Data-driven method for detecting and locating minor faults in central air conditioning actuators

Abstract

This invention provides a data-driven method for detecting and locating minor faults in central air conditioning actuators, belonging to the field of data-driven fault diagnosis technology. It solves the technical problem of effectively detecting and accurately locating minor faults in central air conditioning systems when the mechanistic model is unknown and historical fault data is unavailable. The technical solution includes: a. training data preprocessing; b. calculating the state influence matrix and input influence matrix; c. designing a residual generator set and calculating the residual covariance matrix; d. fault detection and location logic. This invention does not rely on advanced control theory knowledge or a large amount of historical fault data, and can achieve the purpose of fault detection and location.

Description

Technical Field

[0001] This invention relates to the field of data-driven fault diagnosis technology, specifically to a data-driven method for detecting and locating minor faults in central air conditioning actuators. Background Technology

[0002] With the continuous expansion of modern industry and the accelerating pace of industrial intelligence, the difficulty of fault diagnosis and maintenance is also increasing. Traditional fault diagnosis methods rely on the experience and knowledge of maintenance personnel, resulting in low diagnostic efficiency and other technical problems. Therefore, researching efficient and intelligent fault detection methods has become a crucial issue. Fault detection technology can detect and estimate faults in a timely manner, thereby effectively preventing major accidents. Therefore, it is a key technology for improving system safety and reliability and reducing accident risks. On the other hand, many existing fault diagnosis methods require a large amount of historical fault data samples, which brings inconvenience to fault diagnosis.

[0003] Most current research assumes that model parameters are known. However, in industrial processes, the parameters of many system models are difficult to determine, making it extremely difficult to obtain accurate system models. This significantly limits the effectiveness and applicability of model-based methods in practical applications. To avoid complex system modeling, data-driven fault diagnosis methods have received increasing attention. However, many traditional data-driven fault diagnosis methods suffer from drawbacks such as high computational cost or insufficient fault detection accuracy. Therefore, finding a fault detection method for situations where the mechanistic model is unknown and historical fault data is unavailable is of significant practical importance. A data-driven method for detecting and locating minor faults in central air conditioning actuators is proposed to address these issues. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a data-driven method for detecting and locating minor faults in central air conditioning actuators. This method does not rely on advanced control theory or a large amount of historical fault data, yet it can achieve the purpose of fault detection and location.

[0005] The inventive concept of this invention is as follows: This invention proposes a data-driven method for detecting and locating minor faults in central air conditioning actuators. Based on trained input and output data, a Hankel matrix is ​​constructed, and two joint matrices with a time difference are generated. Then, the state influence matrix, the overall input influence matrix, and the input influence matrix of a single actuator are calculated. An optimal equivalent matrix is ​​designed so that it lies within the null space of the state influence matrix and the input influence matrix of a single actuator, and is constrained by its irrelevant influence matrix. A set of residual generators is then constructed, and the covariance of the residuals is calculated based on the obtained optimal equivalent matrix and the training data. Finally, a threshold and test statistics are calculated according to the designed optimal equivalent matrix. When the test statistics are greater than the threshold, it indicates that the fault occurs in an actuator other than the one being tested; when they are less than the threshold, it indicates that there is no fault in any actuator other than the one being tested, thereby achieving the purpose of fault detection and location.

[0006] To achieve the above objectives, the technical solution adopted by this invention is specifically a data-driven method for detecting and locating minor faults in central air conditioning actuators, comprising the following steps:

[0007] Step a. Training data preprocessing: Collect the opening signals of actuators such as air valves and water valves of the central air conditioning system as inputs, and the sensor temperature data of each area as outputs. Stack the input and output into vector sequences from top to bottom according to time sequence, and then arrange them from left to right according to the sampling time to obtain the input and output Hankel matrices. Further stack the input and output Hankel matrices on top of each other to construct two joint matrices with a time difference.

[0008] Step b. Calculate the state influence matrix and the input influence matrix: Perform singular value decomposition on the covariance of the two joint matrices, calculate the left null space of the covariance, and obtain the state influence matrix and the overall input influence matrix from it; further, extract the input influence matrix of a single actuator by column from the overall input influence matrix, and the remaining part of the overall input influence matrix forms the unrelated influence matrix of this actuator.

[0009] Step c. Design a set of residual generators and calculate the residual covariance matrix: Based on the obtained state influence matrix and input influence matrix, design an optimal equivalent matrix that lies in the null space of the state influence matrix and the input influence matrix of a single actuator, and is constrained by its independent influence matrix. Then construct a set of residual generators and calculate the covariance of the residuals based on the obtained optimal equivalent matrix and training data.

[0010] Step d. Fault detection and localization logic: Calculate the threshold and test statistics based on the designed optimal equivalence matrix. When the test statistics of a certain residual generator are less than or equal to the threshold and the test statistics of other residual generators are all greater than the threshold, it indicates that the fault occurs in this actuator; when the test statistics of other residual generators are all less than or equal to the threshold, it indicates that this actuator has not failed, thereby achieving the purpose of fault detection and localization.

[0011] Further, in step a, the training data preprocessing is performed as follows: the opening signals of actuators such as air valves and water valves of the central air conditioning system are collected as inputs, and the sensor temperature data of each area are used as outputs. The inputs and outputs are stacked from top to bottom in time sequence to form vector sequences, and then arranged from left to right according to the sampling time to obtain the Hankel matrices of the inputs and outputs. The Hankel matrices of the inputs and outputs are then stacked vertically to construct two joint matrices with a time difference.

[0012] Specifically as follows:

[0013] Collect the opening signals of air valves and water valves as inputs to the central air conditioning system. Temperature data from sensors in each area are used as output by the central air conditioning system. , They represent 3D real space, Indicates the number of actuators. This indicates the number of sensors, and the input and output signals of the central air conditioning system are stacked separately:

[0014]

[0015] in, Indicates time, This indicates the number of consecutive time steps in the stack. Indicates stacking The input stacked vector at time step, Indicates stacking The output stacked vector at each time step;

[0016] The two joint matrices with a time difference are as follows:

[0017]

[0018] in, Indicates time The initial joint matrix, Indicates time Initial joint matrix;

[0019] and Hankel matrices for input and output, respectively:

[0020]

[0021] in, This indicates the total number of collected sample data.

[0022] Further, in step b, the state influence matrix and the input influence matrix are calculated: singular value decomposition is performed on the covariance of the two joint matrices, the left null space of the covariance is calculated, and the state influence matrix and the overall input influence matrix are obtained from it; further, the overall input influence matrix is ​​extracted column by column to obtain the input influence matrix of a single actuator, and the remaining part of the overall input influence matrix forms the unrelated influence matrix of this actuator.

[0023] Specifically as follows:

[0024] b1) First of all Singular value decomposition of the covariance:

[0025]

[0026]

[0027] Among them, superscript To represent the transpose of a matrix, These are the non-zero singular values ​​and the zero singular value obtained after singular value decomposition, respectively. These are the left and right singular vector submatrices with non-zero singular values, respectively. These are the left and right singular vector submatrices with zero singular values, respectively. b2) Calculate again. left null space Makes the following conditions satisfied:

[0028]

[0029] achievable .

[0030] in, Indicates the number of state variables.

[0031] b3) Then calculate the state influence matrix. and input influence matrix :

[0032] make left null space The part related to the output, left null space The part related to input. The state influence matrix is ​​calculated using the null null space statement in MATLAB. satisfy: ,Right now The input influence matrix is ​​obtained using the generalized inverse statement `pinv` in MATLAB. satisfy: ,Right now .

[0033] b4) Finally, calculate the input influence matrix of a single actuator. The influence matrix unrelated to this actuator :

[0034] Will Divide into equal columns The nth block matrix, extract the nth block matrix from each block matrix The columns are concatenated to obtain the input influence matrix of a single actuator. ,Right now:

[0035]

[0036] in Indicates the actuator number ( ).

[0037] Remove The part is called the irrelevant influence matrix of this actuator. ,Right now:

[0038]

[0039] Further, step c involves designing a set of residual generators and calculating the residual covariance matrix: Based on the obtained state influence matrix and input influence matrix, an optimal equivalent matrix is ​​designed such that it lies in the null space of the state influence matrix and the input influence matrix of a single actuator, and is constrained by its irrelevant influence matrix. In this way, a set of residual generators is constructed, and the covariance of the residuals is calculated based on the obtained equivalent matrix and training data.

[0040] The design is as follows:

[0041] The first design proposal The optimal equivalent matrix of each residual generator ( Only the following three equality constraints need to be satisfied:

[0042]

[0043] in Since the state influence matrix is ​​used, the first equality constraint can eliminate the influence of the initial state on the residual. For the first The input influence matrix of the actuator is such that the second equality constraint can eliminate the first... The actuator for the first The influence of the residual generator ensures that the residual is only affected by other actuators, when the... When the residual generator exhibits a fault, it indicates that, except for the first one... The failure of an actuator outside the actuator itself allows for fault location; the third equality constraint expands the measurement space dimension from... The dimension is reduced to the same dimension as the fault space. Dimension, at this time the noise space also changes from Dimensions reduced to Since the fault space remains unchanged while the noise space decreases, the impact of noise on the measurement space is minimized to the greatest extent possible while keeping the fault information unchanged, thereby achieving optimal diagnosis of minor faults.

[0044] Based on the solution obtained in step b , to solve in detail This can be achieved through the following steps:

[0045] c1) First, broaden for ,when When large enough At this point, there must exist a non-zero space. satisfy Then, the non-zero space is solved using the null function statement in Matlab, i.e. ;

[0046] c2) Further solve using the pinv command in Matlab. generalized inverse satisfy ,Right now Thus, the optimal equivalent matrix is ​​obtained. ;

[0047] c3) Finally, by using the optimal equivalence matrix and the training data... Solve the first Covariance of each residual :

[0048] .

[0049] c4) Collect the opening signals of the air valves and water valves of the central air conditioning system under test online as input. The sensor temperature data of each area to be detected is used as the output. Based on the online input and output data to be detected and the designed optimal equivalence matrix, a set of residual generators is obtained:

[0050] ;

[0051] in, Indicates the first The residual of each actuator

[0052]

[0053] and They represent stacking respectively The input stacked vector and output stacked vector to be detected at each time step;

[0054] Furthermore, the fault detection and localization logic in step d involves calculating a threshold and test statistics based on the designed optimal equivalence matrix. If the test statistics of a certain residual generator are less than or equal to the threshold, and the test statistics of other residual generators are all greater than the threshold, it indicates that a fault has occurred in this actuator. If the test statistics of other residual generators are all less than or equal to the threshold, it indicates that no fault has occurred in this actuator, thus achieving the purpose of fault detection and localization.

[0055] The design is as follows:

[0056] The fault detection logic of the data-driven central air conditioning actuator minor fault detection and location method is as follows:

[0057]

[0058] The test statistics are as follows:

[0059]

[0060] Indicates the first Test statistics for each residual generator Indicates the first Covariance of each residual The inverse matrix.

[0061] The equivalence matrix and test statistics designed in this way are optimal under the generalized likelihood ratio.

[0062] The threshold form is as follows:

[0063]

[0064] in, Indicates the first The threshold for detection by a residual generator. Indicates the chi-square distribution, subscript Indicates the significance level.

[0065] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0066] 1. This invention is entirely based on the input and output data during normal system operation, without relying on precise mechanistic models or requiring the collection of historical fault samples. It can be directly applied to complex central air conditioning systems, overcoming diagnostic obstacles caused by difficulties in model building or a lack of fault data, and broadening the applicability and engineering practicality of data-driven fault diagnosis methods. Each actuator is designed with a separate residual generator, utilizing an optimal equivalence matrix to make it sensitive to faults of specific actuators while being robust to interference from other actuators and changes in system state. When a minor fault occurs in an actuator, its corresponding residual generator will not alarm due to the "shielding" effect of its design, while all other residual generators will alarm upon detecting the anomaly. This not only confirms the existence of a fault in the system but also precisely locates which specific actuator has failed, providing maintenance personnel with extremely clear guidance and significantly improving maintenance efficiency.

[0067] 2. By monitoring the changes in the statistical characteristics of residual signals, this invention can capture subtle changes in the dynamic relationship of the system and issue timely warnings in the early stages of a fault, before it has a significant impact on system performance and energy consumption. This is especially important for energy-intensive systems such as central air conditioning. By maintaining faulty actuators (such as air valves and water valves) in a timely manner, energy waste and equipment damage caused by the expansion of the fault are avoided, and the reliability and energy efficiency of the system are directly improved. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the central air conditioning system mechanism of the present invention.

[0069] Figure 2 shows a performance comparison between the method proposed in this invention and the traditional equivalent space method in detecting minor faults in central air conditioning actuators.

[0070] Among them, (a) is the effect diagram of fault detection using the traditional equivalent space method.

[0071] (b) is a diagram showing the effect of fault detection on the first residual generator of the data-driven central air conditioning actuator micro-fault detection and location method proposed in this invention.

[0072] (c) is a diagram showing the effect of the second residual generator in the data-driven method for detecting and locating minor faults in central air conditioning actuators proposed in this invention.

[0073] (d) is a diagram showing the effect of the third residual generator in the data-driven method for detecting and locating minor faults in central air conditioning actuators proposed in this invention.

[0074] (e) is a diagram showing the effect of the fourth residual generator in the data-driven method for detecting and locating minor faults in central air conditioning actuators proposed in this invention.

[0075] (f) is a diagram showing the effect of the fifth residual generator in the data-driven method for detecting and locating minor faults in central air conditioning actuators proposed in this invention. 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.

[0077] Example 1: Refer to Figure 1 The flowchart illustrates a data-driven method for detecting and locating minor faults in central air conditioning actuators, comprising the following steps:

[0078] Step a. Training data preprocessing: Collect the opening signals of actuators such as air valves and water valves of the central air conditioning system as inputs, and the sensor temperature data of each area as outputs. Stack the input and output into vector sequences from top to bottom according to time sequence, and then arrange them from left to right according to the sampling time to obtain the input and output Hankel matrices. Further stack the input and output Hankel matrices on top of each other to construct two joint matrices with a time difference.

[0079] Specifically as follows:

[0080] Collect the opening signals of air valves and water valves as inputs to the central air conditioning system. Temperature data from sensors in each area are used as output by the central air conditioning system. , They represent 3D real space, Indicates the number of actuators. This indicates the number of sensors, and the input and output signals of the central air conditioning system are stacked separately:

[0081]

[0082] in, Indicates time, This indicates the number of consecutive time steps in the stack. Indicates stacking The input stacked vector at time step, Indicates stacking The output stacked vector at each time step;

[0083] The two joint matrices with a time difference are as follows:

[0084]

[0085] in, Indicates time The initial joint matrix, Indicates time Initial joint matrix;

[0086] and Hankel matrices for input and output, respectively:

[0087]

[0088] in, This indicates the total number of collected sample data.

[0089] Step b. Calculate the state influence matrix and the input influence matrix: Perform singular value decomposition on the covariance of the two joint matrices, calculate the left null space of the covariance, and obtain the state influence matrix and the overall input influence matrix from it; further, extract the input influence matrix of a single actuator by column from the overall input influence matrix, and the remaining part of the overall input influence matrix forms the unrelated influence matrix of this actuator.

[0090] Specifically as follows:

[0091] b1) First of all Singular value decomposition of the covariance:

[0092]

[0093]

[0094] Among them, superscript To represent the transpose of a matrix, These are the non-zero singular values ​​and the zero singular value obtained after singular value decomposition, respectively. These are the left and right singular vector submatrices with non-zero singular values, respectively. These are the left and right singular vector submatrices with zero singular values, respectively. (b2) Calculate again. left null space Makes the following conditions satisfied:

[0095]

[0096] achievable .

[0097] in, This indicates the number of state variables. (b3) Then calculate the state influence matrix. and input influence matrix :

[0098] make left null space The part related to the output, left null space The part related to input. The state influence matrix is ​​calculated using the null null space statement in MATLAB. satisfy: ,Right now The input influence matrix is ​​obtained using the generalized inverse statement `pinv` in MATLAB. satisfy: ,Right now .

[0099] b4) Finally, calculate the input influence matrix of a single actuator. The influence matrix unrelated to this actuator :

[0100] Will Divide into equal columns The nth block matrix, extract the nth block matrix from each block matrix The columns are concatenated to obtain the input influence matrix of a single actuator. ,Right now:

[0101]

[0102] in Indicates the actuator number ( ).

[0103] Remove The part is called the irrelevant influence matrix of this actuator. ,Right now:

[0104]

[0105] Step c: Design a set of residual generators and calculate the residual covariance matrix: Based on the obtained state influence matrix and input influence matrix, design an optimal equivalent matrix that lies in the null space of the state influence matrix and the input influence matrix of a single actuator, and is constrained by its irrelevant influence matrix. Then, construct a set of residual generators and calculate the covariance of the residuals based on the obtained optimal equivalent matrix and training data.

[0106] The design is as follows:

[0107] The first design proposal The optimal equivalent matrix of each residual generator ( Only the following three equality constraints need to be satisfied:

[0108]

[0109] in Since the state influence matrix is ​​used, the first equality constraint can eliminate the influence of the initial state on the residual. For the first The input influence matrix of the actuator is such that the second equality constraint can eliminate the first... The actuator for the first The influence of the residual generator ensures that the residual is only affected by other actuators, when the... When the residual generator exhibits a fault, it indicates that, except for the first one... The failure of an actuator outside the actuator itself allows for fault location; the third equality constraint expands the measurement space dimension from... The dimension is reduced to the same dimension as the fault space. Dimension, at this time the noise space also changes from Dimensions reduced to Since the fault space remains unchanged while the noise space decreases, the impact of noise on the measurement space is minimized to the greatest extent possible while keeping the fault information unchanged, thereby achieving optimal diagnosis of minor faults.

[0110] Based on the solution obtained in step b , to solve in detail This can be achieved through the following steps:

[0111] c1) First, broaden for ,when When large enough At this point, there must exist a non-zero space. satisfy Then, the non-zero space is solved using the null function statement in Matlab, i.e. ;

[0112] c2) Further solve using the pinv command in Matlab. generalized inverse satisfy ,Right now Thus, the optimal equivalent matrix is ​​obtained. ;

[0113] c3) Finally, by using the optimal equivalence matrix and the training data... Solve the first Covariance of each residual :

[0114] .

[0115] c4) Collect the opening signals of the air valves and water valves of the central air conditioning system under test online as input. The sensor temperature data of each area to be detected is used as the output. Based on the online input and output data to be detected and the designed optimal equivalence matrix, a set of residual generators is obtained:

[0116] ;

[0117] in, Indicates the first The residual of each actuator

[0118]

[0119] and They represent stacking respectively The input stacked vector and output stacked vector to be detected at each time step;

[0120] Step d: Fault detection and localization logic: Calculate the threshold and test statistics based on the designed optimal equivalence matrix. When the test statistics of a certain residual generator are less than or equal to the threshold and the test statistics of other residual generators are all greater than the threshold, it indicates that the fault occurs in this actuator. When the test statistics of other residual generators are all less than or equal to the threshold, it indicates that the actuator has not failed, thereby achieving the purpose of fault detection and localization.

[0121] The design is as follows:

[0122] A data-driven method for detecting and locating minor faults in central air conditioning actuators has the following fault detection logic:

[0123]

[0124] The test statistics are as follows:

[0125]

[0126] Indicates the first Test statistics for each residual generator Indicates the first Covariance of each residual The inverse matrix.

[0127] The equivalence matrix and test statistics designed in this way are optimal under the generalized likelihood ratio.

[0128] The threshold form is as follows:

[0129]

[0130] in, Indicates the first The threshold for detection by a residual generator. Indicates the chi-square distribution, subscript Indicates the significance level.

[0131] This embodiment, conducted in the Matlab R2021b environment, focuses on a four-zone HVAC system with high and slowly varying energy consumption. Figure 1 As shown. This example is used to verify the proposed method, aiming to detect changes in the opening signals of air valves and water valves in a central air conditioning system. The opening signals of actuators such as air valves and water valves in the central air conditioning system are collected as input, with a sampling period of... Minutes later, a fault was detected in area A where the air valve was stuck, specifically manifested as the air valve being fixed in the open position. ,Right now:

[0132]

[0133] in, This indicates the position and opening degree of the damper when it is stuck. This indicates a fault signal.

[0134] The differences between the temperature and steady-state temperature in four zones, as well as the difference between the air handling unit outlet temperature and steady-state temperature, were selected as outputs. 500 sets of data were collected. The fault manifested as the damper in zone A being stuck at 78% of its opening. Test statistics were calculated. Given a significance level The threshold is .

[0135] Results explanation:

[0136] In Figure 2, (a) shows the effect of the traditional equivalent space method for fault detection. It can be observed that, When a fault begins to occur in time zone A, the residual generator is basically able to detect the fault, but the effect is not ideal. When the fault occurs, some test statistics curves are below the threshold line, resulting in a large number of missed fault reports.

[0137] In Figure 2, (b) is the effect of the first residual generator in the proposed design method for fault detection. It can be observed that since a fault occurred in region A, and the first residual generator shielded the input signal of the first actuator, most of the test statistics curve was below the threshold line, and no fault was detected. This indicates that no fault occurred in the other four actuators, but there may be a fault in the first actuator.

[0138] Figure 2(c)-(f) shows the fault detection effect of the 2nd-5th residual generators in the proposed design method. It can be observed that, as in the detection logic, since a fault occurs in area A, and each residual generator only masks the input signal of one corresponding actuator, all 2nd-5th residual generators can detect the fault. The figures show that the fault detection effect is good; the test statistics curve is on the threshold line when the fault occurs, and it outperforms the traditional equivalent space method. Table 1 shows a comparison of the fault diagnosis performance of the traditional equivalent space method and the proposed design method when the damper in area A is stuck at 78% opening.

[0139] Table 1

[0140]

[0141] Example 2: Due to the uncertainty of process noise and measurement noise during the operation of a central air conditioning system, to verify the robustness and stability of the method of the present invention under different noise environments, this example performs fault detection under the same central air conditioning system model and actuator fault settings as Example 1. Table 2 shows a comparison of the fault diagnosis performance of the traditional equivalent space method and the design method under different noise conditions compared to Example 1. Under different noise conditions, the residual generator detection performance of the design method is better than that of the traditional equivalent space method, and the fact that only the first residual generator of the design fails to detect the fault indicates that the fault occurs in the first actuator, thus achieving fault detection and location.

[0142] Table 2

[0143]

[0144] Example 3: In this example, using the same central air conditioning system model as Example 1, the actuator fault is modified to a zone A air valve stuck at 75% opening. Fault detection is then performed. Table 3 shows a comparison of the fault diagnosis performance of the traditional equivalent space method and the design method when the zone A air valve is stuck at 75% opening. Similar to the detection situation when the zone A air valve is stuck at 78% opening, the residual generator of the design method has better detection performance than the traditional equivalent space method. Furthermore, only the first residual generator of the design fails to detect the fault, indicating that the fault occurs in the first actuator, thus achieving fault detection and location.

[0145] Table 3

[0146]

[0147] 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 data-driven method for detecting and locating minor faults in central air conditioning actuators, characterized in that, Includes the following steps: Step a. Training data preprocessing: Collect the opening signals of the air valves and water valves of the central air conditioning system as inputs, and the sensor temperature data of each area as outputs. Stack the input and output into vector sequences from top to bottom according to time sequence, and then arrange them from left to right according to the sampling time to obtain the Hankel matrices of the input and output. Stack the input and output Hankel matrices on top of each other to construct two joint matrices with time difference. Step b. Calculate the state influence matrix and the input influence matrix: Perform singular value decomposition on the covariance of the two joint matrices, calculate the left null space of the covariance, and obtain the state influence matrix and the overall input influence matrix from it; extract the input influence matrix of a single actuator by column from the overall input influence matrix, and the remaining part of the overall input influence matrix forms the unrelated influence matrix of this actuator; Step c. Design a set of residual generators and calculate the residual covariance matrix: Based on the obtained state influence matrix and input influence matrix, design an optimal equivalent matrix that lies in the null space of the state influence matrix and the input influence matrix of a single actuator, and is constrained by its independent influence matrix. Calculate the covariance of the residuals based on the obtained optimal equivalent matrix and training data, and then construct a set of residual generators. Step d. Fault detection and localization logic: Calculate the threshold and test statistics based on the designed optimal equivalence matrix. When the test statistics of a certain residual generator are less than or equal to the threshold and the test statistics of other residual generators are all greater than the threshold, it indicates that the fault occurs in this actuator; when the test statistics of other residual generators are all less than or equal to the threshold, it indicates that this actuator has not failed, thereby achieving the purpose of fault detection and localization.

2. The data-driven method for detecting and locating minor faults in central air conditioning actuators according to claim 1, characterized in that, In step a, the training data preprocessing involves collecting the opening signals of the central air conditioning valves and water valves as inputs, and the sensor temperature data of each area as outputs. The inputs and outputs are stacked sequentially from top to bottom into vector sequences, then arranged from left to right according to the sampling time, yielding the input and output Hankel matrices. These Hankel matrices are then stacked vertically to construct two joint matrices with a time difference. The details are as follows: Collect the opening signals of air valves and water valves as inputs to the central air conditioning system. Temperature data from sensors in each area are used as output by the central air conditioning system. , They represent 3D real space, Indicates the number of actuators. This indicates the number of sensors, and the input and output signals of the central air conditioning system are stacked separately: ； in Indicates time, This indicates the number of consecutive time steps in the stack. Indicates stacking The input stacked vector at time step, Indicates stacking The output stacked vector at each time step; The two joint matrices with a time difference are as follows: ； in, Indicates time The initial joint matrix, Indicates time Initial joint matrix; and Hankel matrices for input and output, respectively: ； in, This indicates the total number of collected sample data.

3. The data-driven method for detecting and locating minor faults in central air conditioning actuators according to claim 1, characterized in that, In step b, the state influence matrix and the input influence matrix are calculated as follows: singular value decomposition is performed on the covariance of the two joint matrices, the left null space of the covariance is calculated, and the state influence matrix and the overall input influence matrix are obtained from it; the overall input influence matrix is ​​extracted column by column to obtain the input influence matrix of a single actuator, and the remaining part of the overall input influence matrix forms the unrelated influence matrix of this actuator. Specifically as follows: b1) First of all Singular value decomposition of the covariance: ； ； Among them, superscript To represent the transpose of a matrix, These are the non-zero singular values ​​and the zero singular value obtained after singular value decomposition, respectively. These are the left and right singular vector submatrices with non-zero singular values, respectively. These are the left singular vector submatrices and the right singular vector submatrices with zero singular values, respectively; b2) Recalculate left null space Makes the following conditions satisfied: ； have to ;in, Indicates the number of state variables; b3) Then calculate the state influence matrix. and input influence matrix : make left null space The part related to the output, left null space In the input-related part, the state influence matrix is ​​calculated using the null null space statement in MATLAB. satisfy: ,Right now The input influence matrix is ​​obtained using the generalized inverse statement `pinv` in MATLAB. satisfy: ,Right now ; b4) Finally, calculate the input influence matrix of a single actuator. The influence matrix unrelated to this actuator : Will Divide into equal columns The nth block matrix, extract the nth block matrix from each block matrix The columns are concatenated to obtain the input influence matrix of a single actuator. ,Right now: ； in Indicates the actuator number, ; Remove The part is called the irrelevant influence matrix of this actuator. ,Right now: 。 4. The data-driven method for detecting and locating minor faults in central air conditioning actuators according to claim 1, characterized in that, Step c: Design a set of residual generators and calculate the residual covariance matrix: Based on the obtained state influence matrix and input influence matrix, design an optimal equivalent matrix that lies in the null space of the state influence matrix and the input influence matrix of a single actuator, and is constrained by its irrelevant influence matrix. Construct a set of residual generators, and calculate the covariance of the residuals based on the obtained optimal equivalent matrix and training data. The first design proposal The optimal equivalent matrix of each residual generator , The following three equality constraints must be satisfied: ； The first equality constraint mentioned above eliminates the initial state for the first... The second equality constraint eliminates the influence of the i-th actuator on the j-th residual; The influence of the residual generator ensures that the residual is only affected by other actuators; the third equality constraint reduces the measurement space dimension to the same dimension as the fault space. Based on the solution obtained in step b , to solve in detail This can be achieved through the following steps: c1) First, broaden for ; Then, the non-zero space is solved using the null function statement in Matlab. satisfy ,Right now ; c2) Solve using the pinv command in Matlab. generalized inverse satisfy ,Right now Thus, the optimal equivalent matrix is ​​obtained. ; c3) Finally, by using the optimal equivalence matrix and the training data... Solve the first Covariance of each residual : ； c4) Collect the opening signals of the air valves and water valves of the central air conditioning system under test online as input. The sensor temperature data of each area to be detected is used as the output. Based on the online input and output data to be detected and the designed optimal equivalence matrix, a set of residual generators is obtained: ； in, Indicates the first The residuals of each actuator; ； and They represent stacking respectively The input stacked vector and output stacked vector to be detected at each time step.

5. The data-driven method for detecting and locating minor faults in central air conditioning actuators according to claim 1, characterized in that, In step d, the fault detection and location logic is as follows: based on the designed optimal equivalence matrix, a threshold and test statistics are calculated. When the test statistics of a certain residual generator are less than or equal to the threshold and the test statistics of other residual generators are all greater than the threshold, it indicates that the fault occurs in this actuator; when the test statistics of other residual generators are all less than or equal to the threshold, it indicates that the actuator has not failed, thereby achieving the purpose of fault detection and location. The design is as follows: The fault detection and location logic is as follows: ； The test statistics are as follows: ； Indicates the first Test statistics for each residual generator Indicates the first Covariance of each residual The inverse matrix; the threshold form is as follows: ； in, Indicates the first The threshold for detection by a residual generator. Indicates the chi-square distribution, subscript Indicates the significance level.

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