivalent vectors and the diagnostic observer, the Luenebrger observer is determined, in the following form:

[0024]

[0025] in, Represents the observer state vector. This represents a slow-rate residual signal that does not satisfy the causal constraint. This is the observation parameter matrix to be designed.

[0026] Regarding the past The joint matrix formed by the stacked matrices at time points is represented as .right and Perform singular value decomposition

[0027]

[0028] in .right Rearrange and decompose into QR:

[0029]

[0030] Obtain the equivalent vector: Then slow rate The parameter matrix of the 3D diagnostic observer is

[0031]

[0032]

[0033] in,

[0034]

[0035]

[0036]

[0037] Furthermore, in step c, a post-filter with zero constraints is designed to eliminate the dependence of the residuals introduced by the boosting technique on future input and output data, thereby obtaining a Luenberger observer that satisfies causality constraints, in the form of:

[0038]

[0039]

[0040] in, This represents a slow-rate residual signal that satisfies the constraints.

[0041] Construct satisfying and set ,in Indicates post-filter the number of rows, Represent matrices respectively , The number of columns can be used to obtain the post-filter. The structure is used to obtain diagnostic observer parameters that satisfy causal constraints:

[0042] Same as in step b.

[0043] Finally, in step d, the following steps are performed: and Construct the Hankle matrix and perform QR decomposition on it.

[0044]

[0045] Combining the results obtained in step b We can obtain:

[0046]

[0047] in, Indicates the output stacked matrix The part related to noise.

[0048] For any The following relationship always holds:

[0049]

[0050] From this, the residual signal can be obtained. The variance matrix is:

[0051]

[0052] Simultaneously calculate the threshold as in, Describing the degrees of freedom as Confidence level is The chi-square distribution value.

[0053] The residual signal satisfying causality constraints generated within the base period is converted into a fast-rate residual signal using an inverse boosting technique. This fast-rate residual signal is then reconstructed and evaluated in real time, taking the form of…

[0054]

[0055] in, Indicates the first A fast rate residual signal. Combined with the calculated threshold, online fast rate fault detection is performed. The fault detection logic is described as follows:

[0056] .

[0057] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0058] 1) In the case of an unknown multi-rate sampling dynamic system model, this invention processes multi-rate data based on enhancement techniques, effectively solving the problem of asynchronous sampling of multi-rate data;

[0059] 2) This invention constructs a new output stacking matrix by introducing weighted vectors, and then solves for equivalent vectors based on this matrix, thus designing a... This is a slow-rate diagnostic observer. Based on this, a post-filter is designed. By applying zero constraints to 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 due to the application of lifting techniques is eliminated.

[0060] 3) This invention introduces inverse boosting technology to convert the residual signal that satisfies the causal constraint within the base period into a fast rate residual signal and reconstruct the fast rate residual signal, thereby realizing fast rate fault detection and effectively reducing the fault detection delay problem;

[0061] 4) This invention selects energy-intensive, slow-dynamic systems such as central air conditioning (HVAC) as experimental subjects to verify the proposed method.

[0062] 5) This invention first employs a boosting technique to convert multi-rate sampled data into data based on the same sampling base period, and then introduces a weighted vector to process the boosted output data. Next, within the subspace identification framework, equivalent vectors are solved to construct a diagnostic observer to generate a slow-rate multidimensional residual signal. Subsequently, a post-filter is designed to address the non-causal constraint problem between the residual signal and the input / output signals, and a corresponding diagnostic observer is formed, thereby generating a slow-rate residual signal that satisfies causal constraints. Finally, an inverse boosting technique is used to convert the slow-rate residual signal that satisfies causal constraints into a fast-rate residual signal and reconstruct it, thereby achieving fast-rate fault detection. Attached Figure Description

[0063] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0064] Figure 1 The flowchart illustrates the steps of the fast rate fault detection method for multi-rate dynamic systems with unknown models provided by this invention.

[0065] Figure 2 This is a four-area building model diagram according to an embodiment of the present invention.

[0066] Figure 3 This invention presents a four-zone building HVAC system simulation environment built using the simulation software TRNSYS.

[0067] Figure 4(a) shows the damper in area A of this embodiment of the invention stuck in the open position. PCA method fault detection diagram;

[0068] Figure 4(b) shows the air valve in area A of this embodiment stuck in the open position. Slow-rate fault detection diagram;

[0069] Figure 4(c) shows the air valve in area A of this embodiment of the invention stuck in the open position. High-rate fault detection diagram;

[0070] Figure 5(a) shows the damper in area A of this embodiment of the invention stuck in the open position. PCA method fault detection diagram;

[0071] Figure 5(b) shows the damper in area A of this embodiment of the invention stuck in the open position. High-rate fault detection diagram;

[0072] Figure 5(c) shows the air valve in area A of this embodiment of the invention stuck in the open position. The high-rate fault detection diagram.

[0073] Figure 6(a) shows the damper in area A of this embodiment of the invention stuck in the open position. PCA method fault detection diagram;

[0074] Figure 6(b) shows the damper in area A of this embodiment of the invention stuck in the open position. Slow and fast rate fault detection diagrams;

[0075] Figure 6(c) shows the air valve in area A of this embodiment of the invention stuck in the open position. The high-rate fault detection diagram. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0077] Example 1

[0078] Reference Figure 1The flowchart illustrates a fast rate fault detection method for a multi-rate dynamic system with an unknown model, comprising the following steps:

[0079] Step a: Use lifting techniques to transform asynchronously sampled input and output data in a dynamic system into data based on the same sampling base period, and then construct an input-output stacking matrix, as follows:

[0080] The input and output data in a multi-rate dynamic system are , ,in Updated at a fast rate with a base period h. The Each component The sampling period is Let M be... The least common multiple of , then For the common sampling period, For output The number of samples within the common period, This represents the total number of samples output within the common period. By applying enhancement techniques, the enhanced data can be represented as

[0081]

[0082] in, This represents the time index for updating data with the base period. Construct an input-output stacked matrix for N sets of data, represented as follows:

[0083]

[0084]

[0085] in, Indicates past level number.

[0086] The weighted vector is calculated using the following heuristic algorithm. :

[0087]

[0088] in, , , It is a column vector whose elements are all 1s. It is an identity matrix. The output data will be... The reconstruction of ,in Then the form of the output stacked matrix becomes

[0089]

[0090] .

[0091] Step b: Within 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 for equivalent vectors. Based on the relationship between the equivalent vectors and the diagnostic observer, the Luenberger observer is determined, in the following form:

[0092]

[0093] in, Represents the observer state vector. This represents a slow-rate residual signal that does not satisfy the causal constraint. This is the observation parameter matrix to be designed.

[0094] Regarding the past The joint matrix formed by the stacked matrices at time points is represented as .right and Perform singular value decomposition

[0095]

[0096] in .right Rearrange and decompose into QR:

[0097]

[0098] Obtain the equivalent vector: Then slow rate The parameter matrix of the 3D diagnostic observer is

[0099]

[0100]

[0101] in,

[0102]

[0103]

[0104]

[0105] Step c: Design a post-filter and apply zero constraints to eliminate future data dependencies introduced by the boosting technique. Design a Luenebrger observer that satisfies causal constraints, in the form of:

[0106]

[0107]

[0108] in, This represents a slow-rate residual signal that satisfies causal constraints.

[0109] Construct satisfying and set ,in Indicates post-filter the number of rows, Represent matrices respectively , The number of columns can be used to obtain the post-filter. The structure is used to obtain diagnostic observer parameters that satisfy causal constraints:

[0110] Same as in step b.

[0111] Step d: In the middle and Construct the Hankle matrix and perform QR decomposition on it.

[0112]

[0113] Combining the results obtained in step b We can obtain:

[0114]

[0115] in, Indicates the output stacked matrix The part related to noise.

[0116] For any The following relationship always holds:

[0117]

[0118] From this, the residual signal can be obtained. The variance matrix is:

[0119] .

[0120] Simultaneously calculate the threshold as in, Describing the degrees of freedom as Confidence level is The chi-square distribution value.

[0121] The residual signal satisfying causality constraints within the base period is converted into a fast-rate residual signal using an inverse boosting technique. This reconstructed fast-rate residual signal is then evaluated in real time, taking the form of…

[0122]

[0123] in, Indicates the first A fast rate residual signal. Combined with the calculated threshold, online fast rate fault detection is performed. The fault detection logic is described as follows:

[0124] .

[0125] This embodiment, conducted in the TRNSYS and Matlab R2018b environment, focuses on a four-zone HVAC system with high and slowly varying energy consumption. Figure 2 and 3 As shown. This embodiment is used to verify the proposed method, aiming to detect changes in the damper opening signal in a central air conditioning system. The damper opening signal of each zone is used as the input signal, with a sampling period of... Minutes later, the damper in area A was found to be stuck, specifically manifested as follows: The time valve is fixed in the open position. .

[0126] The temperature signal of each room is selected as the output, and the sampling period of areas A and B is... Minutes, sampling period for regions C and D Minutes. Because the sampling periods of the input and output signals are inconsistent, a boosting technique is used to convert the different sampling periods into a common sampling period. The calculation is based on the following:

[0127] .

[0128] Under the common base period, the number of samples for each output is as follows:

[0129] .

[0130] The diagnostic observer form that satisfies causal constraints is as follows:

[0131]

[0132] The specific dimensions and values ​​of the relevant parameter matrix are as follows:

[0133]

[0134] .

[0135] Calculate the fast rate test statistics and threshold .

[0136] Results Explanation:

[0137] Figure 4(a) shows the effect of the PCA method for fault detection when the damper in area A is stuck in the open position at 10%. Figure 4(b) shows the effect of slow-rate fault detection. Figure 4(c) shows the effect of the proposed fast-rate fault detection. It can be observed that in Figure 4(a), the PCA method... The test statistics failed to identify the fault; the SPE test statistics were in the range... The fault was not detected; Figure 4(b) shows that the detection effect of the slow-rate detection method is improved compared to the PCA method, but the slow-rate detection method still fails to detect the fault. The fault was only detected at that time, indicating a significant detection delay; compared to Figure 4(c), the designed fast-rate detection method showed a significant delay. The fault was detected quickly and accurately, achieving a detection speed one base cycle ahead of slower detection methods.

[0138] Example 2

[0139] The selected area A's damper jamming fault is specifically manifested as follows: The time valve is fixed in the open position. .

[0140] Results explanation:

[0141] Figure 5(a) shows the effect of the PCA method for fault detection when the damper in area A is stuck in the open position at 10%. Figure 5(b) shows the effect of slow-rate fault detection. Figure 5(c) shows the effect of the proposed fast-rate fault detection. As can be seen from Figure 5(a), the shortcomings of the PCA method are more pronounced; only the SPE test statistic detects the fault at a limited number of moments, failing to detect it at other times. Figure 5(b) shows the effect of slow-rate fault detection, where the slow-rate detection delay is more obvious. The fault was only detected when the fault was detected. In this case, the fault detection rate and false alarm rate were 96.66% and 6.44%, respectively. Figure 5(c) shows the effect of fast-rate fault detection. The system can detect faults and quickly capture dynamic characteristics of the system. Its detection rate and false alarm rate are 98.67% and 3.1% respectively, which are significantly better than PCA and slow-rate detection methods.

[0142] Example 3

[0143] The selected area A's damper jamming fault is specifically manifested as follows: The time valve is fixed in the open position. .

[0144] Results explanation:

[0145] Figure 6(a) shows the effect of the PCA method for fault detection when the damper in area A is stuck in the open position at 10%; Figure 6(b) shows the effect of slow-rate fault detection; and Figure 6(c) shows the effect 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. The fault was detected, and compared with the PCA detection method and the slow-rate fault detection method, it showed a strong ability to detect small faults.

[0146] 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 principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting fast rate faults in a multi-rate dynamic system with an unknown model, characterized in that, Includes the following steps: a. Using lifting techniques, the asynchronously sampled input and output data in a dynamic system are transformed into data based on the same sampling base period, thereby constructing an input and output stacking matrix, and then calculating a weighted vector based on a heuristic algorithm to reconstruct the output stacking matrix; b. Under the subspace identification framework, singular value decomposition and QR decomposition are performed on the joint matrix composed of input and output stacked matrices to solve for equivalent vectors. Based on the relationship between the equivalent vectors and the diagnostic observer, the Luenberger observer parameter matrix is ​​determined. c. Design a post-filter with zero constraints to eliminate the dependence of the residuals introduced by the lifting technique on future input and output data, obtain the Luenberger observer parameter matrix that satisfies the causal constraints, and further construct a multidimensional residual generator; In step c, a post-filter with zero constraints is designed to eliminate the dependence of the residuals introduced by the boosting technique on future input and output data, thereby obtaining a Luenebrger observer that satisfies causality constraints, in the form of: ； ； in, This represents a slow-rate residual signal that satisfies the constraints. Construct satisfying and set ,in Indicates post-filter the number of rows, Represent matrices respectively , The number of columns is used to obtain the post-filter. The structure is used to obtain diagnostic observer parameters that satisfy causal constraints: Same as in step b; d. Perform QR decomposition on the joint matrix to calculate the covariance of the residual signal. Simultaneously, calculate the threshold. Use inverse boosting technology to convert the residual signal that satisfies the causal constraint generated within the base period into a fast rate residual signal. Reconstruct the fast rate residual signal sequence and evaluate its fast rate. Combine the threshold with online fault detection logic to achieve fast rate fault detection.

2. The fast rate fault detection method for a multi-rate dynamic system with an unknown model according to claim 1, characterized in that, In step a, the lifting technique is used to transform the asynchronously sampled input and output data in the dynamic system into data based on the same sampling base period, thereby constructing an input and output stacking matrix, as detailed below: The input and output data in a multi-rate dynamic system are , ,in Updated at a fast rate with a base period h. The Each component The sampling period is Let M be The least common multiple of , then For the common sampling period, For output The number of samples within the common period, The total number of samples output within the common period. The data, after enhancement using the applied enhancement technology, is represented as follows: ； in, This indicates a time-based indicator that updates data with a base period. The data sets are used to construct an input-output stacked matrix, in the form of... ； ； in, Indicates past level number; The weighted vector is calculated using the following heuristic algorithm. : ； in, , , It is a column vector whose elements are all 1s. The output data is an identity matrix. The reconstruction of ,in Then the form of the output stacked matrix becomes: ； 。 3. The fast rate fault detection method for a multi-rate dynamic system with an unknown model according to claim 1, characterized in that, In step b, within 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 for equivalent vectors. Based on the relationship between the equivalent vectors and the diagnostic observer, the Luenebrger observer is determined, in the following form: ； ； in, Represents the observer state vector. This represents a slow-rate residual signal that does not satisfy the causal constraint. The observation parameter matrix to be designed; Regarding the past The joint matrix formed by the stacked matrices at time points is represented as ,right and Perform singular value decomposition: ； in ,right Rearrange and decompose into QR: ； ； Obtain the equivalent vector: Then slow rate The parameter matrix of the 3D diagnostic observer is ； ； in, ； ； ； 。 4. The fast rate fault detection method for a multi-rate dynamic system with an unknown model according to claim 1, characterized in that, In step d, the and Construct the Hankle matrix and perform QR decomposition on it. Combined with the result obtained in step b ,get: ； in, This represents the noise-related portion of the output stacking matrix; For any The following relationship always holds: ； ； Obtain residual signal The variance matrix is: ； Simultaneously calculate the threshold as in, Describing the degrees of freedom as Confidence level is The chi-square distribution value; The residual signal satisfying causality constraints generated within the base period is converted into a fast-rate residual signal using an inverse boosting technique. This fast-rate residual signal is then reconstructed and evaluated in real time, taking the form of… ； in, Indicates the first A fast rate residual signal is used, combined with a calculated threshold, to detect online fast rate faults. The fault detection logic is described as follows: 。

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