Dynamic system order reduction method suitable for improving dynamic mode decomposition of wind power signal

Abstract

The invention provides a dynamic system order reduction method suitable for improving dynamic mode decomposition of a wind power signal, and belongs to the technical field of wind power signals, and the method comprises the steps: obtaining a wind power time sequence signal, carrying out the preprocessing, constructing a time delay data matrix, carrying out the dynamic mode decomposition of the time delay data matrix, and obtaining a wind power signal. Obtaining a system order reduction model comprising a modal matrix, an amplitude matrix and a dynamic evolution matrix; arranging the modal matrix by using an improved discrete time coefficient weighting criterion, and obtaining a reconstructed low-order linear model by using an inversion formula and a strategy of increasing a reserved modal number; performing inverse time delay operation and inverse normalization processing on the reconstructed low-order linear model to obtain one-dimensional signal data, and completing original dynamic system order reduction; according to the method, the problems that an existing wind power signal data driving model cannot give consideration to interpretability and accuracy, and errors caused by an original dynamic mode decomposition method in the aspects of mode selection and mode number determination are large are solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wind power signals, and particularly relates to a dynamic system order reduction method suitable for improved dynamic mode decomposition of wind power signals. BACKGROUND

[0002] Wind power, as a renewable, environmentally friendly and widely distributed new energy, plays an important role in peak shaving and valley filling in power systems. However, due to the strong random fluctuation and multi-scale time variation characteristics of wind power, traditional prediction models often rely on a large amount of historical data for training, and it is difficult to obtain intuitive physical meaning, which easily falls into the "black box" dilemma. In order to improve the interpretability and stability of wind power prediction, researchers have begun to focus on dimensionality reduction processing of wind power time domain signals, and by constructing a reduced order model to reveal the potential dynamic structure, so as to provide a basis for subsequent prediction and control.

[0003] The dynamic mode decomposition (DMD) method is to map high-dimensional dynamic data to a low-dimensional linear operator space, which decouples the signal frequency domain mode and shows the evolution rule of each mode over time. Therefore, this method has significant advantages in signal noise reduction and data dimensionality reduction. The existing researches are dedicated to using DMD as a signal decomposition method, and by extracting several dominant modes to reconstruct the dynamic characteristics of the signal, a reduced order representation is provided for the prediction model. The standard DMD algorithm still has the following limitations in the application of complex signal processing: on the one hand, the analytical nature of the reduced order model depends on the consistency of the modal selection criterion and the time series dynamics. On the other hand, the selection of the number of modes is usually based on human experience, and it is difficult to ensure the complete extraction of all dominant dynamic characteristics. The more "effective" modes selected, the more dynamic the constructed model is, and the more obvious the law is, and the more analytical it is. In contrast, the more "noise" modes selected, the more chaotic the constructed model is, and the key dynamic components may be missed.

[0004] The selection of modes is indeed the core of model reduction. Proper orthogonal decomposition (POD) is to carry out decomposition according to the energy characteristics of different modes, so the POD mode can easily realize the contribution degree sorting according to the energy level size. The DMD method is to carry out decomposition according to the frequency characteristics of different modes, and unless the essential frequency mode contained in the system is known in advance, there is no meaning to sort according to the frequency size. Therefore, the standard DMD algorithm gives a mode selection criterion using amplitude sorting, realizing the preliminary screening of the mode. The energy of the mode seems to be hidden, and the mode change rate and evolution time are currently used as variables to form a function, which has clear monotonicity in the definition interval, but because of the existence of the exponential term, when the change rate is far away from the zero axis, the order of magnitude of the numerator and the denominator is large, and due to the Frobenius norm, the method error exists; and the time coefficient weighting method of traversing all time seems to have other thinking ways.

[0005] In order to accurately construct a wind power signal reduction model with explainability and dynamic feature reservation, a new amplitude weighting criterion based on discrete time step and model construction process are needed to overcome the shortcomings of the existing DMD algorithm in mode selection and mode number determination, and to realize efficient reduction and accurate reconstruction of the wind power signal model in a complex dynamic environment. SUMMARY

[0006] In view of the above problems in the prior art, the improved dynamic modal decomposition dynamic system reduction method suitable for wind power signals provided by the present application solves the problems that the existing data-driven model of wind power signals cannot consider explainability and accuracy, and the original modal decomposition method causes large errors in mode selection and mode number determination.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows: an improved dynamic modal decomposition dynamic system reduction method suitable for wind power signals, comprising the following steps: S1, obtaining a wind power time series signal and pre-processing, constructing a time delay data matrix, carrying out dynamic modal decomposition on the time delay data matrix, and obtaining a system reduction model containing a mode matrix, an amplitude matrix and a dynamic evolution matrix; S2, arranging the mode matrix according to the improved discrete time coefficient weighting criterion based on the system reduction model, adjusting the amplitude matrix and the dynamic evolution matrix, using the inversion formula and increasing the number of reserved modes, and obtaining a reconstructed low-order linear model; S3, performing inverse time delay operation and inverse normalization processing on the reconstructed low-order linear model to obtain one-dimensional signal data, and completing dynamic system reduction.

[0008] The beneficial effects of this invention are as follows: Based on the improved amplitude weighting criterion and model construction process of discrete time step, this invention overcomes the large errors caused by existing dynamic mode decomposition algorithms in mode selection and mode number determination, and achieves efficient order reduction and accurate reconstruction of wind power signal models in complex dynamic environments.

[0009] Further, S1 includes the following steps: S101. Obtain wind power time sequence signals and perform standardization processing on the wind power time sequence signals; S102. Using the Hankel time delay matrix, process the standardized wind power time sequence signal to construct a time delay data matrix; S103. Based on dynamic mode decomposition, singular value decomposition and eigenvalue decomposition are performed on the time delay data matrix to obtain a reduced-order system model containing the mode matrix, amplitude matrix and dynamic evolution matrix.

[0010] The beneficial effects of the above-mentioned further solutions are as follows: The present invention uses the dynamic mode decomposition method to extract features and reduce the order of one-dimensional time series signals. Through this method, the linear simplification of complex dynamic systems can be achieved, and the interpretability and robustness of data-driven models can be better improved.

[0011] Furthermore, S2 includes the following steps: S201. Based on the system order reduction model, and based on the improved discrete time coefficient weighting criterion, the mode matrix is ​​arranged using time weighting coefficients, and the preset order modes are retained by the criterion for retaining the number of modes, thus obtaining the mode matrix of retained modes. S202. Adjust the amplitude matrix and dynamic evolution matrix, and based on the mode matrix with preserved modes, the adjusted amplitude matrix and the adjusted dynamic evolution matrix, use the inversion formula to perform inversion reconstruction and calculate the reconstructed low-order linear model. S203. Calculate the error of the reconstructed low-order linear model and judge the error. If the error is less than the preset threshold, output the reconstructed low-order linear model. Otherwise, increase the number of retained modes and return to step S201.

[0012] Furthermore, the expression for the improved discrete-time coefficient weighting criterion is as follows: ; in, Indicates a time scale. Indicates amplitude. Indicates the modal order. Indicates the time step. Indicates the first Each feature value.

[0013] Further, the expression of the inversion formula is as follows: ; Wherein, represents the signal data after inversion, represents the modal matrix, represents the diagonal matrix of the order, represents the amplitude matrix, represents the number of rows of the matrix, represents the first modal.

[0014] Further, the expression of the loss function is as follows: ; Wherein, represents the error, represents the time delay data matrix, represents the reconstruction matrix, represents the F norm.

[0015] The beneficial effects of the above further scheme are: the improved modal selection criterion is defined, the discrete time weighted amplitude sorting method is adopted, the projection of the modal to the snapshot is not needed, only the initial amplitude of each order modal and the characteristic value are used, the magnitude gap caused by the exponential term calculation is simplified, the stability of the algorithm is enhanced, and the main characteristic modal of the dynamic system is beneficial to select and retain; And a modal number selection process is adopted, the function of the modal retention number and the loss between the inversion signal is defined, the problems of insufficient modal number caused by artificial selection of modal number, incomplete extraction of main modal, and introduction of redundant information and noise interference caused by too many modes are avoided.

[0016] Further, the S3 comprises the following steps: S301, according to the reconstructed low-order linear model, the inverse time delay formula is used to average the inverse diagonal elements of the Hankel time delay matrix, and the low-order linear model of the recovered time delay is obtained; S302, the low-order linear model of the recovered time delay is de-normalized, a one-dimensional signal data with consistent shape and amplitude and wind power time sequence signal is obtained, and the dynamic system is reduced.

[0017] Further, the expression of the inverse time delay formula is as follows: ; Wherein, represents the reconstructed one-dimensional sequence , the first k data, denotes a Hankel time-delay matrix, k denotes k is an integer, and , denotes a time step.

[0018] The above further scheme has the beneficial effect that the present application, through inverse time-delaying and renormalization processing, obtains one-dimensional signal data with the same shape and amplitude as the original data, realizes accurate reconstruction, improves the accuracy and efficiency of dynamic system reduction, and ensures the effectiveness of dynamic system reduction. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is a flow chart of the method of the present application.

[0020] Figure 2 is a real wind power monitoring signal graph obtained in the present embodiment.

[0021] Figure 3 is a comparison graph of the effect of the improved discrete time coefficient weighting criterion and the existing modal selection method in the present embodiment.

[0022] Figure 4 is a comparison graph of the inversion signal results of the improved discrete time coefficient weighting criterion and the existing modal selection method when the number of retained modes is 30 in the present embodiment. DETAILED DESCRIPTION

[0023] The specific embodiments of the present application are described below to facilitate understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, any changes that are obvious within the spirit and scope of the present application as defined and determined by the appended claims are obvious, and all applications utilizing the concept of the present application are included in the protection.

[0024] Before the present embodiment is described, the following terms are explained: DMD: dynamic modal decomposition; POD: proper orthogonal decomposition; Hankel time-delay matrix: Hankel time-delay matrix; Frobenius norm: Frobenius norm.

[0025] EMBODIMENT As shown in Figure 1 , the present application provides a dynamic system reduction method for improved dynamic modal decomposition of wind power signals, and the implementation method is as follows: S1, acquire a wind power time series signal and pre-process it, construct a time delay data matrix, perform dynamic modal decomposition on the time delay data matrix, and obtain a system reduced-order model containing a modal matrix, an amplitude matrix and a dynamic evolution matrix, the specific steps being as follows: S101, acquire a wind power time series signal, and perform standardization processing on the wind power time series signal; S102, process the wind power time series signal subjected to standardization processing by using a Hankel time delay matrix, and construct a time delay data matrix.

[0026] In this embodiment, as shown in the figure, Figure 2 a real wind power monitoring signal, i.e., a wind power time series signal, is acquired, and standardization processing and Hankel time delay matrix processing are performed on the wind power time series signal to construct a time delay data matrix, the data form of the time delay data matrix being pre-set as a data matrix of the shape , denotes the number of rows of the matrix, denotes the number of columns of the matrix; The acquired wind power time series signal is a one-dimensional time series signal, and its expression is: wherein, denotes signal data in the wind power time series signal, N denotes a time step of the signal data in the wind power time series signal, and a one-dimensional time series signal at the next moment is defined as , and is expressed as: The expression of the time delay data matrix is: ; wherein, denotes the time delay data matrix, is signal data of time steps.

[0027] S103, based on dynamic modal decomposition, perform singular value decomposition and eigenvalue decomposition on the time delay data matrix to obtain a system reduced-order model containing a modal matrix, an amplitude matrix and a dynamic evolution matrix.

[0028] In this embodiment, the dynamic modal decomposition method is used to perform singular value decomposition on the time delay data matrix, and the expression is as shown below: ; wherein, denotes a first unitary matrix decomposed by the time delay data matrix, denotes a diagonal singular value matrix, denotes a second unitary matrix decomposed by the time delay data matrix; ​The singular value decomposition, by preserving r main singular values and reducing noise by truncation, obtains a similarity matrix by similarity transformation , the similarity matrix , the first eigenvalue of the th column of the similarity matrix , the eigenvector of the th column of the similarity matrix , the first unitary matrix obtained by singular value decomposition of the time-delay data matrix ; ; The control equation of the reduced-order system can be described as: ; , wherein represents the signal data corresponding to the low-dimensional space mapping , represents the high-dimensional matrix of the system linear hypothesis, reflecting the time evolution of the system, i.e. ; Therefore, the expression of the th mode is as follows: ; , wherein represents the th mode, and the mode matrix is obtained by integrating the modes ; The eigenvector is a column vector, the characteristic matrix , the diagonal matrix of singular values , and the characteristic decomposition of the similarity matrix is as follows: ; , wherein represents the diagonal matrix The system reduction in this embodiment refers to a low-dimensional expression method of the high-dimensional operator representing the system evolution, and the whole is a construction of a linear degradation model In the dynamic mode decomposition method, the expression of the amplitude matrix is as follows: ; , wherein represents the signal data at the first time to the low-dimensional space mapping , represents the inverse of the first unitary matrix, and the amplitude represents the contribution of the th mode to the system at the initial timeobtain a system reduced order model including modal matrixes of each order mode , amplitude matrix and dynamic evolution matrix , expressed as follows: ; wherein, denotes the system reduced order model.

[0029] S2, according to the system reduced order model, arranging the modal matrixes by using the improved discrete time coefficient weighting criterion, and adjusting the amplitude matrix and the dynamic evolution matrix, obtaining the reconstructed low order linear model by using the inversion formula and the strategy of increasing the number of reserved modes, the specific steps are as follows: S201, according to the system reduced order model, arranging the modal matrixes by using the time weighting coefficient based on the improved discrete time coefficient weighting criterion, and reserving the preset order mode by using the judgment criterion of the number of reserved modes, obtaining the modal matrix of the reserved mode; S202, adjusting the amplitude matrix and the dynamic evolution matrix, and according to the modal matrix of the reserved mode, the adjusted amplitude matrix and the adjusted dynamic evolution matrix, using the inversion formula to perform inversion reconstruction, and calculating to obtain the reconstructed low order linear model; S203, calculating the error of the reconstructed low order linear model, and judging the error, if the error is less than the preset threshold, outputting the reconstructed low order linear model, otherwise, increasing the number of reserved modes, and returning to step S201.

[0030] In this embodiment, the modal matrixes are arranged by using the time weighting coefficient based on the improved discrete time coefficient weighting criterion; The specific expression of the improved discrete time coefficient weighting criterion is as follows: ; wherein, denotes, the direction is the time scale, denotes the amplitude of the order mode, denotes the order of the mode, denotes the time step, denotes the first eigenvalue.

[0031] and reserving the preset number of modes by using the judgment criterion of the number of reserved modes, obtaining the modal matrix of the reserved mode; Adjust the corresponding feature matrix (amplitude matrix and dynamic evolution matrix), and use the inversion formula to perform inversion reconstruction according to the modal matrix of the retained mode, the adjusted amplitude matrix and the adjusted dynamic evolution matrix, to calculate a high-precision reconstructed low-order linear model ; The expression of the inversion formula is as follows: ; Wherein, represents the signal data after inversion, represents the modal matrix, represents the diagonal matrix of the order, represents the amplitude matrix, represents the number of rows of the matrix, represents the first mode; Calculate the error of the reconstructed low-order linear model, and the expression of the error analysis function, that is, the loss function, is as follows: ; Wherein, represents the error, represents the time delay data matrix, represents the reconstructed low-order linear model, represents the F norm, and the error is judged, if the error is less than a preset threshold , the reconstructed low-order linear model is output, otherwise, the number of retained modes is increased, and the modal matrix of the retained mode is reacquired, and the updated reconstructed low-order linear model is obtained through the inversion formula.

[0032] S3, inverse time delay operation and inverse normalization processing are performed on the reconstructed low-order linear model to obtain one-dimensional signal data, and dynamic system reduction is completed, and the specific steps are as follows: S301, according to the reconstructed low-order linear model, the inverse time delay formula is used to average the anti-diagonal elements of the Hankel time delay matrix, and the low-order linear model with recovered time delay is obtained; S302, the low-order linear model with recovered time delay is subjected to inverse normalization to obtain one-dimensional signal data with consistent shape and amplitude and wind power time sequence signal, and dynamic system reduction is completed.

[0033] In this embodiment, according to the reconstructed low-order linear model, the inverse time delay formula is used to average the anti-diagonal elements of the Hankel time delay matrix, and the low-order linear model with recovered time delay is obtained; The expression of the inverse time delay formula is as follows: ; Wherein, Low-order linear model representing recovery time delay In the first embodiment of the present application, k Data, denotes a Hankel time delay matrix, which is defined as: , Low-order linear model representing recovery time delay, is a reconstructed one-dimensional sequence, and the original one-dimensional time series signal is , .

[0034] And the low-order linear model of the recovery time delay is de-normalized to obtain one-dimensional signal data with consistent shape and amplitude as the wind power time series signal, and the expression of the de-normalization is as follows: ; Where, denotes the data obtained by de-normalization, which has the same shape and amplitude as the original one-dimensional data, denotes the maximum value in the reconstructed one-dimensional sequence, denotes the minimum value in the reconstructed one-dimensional sequence. The more efficient and more accurate reduced-order modeling effect is achieved.

[0035] In the embodiment, as shown in Figure 3 When the number of retained modes , each criterion shows a higher reconstruction loss, where the initial amplitude of the mode The criterion shows a significant defect: when the number of retained modes The Loss value still remains above 95%, and the decline and convergence of the Loss value requires the number of retained modes Trigger, which reflects its invalid truncation of non-physical high-frequency modes; in contrast, the E criterion and the improved discrete-time coefficient weighting criterion produce rapid decay of the Loss function when the number of retained modes As shown in Figure 4 When the number of retained modes The improved discrete-time coefficient weighting criterion stabilizes the Loss at 11.75%, which is significantly lower than the E criterion (13.51%) and the initial amplitude of the mode The criterion (20.02%), which proves that it can achieve a more compact low-order expression through impurity mode filtering.

Claims

1. A dynamic system reduction method suitable for improved dynamic modal decomposition of wind signals, characterized in that, The method comprises the following steps: S1, obtaining a wind power time series signal and performing preprocessing, constructing a time delay data matrix, performing dynamic modal decomposition on the time delay data matrix, and obtaining a system reduced order model comprising a modal matrix, an amplitude matrix, and a dynamic evolution matrix; S2, arranging the modal matrix according to the system reduced order model, adjusting the amplitude matrix and the dynamic evolution matrix by using an improved discrete time coefficient weighting criterion, and obtaining a reconstructed low-order linear model by using an inversion formula and a strategy of increasing a retained modal number; S3, performing inverse time delay operation and inverse normalization processing on the reconstructed low-order linear model to obtain one-dimensional signal data, and completing dynamic system reduction.

2. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 1, wherein, The S1 comprises the following steps: S101, obtaining a wind power time series signal and performing standardization processing on the wind power time series signal; S102, processing the wind power time series signal subjected to the standardization processing by using a Hankel time delay matrix to construct a time delay data matrix; S103, performing singular value decomposition and eigenvalue decomposition on the time delay data matrix based on dynamic modal decomposition to obtain a system reduced order model comprising a modal matrix, an amplitude matrix, and a dynamic evolution matrix.

3. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 1, wherein, The S2 comprises the following steps: S201, arranging the modal matrix by using a time weighting coefficient based on the improved discrete time coefficient weighting criterion according to the system reduced order model, and retaining a preset order modal by using a retained modal number determination criterion to obtain a modal matrix of the retained modal; S202, adjusting the amplitude matrix and the dynamic evolution matrix, and performing inversion reconstruction by using the inversion formula according to the modal matrix of the retained modal, the adjusted amplitude matrix, and the adjusted dynamic evolution matrix to calculate a reconstructed low-order linear model; S203, calculating an error of the reconstructed low-order linear model, and judging the error, if the error is less than a preset threshold, outputting the reconstructed low-order linear model, otherwise, increasing the retained modal number, and returning to step S201.

4. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 3, wherein, An expression of the improved discrete time coefficient weighting criterion is as follows: in, Indicates a time scale. Indicates amplitude, Indicates the modal order. Indicates the time step. Indicates the first Each feature value.

5. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 4, wherein, An expression of the inversion formula is as follows: wherein denotes the signal data after inversion, denotes the modal matrix, denotes a diagonal matrix of order denotes the amplitude matrix, denotes the number of rows of the matrix, denotes the th mode.

6. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 5, wherein, An expression of the loss function is as follows: wherein, denotes an error, denotes a delay data matrix, denotes a reconstruction matrix, denotes an F-norm.

7. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 1, wherein, The S3 comprises the following steps: S301, averaging anti-diagonal elements of the Hankel time delay matrix by using an inverse time delay formula according to the reconstructed low-order linear model to obtain a low-order linear model with restored time delay; S302, performing inverse normalization on the low-order linear model with the restored time delay to obtain one-dimensional signal data with consistent shape and amplitude of the wind power time series signal, and completing dynamic system reduction.

8. The dynamic system reduction method for improved dynamic mode decomposition applicable to wind signals of claim 7, wherein, An expression of the inverse time delay formula is as follows: wherein, denotes the reconstructed one-dimensional sequence the k data, denotes the Hankel time-delay matrix, k denotes k one, and , denotes the time step.

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