CN110210152B - Ultrahigh-order harmonic source modeling method - Google Patents

Ultrahigh-order harmonic source modeling method Download PDF

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CN110210152B
CN110210152B CN201910494902.8A CN201910494902A CN110210152B CN 110210152 B CN110210152 B CN 110210152B CN 201910494902 A CN201910494902 A CN 201910494902A CN 110210152 B CN110210152 B CN 110210152B
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张逸
阮正鑫
方键
邵振国
张嫣
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Fuzhou University
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Abstract

The invention relates to an ultrahigh-order harmonic source modeling method, which comprises the following steps of S1: providing ultra-high harmonic current time series data under different powers in any time period; step S2: training the data of the step S1 by using a neural network algorithm; step S3: generating prediction data of each ultrahigh harmonic current amplitude under different powers by using a neural network algorithm; step S4: error calculation is performed on the predicted data and the measured value generated in step S3, and a performance evaluation coefficient R with the smallest error is selected according to the error calculation result2Selecting R at a given calculation accuracy epsilon2Value fitting curve is used as fitting result; step S5: and (5) analyzing and judging the final fitting result of the step (S4), and if the error between the obtained predicted value and the actually measured value is within the range, obtaining a trained neural network model. The invention can predict the output ultra-high harmonic current characteristic of any one ultra-high harmonic source so as to take necessary treatment measures in advance or filter by a more appropriate filter.

Description

Ultrahigh-order harmonic source modeling method
Technical Field
The invention relates to the field of power electronics, in particular to an ultrahigh harmonic source modeling method.
Background
With the rapid development of modern industries, transportation, finance, information and other industries and the implementation of energy saving, consumption reduction and environmental protection policies, clean and efficient energy utilization becomes the mainstream. The high density access of a large amount of distributed energy sources and the wide application of flexible power transmission technology enable the power distribution network to show a 'source-network-load' tight coupling characteristic. When the power system supplies power to the nonlinear equipment and the loads, the nonlinear equipment and the loads transmit, convert and absorb fundamental wave energy supplied by the system generator, convert part of the fundamental wave energy into harmonic wave energy, and return the harmonic wave energy to the power system to become a main ultrahigh-order harmonic wave source of the power grid.
At present, with the permeability of electrical equipment such as wind power converters, photovoltaic inverters, electric vehicle charging piles and the like in a power grid becoming higher and higher, the generated ultra-high harmonics cause more and more power quality problems, such as intermittent operation or function failure of the equipment, incapability of operating or damage of the equipment, power carrier communication failure, noise emission of the equipment or devices and the like, and the damage becomes more and more serious undoubtedly in the future. Therefore, the propagation characteristic of the ultra-high harmonic in the power grid is accurately estimated, the actual condition of the ultra-high harmonic in the power grid is accurately mastered, and the method is necessary for preventing the harm of the ultra-high harmonic and maintaining the safe operation of the power grid.
The most common harmonic source modeling methods at present mainly include the following methods: (1) constant current source model and norton equivalent model: although the model is easy to process, the model is too simple and rough and is easy to cause large errors. And the atypical running condition is not considered, so that the accuracy and the application range of the model are reduced. (2) Simplified model based on cross-frequency admittance matrix: although the model considers the mechanism of harmonic generation more, no theoretical basis proves that the characteristics of the harmonic source can be linearized at a certain operating point, and the model only corresponds to a certain operating point and has different harmonic source models for different operating points. (3) A harmonic current expression model is established for a topological circuit structure of a common power electronic device, and the amplitude and the phase angle of each harmonic current generated on an alternating current side are obtained through Fourier analysis. The premise of the above-mentioned modeling is that, assuming that the structure of the harmonic source is unchanged, when the structure is slightly changed, the relationship changes, and the analytical modeling must be performed again.
Disclosure of Invention
In view of this, the present invention provides an ultrahigh-order harmonic source modeling method, which can predict the output ultrahigh-order harmonic current characteristic of any one ultrahigh-order harmonic source, so as to take necessary treatment measures in advance or select a more appropriate filter for filtering.
The invention is realized by adopting the following scheme: an ultrahigh-order harmonic source modeling method comprises the following steps:
step S1: providing ultra-high harmonic current time series data under different powers in any time period;
step S2: training the ultra-high harmonic current time series data under different powers by using a neural network algorithm;
step S3: generating prediction data of each ultrahigh harmonic current amplitude under different powers by using a neural network algorithm;
step S4: performing error calculation on the prediction data and the actual measurement value generated in step S3, namely the super-harmonic current time-series data under different powers mentioned in step S1, and selecting a performance evaluation coefficient R with the minimum error according to the error calculation result2Selecting R at a given calculation accuracy epsilon2The value fitting curve is used as a fitting result to obtain the output characteristic of the ultrahigh harmonic source;
step S5: and analyzing and judging the final fitting result of the step S4, if the error between the obtained predicted value and the actually measured value is within 0.0001-0.000001, obtaining a trained neural network model, inputting the power value and the frequency of the ultrahigh harmonic source into the trained neural network model, and outputting the predicted value of the output current amplitude of the ultrahigh harmonic source with the required frequency under the power by the model.
Further, the step S2 specifically includes the following steps:
step S21: providing ultrahigh harmonic current value data corresponding to different frequencies under different powers, comprising: input vector of input layer, hidden layer input vector
Figure BDA0002087608860000031
Hidden layer output vector
Figure BDA0002087608860000032
Output layer input vector
Figure BDA0002087608860000033
And an output vector of the output layer;
wherein the input vector of the input layer includes the power of the ultra-high harmonic source
Figure BDA0002087608860000034
Ultra-high order harmonic frequency
Figure BDA0002087608860000035
And the amplitude of the current actually measured by the ultra-high order harmonic source
Figure BDA0002087608860000036
The output vector of the output layer includes the power of the ultra-high harmonic source
Figure BDA0002087608860000037
Ultra-high order harmonic frequency
Figure BDA0002087608860000038
And ultrahigh harmonic source predicted current amplitude
Figure BDA0002087608860000039
Establishing a neural network model, wherein an input layer has 2 nodes, an output layer has 1 node, and an empirical formula is utilized: s is 2n +1, wherein n is the number of nodes of the input layer, and the number of nodes of the hidden layer is calculated to be 5; the number of the nodes is gradually increased on the hidden layer of 5 nodes, when the number of the nodes is increased to 10, the network error of the node number is increased and is not reduced, and the node selection number is optimal.
Step S22: connection weight omega for input layer and hidden layerihThe connection weight omega of the hidden layer and the output layerhoThreshold b of each neuron in the hidden layerhAnd threshold b of each neuron of output layeroRespectively make one [ -11 ]]Random number inside, and let the error function be:
Figure BDA0002087608860000041
setting the range of the calculation precision value epsilon to be 0.0001-0.000001 as a training termination condition, and setting the range of the maximum learning times M to be 1000-; the learning rate is selected in the range of 0.01-0.8;
step S23: normalizing the ultrahigh harmonic current value data corresponding to different frequencies under different powers in the step S21 to [01] by adopting an S-shaped activation function;
step S24: randomly selecting a group of input samples, i.e. the data x (k) of the ultra-high harmonic current values corresponding to different frequencies at different powers in step S21 and the corresponding expected outputs d (k);
wherein the ultra high harmonic current value data x (k) includes power of an ultra high harmonic source
Figure BDA0002087608860000042
Ultra-high order harmonic frequency
Figure BDA0002087608860000043
And the amplitude of the current actually measured by the ultra-high order harmonic source
Figure BDA0002087608860000044
Step S25: computing input hi for each neuron in the hidden layerh(k) Then using the input and the laser
Live function calculation of output ho of each neuron of hidden layerh(k)：
Figure BDA0002087608860000045
In the formula, ωihWeights, x, for input layer neurons pointing to hidden layer neuronsi(k) For data on the ith neuron in the kth set of data, bhA threshold value for each neuron of the hidden layer;
input hi of neurons in the hidden layerh(k) Passing through Sigmoid type functions:
Figure BDA0002087608860000046
the mapping of (a) yields the output ho of each neuron of the hidden layerh(k)
hoh(k)＝f(hih(k))
Step S26: calculating input yi of each neuron of output layero(k) Then using input and activation function to calculate output yo of each neuron in output layero(k)：
Figure BDA0002087608860000051
In the formula, ωhoWeights, ho, for neurons of the hidden layer to neurons of the output layerh(k) For the output of neurons of the hidden layer, boIs the threshold value of each neuron in the output layer;
input yi of each neuron of output layero(k) Passing through Sigmoid type functions:
Figure BDA0002087608860000052
the mapping of (2) obtains the output yo of each neuron of the output layero(k)
yoo(k)＝f(yio(k))
Step S27: calculating partial derivative delta of error function to each neuron of output layero(k)：
δo(k)＝(do(k)-yoo(k))yoo(k)(1-yoo(k))
Step S28: using the connection weight omega from the hidden layer to the output layerho(k) Partial derivative delta of error function to each neuron of output layero(k) And output ho of hidden layerh(k) Calculating partial derivative delta of error function to each neuron of hidden layerh(k)：
Figure BDA0002087608860000053
Step S29: using error functions for neurons of the output layerPartial derivative deltao(k) And output ho of neurons of the hidden layerh(k) To correct the connection weight omegaho(k) And a threshold value bo(k)：
Figure BDA0002087608860000054
Figure BDA0002087608860000055
Figure BDA0002087608860000056
In order to adjust the connection weight value after the adjustment,
Figure BDA0002087608860000057
in order to adjust the connection weight before the adjustment,
Figure BDA0002087608860000058
in order to achieve the adjusted threshold value, the threshold value is,
Figure BDA0002087608860000059
the threshold before adjustment is adopted, eta is the learning rate and takes a value between (0, 1);
step S210: partial derivative delta of each neuron in hidden layer by using error functionh(k) And input x of each neuron of input layeri(k) Modifying the connection weight and the threshold value;
Figure BDA0002087608860000061
Figure BDA0002087608860000062
Figure BDA0002087608860000063
in order to adjust the connection weight value after the adjustment,
Figure BDA0002087608860000064
in order to adjust the connection weight before the adjustment,
Figure BDA0002087608860000065
in order to achieve the adjusted threshold value, the threshold value is,
Figure BDA0002087608860000066
the threshold before adjustment is adopted, eta is the learning rate and takes a value between (0, 1);
step S211: according to the output vector of the output layer, i.e. including the power of the ultra-high harmonic source
Figure BDA0002087608860000067
Ultra-high order harmonic frequency
Figure BDA0002087608860000068
And ultrahigh harmonic source predicted current amplitude
Figure BDA0002087608860000069
Corresponding desired output do(k) Calculating a global error E:
Figure BDA00020876088600000610
step S212: judging whether the network error meets the requirement, and finishing the algorithm when E is less than epsilon or the learning times is more than the set maximum times M; otherwise, the next learning sample and the corresponding expected output are randomly selected, and the process returns to step S24 to enter the next learning process.
Further, the step S4 specifically includes the following steps:
step S41: if the algorithm is finished, performing inverse normalization on output data of the neural network algorithm result to obtain a real value;
step S42: evaluating the predicted value of the current amplitude of the ultrahigh harmonic source according to the performance evaluation coefficient R of the neural network2：
Figure BDA0002087608860000071
Figure BDA0002087608860000072
The current amplitude prediction value of the ultra-high order harmonic wave of the ith data is obtained; y isiThe current amplitude real value of the ultrahigh harmonic wave of the ith data; n is the number of data to select a final fitting result curve so as to obtain the output characteristic of the ultrahigh harmonic source; evaluation of coefficient R for neural network Performance2Of selected value of R2The closer the value is to 1, the better the training effect is, the better the model fitting is, and the well-trained neural network model can be obtained; so that R under a given calculation accuracy epsilon is selected2And taking a fitting curve of the values as a fitting result, and further obtaining the output characteristic of the ultrahigh harmonic source.
Further, the step S5 specifically includes the following steps:
step S51: the power of the ultra-high harmonic source to the input data of the neural network model trained in step S4
Figure BDA0002087608860000073
And ultra-high harmonic frequency
Figure BDA0002087608860000074
Step S52, the trained neural network model outputs data
Figure BDA0002087608860000075
That is, the predicted current amplitude of the specific frequency input in step S51 at the power specified in step S51 by the ultra-high harmonic source;
step S53: and obtaining the output characteristic of the predicted ultra-high harmonic source.
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention can predict the output ultra-high harmonic current characteristic of any one ultra-high harmonic source so as to take necessary treatment measures in advance or select a more appropriate filter for filtering.
(2) The method realizes the analysis of harmonic sources with complex topological structures and variable operating conditions, has the advantages of short training time, high precision and dynamic modeling, and is an effective method for modeling the harmonic sources.
Drawings
Fig. 1 is a frequency spectrum diagram of ultrahigh harmonic current output by an electric vehicle charging pile under different powers according to an embodiment of the invention.
Fig. 2 is a frequency spectrum diagram of an ultra-high harmonic current output by an electric vehicle charging pile under a certain power according to an embodiment of the invention.
FIG. 3 is a flowchart illustrating ultra-high harmonic source characteristic estimation according to an embodiment of the invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
As shown in fig. 3, the present embodiment provides an ultrahigh-order harmonic source modeling method, including the following steps:
step S1: providing ultra-high harmonic current time sequence data under different powers which can represent the operating conditions of the ultra-high harmonic source within any time period;
step S2: training the ultra-high harmonic current time series data under different powers by using a neural network algorithm;
step S3: generating prediction data of each ultrahigh harmonic current amplitude under different powers by using a neural network algorithm;
step S4: performing error calculation on the predicted data and the measured value generated in step S3, i.e. the super-harmonic current time-series data (or simulated value) under different powers mentioned in step S1, and selecting the performance evaluation coefficient R with the minimum error according to the error calculation result2Selecting R at a given calculation accuracy epsilon2The value fitting curve is used as a fitting result to obtain the output characteristic of the ultrahigh harmonic source; coefficient of performance evaluation R2Value R2The closer the value is to 1, the more variables in the equation in step S42 are indicated
Figure BDA0002087608860000091
(prediction value of ultrahigh harmonic current amplitude of ith data) to yiThe stronger the interpretation ability of the (true value of the ultrahigh harmonic current amplitude of the ith data), the better the training effect, and the better the model fits the data;
step S5: and analyzing and judging the final fitting result of the step S4, if the error between the obtained predicted value and the actually measured value is within 0.0001-0.000001, obtaining a trained neural network model, inputting the power value and the frequency of the ultrahigh harmonic source into the trained neural network model, and outputting the predicted value of the output current amplitude of the ultrahigh harmonic source with the required frequency under the power by the model.
In this embodiment, the step S2 specifically includes the following steps:
step S21: providing ultrahigh harmonic current value data corresponding to different frequencies under different powers, comprising: input vector of input layer, hidden layer input vector
Figure BDA0002087608860000092
Hidden layer output vector
Figure BDA0002087608860000093
Output layer input vector
Figure BDA0002087608860000094
And an output vector of the output layer;
wherein the input vector of the input layer includes the power of the ultra-high harmonic source
Figure BDA0002087608860000095
Ultra-high order harmonic frequency
Figure BDA0002087608860000096
And the amplitude of the current actually measured by the ultra-high order harmonic source
Figure BDA0002087608860000097
The output vector of the output layer includes the power of the ultra-high harmonic source
Figure BDA0002087608860000098
Ultra-high order harmonic frequency
Figure BDA0002087608860000099
And ultrahigh harmonic source predicted current amplitude
Figure BDA00020876088600000910
Establishing a neural network model, wherein an input layer has 2 nodes, an output layer has 1 node, and an empirical formula is utilized: s is 2n +1, wherein n is the number of nodes of the input layer, and the number of nodes of the hidden layer is calculated to be 5; the number of the nodes is gradually increased on the hidden layer of 5 nodes, when the number of the nodes is increased to 10, the network error of the node number is increased, the network error is not obviously reduced, and the node selection number is optimal.
Step S22: connection weight omega for input layer and hidden layerihThe connection weight omega of the hidden layer and the output layerhoThreshold b of each neuron in the hidden layerhAnd threshold b of each neuron of output layeroRespectively make one [ -11 ]]Random number inside, and let the error function be:
Figure BDA0002087608860000101
setting the range of the calculation precision value epsilon to be 0.0001-0.000001 as a training termination condition, and setting the range of the maximum learning times M to be 1000-; the learning rate is selected in the range of 0.01-0.8;
step S23: normalizing the ultrahigh harmonic current value data corresponding to different frequencies under different powers in the step S21 to [01] by adopting an S-shaped activation function;
step S24: randomly selecting a group of input samples, i.e. the data x (k) of the ultra-high harmonic current values corresponding to different frequencies at different powers in step S21 and the corresponding expected outputs d (k);
wherein the ultra high harmonic current value data x (k) includes power of an ultra high harmonic source
Figure BDA0002087608860000102
Ultra-high order harmonic frequency
Figure BDA0002087608860000103
And the amplitude of the current actually measured by the ultra-high order harmonic source
Figure BDA0002087608860000104
Step S25: computing input hi for each neuron in the hidden layerh(k) Then, the output ho of each neuron in the hidden layer is calculated by using the input and the activation functionh(k)：
Figure BDA0002087608860000105
In the formula, ωihWeights, x, for input layer neurons pointing to hidden layer neuronsi(k) For data on the ith neuron in the kth set of data, bhA threshold value for each neuron of the hidden layer;
input hi of neurons in the hidden layerh(k) Passing through Sigmoid type functions:
Figure BDA0002087608860000106
the mapping of (a) yields the output ho of each neuron of the hidden layerh(k)
hoh(k)＝f(hih(k))
Step S26: calculating input yi of each neuron of output layero(k) Then using input and activation function to calculate output yo of each neuron in output layero(k)：
Figure BDA0002087608860000107
In the formula, ωhoWeights, ho, for neurons of the hidden layer to neurons of the output layerh(k) For the output of neurons of the hidden layer, boIs the threshold value of each neuron in the output layer;
input of each neuron of output layeryio(k) Passing through Sigmoid type functions:
Figure BDA0002087608860000111
the mapping of (2) obtains the output yo of each neuron of the output layero(k)
yoo(k)＝f(yio(k))
Step S27: calculating partial derivative delta of error function to each neuron of output layero(k)：
δo(k)＝(do(k)-yoo(k))yoo(k)(1-yoo(k))
Step S28: using the connection weight omega from the hidden layer to the output layerho(k) Partial derivative delta of error function to each neuron of output layero(k) And output ho of hidden layerh(k) Calculating partial derivative delta of error function to each neuron of hidden layerh(k)：
Figure BDA0002087608860000112
Step S29: partial derivative delta of each neuron of output layer by using error functiono(k) And output ho of neurons of the hidden layerh(k) To correct the connection weight omegaho(k) And a threshold value bo(k)：
Figure BDA0002087608860000113
Figure BDA0002087608860000114
Figure BDA0002087608860000115
In order to adjust the connection weight value after the adjustment,
Figure BDA0002087608860000116
in order to adjust the connection weight before the adjustment,
Figure BDA0002087608860000117
in order to achieve the adjusted threshold value, the threshold value is,
Figure BDA0002087608860000118
for the threshold before adjustment, η is the learning rate and is taken between (0, 1).
Step S210: partial derivatives delta of neurons in the hidden layer using error functionsh(k) And input x of each neuron of input layeri(k) Modifying the connection weight and the threshold value;
Figure BDA0002087608860000121
Figure BDA0002087608860000122
Figure BDA0002087608860000123
in order to adjust the connection weight value after the adjustment,
Figure BDA0002087608860000124
in order to adjust the connection weight before the adjustment,
Figure BDA0002087608860000125
in order to achieve the adjusted threshold value, the threshold value is,
Figure BDA0002087608860000126
for the threshold before adjustment, η is the learning rate and is taken between (0, 1).
Step S211: according to the output vector of the output layer, i.e. including the power of the ultra-high harmonic source
Figure BDA0002087608860000127
Ultra-high order harmonic frequency
Figure BDA0002087608860000128
And ultrahigh harmonic source predicted current amplitude
Figure BDA0002087608860000129
Corresponding desired output do(k) Calculating a global error E:
Figure BDA00020876088600001210
step S212: judging whether the network error meets the requirement, and finishing the algorithm when E is less than epsilon or the learning times is more than the set maximum times M; otherwise, the next learning sample and the corresponding expected output are randomly selected, and the process returns to step S24 to enter the next learning process.
In this embodiment, the step S4 specifically includes the following steps:
step S41: if the algorithm is finished, performing inverse normalization on output data of the neural network algorithm result to obtain a real value;
step S42: evaluating the predicted value of the current amplitude of the ultrahigh harmonic source according to the performance evaluation coefficient R of the neural network2：
Figure BDA00020876088600001211
Figure BDA0002087608860000131
The current amplitude prediction value of the ultra-high order harmonic wave of the ith data is obtained; y isiThe current amplitude real value of the ultrahigh harmonic wave of the ith data; n is the number of data to select a final fitting result curve so as to obtain the output characteristic of the ultrahigh harmonic source; evaluation of coefficient R for neural network Performance2Of selected value of R2The closer the value is to 1, the better the training effect is, the better the model fitting is, and the well-trained neural network model can be obtained; so that R under a given calculation accuracy epsilon is selected2And taking a fitting curve of the values as a fitting result, and further obtaining the output characteristic of the ultrahigh harmonic source.
In this embodiment, the step S5 specifically includes the following steps:
step S51: the power of the ultra-high harmonic source to the input data of the neural network model trained in step S4
Figure BDA0002087608860000132
And ultra-high harmonic frequency
Figure BDA0002087608860000133
Step S52, the trained neural network model outputs data
Figure BDA0002087608860000134
That is, the predicted current amplitude of the specific frequency input in step S51 at the power specified in step S51 by the ultra-high harmonic source;
step S53: and obtaining the output characteristic of the predicted ultra-high harmonic source.
Preferably, the implementation process of this embodiment is as follows: the method mainly comprises the following steps:
(1) acquiring ultrahigh harmonic current data or current data obtained by simulation within a period of time, which is acquired by an electric energy quality tester, from an ultrahigh harmonic source output end, and forming time series data;
(2) training the super-high harmonic current time series data under different powers by using a neural network algorithm;
(3) generating prediction data of each sub-ultrahigh harmonic current amplitude under a series of different powers by using a neural network algorithm;
(4) error calculation is carried out on the generated prediction data and the measured value (or the simulated value), and a performance evaluation coefficient R with the minimum error is selected according to the error calculation result2(coefficient of Performance evaluation R2Value R2The closer the value is to 1, the better the training effect, the better the model fitting), the appropriate R is selected2The fitting curve of the values is used as a fitting result, and further the output characteristic of the ultrahigh harmonic source is obtained;
(5) and inputting the power value and the frequency of the ultrahigh harmonic source to the trained neural network model, and outputting the predicted value of the output current amplitude of the ultrahigh harmonic source with the required frequency under the power by the model.
As shown in fig. 1 below, the output ultrahigh harmonic current value of the electric vehicle charging pile under different powers is obtained. FIG. 2 shows the value of the super-high harmonic current at a certain power, which is compared with the predicted value of the harmonic current of the super-high harmonic source at the same power obtained by the neural network algorithm, and R is selected2And analyzing the fitting curve when the voltage is 0.95433 as a fitting result, and further obtaining the output characteristic of the ultrahigh harmonic current of the electric automobile charging pile.
In the embodiment, the model is established by training actual measurement data or data obtained by simulation of the ultra-high harmonic source under different powers. The ultra-high harmonic current output frequency spectrum characteristic of the ultra-high harmonic source under a certain power condition is obtained.
In the embodiment, the ultrahigh harmonic current data (which can be from a large number of actual measurements or simulations) output by the ultrahigh harmonic source is trained, the output data of the network is compared with the actual data, and the weight is changed according to the learning rule until the difference between the output data and the actual data of the network reaches the required error range, so that the ultrahigh harmonic model is established.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (2)

1. An ultrahigh-order harmonic source modeling method is characterized in that: the method comprises the following steps:
step S1: providing ultra-high harmonic current time series data under different powers in any time period;
step S2: training the ultra-high harmonic current time series data under different powers by using a neural network algorithm;
step S3: generating prediction data of each ultrahigh harmonic current amplitude under different powers by using a neural network algorithm;
step S4: the predicted data and actual measurement value generated in step S3The ultra-high harmonic current time-series data under different powers mentioned in the step S1 are subjected to error calculation, and according to the error calculation result, a performance evaluation coefficient R with the minimum error is selected2Selecting R at a given calculation accuracy epsilon2The value fitting curve is used as a fitting result to obtain the output characteristic of the ultrahigh harmonic source;
step S5: analyzing and judging the final fitting result of the step S4, if the error between the obtained predicted value and the measured value is within 0.0001-0.000001, obtaining a trained neural network model, inputting the power value and the frequency of the ultra-high harmonic source to the trained neural network model, and outputting the predicted value of the output current amplitude of the ultra-high harmonic source with the required frequency under the power by the model;
wherein, the step S4 specifically includes the following steps:
step S41: if the algorithm is finished, performing inverse normalization on output data of the neural network algorithm result to obtain a real value;
step S42: evaluating the predicted value of the current amplitude of the ultrahigh harmonic source according to the performance evaluation coefficient R of the neural network2：
Figure FDA0002743729180000021
Figure FDA0002743729180000022
The current amplitude prediction value of the ultra-high order harmonic wave of the ith data is obtained; y isiThe current amplitude real value of the ultrahigh harmonic wave of the ith data; n is the number of data to select a final fitting result curve so as to obtain the output characteristic of the ultrahigh harmonic source; evaluation of coefficient R for neural network Performance2Of selected value of R2The closer the value is to 1, the better the training effect is, the better the model fitting is, and the well-trained neural network model can be obtained; so that R under a given calculation accuracy epsilon is selected2The fitting curve of the values is used as a fitting result, and further the output characteristic of the ultrahigh harmonic source is obtained;
wherein, the step S5 specifically includes the following steps:
step S51: the power of the ultra-high harmonic source to the input data of the neural network model trained in step S4
Figure FDA0002743729180000023
And ultra-high harmonic frequency
Figure FDA0002743729180000024
Step S52, the trained neural network model outputs data
Figure FDA0002743729180000025
That is, the predicted current amplitude of the specific frequency input in step S51 at the power specified in step S51 by the ultra-high harmonic source;
step S53: and obtaining the output characteristic of the predicted ultra-high harmonic source.
2. The modeling method for an ultra-high order harmonic source of claim 1, wherein: the step S2 specifically includes the following steps:
step S21: providing ultrahigh harmonic current value data corresponding to different frequencies under different powers, comprising: input vector of input layer, hidden layer input vector
Figure FDA0002743729180000026
Hidden layer output vector
Figure FDA0002743729180000031
Output layer input vector
Figure FDA0002743729180000032
And an output vector of the output layer;
wherein the input vector of the input layer includes the power of the ultra-high harmonic source
Figure FDA0002743729180000033
Ultra-high order harmonic frequency
Figure FDA0002743729180000034
And the amplitude of the current actually measured by the ultra-high order harmonic source
Figure FDA0002743729180000035
The output vector of the output layer includes the power of the ultra-high harmonic source
Figure FDA0002743729180000036
Ultra-high order harmonic frequency
Figure FDA0002743729180000037
And ultrahigh harmonic source predicted current amplitude
Figure FDA0002743729180000038
Establishing a neural network model, wherein an input layer has 2 nodes, an output layer has 1 node, and an empirical formula is utilized: s is 2n +1, wherein n is the number of nodes of the input layer, and the number of nodes of the hidden layer is calculated to be 5; gradually increasing the number of nodes on the hidden layer by 5 nodes, increasing the number of nodes when the number of nodes is increased to 10, and preventing the network error from being reduced, wherein the number of node selection is optimal;
step S22: connection weight omega for input layer and hidden layerihThe connection weight omega of the hidden layer and the output layerhoThreshold b of each neuron in the hidden layerhAnd threshold b of each neuron of output layeroRespectively make one [ -1, 1 [ -1 [ ]]Random number inside, and let the error function be:
Figure FDA0002743729180000039
setting the range of the calculation precision value epsilon to be 0.0001-0.000001 as a training termination condition, and setting the range of the maximum learning times M to be 1000-; the learning rate is selected in the range of 0.01-0.8;
step S23: normalizing the ultrahigh harmonic current value data corresponding to different frequencies under different powers in the step S21 to [0, 1] by adopting an S-shaped activation function;
step S24: randomly selecting a group of input samples, i.e. the data x (k) of the ultra-high harmonic current values corresponding to different frequencies at different powers in step S21 and the corresponding expected outputs d (k);
wherein the ultra high harmonic current value data x (k) includes power of an ultra high harmonic source
Figure FDA00027437291800000310
Ultra-high order harmonic frequency
Figure FDA00027437291800000311
And the amplitude of the current actually measured by the ultra-high order harmonic source
Figure FDA00027437291800000312
Step S25: computing input hi for each neuron in the hidden layerh(k) Then, the output ho of each neuron in the hidden layer is calculated by using the input and the activation functionh(k)：
Figure FDA0002743729180000041
In the formula, ωihWeights, x, for input layer neurons pointing to hidden layer neuronsi(k) For data on the ith neuron in the kth set of data, bhA threshold value for each neuron of the hidden layer;
input hi of neurons in the hidden layerh(k) Passing through Sigmoid type functions:
Figure FDA0002743729180000042
the mapping of (a) yields the output ho of each neuron of the hidden layerh(k)
hoh(k)＝f(hih(k))
Step S26: calculating input yi of each neuron of output layero(k),Then, the output yo of each neuron in the output layer is calculated by using the input and the activation functiono(k)：
Figure FDA0002743729180000044
In the formula, ωhoWeights, ho, for neurons of the hidden layer to neurons of the output layerh(k) For the output of neurons of the hidden layer, boIs the threshold value of each neuron in the output layer;
input yi of each neuron of output layero(k) Passing through Sigmoid type functions:
Figure FDA0002743729180000043
the mapping of (2) obtains the output yo of each neuron of the output layero(k)
yoo(k)＝f(yio(k))
Step S27: calculating partial derivative delta of error function to each neuron of output layero(k)：
δo(k)＝(do(k)-yoo(k))yoo(k)(1-yoo(k))
Step S28: using the connection weight omega from the hidden layer to the output layerho(k) Partial derivative delta of error function to each neuron of output layero(k) And output ho of hidden layerh(k) Calculating partial derivative delta of error function to each neuron of hidden layerh(k)：
Figure FDA0002743729180000051
Step S29: partial derivative delta of each neuron of output layer by using error functiono(k) And output ho of neurons of the hidden layerh(k) To correct the connection weight omegaho(k) And a threshold value bo(k)：
Figure FDA0002743729180000052
Figure FDA0002743729180000053
Figure FDA0002743729180000054
In order to adjust the connection weight value after the adjustment,
Figure FDA0002743729180000055
in order to adjust the connection weight before the adjustment,
Figure FDA0002743729180000056
in order to achieve the adjusted threshold value, the threshold value is,
Figure FDA0002743729180000057
the threshold before adjustment is adopted, eta is the learning rate and takes a value between (0, 1);
step S210: partial derivative delta of each neuron in hidden layer by using error functionh(k) And input x of each neuron of input layeri(k) Modifying the connection weight and the threshold value;
Figure FDA0002743729180000058
Figure FDA0002743729180000059
Figure FDA00027437291800000510
in order to adjust the connection weight value after the adjustment,
Figure FDA00027437291800000511
in order to adjust the connection weight before the adjustment,
Figure FDA00027437291800000512
in order to achieve the adjusted threshold value, the threshold value is,
Figure FDA00027437291800000513
the threshold before adjustment is adopted, eta is the learning rate and takes a value between (0, 1);
step S211: according to the output vector of the output layer, i.e. including the power of the ultra-high harmonic source
Figure FDA00027437291800000514
Ultra-high order harmonic frequency
Figure FDA00027437291800000515
And ultrahigh harmonic source predicted current amplitude
Figure FDA00027437291800000516
Corresponding desired output do(k) Calculating a global error E:
Figure FDA00027437291800000517
step S212: judging whether the network error meets the requirement, and finishing the algorithm when E is less than epsilon or the learning times is more than the set maximum times M; otherwise, the next learning sample and the corresponding expected output are randomly selected, and the process returns to step S24 to enter the next learning process.
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