CN111259329A - Propagation matrix modulus optimization fitting method and system based on differential evolution algorithm - Google Patents

Propagation matrix modulus optimization fitting method and system based on differential evolution algorithm Download PDF

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CN111259329A
CN111259329A CN202010104407.4A CN202010104407A CN111259329A CN 111259329 A CN111259329 A CN 111259329A CN 202010104407 A CN202010104407 A CN 202010104407A CN 111259329 A CN111259329 A CN 111259329A
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葛青宇
焦重庆
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North China Electric Power University
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Abstract

The invention relates to a propagation matrix modulus optimization fitting method and system based on a differential evolution algorithm, which comprises the following steps: determining target fitting accuracy tol and a fitting frequency range; determining a pole number range; determining the range of the delay tau; determining a maximum value of a delay coding vector based on the range of the delay tau; determining a pole number code vector maximum based on a range of pole numbers; determining the number of solutions to be N; initializing relevant parameters in an iterative process; performing an iterative calculation based on the correlation parameter; reading solution x with minimum delta in population*Obtaining the number of poles and the time delay contained in the pole, and executing the steps to obtain a new pole; and fitting the modulus of the propagation function matrix by using a vector fitting technology according to the pole number, the delay and the new pole obtained in the step, calculating a fitting error, and outputting a fitting result and the fitting error. The above method of the present invention introduces differential feedingThe nonlinear optimization problem can be solved well by the algorithm, and the efficiency is improved.

Description

Propagation matrix modulus optimization fitting method and system based on differential evolution algorithm
Technical Field
The invention relates to the field of power transmission, in particular to an optimal fitting method and system of propagation matrix modulus based on a differential evolution algorithm.
Background
Power transmission lines are important power transmission devices. In addition to electric equipment and power plant, the rest of the electric power system is a power grid formed by transmission lines, so that the transmission lines cannot replace the electric power systemThe generation has the function of generation. Overvoltage caused by power equipment failure, lightning strike or improper operation has a frequency range much larger than that of normal operation of the system, and contains a large amount of high-frequency components. Therefore, in the transient calculation, a traveling wave model is established for the power transmission line. The traveling wave model regards the change of voltage and current on the power transmission line as a wave process, and incident waves are transmitted from one end of the power transmission line to the other end through time tau, are reflected and reversely transmitted, and are reflected endlessly at the two ends of the power transmission line, so that the change of the voltage and current of each point on the power transmission line is caused, as shown in fig. 2. The traveling wave model can be simply expressed by the equation: i.e. ik(t)＝Yc(t)*vk(t)-2iki(t)iki(t)＝H(t)*imr(t) of (d). Where t denotes a certain time, ikRepresenting the current of port k, vkRepresents the voltage of port k, ikiRepresenting the incident current wave of port k, imrRepresenting reflected current wave, Y, of port mcA characteristic admittance matrix representing the power transmission line, and H represents a propagation function matrix of the power transmission line. The two parameters are obtained in a frequency domain, and the specific expression is as follows:
Figure BDA0002388022220000011
wherein, Z represents the impedance parameter matrix of the unit length of the power transmission line, and Y represents the admittance parameter matrix of the unit length of the power transmission line. l represents the distance between the two ends of the power transmission line, i.e., the length of the power transmission line. In order to facilitate convolution in the time domain in the actual modeling process, a vector fitting method is generally adopted for YcAnd fitting the frequency domain response of the H parameters to obtain a corresponding rational fraction, and converting the rational fraction into a time domain for simulation through an iterative convolution technology.
The matrix of the propagation functions of the power transmission lines is an n x n square matrix,
Figure BDA0002388022220000012
by the phase-mode transformation and vector fitting methods, each element in the matrix can be represented as the sum of some functions,
Figure BDA0002388022220000013
Figure BDA0002388022220000014
wherein HijThe ith row and jth column elements, H, of the matrix representing the propagation functionmkK-th modulus H representing the propagation matrixmAnd the total number of the modulus is G, which is obtained by a phase-mode conversion process.
Further, the k modulus can be expressed as a rational sum
Figure BDA0002388022220000021
Where s denotes the complex frequency, τkRepresenting the propagation delay corresponding to the k modulus; p is a radical ofk,mThe m-th pole representing the k-th modulus, which has a total of NkAnd each pole needs to be obtained by a vector fitting method. The poles of different moduli are mutually independent and are respectively solved; r isk,mAnd representing the residue corresponding to the mth pole of the kth modulus.
The traditional fitting process is as follows: knowing the numerical result of the propagation matrix H, given the frequency range (e.g., 0-1MHz) being modeled, given the upper limit of the number of poles (e.g., 50) being fitted to the model, given the target fitting accuracy (e.g., 0.01), a plurality of moduli H are obtained by phase-to-mode transformationmThen for each modulus, the propagation delay τ is found, starting from the number of poles 1, trying on HmAnd fitting, continuously increasing the number of poles, and adjusting the delay tau until the target fitting precision is reached or the upper limit of the number of poles is reached. In this process, one HmThe final effect of the fitting model can be determined by two parameters, namely the number of poles and the delay size.
The problem is that fitting methods employing successively increasing numbers of poles typically take a significant amount of time to try different numbers of poles one by one given the accuracy of the target fit. The differential evolution algorithm has the characteristics of concise concept, convenient realization and high convergence rate for the nonlinear optimization problem. The basic idea is to simulate the genetic selection and natural elimination of Darwin, and is a method for searching the optimal solution by simulating the natural evolution process.
Therefore, a fitting scheme is improved by combining a differential evolution algorithm, so that model parameters (pole number and delay size) meeting the precision requirement can be quickly found, and a corresponding fitting model is obtained.
Disclosure of Invention
The invention aims to provide an optimal fitting method and system of propagation matrix modulus based on a differential evolution algorithm.
In order to achieve the purpose, the invention provides the following scheme:
a propagation matrix modulus optimization fitting method based on a differential evolution algorithm comprises the following steps:
s1: determining target fitting accuracy tol and a fitting frequency range;
s2: determining a pole number range;
s3: determining the range of the delay tau;
s4: determining a maximum value of a delay coding vector based on the range of the delay τ;
s5: determining a pole number encoding vector maximum based on the range of pole numbers;
s6: determining the number of solutions to be N, wherein N is more than or equal to 100;
s7: initializing relevant parameters in an iterative process;
s8: performing an iterative calculation based on the correlation parameter;
s9: reading solution x with minimum delta in population*Obtaining the number of poles and the time delay contained in the pole, and executing the step S7 to obtain a new pole; the delta represents the difference between the fitting error of the model corresponding to the solution and the target fitting precision tol;
s10: and fitting the modulus of the propagation function matrix by using a vector fitting technology according to the pole number, the delay and the new pole obtained in the step S9, calculating a fitting error, and outputting a fitting result and the fitting error.
Optionally, the following formula is specifically adopted for determining the range of the delay τ:
Figure BDA0002388022220000031
wherein, tauRFor the upper delay limit, τLFor the lower delay limit,. l.is the length of the transmission line, β is the maximum frequency f of the transmission lineRThe phase constant at c is the speed of light.
Optionally, the determining the maximum value of the delay coding vector based on the range of the delay τ specifically adopts the following formula:
Δτmax＝τR-τLwherein, τRFor the upper delay limit, τLIs the lower delay limit.
Optionally, the determining the maximum value of the pole number coding vector based on the range of the pole number specifically adopts the following formula:
Δnmax＝nR-nLwherein n isRUpper limit of the number of poles, nLThe lower limit of the number of poles.
Optionally, the relevant parameters in the computer initialization iterative process specifically include:
s701, setting a threshold belonging to the same category, a mutation operator α and a cross probability β;
s702: generating N initial solutions xi，1≤i≤N：
For the ith initial solution xiGenerating 6+ Z random integers between 0 and 9, and forming a vector according to the sequence; the first six elements of the vector are used as time-delay coding vectors
Figure BDA0002388022220000032
Coding vector delta n with last Z elements as pole numbersi(ii) a Wherein Z represents the maximum value of the pole number code vector Δ nmaxThe number of significant digits of (from the first non-zero high-order digit to the end of the single digit).
The true value of the delay is recovered using the following equation:
Figure BDA0002388022220000041
wherein,
Figure BDA0002388022220000042
represents the vector
Figure BDA0002388022220000043
Converting into a number;
determination of tauiWhether or not greater than τRIf yes, recalculating by using the following formula
Figure BDA0002388022220000044
Figure BDA0002388022220000045
Wherein the symbol [ 2 ]]-1Representing the conversion of numbers into vectors;
the true number of poles is restored using the following equation:
ni＝nL+[Δni]wherein [ Δ n ]i]Representing the vector Δ niConverting into a number;
judging niWhether or not it is greater than nRIf yes, recalculate Δ n using the following equationi，Δni＝[Δnmax]-1Wherein, the symbol [ 2 ]]-1Representing the conversion of numbers into vectors;
s703: for each solution xiDetermining niThe poles required for the fit:
sampling at logarithmic intervals over a range of frequencies to obtain niAt one frequency point, then x is solvediOf the u-th pole puGiven by:
Imu＝2πfu
Figure BDA0002388022220000046
pu＝Reu+jImu
wherein f isuAt the u-th frequency point, ImuIs the u-thImaginary part of individual poles, ReuThe real part of the u-th pole;
s704: fitting the modulus of the propagation function matrix by using a vector fitting technology according to the number and the delay size of the poles required by each solution for fitting and the poles obtained in the step S703, calculating a fitting error and comparing the fitting error with the target fitting precision tol set in the step S1;
fitting error E of ith solution corresponding modeliThe difference value from the target fitting accuracy tol is obtained by the following formula:
δi＝|Ei-tol|
determination of EiSolutions ≦ tol and labeled as potentially optimal solutions xjWherein j is more than or equal to 1 and less than or equal to N*，N*Number of solutions for potential optimization, N*≤N；
Judgment of N*And if the value is equal to 0, returning to the step S701.
Optionally, the performing iterative computation based on the relevant parameter specifically includes:
s801: from the potentially optimal solutions, find the solution x with the minimum δ*If delta is less than or equal to the epsilon, stopping iterative calculation, and turning to the step S9, otherwise, continuing to execute the step S802;
s802: for each potentially optimal solution xjRandomly selecting two solutions from all the solutions, performing difference to obtain a difference vector d, and generating a new solution, x'i＝xj+αd；
S803: to each x'iThe encoded vector of (a) is checked digit by digit as follows:
generating a random number r between 0 and 1, if r > β, x'iThe value on the current digit in the encoded vector is replaced with the solution x with the smallest delta in S801*Encoding the value on the corresponding digit in the vector; x 'after replacement'iIs still recorded as x'i；
S804: executing S702 and S703 once respectively to obtain a new pole;
s805: according to each new solution x'iThe number of poles and the time delay required by the current corresponding fitting are largeFitting the propagation function by using a vector fitting technology, calculating a fitting error and comparing the fitting error with the target fitting accuracy tol set in the step S1, wherein the pole is smaller than the pole obtained in the step 804;
fitting error E of ith new solution corresponding modeliDifference value delta from standard fitting accuracy toliIs obtained by the following formula: delta 'of'i＝|E′i-tol |; if delta'i＜δiAnd E'iLess than or equal to tol, then use x'iReplacement of xi，xiAll replaced, are still recorded as x'i；
S801-S805 are repeated until the preset number of iterations is completed.
Optionally, the preset number of iterations is 50.
Alternatively, α -0.5 and β -0.1.
The invention further provides a propagation matrix modulus optimization fitting system based on a differential evolution algorithm, which comprises:
the target fitting precision and fitting frequency range determining module is used for determining target fitting precision tol and a fitting frequency range;
a pole number range determination module for determining a pole number range;
a delay range determining module, configured to determine a range of the delay τ;
a maximum delay coding vector determining module, configured to determine a maximum delay coding vector based on the range of the delay τ;
a maximum code vector determination module for determining a maximum pole number code vector based on the range of pole numbers;
the number determining module of the solutions is used for determining the number of the solutions to be N, wherein N is more than or equal to 100;
the initialization module is used for initializing relevant parameters in the iterative process;
an iterative calculation module for performing iterative calculation based on the relevant parameters;
a new pole determination module for reading a solution x in a population with a minimum delta*Obtaining the number of poles contained in the magnetic fieldAnd (4) delaying, and executing an initialization module to obtain a new pole.
And the output module is used for fitting the modulus of the propagation function matrix by using a vector fitting technology according to the pole number, the delay and the new pole obtained by the new pole determining module in the step, calculating a fitting error and outputting a fitting result and the fitting error.
Optionally, the following formula is specifically adopted for determining the range of the delay τ:
Figure BDA0002388022220000061
wherein, tauRFor the upper delay limit, τLFor the lower delay limit,. l.is the length of the transmission line, β is the maximum frequency f of the transmission lineRThe phase constant at c is the speed of light.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
compared with the existing fitting process of increasing the number of poles one by one and then adjusting the time delay to search an optimal model, the method introduces a differential evolution algorithm, can well solve the nonlinear optimization problem, and improves the efficiency. The reason is that the differential evolution algorithm tries multiple sets of parameter combinations at the same time, and the parameter combinations are uniformly distributed in the solving range, so that one parameter combination is close to the optimal parameter combination (optimal solution). And in multiple iterations, more and more parameter combinations tend to be the optimal parameter combinations, and one closest optimal parameter combination always exists. Thus, satisfactory parameter combinations can be easily found without a plurality of iterations, and the efficiency is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flowchart of a propagation matrix modulus optimization fitting method based on a differential evolution algorithm according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating the magnitude fitting result of the modulus Hm of the propagation function matrix according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the phase angle fitting result of the modulus Hm of the propagation function matrix according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of a propagation matrix modulus optimization fitting system based on a differential evolution algorithm according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an optimal fitting method and system of propagation matrix modulus based on a differential evolution algorithm.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Take a 100km horizontal three-phase overhead transmission line as an example. The three-phase wires of the circuit are horizontally arranged, and the ground height is 30 m; the horizontal distance between every two is 26.56 m; the lead 8 is split, the outer diameter of the lead is 15mm, and the direct current resistance of the lead is 0.05812 omega/km. The horizontal distance between the two ground wires and the ground is 57.12m, the height of the ground wire is 50m, the outer diameter of the ground wire is 10mm, and the direct current resistance of the ground wire is 0.3601 omega/km. The relative dielectric constant of the soil is 10, and the relative magnetic permeability of the soil is 1. Obtaining three moduli H after propagation function matrix H-phase mode conversionmAnd finding out the first modulus optimal fitting parameter to obtain an optimal fitting result.
Fig. 1 is a flowchart of a propagation matrix modulus optimization fitting method based on a differential evolution algorithm according to an embodiment of the present invention, and as shown in fig. 1, the method includes:
s1: and determining target fitting accuracy tol and a fitting frequency range.
According to the modeling requirement of the power transmission line, the target fitting accuracy tol is set to be 0.002 and the fitting frequency range is set to be 0.5-1MHz in consideration of lightning overvoltage. f. ofR1MHZ is the upper frequency limit, fL0.5MHZ is the lower frequency limit. The set accuracy is used for the accuracy comparison of step 704 with step 805 and the resulting frequency range is used for the frequency sampling in step 702.
S2: a range of pole numbers is determined.
n L1, is the lower limit of the number of poles, n R100 is the upper limit on the number of poles.
S3: the range of the delay τ is determined.
Figure BDA0002388022220000081
Figure BDA0002388022220000082
Wherein, tauRFor the upper delay limit, τLFor lower delay limit, l is the length of transmission line, 1 × 105m, β shows the transmission line is at the highest frequency, β is 0.0217, fRThe phase constant of (c) is the speed of light (c) is 3 × 108m/s。
S4: and determining the maximum value of the delay coding vector based on the range of the delay tau.
Δτmax＝τR-τL＝(3.461284-3.333333)×10-4＝1.30951×10-5S, taking 6 significant digits and recording the significant digits
Figure BDA0002388022220000083
Wherein
Figure BDA0002388022220000084
Equals to the maximum value of the number of poles code vector Δ n calculated in step S5max；Δnmax＝nR-nL100-1-99, giving the number of significant digits, z-2.
S5: determining a pole number encoding vector maximum based on the range of pole numbers.
S6: the number of solutions is determined to be N, N being 100.
S7: the relevant parameters in the iterative process are initialized for the iterative calculation of step S8.
S701: setting threshold e to 1 × 10-6The mutation operator α is 0.5, and the crossover probability β is 0.1.
S702: the N initial solutions x are generated by the following methodi，1≤i≤N：
Taking the first initial solution as an example, 8 random integers (6+ Z) are generated between 0 and 9, and a vector [0,0,8,1,0,9,2,1 ] is formed in sequence]The first six elements "0, 0,8,1,0, 9" of the vector are used as time-lapse encoding vectors
Figure BDA0002388022220000085
The last Z ═ 2 elements "2, 1" as the pole number code vector Δ n1The vector then constitutes the solution x1And recovering the real value of the delay by adopting the following formula:
Figure BDA0002388022220000086
wherein,
Figure BDA0002388022220000087
represents the vector
Figure BDA0002388022220000088
Converting into a number;
determination of tauiWhether or not greater than τRIf yes, recalculating by using the following formula
Figure BDA0002388022220000089
Wherein the symbol [ 2 ]]-1Indicating conversion of numbers into vectors, τ in the above embodiments1＞τRDo not stand and therefore do not need toRecalculation
Figure BDA00023880222200000810
Likewise, the true number of poles is restored using the following equation:
ni＝nL+[Δni]1+ 21-22, where [ Δ n [ ]i]Representing the vector Δ niConverting into a number;
judging niWhether or not it is greater than nRIf yes, recalculate Δ n using the following equationi，Δni＝[Δnmax]-1Wherein, the symbol [ 2 ]]-1Indicating conversion of numbers into vectors, n in the above embodiments1＞nRDoes not hold, so it is not necessary to recalculate Δ n1。
S703: for each solution xiDetermining niThe poles required for the fit:
with x1For example, n is sampled at logarithmic intervals over a frequency range122 frequency points, as shown in table 2:
TABLE 2 initial solution x1Frequency sampling result in step 704
Figure BDA0002388022220000091
Then x is solvediOf the u-th pole puGiven by:
Imu＝2πfu
Figure BDA0002388022220000092
pu＝Reu+jImu
wherein f isuAt the u-th frequency point, ImuIs the imaginary part of the u-th pole, ReuThe real part of the u-th pole, the results are shown in Table 3.
TABLE 3 initial solution x1Step 704, the pole result
Figure BDA0002388022220000093
Figure BDA0002388022220000101
S704: and (4) fitting the modulus of the propagation function matrix by using a vector fitting technology according to the number and the delay size of the poles required by each solution for fitting and the poles obtained in the step (S703), calculating a fitting error and comparing the fitting error with the target fitting accuracy tol set in the step (S1).
Fitting error E of ith solution corresponding modeli(see Table 4) difference value delta from target fitting accuracy toliIs obtained by the following formula:
δi＝|Ei-tol|
TABLE 4 fitting error E of 100 solutions in step 704i
Figure BDA0002388022220000102
Figure BDA0002388022220000111
Find out EiSolutions ≦ tol and labeled as potentially optimal solutions xj(see Table 5), wherein j is 1. ltoreq. N*，N*Number of solutions for potential optimization, N*＝45；
TABLE 5 latent optimal solution numbering
Figure BDA0002388022220000112
Figure BDA0002388022220000121
S8: performing an iterative calculation based on the correlation parameter.
S801: from the potentially optimal solution, find the solution with the minimum δ of 2.71 × 10-5Solution x of*＝[3,6,1,2,9,9,0,6]If delta ≦ e is not satisfied, continue to execute step S802;
s802: for each potentially optimal solution xjE.g. x1Arbitrarily selecting two solutions x from all solutions1,x38And differenced to give a difference vector d, and a new solution was generated by the following equation (see Table 6), x'i＝xj+ α d, rounding down if a decimal occurs in α d, or if x'1If the number in a digit is not in the range 0 to 9, the negative number is directly set to zero and the number greater than 9 is directly set to 9.
TABLE 6 x1In the first iteration step 802, the operation result is obtained
x1 [0,0,8,1,0,9,2,1]
x38 [2,9,9,9,7,3,4,3]
d [-2,-9,-1,-8,-3,6,-2,-2]
x1′ [0,0,8,0,0,9,1,0]
Because, N*45 < N100, all potentially optimal solutions are used at least 2 times, and the first 10 potentially optimal solutions are used three times.
S803: to each x'iThe encoded vector of (a) is checked digit by digit as follows:
with x1For example, a value of 0 to 1 is generatedM-random number r ═ 0.978, r > β ═ 0.1, and x'iThe value on the current digit in the encoded vector is replaced with the solution x with the smallest delta in S801*Encoding the value on the corresponding digit in the vector; x 'after replacement'iIs still recorded as x'i. After checking for 8 bits, x'iOnly bit 5 has no substitution, see Table 7.
TABLE 7 x'iResult after replacement
x* [3 Net 6 Net 1 Net 2 Net 9 Net 0 Net 6]
x′1Before replacement [0,0,8,0,0,9,1,0]
x′1After replacement [3,6,1,2,0,9,0,6]
S804: s702 and S703 are performed once each to obtain a new pole.
X'1For example, at this time, τ1＝3.369463×10-4And 6 poles are shown in table 8.
TABLE 8 x 'in the first iteration'1Pole generated correspondingly
Figure BDA0002388022220000131
S805: according to each new solution x'iFitting the propagation function by using a vector fitting technology according to the number and the delay size of poles required by the current corresponding fitting and the poles obtained in the step 804, calculating a fitting error and comparing the fitting error with the target fitting accuracy tol set in the step S1Comparing;
taking the 1 st new solution as an example, the 1 st new solution corresponds to the fitting error E 'of the model'1Difference value delta 'between 0.00066212090 and standard fitting accuracy tol'1Is obtained by the following formula: delta 'of'i＝|E′i-tol | ═ 0.00066212090-0.002| ═ 0.0013378791, where δ is satisfied'i＜δiAnd E'iLess than or equal to tol, then use x'1Replacement of x1，x1After all are replaced, it is still marked as x1See table 9.
TABLE 9 x in the first iteration1The result after the substitution in step 805
x1Before replacement [0,0,8,1,0,9,2,1]
x1After replacement [3,6,1,2,0,9,0,6]
S806, repeating S801-S805 until 50 iterations are completed.
S9: reading solution x with minimum delta in population*The number of poles contained in the signal is 6 and the time delay is 3.397484 multiplied by 10-4S, (the δ represents the difference between the fitting error of the model corresponding to the solution and the target fitting accuracy tol), and step S702 and step S703 are executed once respectively to obtain a new pole. As shown in table 1:
TABLE 1 computer x after completion of the iteration*Corresponding pole
Figure BDA0002388022220000132
S10: using the vector according to the number of poles, the delay and the new poles obtained in step S9Fitting technique, fitting the modulus of propagation function matrix, calculating fitting error 9.7878 × 10-4And outputting the fitting result and the fitting error. As shown in particular in fig. 2 and 3.
Fig. 4 is a schematic structural diagram of a propagation matrix modulus optimization fitting system based on a differential evolution algorithm according to an embodiment of the present invention, and as shown in fig. 4, the system includes: a target fitting precision and fitting frequency range determination module 201, a pole number range determination module 202, a delay range determination module 203, a delay coding vector maximum determination module 204, a coding vector maximum determination module 205, a number of solutions determination module 206, an initialization module 207, an iterative computation module 208, a new pole determination module 209, and an output module 210;
the target fitting precision and fitting frequency range determining module 201 is configured to determine a target fitting precision tol and a fitting frequency range;
the pole number range determination module 202 is configured to determine a pole number range;
the delay range determining module 203 is used for determining the range of the delay τ;
the maximum delay coding vector determining module 204 is configured to determine a maximum delay coding vector based on the range of the delay τ;
the maximum code vector determination module 205 is configured to determine a maximum pole number code vector based on the range of pole numbers;
the number of solutions determining module 206 is used for determining the number of solutions to be N, wherein N is more than or equal to 100;
the initialization module 207 is used for initializing relevant parameters in an iterative process;
the iterative computation module 208 is configured to perform an iterative computation based on the relevant parameters;
the new pole determination module 209 is used to read the solution x in the population with the minimum delta*And obtaining the number of poles and the time delay contained in the signal, and executing an initialization module to obtain a new pole.
The output module 210 is configured to fit the modulus of the propagation function matrix by using a vector fitting technique according to the number of poles, the delay and the new poles obtained by the new pole determination module in the step, calculate a fitting error, and output a fitting result and the fitting error.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A propagation matrix modulus optimization fitting method based on a differential evolution algorithm is characterized by comprising the following steps:
s1: determining target fitting accuracy tol and a fitting frequency range;
s2: determining a pole number range;
s3: determining the range of the delay tau;
s4: determining a maximum value of a delay coding vector based on the range of the delay τ;
s5: determining a pole number encoding vector maximum based on the range of pole numbers;
s6: determining the number of solutions to be N, wherein N is more than or equal to 100;
s7: initializing relevant parameters in an iterative process;
s8: performing an iterative calculation based on the correlation parameter;
s9: reading solution x with minimum delta in population*Obtaining the number of poles and the time delay contained in the pole, and executing the step S7 to obtain a new pole; the delta represents the difference between the fitting error of the model corresponding to the solution and the target fitting precision tol;
s10: and fitting the modulus of the propagation function matrix by using a vector fitting technology according to the pole number, the delay and the new pole obtained in the step S9, calculating a fitting error, and outputting a fitting result and the fitting error.
2. The propagation matrix modulus optimization fitting method based on the differential evolution algorithm as claimed in claim 1, wherein the range of the determined delay τ is specifically defined by the following formula:
Figure FDA0002388022210000011
wherein, tauRFor the upper delay limit, τLFor the lower delay limit,. l.is the length of the transmission line, β is the maximum frequency f of the transmission lineRThe phase constant at c is the speed of light.
3. The propagation matrix modulus optimization fitting method based on the differential evolution algorithm as claimed in claim 1, wherein the maximum value of the delay coding vector determined based on the range of the delay τ is specifically determined by using the following formula:
Δτmax＝τR-τLwherein, τRFor the upper delay limit, τLIs the lower delay limit.
4. The propagation matrix modulus optimization fitting method based on the differential evolution algorithm as claimed in claim 1, wherein the maximum value of the pole number code vector is determined based on the range of the pole number by using the following formula:
Δnmax＝nR-nLwherein n isRUpper limit of the number of poles, nLThe lower limit of the number of poles.
5. The propagation matrix modulus optimization fitting method based on the differential evolution algorithm as claimed in claim 1, wherein the computer initialization iteration process related parameters specifically include:
s701, setting a threshold belonging to the same category, a mutation operator α and a cross probability β;
s702: generating N initial solutions xi，1≤i≤N：
For the ith initial solution xiGenerating 6+ Z random integers between 0 and 9, and forming a vector according to the sequence; the first six elements of the vector are used as time-delay coding vectors
Figure FDA0002388022210000021
Coding vector delta n by taking last Z noon element as pole numberi(ii) a Wherein Z represents the maximum value of the pole number code vector Δ nmaxThe number of significant digits of (c);
the true value of the delay is recovered using the following equation:
Figure FDA0002388022210000022
wherein,
Figure FDA0002388022210000023
represents the vector
Figure FDA0002388022210000024
Converting into a number;
determination of tauiWhether or not greater than τRIf yes, recalculating by using the following formula
Figure FDA0002388022210000025
Figure FDA0002388022210000026
Wherein the symbol [ 2 ]]-1Representing the conversion of numbers into vectors;
the true number of poles is restored using the following equation:
ni＝nL+[Δni]wherein [ Δ n ]i]Representing the vector Δ niConverting into a number;
judging niWhether or not it is greater than nRIf yes, recalculate Δ n using the following equationi，Δni＝[Δnmax]-1Wherein, the symbol [ 2 ]]-1Indicating conversion of numbers toConverting into a vector;
s703: for each solution xiDetermining niThe poles required for the fit:
sampling at logarithmic intervals over a range of frequencies to obtain niAt one frequency point, then x is solvediOf the u-th pole puGiven by:
Imu＝2πfu
Figure FDA0002388022210000027
pu＝Reu+jImu
wherein f isuAt the u-th frequency point, ImuIs the imaginary part of the u-th pole, ReuThe real part of the u-th pole;
s704: fitting the modulus of the propagation function matrix by using a vector fitting technology according to the number and the delay size of the poles required by each solution for fitting and the poles obtained in the step S703, calculating a fitting error and comparing the fitting error with the target fitting precision tol set in the step S1;
fitting error E of ith solution corresponding modeliThe difference value from the target fitting accuracy tol is obtained by the following formula:
δi＝|Ei-tol|
determination of EiSolutions ≦ tol and labeled as potentially optimal solutions xjWherein j is more than or equal to 1 and less than or equal to N*，N*Number of solutions for potential optimization, N*≤N；
Judgment of N*And if the value is equal to 0, returning to the step S701.
6. The propagation matrix modulus optimization fitting method based on the differential evolution algorithm as claimed in claim 5, wherein the performing iterative computation based on the relevant parameters specifically comprises:
s801: from the potentially optimal solutions, find the solution x with the minimum δ*If delta is less than or equal to epsilon, stopping iterative calculation, and going to step S9, otherwise, continuing to executeStep S802 is performed;
s802: for each potentially optimal solution xjRandomly selecting two solutions from all the solutions, performing difference to obtain a difference vector d, and generating a new solution, x'i＝xj+αd；
S803: to each x'iThe encoded vector of (a) is checked digit by digit as follows:
generating a random number r between 0 and 1, if r > β, x'iThe value on the current digit in the encoded vector is replaced with the solution x with the smallest delta in S801*Encoding the value on the corresponding digit in the vector; x 'after replacement'iIs still recorded as x'i；
S804: executing S702 and S703 once respectively to obtain a new pole;
s805: according to each new solution x'iFitting the propagation function by using a vector fitting technology according to the number and the delay size of the poles required by the current corresponding fitting and the poles obtained in the step 804, calculating a fitting error and comparing the fitting error with the target fitting accuracy tol set in the step S1;
fitting error E of ith new solution corresponding modeliDifference value delta from standard fitting accuracy toliIs obtained by the following formula: delta 'of'i＝|E′i-tol |; if delta'i＜δiAnd E'iLess than or equal to tol, then use x'iReplacement of xi，xiAll replaced, are still recorded as x'i；
S801-S805 are repeated until the preset number of iterations is completed.
7. The differential evolution algorithm-based propagation matrix modulus optimization fitting method according to claim 6, wherein the preset iteration number is 50.
8. The differential evolution algorithm-based propagation matrix modulus optimization fitting method according to claim 5, wherein α -0.5 and β -0.1.
9. A propagation matrix modulus optimization fitting system based on a differential evolution algorithm is characterized by comprising:
the target fitting precision and fitting frequency range determining module is used for determining target fitting precision tol and a fitting frequency range;
a pole number range determination module for determining a pole number range;
a delay range determining module, configured to determine a range of the delay τ;
a maximum delay coding vector determining module, configured to determine a maximum delay coding vector based on the range of the delay τ;
a maximum code vector determination module for determining a maximum pole number code vector based on the range of pole numbers;
the number determining module of the solutions is used for determining the number of the solutions to be N, wherein N is more than or equal to 100;
the initialization module is used for initializing relevant parameters in the iterative process;
an iterative calculation module for performing iterative calculation based on the relevant parameters;
a new pole determination module for reading a solution x in a population with a minimum delta*And obtaining the number of poles and the time delay contained in the signal, and executing an initialization module to obtain a new pole.
And the output module is used for fitting the modulus of the propagation function matrix by using a vector fitting technology according to the pole number, the delay and the new pole obtained by the new pole determining module in the step, calculating a fitting error and outputting a fitting result and the fitting error.
10. The propagation matrix modulus optimization fitting system based on the differential evolution algorithm as claimed in claim 9, wherein the range of the determined delay τ is specifically defined by the following formula:
Figure FDA0002388022210000041
wherein, tauRFor the upper delay limit, τLFor lower delay limit, | is transmission lineLength, β, of the transmission line at the highest frequency fRThe phase constant at c is the speed of light.
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