CN114254713A - Classification system and method based on time-frequency transformation and dynamic mode decomposition - Google Patents
Classification system and method based on time-frequency transformation and dynamic mode decomposition Download PDFInfo
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Abstract
The invention relates to a classification system and a classification method based on time-frequency transformation and dynamic mode decomposition, and belongs to the technical field of data classification, image classification and signal identification. The system comprises a preprocessing module, a time-frequency analysis module, a dynamic mode decomposition module, an energy feature extraction module, each order moment solving module and a classification module; the method comprises the following steps: preprocessing the acquired data to obtain effective signals; performing time-frequency analysis and dynamic mode decomposition on the effective signals to obtain a plurality of characteristic values and dynamic modes, sequencing the characteristic values and the dynamic modes to obtain energy values from large to small, corresponding characteristic values and dynamic modes, and combining the energy values and the dynamic modes to form an energy characteristic matrix; extracting the first S elements of the energy characteristic matrix, discarding subsequent data, updating the energy characteristic matrix, and solving the two-norm of the energy characteristic matrix to obtain a transformed characteristic matrix; and performing threshold classification and outputting a classification result based on the transformed characteristic matrix as data to be classified. The method can realize higher classification accuracy.
Description
Technical Field
The invention relates to a classification system and a classification method based on time-frequency transformation and dynamic mode decomposition, and belongs to the technical field of data classification, image classification and signal identification.
Background
Data classification is the grouping together of data having some common attribute or characteristic, and the data are distinguished by the attribute or characteristic of its category. In other words, the information with the same content or the same property is classified into a category, and the different information is distinguished, and then the relationship between the sets is determined, so as to form an organized classification system. For signal processing and classification, for example: the data classification is also widely applied in the related fields of Internet of things identification, space spectrum resource management and control, radio frequency security and the like, and the signal classification and identification have great application value and practical significance.
In practical applications, signals received after the signals sent by the radio frequency signal source pass through a complex channel are often unstable and statistics of the signals are time-varying. In order to classify the radio frequency signals, the radio frequency signal features are often required to be extracted. The methods for extracting features generally include fourier analysis, short-time fourier transform, wavelet transform, power spectrum, cepstrum, and the like. The Fourier analysis method cannot perform local characterization on non-stationary radio frequency signal characteristics, and can only be used for knowing the global characteristics of the signal in a time frequency domain. Although short-time fourier transform can describe frequency information in a certain local time period, the stability of a signal in a short time is difficult to guarantee as the signal time increases. The wavelet transform can characterize local characteristics of signals in a time-frequency domain, but the wavelet transform belongs to a linear time-frequency analysis method as the traditional Fourier analysis method, and cannot describe the instantaneous power spectral density of the signals. Therefore, neither time-frequency analysis nor spectrogram analysis can comprehensively and intuitively reflect all the characteristics of the radio-frequency signal in the time domain and the frequency domain, and the problem of time-frequency resolution compromise becomes the bottleneck of time-frequency characteristic extraction. Furthermore, the frequency information of the signal varies at different times, and it is difficult to find a suitable analysis window to accommodate the entire time period of the signal.
Besides linear time-frequency analysis, a quadratic time-frequency analysis method is also provided. The existing research results show that the time frequency resolution obtained by using quadratic time frequency analysis to process the non-stationary signals is higher, and the quadratic time frequency analysis method is an effective method for processing the non-stationary signals. Such as the Cohen-like time-frequency distribution and the Wigner-Ville distribution (WVD). The Cohen-like time-frequency distribution is proposed by Cohen in the middle of the 60's of the 20 th century, and Cohen finds that many time-frequency distributions are the deformation of WVD and can be uniformly expressed. The Cohen-class time-frequency distribution is two-dimensional Fourier transform of a kernel-weighted fuzzy function, and is also called generalized bilinear time-frequency distribution, WVD has good time-frequency aggregation characteristics, but for multi-component signals, the W-V distribution can generate cross terms, generate false signals and cause interference on the time-frequency characteristics of radio frequency signals, thereby bringing serious influence to signal classification.
The Wigner-Hough transform (WHT) is used for carrying out Hough transform on a signal time-frequency diagram on the basis of WVD, and can inhibit cross term interference. The Hough transform transforms a given curve in the original image space into one point in the parameter space, using the duality of points and lines. The detection problem of a given curve in an original image is converted into a peak value in a parameter space, so that the overall detection characteristic is converted into a local detection characteristic. However, the Hough transform again results in a matrix with too high dimensions after the transform. Dynamic Mode Decomposition (DMD) is physically more significant than conventional dimensionality reduction methods such as Principal Component Analysis (PCA). Therefore, the energy of the matrix can be calculated by the DMD, and the characteristics of the matrix are reflected from the energy perspective. The dynamic information extracted by the DMD is called a dynamic modality, and is used for describing a potential physical mechanism in a dynamic system, or projecting a complex system onto a dynamic system with a very small degree of freedom, so as to extract the dynamic information from the dynamic system. The DMD avoids extracting dynamic information by a model-based method, adopts a data-based process, and is also suitable for experimental and numerical dynamic data. The DMD can reduce the dimensionality of data, and the processed modal matrix can also be used as a characteristic matrix for reflecting matrix information.
Disclosure of Invention
The invention aims to provide a classification system and a classification method based on time-frequency transformation and dynamic mode decomposition aiming at the defects of difficult classification of complex data and low radio frequency signal identification rate transmitted through a complex channel.
In order to achieve the purpose, the following technical scheme is adopted:
the classification system based on time-frequency transformation and dynamic mode decomposition comprises a preprocessing module, a time-frequency analysis module, a dynamic mode decomposition module, an energy feature extraction module, each order moment solving module and a classification module;
the preprocessing module comprises a data truncation unit, a denoising unit and an enhancement unit; the time-frequency analysis module comprises a time-frequency distribution solving unit, a time-frequency relation graph output unit and a Hough transformation unit;
the preprocessing module cuts, denoises and enhances input data and outputs preprocessed signals; the preprocessed signals are output to an H matrix through a time-frequency analysis module, and the H matrix is subjected to dynamic mode decomposition by a dynamic mode decomposition module to obtain a plurality of characteristic values and dynamic modes; the energy characteristic extraction module extracts the first S energy values and the corresponding characteristic values thereof and the dynamic modes according to the sequence from big to small according to the energy value difference between different modes, rearranges the S energy values and the corresponding characteristic values to obtain a transformed characteristic matrix, and each order moment solving module calculates each order moment of the characteristic matrix; the classification module classifies according to each order moment;
the preprocessing module is connected with the video analysis module, the video analysis module is connected with the dynamic mode decomposition module, the dynamic mode decomposition module is connected with the energy feature extraction module, the energy feature extraction module is connected with each order moment solving module, and each order moment solving module is connected with the classification module;
the data truncation unit in the preprocessing module is connected with the denoising unit, and the denoising unit is connected with the enhancement unit;
the classification method based on time-frequency transformation and dynamic mode decomposition comprises the following steps:
step 1, preprocessing acquired data to obtain effective signals;
the preprocessing comprises signal truncation, denoising and enhancement operations;
step 2, performing time-frequency analysis on the effective signals obtained in the step 2 to obtain an H matrix;
the preferable time-frequency analysis is Wigner-Hough transformation, which comprises the steps of solving time-frequency distribution, outputting a time-frequency relation graph and Hough transformation to obtain an H matrix, and the method specifically comprises the following substeps:
step 2.1, solving Wigner-Ville distribution of the effective signals, namely solving Fourier transformation of instantaneous correlation functions of the effective signals, solving time-frequency relations corresponding to the signals, and drawing corresponding time-frequency graphs;
step 2.2, carrying out Hough transformation on the time-frequency diagram to obtain an H matrix reflecting W-H transformation characteristics of the signal;
step 3, performing dynamic mode decomposition on the H matrix obtained in the step 3 to obtain a plurality of characteristic values and dynamic modes;
step 5, extracting the first S elements of the energy characteristic matrix, discarding subsequent data, updating the energy characteristic matrix, and solving the two-norm of the energy characteristic matrix to obtain a transformed characteristic matrix;
s is greater than or equal to 2;
step 6.1, whether the classification is finished or not is judged firstly when the classification starts, if only 1 type of data exists in the data to be classified at the moment, the classification is finished, and if not, the step 6.2 is skipped;
step 6.2, comparing various types of data to be classified, if the mean value of the energy characteristic matrix of certain type of data is always larger than the signals of other types, separating the data, removing the data from the data to be classified, skipping to step 6.1 to judge whether the classification is finished, and skipping to step 6.3 if not;
6.3, comparing various energy characteristic matrixes, if the energy characteristic variance of certain data is always larger than that of other data, classifying the data, removing the data from the data to be classified, skipping to the step 6.1 to judge whether the classification is finished, and if not, skipping to the step 6.4;
step 6.4, comparing the third moment of the energy characteristic matrixes of various types, if the third moment of the energy characteristic matrix of certain type of data is always larger than that of other types of data, classifying the data, removing the data from the data to be classified, skipping to step 6.1 to judge whether the classification is finished, and if not, skipping to step 6.5;
step 6.5, continuously comparing the higher-order moments of the various energy characteristic matrixes until one type of data is removed from the data to be classified;
6.6, sequentially circulating the steps 6.1 to 6.5 until all data are separated;
and 7, outputting a classification result.
Advantageous effects
Compared with the existing classification method, the classification system and method based on time-frequency transformation and dynamic mode decomposition have the following beneficial effects:
1. the classification method adopts W-H transformation, namely Hough transformation is carried out on the basis of Wigner-Ville distribution; the W-H conversion can inhibit noise in signals and reduce interference of cross terms generated in Wigner-Ville distribution;
2. the classification method adopts the DMD, which is a dynamic information extraction mode focusing on data, so that the defect of poor algorithm applicability caused by model-based processing of some extraction algorithms is overcome, and the method is more suitable for processing different types of data; the DMD can conveniently extract time domain change corresponding to the space domain component, the change is called as a dynamic mode and is related to dynamic oscillation frequency attenuation and growth rate;
3. the classification method aims at image data and wireless signals passing through complex channels, and achieves high classification accuracy through preprocessing, time-frequency transformation, DMD decomposition and moment calculation of an energy matrix.
Drawings
FIG. 1 is a diagram of the composition and connection relationship of a classification system based on time-frequency transformation and dynamic mode decomposition according to the present invention;
FIG. 2 is a flowchart illustrating the specific implementation of time-frequency transformation in a classification method based on time-frequency transformation and dynamic mode decomposition according to the present invention;
FIG. 3 is a flowchart of a classification method based on time-frequency transformation and dynamic mode decomposition according to the present invention;
FIG. 4 is a block diagram of a signal processing system for a classification system based on time-frequency transformation and dynamic mode decomposition according to an embodiment of the present invention;
FIG. 5 shows the first moment and second moment results of Iris data set classification when the classification method based on time-frequency transformation and dynamic mode decomposition is implemented.
Detailed Description
The classification system and method based on time-frequency transformation and dynamic mode decomposition according to the present invention will be further described and illustrated in detail with reference to the accompanying drawings and embodiments.
Example 1
This embodiment illustrates a process of classifying an Iris data set in a UCI database by using the method of the present invention. The total amount of data in the Iris dataset is 150; the data dimension is 1x4, and the data category is 3 types. Attributes of data in the Iris dataset include: 1. sepal length in cm, 2 sepal width in cm, 3 petal length in cm, 4 petal width in cm, 5 Class Iris Setosa, Iris Versicolour, and Iris Virginica.
FIG. 1 is a diagram illustrating the components and connections of the classification system based on time-frequency transformation and dynamic mode decomposition; as can be seen from fig. 1, the classification system includes a preprocessing module, a time-frequency analysis module, a dynamic mode decomposition module, an energy feature extraction module, an order moment solving module, and a classification module; and the preprocessing module is connected with the video analysis module, the video analysis module is connected with the dynamic mode decomposition module, the dynamic mode decomposition module is connected with the energy feature extraction module, the energy feature extraction module is connected with each order moment solving module, and each order moment solving module is connected with the classification module.
FIG. 2 is a flow chart of the time-frequency transformation implementation of the classification method based on time-frequency transformation and dynamic mode decomposition; the time-frequency analysis is specifically W-H transform in this embodiment. As can be seen from fig. 2, first, the Wigner-Ville distribution of valid data is obtained, that is, the fourier transform of the instantaneous correlation function of the valid data is obtained, a corresponding time-frequency relationship is obtained, a corresponding time-frequency graph is drawn, then Hough transform is performed on the time-frequency graph, and an H matrix reflecting the W-H transform characteristics of the signal is obtained, because the Hough transform is thought to find the peak value problem of a parameter space, that is, the edge of the image is detected and enhanced, low-frequency noise is generally widely and uniformly distributed in the image, and therefore is not easily detected, the purpose of suppressing noise is achieved, and meanwhile, an interference cross term generated by the Wigner-Ville distribution is also difficult to be detected as the peak value after the Hough transform, so that the purpose of suppressing the interference cross term is also achieved; then decomposing the W-H transformation characteristic matrix H through the DMD, and decomposing the W-H transformation characteristic matrix H into a plurality of characteristic values and dynamic modes; and then rearranging the energy values and the corresponding characteristic values thereof with the dynamic modes according to the difference of the energy values among different modes from large to small to obtain a transformed characteristic matrix.
Fig. 4 and fig. 3 are schematic diagrams of the classification system and the classification method based on time-frequency transformation and dynamic mode decomposition, respectively. As can be seen from fig. 3, the method adopts threshold classification, specifically:
s10, preprocessing the three types of data to be classified in the Iris data set to obtain effective data;
the preprocessing comprises truncation, denoising and enhancement in specific implementation;
s20, performing time-frequency analysis on the effective data obtained in the step S10, wherein Wigner-Hough transformation is obtained to obtain an H matrix;
s20 specifically includes the following substeps:
s21, solving Wigner-Ville distribution of effective data, namely solving Fourier transform of an instantaneous correlation function of the effective signal, solving a time-frequency relation corresponding to the data, and drawing a corresponding time-frequency graph;
s22, carrying out Hough transformation on the time-frequency diagram to obtain an H matrix reflecting W-H transformation characteristics of the signal;
s30, performing DMD decomposition on the H matrix which is obtained in S20 and reflects the W-H transformation characteristics of the signals to obtain a plurality of characteristic values and dynamic modes, and specifically comprising the following substeps:
s31 matrix H obtained based on Hough transformation1 NBy H1 N-1=[H1H2…H N-1 ]And H2 N=[H2…H N-1 H N ]Construction matrix H1 N-1And H2 NAnd H is1 N=[ H1H2…H N-1 H N ]；
S32 according to the matrix H1 N-1And H2 NBy A = H2 NH1 N-1+Constructing a relationship matrix A, H1 N-1+Represents a timing matrix H1 N-1The generalized inverse matrix of (2);
s33, general formula H1 N-1=UΣV*To H1 N-1Performing singular value decomposition;
wherein, the decomposed U and V are unitary matrixes, the matrix sigma is an orthogonal matrix of singular value decomposition, the matrix sigma is a diagonal matrix, and V is*Is the adjoint of V;
s34 according to the matrix H2 NAnd the relation matrix A is formed by B = U*AU constructs an approximate relation matrix B;
wherein, U*Is the companion matrix of U;
s35, performing characteristic decomposition on the approximate relation matrix B to obtain a characteristic value lambda, a characteristic vector omega and a matrix Q consisting of the characteristic vectors;
s36 according to the matrix H2 NMatrix U, matrix Σ, and matrix Q pass Φ = H2 NUΣ+Q, calculating the mode phi of dynamic mode decomposition; wherein, sigma+Is the generalized inverse of the matrix Σ;
thereby decomposing the matrix H into a plurality of eigenvalues and dynamic modes;
s40 rearranging the energy values and the corresponding characteristic values and the dynamic modes from large to small according to the energy values among different modes to form an energy characteristic matrix; then extracting the first three energy values of the energy characteristic matrix, discarding subsequent data, taking the logarithm of the energy values, and then solving the two norms to obtain a transformed characteristic matrix;
s50, threshold classification is carried out based on the characteristic matrix, and the threshold classification method specifically comprises the following substeps:
s51, firstly judging whether the classification is finished when the classification is started, finishing the classification if only 1 type of data exists in the data to be classified at the moment, and jumping to S52 if not;
s52, comparing various energy characteristic matrixes, if the energy characteristic mean value of a certain signal is always larger than that of other signals, separating the signals, removing the signals from the signals to be classified, jumping to S51 to judge whether the classification is finished, and otherwise jumping to the step 8.3;
s53, comparing various energy characteristic matrixes, if the energy characteristic variance of a certain signal is always larger than that of other signals, separating the signals, removing the signals from the signals to be classified, jumping to S51 to judge whether the classification is finished, and otherwise, jumping to S54;
s54, comparing the third moment of the energy characteristic matrixes of various types, if the third moment of the energy characteristic matrix of a certain type of signals is always larger than the signals of other types, separating the signals, removing the signals from the signals to be classified, jumping to S51 to judge whether the classification is finished, and otherwise, jumping to S55;
s55, continuously comparing higher-order moments of various energy characteristic matrixes until one signal is removed from the signals to be classified;
s56, sequentially circulating S51 to S55 until all signals are separated;
and repeating the steps S10 to S56 for multiple times, and counting the classification accuracy.
In specific implementation, WHT is performed on each 1 × 4 data, and an energy average is obtained by DMD. The total number of each kind of data is 50, and the energy of 25 data is taken as the mean value and the variance, so that the results of two experiments are obtained. Selecting 75 data as a first experiment result, and taking the first 25 data of each type; the second experiment result selects 75 data, and takes the last 25 data of each type.
The first moment and second moment results of the two experimental energy matrices are shown in tables 1 and 2, respectively.
TABLE 1 mean (first moment) results of two experiments
| UCI database Iris data Mean | First experiment | Second experiment |
| Iris Setosa | 10.3153 | 10.11495 |
| Iris Versicolour | 10.40695 | 10.30931 |
| Iris Virginica | 12.93793 | 13.12349 |
TABLE 2 mean variance (second moment) results of two experiments
| UCI database Iris data Var | First experiment | Second experiment |
| Iris Setosa | 10.3153 | 10.11495 |
| Iris Versicolour | 10.40695 | 10.30931 |
| Iris Virginica | 12.93793 | 13.12349 |
FIG. 5 shows the first moment and second moment results of Iris data set classification when the classification method based on time-frequency transformation and dynamic mode decomposition is implemented. 5a, the two experiments can be ensured, and the Mean of the Iris Virginica energy matrix is the highest; further based on the second moment value obtained in 5b, Iris Setosa and Iris Versicolor can be distinguished in two experiments.
While the foregoing is directed to the preferred embodiment of the present invention, it is not intended that the invention be limited to the embodiment and the drawings disclosed herein. Equivalents and modifications may be made without departing from the spirit of the disclosure, which is to be considered as within the scope of the invention.
Claims (7)
1. A classification system based on time-frequency transformation and dynamic mode decomposition is characterized in that: the system comprises a preprocessing module, a time-frequency analysis module, a dynamic mode decomposition module, an energy feature extraction module, each order moment solving module and a classification module;
the preprocessing module comprises a data truncation unit, a denoising unit and an enhancement unit; the time-frequency analysis module comprises a time-frequency distribution solving unit, a time-frequency relation graph output unit and a Hough transformation unit;
the preprocessing module is connected with the video analysis module, the video analysis module is connected with the dynamic mode decomposition module, the dynamic mode decomposition module is connected with the energy feature extraction module, the energy feature extraction module is connected with each order moment solving module, and each order moment solving module is connected with the classification module; the data truncation unit in the preprocessing module is connected with the denoising unit, and the denoising unit is connected with the enhancement unit; the preprocessing module cuts, denoises and enhances input data and outputs preprocessed signals; the preprocessed signals are output to an H matrix through a time-frequency analysis module, and the H matrix is subjected to dynamic mode decomposition by a dynamic mode decomposition module to obtain a plurality of characteristic values and dynamic modes; the energy characteristic extraction module extracts the first S energy values and the corresponding characteristic values thereof and the dynamic modes according to the sequence from big to small according to the energy value difference between different modes, rearranges the S energy values and the corresponding characteristic values to obtain a transformed characteristic matrix, and each order moment solving module calculates each order moment of the characteristic matrix; the classification module classifies according to each order moment.
2. A classification method based on time-frequency transformation and dynamic mode decomposition is characterized in that: the method comprises the following steps:
step 1, preprocessing acquired data to obtain effective signals;
step 2, performing time-frequency analysis on the effective signals obtained in the step 2 to obtain an H matrix;
step 3, performing dynamic mode decomposition on the H matrix obtained in the step 3 to obtain a plurality of characteristic values and dynamic modes;
step 4, arranging the energy values of the plurality of dynamic modes in a descending order to obtain ascending energy values, corresponding characteristic values and rearranged dynamic modes, and combining to form an energy characteristic matrix;
step 5, extracting the first S elements of the energy characteristic matrix, discarding subsequent data, updating the energy characteristic matrix, and solving the two-norm of the energy characteristic matrix to obtain a transformed characteristic matrix;
step 6, performing threshold classification based on the transformed feature matrix as data to be classified;
and 7, outputting a classification result.
3. The classification method according to claim 2, characterized in that: and the preprocessing comprises signal truncation, denoising and enhancement operations.
4. The classification method according to claim 2, characterized in that: the time-frequency analysis is Wigner-Hough transformation, and comprises the steps of solving time-frequency distribution, outputting a time-frequency relation graph and Hough transformation to obtain an H matrix.
5. The classification method according to claim 2, characterized in that: step 2, specifically comprising the following substeps:
step 2.1, solving Wigner-Ville distribution of the effective signals, namely solving Fourier transformation of instantaneous correlation functions of the effective signals, solving time-frequency relations corresponding to the signals, and drawing corresponding time-frequency graphs;
and 2.2, carrying out Hough transformation on the time-frequency diagram to obtain an H matrix reflecting the W-H transformation characteristics of the signal.
6. The classification method according to claim 2, characterized in that: and S is more than or equal to 2.
7. The classification method according to claim 2, characterized in that: step 6, specifically comprising the following substeps:
step 6.1, whether the classification is finished or not is judged firstly when the classification starts, if only 1 type of data exists in the data to be classified at the moment, the classification is finished, and if not, the step 6.2 is skipped;
step 6.2, comparing various types of data to be classified, if the mean value of the energy characteristic matrix of certain type of data is always larger than the signals of other types, separating the data, removing the data from the data to be classified, skipping to step 6.1 to judge whether the classification is finished, and skipping to step 6.3 if not;
6.3, comparing various energy characteristic matrixes, if the energy characteristic variance of certain data is always larger than that of other data, classifying the data, removing the data from the data to be classified, skipping to the step 6.1 to judge whether the classification is finished, and if not, skipping to the step 6.4;
step 6.4, comparing the third moment of the energy characteristic matrixes of various types, if the third moment of the energy characteristic matrix of certain type of data is always larger than that of other types of data, classifying the data, removing the data from the data to be classified, skipping to step 6.1 to judge whether the classification is finished, and if not, skipping to step 6.5;
step 6.5, continuously comparing the higher-order moments of the various energy characteristic matrixes until one type of data is removed from the data to be classified;
and 6.6, sequentially circulating the step 6.1 to the step 6.5 until all data are separated.
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