CN101478069B - Microwave filter assistant debugging method based on nuclear machine learning - Google Patents

Abstract

The invention discloses a microwave filter auxiliary debugging method based on kernel machine study, which mainly solves the problem that the prior art that does not construct a relationship model between the bolt adjustment amount and variable quantities of a coupling matrix. The method comprises the following steps: extracting the coupling matrix and processing data according to parameters of a filter S in engineering measurement to obtain normalized data sample sets of the bolt adjustment amount and the variable quantities of the coupling matrix; constructing the model of the influences of the bolt adjustment amount on the variable quantities of the coupling matrix by using the kernel machine study algorithm according to the sample sets; constructing an optimal adjustment model of the bolt adjustment amount of the filter according to the study model of the machine; and solving the optimal adjustment model to obtain the adjustment amount of each adjusting bolt of the filter. The method can rapidly and accurately carry out auxiliary debugging of the filter, and can be used for auxiliary debugging of mass-produced filters.

Description

Microwave filter assistant debugging method based on nuclear machine learning

Technical field

The invention belongs to the art of microwave filters field, specifically a kind of microwave filter assistant debugging method based on nuclear machine learning is used for the debugging of guidance or assisted microwave synthesis filter.

Background technology

Microwave filter is widely used in the communication system.In actual production, because the impact of machining accuracy and rigging error, the debugging of filter is indispensable.Yet, since the adjustment bolt of filter on electrical property to affect rule very complicated so that the debugging operational difficulties.At present all be to rely on artificial experience to debug in the engineering, more time-consuming, the effort of debug process, and need that the commissioning staff's is experienced; For new commissioning staff, be difficult to competent such work.If the production in enormous quantities filter will be engaged a lot of veteran commissioning staffs usually, so that the production cost of filter increases cycle stretch-out.Therefore, in order to alleviate the difficulty of filter debugging, shorten debug time and to reducing the requirement of commissioning staff's commissioning experience, study microwave filter assistant debugging method with the debugging of guidance and help filter, this is very important.

At present, at home and abroad disclosed microwave filter assistant debugging method mainly contains following several:

(1) Optimization Debugging of use equivalent-circuit model and coupling matrix.According to the actual measurement S parameter of filter, adopt optimization method to approach the coupling matrix that obtains time domain and frequency-domain equivalent circuit model, then compare with desirable (design) coupling matrix, instruct debugging according to the difference between them.This method only provides the difference between the coupling matrix, can not obtain filter and adjust the adjustment amount of bolt directly to instruct the engineering staff to debug.As at Masoud Kahrzi, Safieddin Safavi-Naeini, Sujeet K.Chaudhuri, et al.Computer Diagnosis and Tuning of RF and Microwave Filters Using Model-Based Parameter Estimation.IEEE Transactions on Circuits and Systems, vol.49, no.9 has adopted the equivalent model of frequency domain to obtain coupling matrix in 2002..In " space electronic technology " document of the 1st phase in 2004 " a kind of new method of the auxiliary debugging of machine of microwave filter " (Li Shengxian waits), adopted time domain approach to obtain its coupling matrix.

(2) method of adjustment of the extraction of use coupling matrix and sensitivity.The method extracts by the method for optimizing and obtains coupling matrix, and then the linearisation hypothesis is adopted in sensitivity, has set up the approximate model between bolt adjustment amount and the coupling matrix variable quantity.Because the relation between bolt adjustment amount and the coupling matrix variable quantity is nonlinear, linearizing restriction of assumption the range of application of the method.This method is at Peter Harscher, Rudiger Vahldieck, Smain Amari.Automated Filter Tuning Using Generalized Low-Pass Prototype Networks and Gradient-Based Parameter Extraction.IEEE Transaction on Microwave Theory and Techniques, vol.49, no.12 has report in 2001..

(3) the machine learning method of adjustment of Schema-based identification and Adaptive Signal Processing technology.The method adopts the clustering method in the pattern recognition that the S supplemental characteristic of actual measurement is extracted and obtains characteristic parameter, use the Adaptive Signal Processing technology set up bolt adjustment amount and characteristic parameter between relational model.The deficiency that the method is used is the accuracy of feature extracting.The method is at document Ahmad R.Mirzai, Colin F.N.Cowean, Tom M.Crawford.Intelligent Alignment of Waveguide Filters Using a Machine Learning Approach.IEEE Transaction on Microwave Theory and Techniques, vol.37, no.1 has report in 1989..

(4) based on the aided debugging method of fuzzy logic.The method is utilized the integrated approach of fuzzy logic, coupling matrix and the human expert info realization assistant adjustment that combines.Yet the method can only provide the difference between the coupling matrix, can not the amount of being adjusted directly instructing the engineering staff to debug, and exist and need more fuzzy rule base and the difficulty of data sample and acquirement of expert knowledge.The method is at document Vahid Miraftab, Raafat R.Computer-aided Tuning of Microwave Filters Using Fuzzy Logic, IEEE Transaction on Microwave Theory and Techniques, vol.50, no.12 has report in 2002..

There is following defective in the filter assistant debugging method that top document proposes: 1) extract coupling matrix from filter actual measurement S parameter, and with design coupling matrix contrast, the method can only provide the difference between the two, can not directly provide the adjustment amount of filter bolt, can't in the engineering of reality, use.2) adjustment amount adopts the linearisation hypothesis to the sensitivity of coupling matrix variable quantity impact, and this hypothesis does not conform to the actual conditions and closes, so that the debugging effect is restricted.3) there is the difficulty that needs the accurate extraction of more fuzzy rule base and data sample and characteristic parameter and acquirement of expert knowledge in the method for adjustment based on fuzzy logic and pattern recognition.

Summary of the invention

The objective of the invention is to avoid now methodical deficiency, a kind of microwave filter assistant debugging method based on nuclear machine learning is provided, it can be used for the debugging of guidance or assisted microwave synthesis filter.It relatively is fit to shorten debug time, improve the debugging efficiency of filter in the microwave filter debugging of large-scale mass production.

The technical scheme that realizes the object of the invention is according to the filter S parameter of measuring in the engineering, by extracting its coupling matrix and carrying out data and process, to obtain the set of data samples of normalized bolt adjustment amount and coupling matrix variable quantity; According to these sample sets, use the nuclear machine learning algorithm to set up the model of bolt adjustment amount on the impact of coupling matrix variable quantity, by revising desirable coupling matrix, obtained the machine learning model of bolt adjustment amount on the electrical property impact; According to this machine learning model, made up the optimum adjustment model of filter bolt adjustment amount at last; Find the solution this optimum adjustment model, each adjusts the adjustment amount of bolt to calculate filter.Detailed process comprises:

(1) presets benchmark D for one ₀Filter, vow that by changing bolt adjustment amount Δ D, using net measures corresponding filter transformation parameter S ₂₁With reflection parameters S ₁₁

(2) according to the S that measures ₂₁And S ₁₁, extract corresponding coupling matrix, obtain bolt adjustment amount and the corresponding coupling matrix set of data samples Г of experiment;

(3) data sample set Г is carried out normalization, the data set Z of the coupling matrix variable quantity of the bolt adjustment amount that obtains testing and correspondence;

(4) according to resulting data set Z, utilize the nuclear machine learning algorithm to set up nuclear machine learning model Δ M between bolt adjustment amount and the coupling matrix variable quantity:

4a) set of the data sample after normalization Z is divided into training sample T and test samples V two parts, wherein training sample T accounts for 4/5 of data sample sum, and remaining data sample is test samples V;

4b) according to training sample T, the least square support vector regression in the use nuclear machine learning algorithm is set up respectively the meta-model Δ m of each unit variation amount in bolt adjustment amount and the coupling matrix _Ij:

4b1) according to training sample set T, use the least square support vector regression, in high-dimensional feature space, make up respectively the meta-model Δ m of each unit of coupling matrix and bolt adjustment amount Δ D _Ij:

ω is weight vectors in the formula, and b is bias term, Expression Nonlinear Mapping function;

4b2) regression model with above-mentioned high-dimensional feature space is converted into:

Min：

s.t.

...，M

E in the formula _kBe ij the error that the relative measured data of meta-model is calculated, C is the compromise of models fitting precision and model complexity, K data sample of ij unit in the expression coupling matrix, M represents the number of samples of training sample T, Δ D _kRepresent k bolt adjustment amount data sample;

4b3) introduce Lagrange multiplier α=[α ₁, α ₂..., α _M] ^T, structure LagrangianL (ω, b, e _k, α) be:

4b4) respectively to the variable ω in the above-mentioned formula, b, e _k, α asks local derviation, obtains system of linear equations after the arrangement:

$\left(\begin{array}{cc}\mathrm{\&Omega;}+\frac{1}{C}I& I\\ I^{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="H2009100209533E00042.png,H2009100209533E00051.png"\; state="\{\{state\}\}">T</figure-callout>}}& 0\end{array}\right)\left(\begin{array}{c}\mathrm{\&alpha;}\\ b\end{array}\right)=\left(\begin{array}{c}\mathrm{\&Delta;<figure-callout\; id="0"\; label="m"\; filenames="H2009100209533E00042.png,H2009100209533E00051.png"\; state="\{\{state\}\}">m</figure-callout>}\\ 0\end{array}\right)$

Each element in the formula among the matrix in block form Ω satisfies I is unit matrix,

The vector that expression coupling matrix unit variable quantity forms;

4b5) find the solution above-mentioned system of linear equations, obtain And b;

4b6) introduce kernel function Finally obtain the meta-model in the ij unit variation amount in the coupling matrix:

$\mathrm{\&Delta;}{m}_{\mathrm{ij}}=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{k}K(\mathrm{\&Delta;D},\mathrm{\&Delta;}{D}_k)+b,$

K(ΔD，ΔD _k)＝exp(-σ ^-2||ΔD-ΔD _k|| ²)，

Or $K(\mathrm{\&Delta;D},\mathrm{\&Delta;}{D}_k)=\underset{h=1}{\overset{n}{\mathrm{\&Pi;}}}(1-\frac{{\left|\right|\mathrm{\&Delta;D}-\mathrm{\&Delta;}{D}_k^h\left|\right|}^2}{{\mathrm{\&sigma;}}^2})\exp (-\frac{{\left|\right|\mathrm{\&Delta;D}-\mathrm{\&Delta;}{D}_k^h\left|\right|}^2}{{2\mathrm{\&sigma;}}^2}),$

In the formula

Represent h component of k data sample, σ represents nuclear parameter, and n represents the number of translation invariant Mexico hat wavelet function base;

4c) utilize all meta-model Δ m among the test samples V checking nuclear machine learning model Δ M _IjAccuracy, if the accuracy of model the expectation scope in, then use these models; Otherwise, turn back to step 4b) again modeling, until the accuracy of model meets the demands, the Accuracy evaluation formula that uses in the checking is:

$\mathrm{AAE}=L^{-1}\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}\left|(\mathrm{\&Delta;}{m}_{\mathrm{ij}}^k-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^k)\right|,$

$\mathrm{MAE}=\max \left(\right|\mathrm{\&Delta;}{m}_{\mathrm{ij}}^1-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{<figure-callout\; id="1"\; label="ij"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">ij</figure-callout>}}^1|,...,|\mathrm{\&Delta;}{m}_{\mathrm{ij}}^L-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^L\left|\right),$

In the formula: AAE is the average absolute value error, and MAE is the maximum value error,

Ij unit variation value in the coupling matrix that represents to measure for the k time,

Be k the numerical value that sample calculates by ij meta-model, L represents the number of samples of test samples V;

4d) to verifying each correct meta-model, according to the structure composition form of filter, combination obtains the nuclear machine learning model Δ M of the actual adjustment amount of bolt and coupling matrix variable quantity:

ΔM＝f(ΔD)，

ΔL＝ΔD ^Tr，

F represents above-mentioned meta-model Δ m in the formula _IjAccording to the Nonlinear Mapping function that the combination of filter construction form obtains, r represents the bolt pitch that microwave filter uses, after Δ L represents that bolt has rotated Δ D circle when adjusting, and the variable quantity that the screw-in depth relative datum of bolt occurs;

(5) use Δ M to the coupling matrix correction, set up the bolt adjustment amount of experiment to the machine learning model of filter electrical property impact

With

5a) use machine learning model Δ M to revise desirable coupling matrix M ₀, obtaining the bolt adjustment amount is actual coupling matrix M corresponding to Δ D:

M＝M ₀+ΔM；

5b) according to actual coupling matrix M, set up coupling matrix and filter electrical property

With

Relation:

$S_{21}^{\mathrm{mode}l}\left(f\right)=-2j\sqrt{R_1{R}_2}{\left[A^{-1}\right]}_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">n</figure-callout>}1}$

${\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{mode}l}\left(f\right)=1+2j\sqrt{R_1}{\left[A^{-1}\right]}_{11},$

$A=\frac{f_0}{\mathrm{BW}}(\frac{f}{f_0}-\frac{f_0}{f})I-\mathrm{jR}+M$

I is unit matrix in the formula, and BW represents the filter bandwidht that designs, f ₀The filter center frequency of expression design, f represents the actual operating frequency of filter, R ₁The coupling of expression filter input end mouth and adjacent resonators, R ₂The coupling of expression filter output mouth and adjacent resonators, j represents the imaginary part of plural number, matrix A ^-1In subscript n 1 and 11 represent that respectively transmission characteristic and the reflection characteristic of n rank filter, R represent filter input and output and outside coupling matrix:

$R=\left[\begin{array}{ccccc}{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">R</figure-callout>}}_1& 0& 0& ....& 0\\ 0& 0& 0& ...& 0\\ 0& 0& 0& ...& 0\\ .& .& .& & .\\ .& .& .& ...& .\\ .& .& .& & .\\ 0& 0& 0& ...& {\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="H2009100209533E00042.png,H2009100209533E00052.png"\; state="\{\{state\}\}">R</figure-callout>}}_2\end{array}\right];$

(6) according to machine learning model

With

Off-line set up microwave filter experiment the bolt adjustment amount optimize and revise model:

6a) according to above-mentioned 5b) process foundation

With

Relation, corresponding off resonance adjustment amount Δ D before calculating filter is adjusted ₁:

Find：ΔD ₁

Min： $\underset{f_i=\mathrm{Sfreq}}{\overset{\mathrm{Efreq}}{\mathrm{\&Sigma;}}}[{(S_{21}^{\mathrm{measure}}\left(f_i\right)-S_{21}^{\mathrm{mode}l}\left(f_i\right))}^2+{({\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{measure}}\left(f_i\right)-{\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{mode}l}\left(f_i\right))}^2],$

s.t. $\mathrm{\&Delta;}{D}_1^L\&le;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\&le;\mathrm{\&Delta;}{D}_1^U$

In the formula

With

The lower bound and the upper bound that represent respectively the filter bolt adjustment amount of permission,

With

Be illustrated respectively in f _iThe transformation parameter that individual Frequency point measures and reflection parameters numerical value,

With

Be illustrated respectively in f _iTransformation parameter and reflection parameters numerical value that individual Frequency point utilizes machine learning model to calculate, Sfreq and Efreq represent respectively the sample initial frequency point that obtains and finish Frequency point of filter operating frequency;

6b) according to 5b) set up

With

Relation, the bolt adjustment amount Δ D that needs when calculating filter is transferred to target by current off resonance state ₂

Find：ΔD ₂

Min： $\underset{f_i=\mathrm{Sfreq}}{\overset{\mathrm{Efreq}}{\mathrm{\&Sigma;}}}[{(S_{21}^{t\arg \mathrm{et}}\left(f_i\right)-S_{21}^{\mathrm{mode}l}\left(f_i\right))}^2+{(S_{11}^{t\arg \mathrm{et}}\left(f_i\right)-{\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{mode}l}\left(f_i\right))}^2],$

s.t. $\mathrm{\&Delta;}{D}_2^L\&le;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="H2009100209533E00042.png,H2009100209533E00052.png"\; state="\{\{state\}\}">D</figure-callout>}}_2\&le;\mathrm{\&Delta;}{D}_2^U$

In the formula With

Be illustrated respectively in f _iTarget debugging transformation parameter and the reflection parameters numerical value of individual Frequency point, it is given by design in advance,

With Be illustrated respectively in f _iTransformation parameter and reflection parameters numerical value that individual Frequency point utilizes machine learning model to calculate,

With

Respectively lower bound and the upper bound of the bolt adjustment amount of the filter that allows of expression; Sfreq and Efreq represent respectively the sample initial frequency point that obtains and finish Frequency point of filter operating frequency;

The as a result Δ D that 6c) obtains according to above-mentioned optimization ₁With Δ D ₂, the bolt adjustment amount that calculates filter is Δ D:

ΔD＝ΔD ₂-ΔD ₁；

(7) with described transformation parameter S ₂₁With reflection parameters S ₁₁Be input to above-mentioned optimizing and revising in the model, in line computation, obtain the actual adjustment amount of each bolt of filter by computer, ancillary works personnel carry out the filter debugging.

The present invention has following advantage:

(1) the present invention can directly obtain the adjustment amount of each bolt owing to the relational model of having set up between bolt adjustment amount and the filter electrical property when optimizing and revising, thereby uses step examination just can adjust to filter the target of expectation.

(2) the present invention assists adjustment model because off-line is set up the filter that contains the engineering debug experience, and adopts in line computation when using, and can obtain fast the concrete adjustment amount of bolt, has shortened debug time, has improved debugging efficiency.

(3) the present invention uses in the filter assistant adjustment of the same type that is suitable for producing in enormous quantities in engineering because the nuclear machine learning algorithm in the employing artificial intelligence is set up the assistant adjustment model of filter.

Description of drawings

Fig. 1 is the structural representation of existing microwave filter;

Fig. 2 is the equivalent circuit diagram of existing microwave filter;

Fig. 3 is aided debugging method flow chart of the present invention;

Fig. 4 is the bright flow charts of setting up bolt adjustment amount and electrical property relation of we;

Fig. 5 is the experimental system of existing four chamber spiral microwave filters;

Fig. 6 uses the filter bolt adjustment amount that the present invention obtains;

Fig. 7 uses filter that the present invention the obtains S21 performance comparison before and after adjusting;

Fig. 8 uses filter that the present invention the obtains S11 performance comparison before and after adjusting;

Fig. 9 uses filter that the present invention the obtains group delay performance comparison before and after adjusting.

Embodiment

Referring to accompanying drawing the present invention is described in further detail.

With reference to Fig. 1, assistant adjustment of the present invention uses existing microwave filter mainly by n resonant element, tuning bolt t _iWith coupling bolt c _iConsist of.In the aided debugging method of filter, its physical structure is converted into corresponding equivalent electric circuit, such as Fig. 2, m among Fig. 2 _IjCoupling between expression resonant element i and the resonant element j, it is cell value in the filter coupled matrix M, ω _iThe resonance frequency that represents i resonant element, R ₁And R ₂Be respectively the coupling of filter input end mouth and output port and adjacent resonant element.

With reference to Fig. 3, the implementation process of the inventive method is as follows:

The first step changes bolt adjustment amount Δ D, uses and vows that net measures corresponding filter transformation parameter S ₂₁With reflection parameters S ₁₁

For a concrete filter, before producing in enormous quantities, the Design of microwave filters personnel by specialty ask according to technique, at first filter are debugged optimum state, and are this setting state benchmark.This benchmark has been specified the initial position D of the filter bolt of producing in enormous quantities ₀And corresponding target coupling matrix M ₀Experiment according to design changes bolt adjustment amount Δ D at every turn, then obtains the transformation parameter S of filter from vector network analyzer ₂₁With reflection parameters S ₁₁

Second step is according to the S that measures ₂₁And S ₁₁, extract coupling matrix, obtain bolt adjustment amount and corresponding coupling matrix set of data samples Г.

In order to obtain coupling matrix M _i, use the equivalent electric circuit of Fig. 2, and be optimized extraction with following objective function F:

$F=\underset{\mathrm{freq}}{\mathrm{\&Sigma;}}\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{2}{\mathrm{\&Sigma;}}}[{(\mathrm{Re}\left(S_{\mathrm{ij}}^m\right)-\mathrm{Re}\left(S_{\mathrm{ij}}^c\right))}^2+{(\mathrm{Im}\left(S_{\mathrm{ij}}^m\right)-\mathrm{Im}\left(S_{\mathrm{ij}}^c\right))}^2]---\left(1\right)$

In the formula

With The S that represents respectively actual measurement _IjThe S that parameter and equivalent-circuit model calculate _IjParameter, Re and Im represent respectively S _IjThe real part of parameter and imaginary part, freq represent the to sample frequency of the filter that obtains.

According to objective function F and microwave designing software ADS, the S that respectively vector network analyzer is recorded ₂₁And S ₁₁, extract corresponding coupling matrix M _i, obtain N data sample Г={ (Δ D _i, M _i), i=1,2 ..., N}.

In the 3rd step, normalized data sample Г obtains the data set Z of bolt adjustment amount and corresponding coupling matrix variable quantity.

Before data sample normalization, at first calculate the variation delta M that corresponding coupling matrix produces _i:

ΔM _i＝M _i-M ₀ (2)

Then, use the linear-scale method for normalizing to data set { (Δ D _i, Δ M _i), i=1,2 ..., N} processes, and obtains data sample set after the normalization

Wherein With

The variable quantity that represents respectively normalized bolt adjustment amount and coupling matrix.

In the 4th step, set up the bolt adjustment amount to the machine learning model of filter electrical property impact

With

According to the data sample set Z that obtains, at first utilize the nuclear machine learning algorithm to set up nuclear machine learning model Δ M between bolt adjustment amount and the coupling matrix variable quantity, then use Δ M to the coupling matrix correction, set up at last the bolt adjustment amount of experiment to the machine learning model of filter electrical property impact

With

As shown in Figure 4.

With reference to Fig. 4, the specific implementation process is as follows:

1) set of the data sample after normalization Z is divided into training sample T and test samples V two parts, wherein training data sample T accounts for 4/5 of data sample sum, is used for setting up the nuclear machine learning model between bolt adjustment amount and the coupling matrix variable quantity; Check data sample V is used for the accuracy of verification model.

2) according to training sample T, use the nuclear machine learning algorithm to set up respectively the meta-model Δ m of each unit variation amount in bolt adjustment amount and the coupling matrix _Ij

At data acquisition system Z={ (Δ D _i, Δ M _i), i=1,2 ..., among the N}, according to the physical structure that filter adopts, the coupling matrix Δ M of filter _iGenerally be expressed as:

$\mathrm{\&Delta;}{M}_i=\left[\begin{array}{cccc}\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="11"\; label="m"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">m</figure-callout>}}_{11}& \mathrm{\&Delta;}{m}_{12}& ...& \mathrm{\&Delta;}{m}_{1n}\\ \mathrm{\&Delta;}{m}_{21}& \mathrm{\&Delta;}{m}_{22}& ...& \mathrm{\&Delta;}{m}_{2n}\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ \mathrm{\&Delta;}{m}_{n1}& \mathrm{\&Delta;}{m}_{n2}& ...& \mathrm{\&Delta;}{m}_{\mathrm{nn}}\end{array}\right]---\left(3\right)$

Δ m in the formula _Ij=Δ m _Ji, nonzero element Δ m _IjThe variable quantity of the coupling value between expression resonant element i and the resonant element j, Δ m _IiRepresent that the resonance frequency of each resonant element departs from the value of its centre frequency.

In data acquisition system Z, because the variable quantity of each unit belongs to many inputs to the relations of many outputs in bolt adjustment amount and the coupling matrix, and reasonable algorithm such as least square support vector regression can only be set up many inputs to the data models of single output in the nuclear machine learning.For this reason, the present invention proposes use least square support vector regression and set up respectively bolt adjustment amount Δ D to unit Δ m among the coupling matrix Δ M _IjThe method of meta-model.

When making up ij meta-model, the input data are Δ D ∈ R ⁿ, the output data are Δ m _IjThe M of ∈ R training data sample set

Use the nonlinear mapping function

Least square support vector regression model below making up:

ω is weight vectors in the formula, and b is bias term.According to Statistical Learning Theory, the problems referred to above can be converted into following optimization problem:

Min：

s.t.

...，M

E in the formula _kBe model error, C is the compromise of models fitting precision and model complexity.

In order to find the solution this optimization problem, introduce Lagrange multiplier α=[α ₁, α ₂..., α _M] ^T, LagrangianL (ω, b, e that structure is following; α):

To the parameter ω in the formula (6), b, e, α ask respectively local derviation, and cancellation intermediate variable ω and e obtain system of linear equations after the arrangement:

$\left(\begin{array}{cc}\mathrm{\&Omega;}+\frac{1}{C}I& \mathrm{<figure-callout\; id="0"\; label="I\; I\; T"\; filenames="H2009100209533E00042.png,H2009100209533E00051.png"\; state="\{\{state\}\}">I</figure-callout>}& \\ I^T{}^{}& 0\end{array}\right)\left(\begin{array}{c}\mathrm{\&alpha;}\\ b\end{array}\right)=\left(\begin{array}{c}\mathrm{\&Delta;m}\\ 0\end{array}\right)---\left(7\right)$

Each element in the formula among the matrix in block form Ω satisfies

Matrix in block form I is unit matrix,

The vector that the unit variable quantity forms in the expression coupling matrix;

Find the solution this system of linear equations, obtain

With b, and by introducing kernel function

Obtain meta-model:

$\mathrm{\&Delta;}{m}_{\mathrm{ij}}=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{k}K(\mathrm{\&Delta;D},\mathrm{\&Delta;}{D}_k)+b---\left(8\right)$

K in the formula (Δ D, Δ D _k) be the nonlinear mapping function

Inner product in high-dimensional feature space, the use of kernel function have been avoided direct searching nonlinear mapping function

Difficulty, kernel function is used Gaussian kernel or translation invariant Mexico hat wavelet kernel function, their mathematic(al) representation is as follows respectively:

K(ΔD，ΔD _k)＝exp(-σ ^-2||ΔD-ΔD _k|| ²) (9)

$K(\mathrm{\&Delta;D},\mathrm{\&Delta;}{D}_k)=\underset{h=1}{\overset{n}{\mathrm{\&Pi;}}}(1-\frac{{\left|\right|\mathrm{\&Delta;D}-\mathrm{\&Delta;}{D}_k^h\left|\right|}^2}{{\mathrm{\&sigma;}}^2})\exp (-\frac{{\left|\right|\mathrm{\&Delta;D}-\mathrm{\&Delta;}{D}_k^h\left|\right|}^2}{{2\mathrm{\&sigma;}}^2})---\left(10\right)$

In the formula Represent h component of k data sample, σ represents nuclear parameter.When practical application, according to the requirement of model accuracy, select one of them kernel function to carry out modeling.

3) each meta-model Δ m that utilizes check data sample V checking to set up _IiAccuracy.

If the accuracy of model is then used these models in the scope of expectation; Otherwise, turn back to process 2) in again modeling, the parameter that reselects model is carried out modeling, until the accuracy of model meets the demands.In the process of verification model accuracy, be the accuracy that index is come assessment models with average absolute value error AAE and maximum value error MAE:

$\mathrm{AAE}=L^{-1}\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}\left|(\mathrm{\&Delta;}{m}_{\mathrm{ij}}^k-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^k)\right|---\left(11\right)$

$\mathrm{MAE}=\max \left(\right|\mathrm{\&Delta;}{m}_{\mathrm{ij}}^1-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^1|,...,|\mathrm{\&Delta;}{m}_{\mathrm{ij}}^L-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^L\left|\right)---\left(12\right)$

In the formula

Ij unit variation value in the coupling matrix that represents to measure for the k time, Be k the numerical value that sample calculates by ij meta-model, L represents the test samples number.

4) combination obtains the nuclear machine learning model Δ M of the actual adjustment amount of bolt and coupling matrix variable quantity.

According to process 2) in the meta-model modeling method, use respectively the nuclear machine learning algorithm to set up bolt adjustment amount Δ D to each unit Δ m among the coupling matrix Δ M _IjMeta-model; Then, according to the practical structures composition form of filter, each unit Δ m _IjMeta-model be combined into coupling matrix, obtain the bolt adjustment amount to the model Δ M of coupling matrix variable quantity impact:

ΔM＝f(ΔD) (13)

ΔL＝ΔD ^Tr (14)

R represents the bolt pitch that microwave filter uses in the formula, when Δ L represents that bolt is adjusted because after having rotated Δ D circle, the screw-in depth relative datum D of bolt ₀The variable quantity that occurs.

5) use machine learning model Δ M to revise desirable coupling matrix M ₀, when acquisition bolt adjustment amount is Δ D, corresponding actual coupling matrix M.

M＝M ₀+ΔM (15)

6) according to actual coupling matrix M, set up coupling matrix and filter electrical property

With

Relation.

$S_{21}^{\mathrm{mode}l}\left(f\right)=-2j\sqrt{R_1{R}_2}{\left[A^{-1}\right]}_{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">n</figure-callout>}1}$

${\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{mode}l}\left(f\right)=1+2j\sqrt{R_1}{\left[A^{-1}\right]}_{11}---\left(16\right)$

$A=\frac{{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="H2009100209533E00042.png,H2009100209533E00051.png"\; state="\{\{state\}\}">f</figure-callout>}}_0}{\mathrm{BW}}(\frac{f}{f_0}-\frac{f_0}{f})I-\mathrm{jR}+M$

M is the actual coupling matrix of considering after bolt adjustment amount Δ D affects in the formula, M ₀The target coupling matrix of expression expectation, Δ M represent because the coupling matrix variable quantity that the impact of bolt adjustment amount Δ D causes.I is unit matrix.BW represents the filter bandwidht that designs.f ₀The centre frequency of expression filter, f represents the actual operating frequency of filter.R ₁The coupling of expression filter input end mouth and adjacent resonators, R ₂The coupling of expression filter output mouth and adjacent resonators, R represents the coupling matrix of filter input and output and outside, the R matrix notation is:

$R=\left[\begin{array}{ccccc}{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">R</figure-callout>}}_1& 0& 0& ....& 0\\ 0& 0& 0& ...& 0\\ 0& 0& 0& ...& 0\\ .& .& .& & .\\ .& .& .& ...& .\\ .& .& .& & .\\ 0& 0& 0& ...& R_2\end{array}\right]---\left(17\right)$

The 5th step, set up microwave filter experiment the bolt adjustment amount optimize and revise model, detailed process is as follows:

According to the filter off resonance state outcome of vowing that net measures With Then utilize process 6) the middle machine learning model of setting up

Off resonance state with current measurement The principle of error sum of squares minimum, the Optimized model below making up:

Find：ΔD ₁

Min： $\underset{f_i=\mathrm{Sfreq}}{\overset{\mathrm{Efreq}}{\mathrm{\&Sigma;}}}[{(S_{21}^{\mathrm{measure}}\left(f_i\right)-S_{21}^{\mathrm{mode}l}\left(f_i\right))}^2+{({\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{measure}}\left(f_i\right)-{\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{mode}l}\left(f_i\right))}^2]---\left(18\right)$

s.t. $\mathrm{\&Delta;}{D}_1^L\&le;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="H2009100209533E00011.png,H2009100209533E00012.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\&le;\mathrm{\&Delta;}{D}_1^U$

In the formula With Represent respectively lower bound and the upper bound of the filter bolt adjustment amount of permission, their value is determined in advance by the designer;

With

Be illustrated respectively in f _iThe off resonance state transfer parameter that individual Frequency point measures and off resonance attitudinal reflexes parameter values;

With Be illustrated respectively in f _iIndividual Frequency point utilizes process 6) in the machine learning model the set up transformation parameter and the reflection parameters numerical value that calculate, Sfeq and Efeq represent respectively initial frequency point and end Frequency point that the filter operating frequency is sampled and obtained.

Find the solution above-mentioned Optimized model, find and to approach current off resonance state

With

Optimum machine learning model

With

And corresponding bolt off resonance adjustment amount Δ D ₁

The machine learning model of approaching with the current off resonance state of filter according to above-mentioned acquisition With

Filter debug target with prior setting With

Adopt the principle of the two error sum of squares minimum, the optimization formula below making up makes the machine learning model that is in the off resonance state

With

Adjust to the filter debug target of prior setting:

Find：ΔD ₂

Min： $\underset{f_i=\mathrm{Sfreq}}{\overset{\mathrm{Efreq}}{\mathrm{\&Sigma;}}}[{(S_{21}^{t\arg \mathrm{et}}\left(f_i\right)-S_{21}^{\mathrm{mode}l}\left(f_i\right))}^2+{(S_{11}^{t\arg \mathrm{et}}\left(f_i\right)-{\mathrm{<figure-callout\; id="11"\; label="S"\; filenames="H2009100209533E00052.png"\; state="\{\{state\}\}">S</figure-callout>}}_{11}^{\mathrm{mode}l}\left(f_i\right))}^2]---\left(19\right)$

s.t. $\mathrm{\&Delta;}{D}_2^L\&le;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="H2009100209533E00042.png,H2009100209533E00052.png"\; state="\{\{state\}\}">D</figure-callout>}}_2\&le;\mathrm{\&Delta;}{D}_2^U$

In the formula

With

Be illustrated respectively in f _iThe target debugging transformation parameter of individual Frequency point and target debugging reflection parameters numerical value, they are given by design in advance;

With

Respectively lower bound and the upper bound of the filter bolt adjustment amount that allows of expression, their value also determined in advance by the designer, and Sfeq and Efeq represent respectively initial frequency point and end Frequency point that the filter operating frequency is sampled and obtained.

Find the solution the Optimized model of formula (19), obtain the bolt adjustment amount Δ D that needs when filter is adjusted to the debug target of prior setting by current off resonance state ₂

At last, the as a result Δ D that obtains according to above-mentioned seismic responses calculated ₁With Δ D ₂, the bolt adjustment amount Δ D of calculating filter:

ΔD＝ΔD ₂-ΔD ₁。(20)

In the 6th step, the optimizing application adjustment model obtains the actual adjustment amount of each bolt of filter, carries out the filter debugging.

When practical engineering application, at first should arrive predefined benchmark by the correcting filter bolt; Then in debugging, what measure from the arrow net

With

Data directly be sent to optimizing and revising in modular form (18) and (19) that off-line is set up in the 5th step, utilize computer in line computation, obtain filter bolt adjustment amount, according to this adjustment amount filter is debugged.

Advantage of the present invention can be used by the debugging of the filter in the following Practical Project and further specify:

Microwave filter assistant debugging method of the present invention is carried out experimental verification at four chamber screw-filters.The experimental system of this filter is seen accompanying drawing 5.The design objective of this filter is: centre frequency f ₀For 397.7MHz, bandwidth are that return loss is 20dB in 8.31MHz, the band.According to the structure of filter shown in Figure 7, obtain its coupling matrix and be:

$M=\left[\begin{array}{cccc}{m}_{11}& m_{12}& 0& 0\\ m_{12}& m_{22}& m_{23}& 0\\ 0& m_{23}& m_{33}& m_{34}\\ 0& 0& m_{34}& m_{44}\end{array}\right]---\left(21\right)$

Use filter coupled matrix integrated approach, the R that obtains designing ₁=R ₂The no-load Q=540 of=1.0352, four cavitys, in the coupling matrix except m ₁₂=0.9211, m ₂₃=0.6999, m ₃₄=0.9211, other unit is zero.

Collect in the experiment at data sample, as benchmark, measured corresponding S parameter by the vector network analyzer device this moment, then extracts coupling matrix when the inventive method was debugged the electrical property optimum take filter, acquisition target coupling matrix M ₀, its each unit is respectively m ₁₁=-0.0355, m ₂₂=-0.0263, m ₃₃=-0.0089, m ₄₄=0.0034, m ₁₂=0.969, m ₂₃=0.7177, m ₃₄=0.9043.

Take above-mentioned optimum debug results as benchmark, and the number of turns that turns clockwise of regulation bolt relative datum on the occasion of, instead then for negative.Adopted the uniform experiments method for designing.In each experiment, measure the S supplemental characteristic from the vector network analyzer device, then extract and obtain corresponding coupling matrix data.Again bolt is reset to benchmark, restart experiment next time.By experiment repeatedly, can obtain the set of data samples E={ Δ D that some bolts are adjusted variable quantity and coupling matrix _i, M _i), i=1,2 ..., N}.After the processing of data sample set, directly used the normalized bolt adjustment amount of modeling and data set Z={ (the Δ D of the coupling matrix variable quantity of correspondence _i, Δ M _i), i=1,2 ..., N}.

According to set of data samples Z, utilize the present invention to set up nuclear machine learning model between bolt adjustment amount and the coupling matrix variable quantity.Because coupling matrix is very responsive on the impact of electrical property, for accuracy set up bolt adjustment amount and coupling matrix variable quantity model, the nuclear machine learning algorithm such as RBF nuclear least square support vector regression RBFLSSVR, the Mexico hat wavelet nuclear least square support vector regression LSWSVR that have used respectively the present invention to propose, and traditional machine learning algorithm such as BP neural net are carried out modeling.For accuracy and the generalization that guarantees model, use parameter and BP network configuration that cross validation method is selected the least square support vector regression.

For the accuracy of verification model, come the accuracy of verification model with 5 test samples, and average absolute value error AAE and maximum value error MAE are the accuracy that index is come assessment models.Table 1 has provided the AAE of three kinds of modeling methods and the performance comparison result of MAE.

Table 1 model accuracy comparing result

Can see from table 1: LSWSVR is higher than accuracy and the generalization of RBFLSSVR, and the accuracy of BP network and generalization are the poorest.

According to the comparing result of table 1, the machine learning model of using above-mentioned Wavelet Kernel least square support vector regression LSWSVR to set up, and optimize and revise the adjustment amount that model is found the solution bolt in conjunction with what the present invention proposed.Obtain the concrete adjustment amount of each bolt of filter after finding the solution, see accompanying drawing 6.6 bolt adjustment amounts that provide with reference to the accompanying drawings, the commissioning staff adjusts the adjustment bolt of respective filter, only needs can finish adjustment once going on foot.

Before accompanying drawing 7, accompanying drawing 8 and accompanying drawing 9 have provided respectively the adjustment of this filter, adjust after and S21, the S11 of debug target and the comparing result of group delay.From these figure, can see: the adjustment amount that uses the present invention to calculate, only need step examination just the electrical property of filter to be adjusted near optimum state, satisfy the designing requirement of filter, having overcome needs repeatedly to debug filter, too much drawback of time in the engineering, improved the debugging efficiency of filter.

The experimental result of above-mentioned filter shows, adopt the present invention can be than more quickly, finish the debugging of filter exactly.

Claims (1)

1. microwave filter assistant debugging method based on nuclear machine learning comprises following process:

(1) presets benchmark D for one ₀Filter, vow that by changing bolt adjustment amount Δ D, using net measures corresponding filter transformation parameter S ₂₁With reflection parameters S ₁₁

(2) according to the S that measures ₂₁And S ₁₁, extract corresponding coupling matrix, obtain bolt adjustment amount and the corresponding coupling matrix set of data samples Г of experiment;

(3) data sample set Г is carried out normalization, the data set Z of the coupling matrix variable quantity of the bolt adjustment amount that obtains testing and correspondence;

(4) according to resulting data set Z, utilize the nuclear machine learning algorithm to set up nuclear machine learning model Δ M between bolt adjustment amount and the coupling matrix variable quantity:

4a) set of the data sample after normalization Z is divided into training sample T and test samples V two parts, wherein training sample T accounts for 4/5 of data sample sum, and remaining data sample is test samples V;

4b) according to training sample T, the least square support vector regression in the use nuclear machine learning algorithm is set up respectively the meta-model Δ m of each unit variation amount in bolt adjustment amount and the coupling matrix _Ij:

4b1) according to training sample set T, use the least square support vector regression, in high-dimensional feature space, make up respectively the meta-model Δ m of each unit of coupling matrix and bolt adjustment amount Δ D _Ij:

ω is weight vectors in the formula, and b is bias term, Expression Nonlinear Mapping function;

4b2) regression model with above-mentioned high-dimensional feature space is converted into:

Min：

s.t.

...，M

E in the formula _kBe ij the error that the relative measured data of meta-model is calculated, C is the compromise of models fitting precision and model complexity,

K data sample of ij unit in the expression coupling matrix, M represents the number of samples of training sample T, Δ D _kRepresent k bolt adjustment amount data sample;

4b3) introduce Lagrange multiplier α=[α ₁, α ₂..., α _M] ^T, structure LagrangianL (ω, b, e _k, α) be:

4b4) respectively to the variable ω in the above-mentioned formula, b, e _k, α asks local derviation, obtains system of linear equations after the arrangement:

$\left(\begin{array}{cc}\mathrm{\&Omega;}+\frac{1}{C}I& I\\ I^T& 0\end{array}\right)\left(\begin{array}{c}\mathrm{\&alpha;}\\ b\end{array}\right)=\left(\begin{array}{c}\mathrm{\&Delta;m}\\ 0\end{array}\right)$

Each element in the formula among the matrix in block form Ω satisfies

I is unit matrix,

The vector that expression coupling matrix unit variable quantity forms;

4b5) find the solution above-mentioned system of linear equations, obtain

And b;

4b6) introduce kernel function

Finally obtain the meta-model in the ij unit variation amount in the coupling matrix:

$\mathrm{\&Delta;}{m}_{\mathrm{ij}}=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{k}K(\mathrm{\&Delta;D},\mathrm{\&Delta;}{D}_k)+b,$

K(ΔD，ΔD _k)＝exp(-σ ^-2||ΔD-ΔD _k|| ²)，

Or $K(\mathrm{\&Delta;D},\mathrm{\&Delta;}{D}_k)=\underset{h=1}{\overset{n}{\mathrm{\&Pi;}}}(1-\frac{{\left|\right|\mathrm{\&Delta;D}-\mathrm{\&Delta;}{D}_k^h\left|\right|}^2}{{\mathrm{\&sigma;}}^2})\exp (-\frac{{\left|\right|\mathrm{\&Delta;D}-\mathrm{\&Delta;}{D}_k^h\left|\right|}^2}{{2\mathrm{\&sigma;}}^2}),$

In the formula

Represent h component of k data sample, σ represents nuclear parameter, and n represents the number of translation invariant Mexico hat wavelet function base;

4c) utilize all meta-model Δ m among the test samples V checking nuclear machine learning model Δ M _IjAccuracy, if the accuracy of model the expectation scope in, then use these models; Otherwise, turn back to step 4b) again modeling, until the accuracy of model meets the demands, the Accuracy evaluation formula that uses in the checking is:

$\mathrm{AAE}=L^{-1}\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}\left|(\mathrm{\&Delta;}{m}_{\mathrm{ij}}^k-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^k)\right|,$

$\mathrm{MAE}=\max \left(\right|\mathrm{\&Delta;}{m}_{\mathrm{ij}}^1-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^1|,...,|\mathrm{\&Delta;}{m}_{\mathrm{ij}}^L-\mathrm{\&Delta;}{\hat{m}}_{\mathrm{ij}}^L\left|\right),$

In the formula: AAE is the average absolute value error, and MAE is the maximum value error,

Ij unit variation value in the coupling matrix that represents to measure for the k time,

Be k the numerical value that sample calculates by ij meta-model, L represents the number of samples of test samples V;

4d) to verifying each correct meta-model, according to the structure composition form of filter, combination obtains the nuclear machine learning model Δ M of the actual adjustment amount of bolt and coupling matrix variable quantity:

ΔM＝f(ΔD)，

ΔL＝ΔD ^Tr，

F represents above-mentioned meta-model Δ m in the formula _IjAccording to the Nonlinear Mapping function that the combination of filter construction form obtains, r represents the bolt pitch that microwave filter uses, after Δ L represents that bolt has rotated Δ D circle when adjusting, and the variable quantity that the screw-in depth relative datum of bolt occurs;

(5) use Δ M to the coupling matrix correction, set up the bolt adjustment amount of experiment to the machine learning model of filter electrical property impact

With

5a) use machine learning model Δ M to revise desirable coupling matrix M ₀, obtaining the bolt adjustment amount is actual coupling matrix M corresponding to Δ D:

M＝M ₀+ΔM；

5b) according to actual coupling matrix M, set up coupling matrix and filter electrical property

With

Relation:

$S_{21}^{\mathrm{mode}l}\left(f\right)=-2j\sqrt{R_1{R}_2}{\left[A^{-1}\right]}_{n1}$

$S_{11}^{\mathrm{mode}l}\left(f\right)=1+2j\sqrt{R_1}{\left[A^{-1}\right]}_{11},$

$A=\frac{f_0}{\mathrm{BW}}(\frac{f}{f_0}-\frac{f_0}{f})I-\mathrm{jR}+M$

I is unit matrix in the formula, and BW represents the filter bandwidht that designs, f ₀The filter center frequency of expression design, f represents the actual operating frequency of filter, R ₁The coupling of expression filter input end mouth and adjacent resonators, R ₂The coupling of expression filter output mouth and adjacent resonators, j represents the imaginary part of plural number, matrix A ^-1In subscript n 1 and 11 represent that respectively transmission characteristic and the reflection characteristic of n rank filter, R represent filter input and output and outside coupling matrix:

$R=\left[\begin{array}{ccccc}{R}_1& 0& 0& ....& 0\\ 0& 0& 0& ...& 0\\ 0& 0& 0& ...& 0\\ .& .& .& & .\\ .& .& .& ...& .\\ .& .& .& & .\\ 0& 0& 0& ...& R_2\end{array}\right];$

(6) according to machine learning model

With

Off-line set up microwave filter experiment the bolt adjustment amount optimize and revise model:

6a) according to above-mentioned 5b) process foundation

With

Relation, corresponding off resonance adjustment amount Δ D before calculating filter is adjusted ₁:

Find：ΔD ₁

Min： $\underset{f_i=\mathrm{Sfreq}}{\overset{\mathrm{Efreq}}{\mathrm{\&Sigma;}}}[{(S_{21}^{\mathrm{measure}}\left(f_i\right)-S_{21}^{\mathrm{mode}l}\left(f_i\right))}^2+{(S_{11}^{\mathrm{measure}}\left(f_i\right)-S_{11}^{\mathrm{mode}l}\left(f_i\right))}^2],$

s.t. $\mathrm{\&Delta;}{D}_1^L\&le;\mathrm{\&Delta;}{D}_1\&le;\mathrm{\&Delta;}{D}_1^U$

In the formula With The lower bound and the upper bound that represent respectively the filter bolt adjustment amount of permission,

With

Be illustrated respectively in f _iThe transformation parameter that individual Frequency point measures and reflection parameters numerical value,

With

Be illustrated respectively in f _iTransformation parameter and reflection parameters numerical value that individual Frequency point utilizes machine learning model to calculate, Sfreq and Efreq represent respectively the sample initial frequency point that obtains and finish Frequency point of filter operating frequency;

6b) according to 5b) set up

With

Relation, the bolt adjustment amount Δ D that needs when calculating filter is transferred to target by current off resonance state ₂

Find：ΔD ₂

Min： $\underset{f_i=\mathrm{Sfreq}}{\overset{\mathrm{Efreq}}{\mathrm{\&Sigma;}}}[{(S_{21}^{t\arg \mathrm{et}}\left(f_i\right)-S_{21}^{\mathrm{mode}l}\left(f_i\right))}^2+{(S_{11}^{t\arg \mathrm{et}}\left(f_i\right)-S_{11}^{\mathrm{mode}l}\left(f_i\right))}^2],$

s.t. $\mathrm{\&Delta;}{D}_2^L\&le;\mathrm{\&Delta;}{D}_2\&le;\mathrm{\&Delta;}{D}_2^U$

In the formula With

Be illustrated respectively in f _iTarget debugging transformation parameter and the reflection parameters numerical value of individual Frequency point, it is given by design in advance,

With Be illustrated respectively in f _iTransformation parameter and reflection parameters numerical value that individual Frequency point utilizes machine learning model to calculate,

With

Respectively lower bound and the upper bound of the bolt adjustment amount of the filter that allows of expression; Sfreq and Efreq represent respectively the sample initial frequency point that obtains and finish Frequency point of filter operating frequency;

The as a result Δ D that 6c) obtains according to above-mentioned optimization ₁With Δ D ₂, the bolt adjustment amount that calculates filter is Δ D:

ΔD＝ΔD ₂-ΔD ₁；

(7) with described transformation parameter S ₂₁With reflection parameters S ₁₁Be input to above-mentioned optimizing and revising in the model, in line computation, obtain the actual adjustment amount of each bolt of filter by computer, ancillary works personnel carry out the filter debugging.

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