Adaptive online dynamic mode decomposition method and system for a target system
By adaptively adjusting the data window length and causal pattern quantization, the accuracy problem of the online DMD algorithm during system mutations is solved, achieving rapid response and improved noise resistance. It is suitable for complex system state monitoring in fluid mechanics, electromechanical systems and power grid monitoring.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGNAN UNIV
- Filing Date
- 2026-02-27
- Publication Date
- 2026-06-05
AI Technical Summary
Existing online DMD algorithms cannot accurately characterize the current state when the target system undergoes non-stationary changes. Fixed-length sliding windows or constant forgetting factors lead to model tracking delays and prediction distortions, or they are susceptible to noise interference and cannot extract patterns with stable physical meaning.
By adaptively adjusting the data window length, combining local low-order regression models and similarity calculations, the data memory of the online DMD model is dynamically managed. The current causal pattern feature vector is constructed using physical causal relationships, and the data window scaling strategy is optimized to adapt to system changes.
It enables rapid response and discarding of inapplicable data after system mutations, improves the accuracy and noise resistance of the model, reduces reconstruction and prediction errors during the transition period, and can capture changes in system structure or parameters earlier.
Smart Images
Figure CN122153478A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of complex system state monitoring technology, and in particular to an adaptive online dynamic mode decomposition method and system for a target system. Background Technology
[0002] In many scientific and engineering fields (such as fluid mechanics, electromechanical systems, and power grid monitoring), the analysis and modeling of complex dynamic systems are crucial. Dynamic Mode Decomposition (DMD), as a powerful equation-free data-driven tool, provides a finite-dimensional linear approximation of the underlying nonlinear dynamics Koopman operator. It decomposes high-dimensional data into a series of spatially coherent modes with specific oscillation frequencies and growth / decay rates, thus finding wide application in system identification and feature extraction.
[0003] Traditional batch DMD algorithms typically assume that the underlying dynamics of the system are static or change very slowly throughout the observation period. To address time-varying systems and streaming data processing scenarios, various online DMD (ODMD) algorithms have emerged in recent years, such as those employing recursive SVD or sliding window techniques incorporating forgetting factors to adapt to the dynamics of evolution.
[0004] However, existing online DMD technologies still have a common drawback: they inherently assume that the system is in a "quasi-stationary" or "slowly evolving" state. When the target system experiences a sudden and significant regime shift due to changes in external conditions (such as electromechanical systems in the early stages of a variable load or fault), internal parameter drift, or the occurrence of a fault, the model built on historical outdated data will not be able to accurately characterize the current state of the system.
[0005] Current online DMD models primarily employ fixed-length sliding windows or constant forgetting factors. If the window is too long, the model will contain a large amount of outdated physical dynamics, leading to tracking delays and severe prediction distortion. If the window is too short, while the model is agile, it becomes highly susceptible to measurement noise and fails to extract stable and physically meaningful patterns. Therefore, how to intelligently and dynamically manage the "data memory" (i.e., data window length) of online DMD models when non-stationary changes occur in the system has become a pressing technical challenge in the field of data-driven modeling. Summary of the Invention
[0006] Therefore, the technical problem to be solved by the present invention is to overcome the inherent assumption that the target system is in a stable state in the existing online DMD and the use of a fixed-length sliding window, which makes the dynamic pattern decomposition (DMD) model built from historical outdated data unable to accurately represent the current state of the system.
[0007] To address the aforementioned technical problems, this invention provides an adaptive online dynamic mode decomposition method for a target system, comprising:
[0008] Step S1: Obtain multivariate time series data of the target system, and extract a set of core feature variables from the multivariate time series data;
[0009] Step S2: Based on the preset physical causal relationship, construct a local low-order regression model between the core feature variable sets within the current monitoring window of the dynamic pattern decomposition model to quantify the causal interaction pattern at the current moment, and construct the current causal pattern feature vector based on the local low-order regression model.
[0010] Step S3: Calculate the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector;
[0011] Step S4: Based on the similarity and the reconstruction error of the current dynamic pattern decomposition model, dynamically adjust the length of the data window used for updating the dynamic pattern decomposition model;
[0012] Step S5: Based on the time series data of the target system extracted by the adjusted data window length, update the dynamic mode decomposition model and output the current dynamic mode information of the target system.
[0013] In one embodiment of the present invention, the local low-order regression model in step S2 is an autoregressive model with exogenous input, expressed as:
[0014] ;
[0015] In the formula, For time points The target feature variable The intercept is... These are the autoregressive coefficients. For time points The target feature variable The total number of known influencing variables. For time points The There are 10 known influencing variables, which are selected from the core feature variable set or external environmental variables. and These are the preset maximum lag orders. For exogenous input coefficients, This represents the model residuals.
[0016] In one embodiment of the present invention, the method for constructing the current causal pattern feature vector based on the local low-order regression model in step S2 includes:
[0017] The parameter combination estimated by the local low-order regression model constitutes the current causal pattern feature vector, which is expressed as:
[0018] ;
[0019] In the formula, This is the feature vector of the current causal pattern. For is equal to, This represents a vectorized straightening operation for a matrix or set. This indicates transpose.
[0020] In one embodiment of the present invention, step S3 calculates the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector, using cosine similarity, expressed as:
[0021] ;
[0022] In the formula, For causal pattern similarity, This is the feature vector of the current causal pattern. The baseline causal pattern feature vector is learned during the initial stable operation phase of the target system. Let be the 2-norm of the vector.
[0023] In one embodiment of the present invention, if multiple preset physical causal relationships exist, the minimum or average value of the similarity of each causal pattern is taken as the overall causal pattern similarity of the target system, expressed as:
[0024] ;
[0025] In the formula, For the overall causal pattern similarity of the target system, For the first The similarity of causal patterns of a pre-defined physical causal relationship.
[0026] In one embodiment of the present invention, the method for dynamically adjusting the data window length for model updates in step S4 includes:
[0027] If the overall causal pattern similarity Below the preset mutation threshold Or the reconstruction error of the current dynamic mode decomposition model Higher than the preset high error threshold If this indicates a sudden change in the underlying physical operating conditions or a failure, then the window shortening strategy will be executed:
[0028] ;
[0029] In the formula, The current data window length, For assignment operations, To obtain the maximum value, Shorten the step size for the preset window. The minimum window length limit is set.
[0030] If the overall causal pattern similarity Higher than the preset mutation threshold Furthermore, the reconstruction error of the current dynamic mode decomposition model... Below the preset high error threshold This indicates that the causal pattern is consistent with the baseline and the dynamic mode decomposition model fits well, meaning the target system is in a steady state. Therefore, the window growth strategy is executed.
[0031] ;
[0032] In the formula, To obtain the minimum value, The preset window growth step size, The maximum window length limit is set;
[0033] If neither of the above two conditions is met, the window length will be adjusted to the preset medium length. Smooth adjustment, and satisfy: .
[0034] In one embodiment of the present invention, the reconstruction error of the current dynamic mode decomposition model in step S4 is calculated by the following formula:
[0035] ;
[0036] In the formula, For reconstruction error, This is the original data matrix within the current data window. The data matrix is reconstructed based on the current dynamic mode decomposition model. Let Frobenius norm denote the matrix.
[0037] To address the aforementioned technical problems, this invention provides an adaptive online dynamic pattern decomposition system for a target system, comprising:
[0038] Data acquisition module: acquires multivariate time series data of the target system and extracts a set of core feature variables from the multivariate time series data, wherein the target system is any one of fluid mechanics, electromechanical system or power grid monitoring;
[0039] Causal pattern quantification module: Based on the preset physical causal relationship, a local low-order regression model is constructed within the current monitoring window of the dynamic pattern decomposition model to quantify the causal interaction pattern at the current moment, and the current causal pattern feature vector is constructed based on the local low-order regression model.
[0040] Similarity calculation module: Calculates the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector;
[0041] Adaptive window adjustment module: Based on the similarity and the reconstruction error of the current dynamic pattern decomposition model, dynamically adjust the length of the data window used for updating the dynamic pattern decomposition model;
[0042] Update and output module: Based on the time series data of the target system extracted by the adjusted data window length, update the dynamic mode decomposition model and output the current dynamic mode information of the target system.
[0043] To address the aforementioned technical problems, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the adaptive online dynamic mode decomposition method for a target system as described above.
[0044] To address the aforementioned technical problems, the present invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the adaptive online dynamic pattern decomposition method for a target system as described above.
[0045] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:
[0046] This invention guides the adaptive scaling of the underlying data window in the DMD by quantifying the interaction patterns between core variables, thereby achieving an optimal balance between filtering smoothing and fast response. By monitoring the causal patterns between core physical characteristic variables (such as the voltage-drive-current relationship in a motor system), this invention can more directly and earlier capture essential changes in system structure or parameters (such as changes in winding resistance with temperature or faults). Once a sudden change is detected, the algorithm decisively shortens the data window and actively discards historical data that is no longer applicable, allowing the model to quickly anchor to the new operating conditions.
[0047] This invention introduces and The dual-threshold adaptive logic prioritizes the nearest related data to accelerate convergence after a sudden change in the target system; and after confirming that the system has returned to stability, it smoothly extends the window to improve noise resistance. This targeted data memory management greatly reduces reconstruction and prediction errors during the transition period.
[0048] The adaptive triggering mechanism of this invention is based on a pre-identified core physical causal link, rather than blindly conducting data-driven causal discovery from scratch (the latter is prone to producing spurious correlations in short-window, non-stationary data). This makes the window-adaptive triggering signal more reliable and has a high degree of physical interpretability. Attached Figure Description
[0049] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.
[0050] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation
[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.
[0052] Example 1
[0053] Reference Figure 1 As shown, this invention relates to an adaptive online dynamic mode decomposition method for a target system.
[0054] Step S1: Obtain multivariate time series data of the target system and extract a set of core feature variables from the multivariate time series data, wherein the target system includes, but is not limited to, any one of a fluid dynamics system, an electromechanical control system, or a smart grid system;
[0055] Step S2: Based on the preset physical causal relationship, construct a local low-order regression model between the core feature variable sets within the current monitoring window of the dynamic pattern decomposition model to quantify the causal interaction pattern at the current moment, and construct the current causal pattern feature vector based on the local low-order regression model.
[0056] Step S3: Calculate the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector;
[0057] Step S4: Based on the similarity and the reconstruction error of the current dynamic pattern decomposition model, dynamically adjust the length of the data window used for updating the dynamic pattern decomposition model;
[0058] Step S5: Based on the time series data of the target system extracted by the adjusted data window length, update the dynamic mode decomposition model and output the current dynamic mode information of the target system. The dynamic mode information includes the characteristic values, oscillation frequency, decay or growth rate and spatial coherence mode of the target system modes. This dynamic mode information can be used for short-term state prediction, equipment health assessment or as input data for the next level control strategy.
[0059] The following is a detailed description of this embodiment:
[0060] Step S1: System Initialization and Core Feature Selection
[0061] Acquire streaming multivariate time series data of the target system. To avoid high-dimensional noise interference, select the feature set that best represents the core dynamics of the system based on prior knowledge of domain physics. Its dimension is denoted as Initialize the DMD sliding data window length to... And using the system's initial validated stable operating data segment, baseline causal pattern feature vectors are learned. .
[0062] Step S2: Online Quantification and Monitoring of Causal Patterns
[0063] Physical systems typically exhibit clear causal relationships. (Setting the target variable...) and the known set of influencing variables , For the first Several known influencing variables. Within a relatively short monitoring sliding window. Within this model, a local low-order autoregressive (ARX) model with exogenous input is established as a local low-order regression model. The specific formula is as follows:
[0064]
[0065] In the formula, For time points The target feature variable The intercept is... These are the autoregressive coefficients. For time points The target feature variable The total number of known influencing variables. For time points The There are 10 known influencing variables, which are selected from the core feature variable set or external environmental variables. and These are the preset maximum lag orders. For exogenous input coefficients, This represents the model residuals.
[0066] Further, the method for constructing the current causal pattern feature vector based on the local low-order regression model in step S2 includes: constructing the current causal pattern feature vector based on the parameter combination estimated by the local low-order regression model, expressed as:
[0067]
[0068] In the formula, This is the feature vector of the current causal pattern. For is equal to, This represents a vectorized straightening operation for a matrix or set. This indicates transpose.
[0069] Further, step S3 calculates the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector, using cosine similarity, expressed as:
[0070]
[0071] In the formula, For causal pattern similarity, This is the feature vector of the current causal pattern. The baseline causal pattern feature vector is learned during the initial stable operation phase of the target system. Let L be the norm of the vector. If multiple preset physical causal relationships exist, the minimum or average value of the similarity of each causal pattern is taken as the overall causal pattern similarity of the target system, expressed as:
[0072]
[0073] In the formula, For the overall causal pattern similarity of the target system, For the first The similarity of causal patterns of a pre-defined physical causal relationship.
[0074] Furthermore, the method for dynamically adjusting the data window length used for model updates in step S4 includes:
[0075] Extract the relative reconstruction error of the current online DMD model , combined Perform joint state determination:
[0076] (1) If or This indicates a deviation from the underlying physical state of the system (a sudden change in operating conditions or a failure). In this case, an aggressive window shortening strategy is implemented:
[0077]
[0078] In the formula, The current data window length, For assignment operations, To obtain the maximum value, Shorten the step size for the preset window. This is the minimum window length limit set.
[0079] (2) If and This indicates that the causal pattern is consistent with the baseline and the DMD fits well, suggesting the system is in a steady state. At this point, a gradual window growth strategy is implemented:
[0080]
[0081] In the formula, To obtain the minimum value, The preset window growth step size, This is the maximum window length limit set.
[0082] (3) If neither of the above two conditions is met, the window length will be adjusted to the preset medium length. Smooth adjustment, and satisfy: .
[0083] Furthermore, the reconstruction error of the current dynamic mode decomposition model in step S4 is calculated using the following formula:
[0084] ;
[0085] In the formula, For reconstruction error, This is the original data matrix within the current data window. The data matrix is reconstructed based on the current dynamic mode decomposition model. Let Frobenius norm denote the matrix.
[0086] Step S4: Dynamic Mode Decomposition (DMD) Underlying Matrix Calculation and Mode Extraction
[0087] Based on the data window length dynamically determined in step S3 The latest state snapshot matrix is extracted from the real-time streaming data buffer pool. The data is then divided into a preceding matrix. and the post-order matrix ,in It is a general representation of a snapshot vector. Under the index... Belonging to 1 to At that time, it belonged to ; under current subscript Belongs to 2 At that time, it belonged to .in For the first A column vector of state snapshots at each moment. , This represents the total number of snapshot sampling points within the current data window.
[0088] DMD aims to find an optimal linear operator. Make The specific calculation includes the following sub-steps:
[0089] S4.1 Preorder Matrix Perform reduced-rank singular value decomposition (SVD): ,in To preserve the system order, It is a left singular matrix. It is a right singular matrix. This indicates the conjugate transpose. For inclusion A diagonal matrix with a maximum singular value;
[0090] S4.2 Calculate the system matrix after dimension reduction and projection : ;
[0091] S4.3 Perform eigenvalue decomposition to obtain eigenvalues. and eigenvectors ;
[0092] S4.4 Calculate the full-state DMD mode matrix (Its column vector is) ): Or more precisely ,in The eigenvectors obtained in the previous step The eigenvector matrix formed by these vectors;
[0093] S4.5 Calculate continuous-time eigenvalues , The real part represents the growth / decay rate of the mode, and the imaginary part represents the oscillation frequency. The physical time interval for system data sampling.
[0094] Therefore, the real-time state of the system can be approximately reconstructed as a linear combination of the modes: ,in, This represents the initial amplitude of the corresponding mode (determined by the initial state of the system). This result can be directly used for short-term prediction, equipment health assessment, or as input for the next level of control strategy.
[0095] The following section introduces specific application scenarios for DC motor systems (gray box systems):
[0096] To further illustrate the applicability of this invention, a DC motor system affected by variable load and fault injection is taken as an example: In this scenario, the core feature variable set is set as follows: Based on the physical equations of the electric motor ( ),Voltage and rotational speed The common cause determines the current. (Results). Therefore, the key causal pattern monitored by the CPM module is: As the target variable ,Will and As an influencing variable Construct an ARX model. When a partial short circuit or overheating occurs in the windings inside the motor, it increases the armature resistance. During abrupt changes, although the system still outputs data, the causal response coefficients (i.e., vector coefficients) between the voltage and current mentioned above will be lost. A significant deviation will occur immediately. The method of this invention can detect similarity instantaneously. Falling below the threshold Furthermore, the data window of the DMD is immediately shortened in the next operation cycle, discarding normal data before the fault occurred. Compared to traditional ODMD algorithms that rely on fixed decay factors and are still "dragged down" by a large amount of health data, resulting in slow response, this embodiment can output fault characteristic modes with new decay rates and frequencies extremely quickly, achieving highly agile state tracking in non-stationary systems.
[0097] Example 2
[0098] This embodiment provides an adaptive online dynamic pattern decomposition system for a target system, including:
[0099] Data acquisition module: acquires multivariate time series data of the target system and extracts a set of core feature variables from the multivariate time series data;
[0100] Causal pattern quantification module: Based on the preset physical causal relationship, a local low-order regression model is constructed within the current monitoring window of the dynamic pattern decomposition model to quantify the causal interaction pattern at the current moment, and the current causal pattern feature vector is constructed based on the local low-order regression model.
[0101] Similarity calculation module: Calculates the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector;
[0102] Adaptive window adjustment module: Based on the similarity and the reconstruction error of the current dynamic pattern decomposition model, dynamically adjust the length of the data window used for updating the dynamic pattern decomposition model;
[0103] Update and output module: Based on the time series data of the target system extracted by the adjusted data window length, update the dynamic mode decomposition model and output the current dynamic mode information of the target system.
[0104] Example 3
[0105] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the adaptive online dynamic pattern decomposition method for a target system described in Embodiment 1.
[0106] Example 4
[0107] This embodiment provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the steps of the adaptive online dynamic pattern decomposition method for a target system described in Embodiment 1.
[0108] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.
[0109] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0110] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0111] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0112] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.
Claims
1. An adaptive online dynamic mode decomposition method for a target system, characterized in that, include: Step S1: Obtain multivariate time series data of the target system, and extract a set of core feature variables from the multivariate time series data; Step S2: Based on the preset physical causal relationship, construct a local low-order regression model between the core feature variable sets within the current monitoring window of the dynamic pattern decomposition model to quantify the causal interaction pattern at the current moment, and construct the current causal pattern feature vector based on the local low-order regression model. Step S3: Calculate the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector; Step S4: Based on the similarity and the reconstruction error of the current dynamic pattern decomposition model, dynamically adjust the length of the data window used for updating the dynamic pattern decomposition model; Step S5: Based on the time series data of the target system extracted by the adjusted data window length, update the dynamic mode decomposition model and output the current dynamic mode information of the target system.
2. The adaptive online dynamic mode decomposition method for a target system according to claim 1, characterized in that: The local low-order regression model in step S2 is an autoregressive model with exogenous input, expressed as: ； In the formula, For time points The target feature variable The intercept is... These are the autoregressive coefficients. For time points The target feature variable The total number of known influencing variables. For time points The There are 10 known influencing variables, which are selected from the core feature variable set or external environmental variables. and These are the preset maximum lag orders. For exogenous input coefficients, This represents the model residuals.
3. The adaptive online dynamic mode decomposition method for a target system according to claim 2, characterized in that: The method for constructing the current causal pattern feature vector based on the local low-order regression model in step S2 includes: The parameter combination estimated by the local low-order regression model constitutes the current causal pattern feature vector, which is expressed as: ； In the formula, This is the feature vector of the current causal pattern. For is equal to, This represents a vectorized straightening operation for a matrix or set. This indicates transpose.
4. The adaptive online dynamic mode decomposition method for a target system according to claim 1, characterized in that: Step S3 calculates the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector, using cosine similarity, expressed as: ； In the formula, For causal pattern similarity, This is the feature vector of the current causal pattern. The baseline causal pattern feature vector is learned during the initial stable operation phase of the target system. Let be the 2-norm of the vector.
5. The adaptive online dynamic mode decomposition method for a target system according to claim 4, characterized in that: If multiple preset physical causal relationships exist, the minimum or average value of the similarity of each causal pattern is taken as the overall causal pattern similarity of the target system, expressed as: ； In the formula, For the overall causal pattern similarity of the target system, For the first The similarity of causal patterns of a pre-defined physical causal relationship.
6. The adaptive online dynamic mode decomposition method for a target system according to claim 1, characterized in that: The method for dynamically adjusting the length of the data window used for model updates in step S4 includes: If the overall causal pattern similarity Below the preset mutation threshold Or the reconstruction error of the current dynamic mode decomposition model Higher than the preset high error threshold If this indicates a sudden change in the underlying physical operating conditions or a failure, then the window shortening strategy will be executed: ； In the formula, The current data window length, For assignment operations, To obtain the maximum value, Shorten the step size for the preset window. The minimum window length limit is set. If the overall causal pattern similarity Higher than the preset mutation threshold Furthermore, the reconstruction error of the current dynamic mode decomposition model... Below the preset high error threshold This indicates that the causal pattern is consistent with the baseline and the dynamic mode decomposition model fits well, meaning the target system is in a steady state. Therefore, the window growth strategy is executed. ； In the formula, To obtain the minimum value, The preset window growth step size, The maximum window length limit is set; If neither of the above two conditions is met, the window length will be adjusted to the preset medium length. Smooth adjustment, and satisfy: .
7. The adaptive online dynamic mode decomposition method for a target system according to claim 1, characterized in that: The reconstruction error of the current dynamic mode decomposition model in step S4 is calculated using the following formula: ； In the formula, For reconstruction error, This is the original data matrix within the current data window. The data matrix is reconstructed based on the current dynamic mode decomposition model. Let Frobenius norm denote the matrix.
8. An adaptive online dynamic pattern decomposition system for a target system, characterized in that, include: Data acquisition module: acquires multivariate time series data of the target system and extracts a set of core feature variables from the multivariate time series data; Causal pattern quantification module: Based on the preset physical causal relationship, a local low-order regression model is constructed within the current monitoring window of the dynamic pattern decomposition model to quantify the causal interaction pattern at the current moment, and the current causal pattern feature vector is constructed based on the local low-order regression model. Similarity calculation module: Calculates the similarity between the current causal pattern feature vector and the pre-established baseline causal pattern feature vector; Adaptive window adjustment module: Based on the similarity and the reconstruction error of the current dynamic pattern decomposition model, dynamically adjust the length of the data window used for updating the dynamic pattern decomposition model; Update and output module: Based on the time series data of the target system extracted by the adjusted data window length, update the dynamic mode decomposition model and output the current dynamic mode information of the target system.
9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the steps of the adaptive online dynamic pattern decomposition method for a target system as described in any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the adaptive online dynamic pattern decomposition method for a target system as described in any one of claims 1 to 7.