1. A fitting analysis method of a multi-port system sampling signal is characterized by comprising the following steps:

step S1, data sampling is performed on each port of the multi-port system in sequence to obtain each sampling data f^(p)(0),f^(p)(1)，…，f^(p)(N-1), wherein P is a port number, and P ═ 1,2, …, P being the number of ports; n is the sampling number of each port;

step S2, respectively forming Hankel matrix by the data adopted by each port, numbering the Hankel matrix from 1 to P according to the sequence of the ports, and respectively forming F⁽¹⁾、F⁽²⁾、…、F^(P)；

Step S3, a line vector F is constructed by the Hankel matrix formed by the sampling data of each port according to the port sequence, wherein each vector element is the Hankel matrix of the corresponding numbered port, and the line vector is defined as a Hankel block matrix, namely

F＝[F⁽¹⁾F⁽²⁾…F^(P)]；

Step S4, singular value decomposition is carried out on the row vector F to obtain a left singular matrix U, a right singular matrix V and a characteristic value matrix, and the calculation formula is as follows:

F＝UΣV^H，

wherein, V^HRepresents the conjugate transpose of matrix V;

determining the number m of main eigenvalues according to the ratio of all eigenvalues to the maximum eigenvalue, i.e.

Where λ is a characteristic value, ε is an artificially set threshold value, and m₀＝1,2,…,P；

Then, the right singular vector V is subjected to order reduction treatment according to the number of the obtained main eigenvalues to obtain V',

V'＝[v₁,v₂,…,v_m]，

construction of a reduced order matrix F₁And F₂，

Wherein, V'₁Equal to V 'to delete last line, V'₂Equal to V' deletes the first row;

a reduced matrix bundle F is then constructed₂-λF₁Then, solving generalized eigenvalues of the matrix bundles to obtain a common pole lambda suitable for a plurality of ports to form a common pole matrix;

step S5: respectively forming the sampling data of each port into a column vector f^(p)，

f^(p)＝[f^(p)(0) f^(p)(1) … f^(p)(N-1)]^T，

And the column vectors of the sampled data for all ports form a matrix f,

f＝[f⁽¹⁾ f⁽²⁾ … f^(P)]，

analyzing a matrix f formed by the column vectors of the sampled data and a common pole matrix applicable to a plurality of ports by using a least square method to obtain a residue R meeting the characteristics of sampled signals of each port,

R＝(Z^TZ)^-1Z^Tf，

z is a diagonal matrix formed by the characteristic values lambda, namely the diagonal matrix Z is the same as the diagonal matrix formed by the m common-pole points;

step S6: according to the common pole obtained in the step S4 and the residue obtained in the step S5, respective fitting formulas of different ports are constructed

Where Δ t is the calculation time interval, k is the sampling time sequence number, S is the common-pole, and p is the port sequence number.

And fitting and evaluating transient signals of different ports.

2. The method of claim 1, wherein in step S1, data is sampled sequentially for each port of the multi-port system, and the number of each port is the same.

3. The method for fitting analysis of multi-port system sampling signals according to claim 1, wherein in step S2, the adopted data of each port are respectively formed into Hankel matrix, and the size of different port matrix is the same.

4. The method for fitting analysis of multi-port system sampling signals according to claim 1, wherein in step S6, the calculation time interval Δ t is controlled according to the fitting formula, so as to realize the estimation of the transient response signals of the ports at any time position.

Background

Systems such as power, communication, control and the like generally have complex geometric structures and numerous internal elements, and the entire structure or a part of the structure is subjected to fine modeling in the process of analyzing the transient response characteristics, which is time-consuming and prone to errors. However, in many cases, the analysis of the transient characteristics of a complex system mainly focuses on the performance of a port where information interaction is performed with the outside, and the whole system is regarded as a "black box", and the analysis of the transient response of the system is realized by performing equivalent modeling on the port. To achieve this, a number of techniques of equivalent modeling analysis have been proposed and used. The method for analyzing the limited sampling data at the port and constructing the rational approximation formula capable of reflecting the port characteristics has attracted much attention, especially the Vector Fitting (VF) technique and the matrix bundle method (MPM) therein. However, although the vector fitting technique has better fitting accuracy, it needs a starting pole obtained through multiple iterations before formal analysis, which is not favorable for improving the calculation efficiency of the algorithm.

For the case of multiple ports, a person in the prior art has proposed an MPM with a common pole to handle the data fitting problem of multiple ports, but the proposed method needs to perform superposition processing on the sampled signals of the ports first, which may inevitably result in the loss of information carried in the sampled signals, and the conjugate symmetry condition of the common pole and the residue cannot be automatically realized in the analysis process, thereby increasing the difficulty of the analysis process.

Therefore, the invention provides a fitting analysis method of a multi-port system sampling signal, which can completely reserve the sampling data information of each port and can automatically realize extended MPM (multi-point modulation), namely EMPM (empirical mode modulation) of common pole and residue conjugate matching.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a fitting analysis method of a multi-port system sampling signal, which is different from the prior matrix bundle method for analyzing multi-port sampling data; meanwhile, the method finally realizes the evaluation of the transient signal of the port of the multi-port system, has the characteristics of simple analysis process and complete retention of the port signal, and can effectively improve the efficiency and goodness of fit of the transient characteristic evaluation and equivalent modeling of the port of the complex equipment when being applied to the fields of communication, electric power, control and the like.

The purpose of the invention is realized by the following technical scheme:

a fitting analysis method of a multi-port system sampling signal comprises the following steps:

step S1, data sampling is performed on each port of the multi-port system in sequence to obtain each sampling data f^(p)(0),f^(p)(1)，…，f^(p)(N-1), wherein P is a port number, and P ═ 1,2, …, P being the number of ports; n is the sampling number of each port;

step S2, respectively forming Hankel matrix by the data adopted by each port, numbering the Hankel matrix from 1 to P according to the sequence of the ports, and respectively forming F⁽¹⁾、F⁽²⁾、…、F^(P)；

Step S3, a line vector F is constructed by the Hankel matrix formed by the sampling data of each port according to the port sequence, wherein each vector element is the Hankel matrix of the corresponding numbered port, and the line vector is defined as a Hankel block matrix, namely

F＝[F⁽¹⁾F⁽²⁾…F^(P)]；

Step S4, singular value decomposition is carried out on the row vector F to obtain a left singular matrix U, a right singular matrix V and a characteristic value matrix, and the calculation formula is as follows:

F＝UΣV^H，

wherein, V^HRepresenting the conjugate transpose of matrix V.

Determining the number m of main eigenvalues according to the ratio of all eigenvalues to the maximum eigenvalue, i.e.

Where λ is a characteristic value, ε is an artificially set threshold value, and m₀＝1,2,…,P；

Then, the right singular vector V is subjected to order reduction treatment according to the number of the obtained main eigenvalues to obtain V',

V'＝[v₁,v₂,…,v_m]，

construction of a reduced order matrix F₁And F₂，

F₁＝UΣ'V₁'^H，

F₂＝UΣ'V₂'^H，

Wherein, V₁'equal to V' deletes the last row, V₂'equal to V' deletes the first row;

a reduced matrix bundle F is then constructed₂-λF₁Then, solving generalized eigenvalues of the matrix bundles to obtain a common pole lambda suitable for a plurality of ports to form a common pole matrix;

step S5: respectively forming the sampling data of each port into a column vector f^(p)，

f^(p)＝[f^(p)(0) f^(p)(1)…f^(p)(N-1)]^T，

And the column vectors of the sampled data for all ports form a matrix f,

f＝[f⁽¹⁾ f⁽²⁾…f^(P)]，

analyzing a matrix f formed by the column vectors of the sampled data and a common pole matrix applicable to a plurality of ports by using a least square method to obtain a residue R meeting the characteristics of sampled signals of each port,

R＝(Z^TZ)^-1Z^Tf，

z is a diagonal matrix formed by the characteristic values lambda, namely the diagonal matrix Z is the same as the diagonal matrix formed by the m common-pole points;

step S6: according to the common pole obtained in the step S4 and the residue obtained in the step S5, respective fitting formulas of different ports are constructed

Where Δ t is the calculation time interval, k is the sampling time sequence number, S is the common pole, p is the port sequence number, and e is the natural constant.

And fitting and evaluating transient signals of different ports.

Further, in step S1, data is sequentially sampled for each port of the multi-port system, and the number of the ports is the same.

Further, in step S2, the adopted data of each port are respectively formed into Hankel matrices, and the sizes of different port matrices are the same.

Further, in step S6, the calculation time interval Δ t is controlled according to the fitting formula, so as to realize the estimation of the transient response signal of the port at any time position.

The invention has the beneficial effects that: the invention relates to a fitting analysis method of a multi-port system sampling signal, which is different from the prior matrix bundle method for analyzing multi-port sampling data, and the method does not perform additional processing such as superposition on the sampling signal of a port and the like, thereby completely retaining the sampling information of the port; the least square method is adopted to realize the calculation of the residue number of each port, so that the solution of multiple generalized inversions is avoided, and the calculation complexity is reduced; meanwhile, the method can automatically realize the conjugate symmetry condition of the pole and the residue, and compared with the prior art, the method avoids secondary processing of the relevant matrix of the pole, simplifies the analysis process and reduces the complexity of the analysis process; in addition, the method finally realizes the evaluation of the transient signal of the port of the multi-port system, has the characteristics of simple analysis process and complete retention of the port signal, and can effectively improve the efficiency and goodness of fit of the transient characteristic evaluation and equivalent modeling of the port of the complex equipment when being applied to the fields of communication, electric power, control and the like.

Drawings

FIG. 1 is a flow chart of a fitting analysis method of the present invention;

FIG. 2 is a circuit diagram of a multi-port system (a sinusoidal function pulsed three-port circuit system) in an experimental example of the present invention;

FIG. 3 is a time domain plot of raw measurement results, sampled data, and fit results of the proposed spread matrix bundle method for port P1 in the experimental example;

FIG. 4 is a time domain plot of raw measurement results, sampled data, and fit results of the proposed spread matrix bundle method for port P2 in the experimental example;

FIG. 5 is a time domain plot of the raw measurement results, sampled data, and the fitting results of the proposed spread matrix bundle method for port P3 in the experimental example.

Detailed Description

The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.

As shown in fig. 1, a fitting analysis method for a multi-port system sampling signal includes the following steps:

step S1, data sampling is performed on each port of the multi-port system in sequence to obtain each sampling data f^(p)(0),f^(p)(1)，…，f^(p)(N-1), wherein P is a port number, and P ═ 1,2, …, P being the number of ports; n is the sampling number of each port;

step S2, respectively forming Hankel matrix by the data adopted by each port, numbering the Hankel matrix from 1 to P according to the sequence of the ports, and respectively forming F⁽¹⁾、F⁽²⁾、…、F^(P)；

Step S3, a line vector F is constructed by the Hankel matrix formed by the sampling data of each port according to the port sequence, wherein each vector element is the Hankel matrix of the corresponding numbered port, and the line vector is defined as a Hankel block matrix, namely

F＝[F⁽¹⁾F⁽²⁾…F^(P)]；

Step S4, singular value decomposition is carried out on the row vector F to obtain a left singular matrix U, a right singular matrix V and a characteristic value matrix, and the calculation formula is as follows:

F＝UΣV^H，

wherein, V^HRepresenting the conjugate transpose of matrix V.

Determining the number m of main eigenvalues according to the ratio of all eigenvalues to the maximum eigenvalue, i.e.

Where λ is a characteristic value, ε is an artificially set threshold value, and m₀＝1,2,…,P；

Then, the right singular vector V is subjected to order reduction treatment according to the number of the obtained main eigenvalues to obtain V',

V'＝[v₁,v₂,…,v_m]，

construction of a reduced order matrix F₁And F₂，

F₁＝UΣ'V₁'^H，

F₂＝UΣ'V₂'^H，

Wherein, V₁'equal to V' deletes the last row, V₂'equal to V' deletes the first row;

a reduced matrix bundle F is then constructed₂-λF₁Then, solving generalized eigenvalues of the matrix bundles to obtain a common pole lambda suitable for a plurality of ports to form a common pole matrix;

step S5: respectively forming the sampling data of each port into a column vector f^(p)，

f^(p)＝[f^(p)(0) f^(p)(1)…f^(p)(N-1)]^T，

And the column vectors of the sampled data for all ports form a matrix f,

f＝[f⁽¹⁾ f⁽²⁾…f^(P)]，

analyzing a matrix formed by the column vectors of the sampled data and a public pole matrix applicable to a plurality of ports by using a least square method to obtain a residue R meeting the characteristics of sampled signals of each port,

R＝(Z^TZ)^-1Z^Tf，

z is a diagonal matrix formed by the characteristic values lambda, namely the diagonal matrix Z is the same as the diagonal matrix formed by the m common-pole points;

step S6: according to the common pole obtained in the step S4 and the residue obtained in the step S5, respective fitting formulas of different ports are constructed

Where Δ t is the calculation time interval, k is the sampling time sequence number, S is the common pole, p is the port sequence number, and e is the natural constant.

And fitting and evaluating transient signals of different ports.

Specifically, in step S1, data is sampled sequentially for each port of the multi-port system, and the number of the ports is the same.

Specifically, in step S2, the adopted data of each port are respectively combined into Hankel matrices, and the sizes of different port matrices are the same.

Specifically, in step S6, the calculation time interval Δ t is controlled according to the fitting formula, and the estimation of the transient response signal of the port at any time position is realized.

Examples of the experiments

The fitting analysis method for the multi-port system sampling signal is adopted to carry out fitting analysis, and specifically comprises the following steps:

step 1, firstly, sampling port data of a multi-port object (as shown in figure 2) to be researched, wherein the sampling number of each port is the same and is set as N;

step 2, respectively using the sampling data of each port to construct a corresponding Hankel matrix, wherein the sizes of different port matrixes are the same, and numbering is carried out on all Hankel matrixes according to the sequence set for the ports, and the number is 1 to 3 because the number of the ports is 3 in the example;

step 3, arranging the Hankel matrixes of the three ports into a row vector F, wherein each element of the vector is the Hankel matrix corresponding to the port with the corresponding serial number, and the vector is defined as a Hankel block matrix;

step 4, carrying out singular value decomposition on the Hankel block matrix to obtain a left singular matrix U, a right singular matrix V and a characteristic value matrix;

step 5, determining the number m of eigenvalues playing an important role in the data according to the characteristics of each eigenvalue in the eigenvalue matrix;

step 6, processing the right singular matrix V according to m, and constructing a reduced matrix F of the F₁And F₂；

Step 7, for F₁And F₂Formed matrix bundle F₂-λF₁Processing and solving F₂Relative to F₁The corresponding element of the eigenvalue lambda is the common pole point of the three ports;

step 8, three column vectors are formed by the sampling data of the three ports, an Nx 3 matrix f is formed by the three column vectors, the matrix formed by the sampling data and the common pole matrix applicable to the plurality of ports are analyzed by using a least square method, and the residue R-Z (Z) meeting the sampling signal characteristics of each port is obtained^TZ)^-1Z^TAnd f, wherein Z is a diagonal matrix formed by the characteristic values lambda.

Step 9, constructing respective fitting formulas of different ports according to the common poles and the residue numbers obtained in the steps 7 and 8,

step 10, according to the fitting formula in step 9, the size of the time interval Δ t is controlled and calculated, and the evaluation of the port transient response signal at any time position can be realized, as shown in fig. 3, 4 and 5, at the ports P1, P2 and P3, on the basis of the sampling data, the sampling data is analyzed by using the method, and the fitting result obtained has very good coincidence with the actual original test data.

The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.