Microwave filter design method based on neural network space mapping reverse model

Abstract

The invention relates to a microwave filter design method based on a neural network space mapping reverse model. According to the method, fast Fourier transform (FFT) is utilized, an input electromagnetic response (S parameter) curve is converted into a low-frequency spectrum with concentrated energy, and therefore the input dimension of a reverse model is reduced. In addition, the invention further provides a two-stage development algorithm of the NSM-based reverse model and an application method of the NSM-based reverse model in microwave filter design. The design parameter value (geometric parameter value) of the microwave filter can be directly obtained at one time according to the design index through the fully trained NSM reverse model without depending on a complete S parameter curve. Compared with an existing ANN-based reverse modeling method, the method has remarkable advantages in modeling speed and convenience in extraction of design parameters of the microwave filter.

Description

Technical Field

[0001] The invention relates to the field of microwave device reverse modeling and the application of artificial neural network and space mapping technology in the field of microwave filter modeling and design. Background Art

[0002] In the new generation of communication systems, microwave filters play a key role in ensuring the stability and reliability of signal transmission, showing a wide range of application prospects. [1] With the rapid development of wireless communication technology, efficient filter design methods have become a research hotspot. Traditional design methods rely on repeated full-wave electromagnetic simulations to iteratively adjust the filter design parameters (geometric parameters) to meet specific design requirements. [2-3] This design process is usually called forward optimization of the filter. However, the full-wave electromagnetic simulation process usually consumes a lot of CPU computing time, resulting in low design efficiency.

[0003] In recent years, modeling technology based on artificial neural network (ANN) has been widely used in the optimization design of various microwave devices. [4-5] . ANN has a powerful ability to handle complex nonlinear relationships by simulating the way human brain nerves process information. In the ANN-based microwave filter optimization design, ANN technology is usually used to develop a forward substitution model of the filter. The input of the forward model usually includes the geometric parameters and physical parameters of the filter, and the output is the electromagnetic response of the filter. This type of ANN-based forward substitution model effectively solves the problem of time-consuming electromagnetic full-wave simulation process. However, for different design indicators, the optimization process still needs to be repeated, and the design time of the filter is still too long.

[0004] In order to further improve design efficiency and avoid time-consuming iterative optimization process, researchers proposed an ANN-based inverse modeling method. [6-7] The core idea of ​​inverse modeling is to use the electromagnetic response of microwave devices as model input and geometric parameters as output to develop ANN models. Through the inverse model, the optimal geometric parameters can be directly obtained through electromagnetic design indicators. However, inverse modeling based on ANN faces many challenges, such as high input dimensions, complex model structure, and the need for a large amount of training data.

[0005] In recent years, ANN-based neural space mapping (NSM) technology has received extensive attention in microwave filter design. [8-12]This technology combines the powerful fitting ability of ANN with the efficient optimization of space mapping (SM). By using ANN to establish an accurate mapping relationship between the coarse model (usually the equivalent circuit of the filter) and the fine model (usually the full-wave electromagnetic simulation of the filter), a high-precision filter model can be quickly obtained using less training data. Although NSM technology has achieved remarkable success in forward modeling of microwave filters, its application in inverse modeling remains to be studied to further improve the design efficiency of filters.

[0006] The present invention proposes a microwave filter inverse design method based on NSM. In view of the problem of high input dimension of ANN inverse model, the present invention uses Fast Fourier Transform (FFT) to convert the input electromagnetic response (S parameter) curve into a low-frequency spectrum with concentrated energy, thereby reducing the input dimension of the inverse model. In addition, the present invention also proposes a two-stage development algorithm based on NSM inverse model, and an application method of the NSM inverse model in microwave filter design. The fully trained NSM inverse model can directly obtain the design parameter value (geometric parameter value) of the microwave filter at one time according to the design index without relying on the complete S parameter curve. Compared with the existing ANN-based inverse modeling method, the method proposed by the present invention has significant advantages in modeling speed and convenience of microwave filter design parameter extraction.

[0007] References:

[0008] [1] RJ Cameron, CM Kudsia, and RR Mansour, Microwave Filters For Communication Systems: Fundamentals, Design, and Applications. Hoboken, NJ, USA: Wiley, 2007.

[0009] [2] JERayas-Sánchez, Q.-J.Zhang, JCRautio, NK Nikolova, VE Boria, QSCheng, M. Yu, and WJRHoefer, "Microwave modeling and design optimization: The legacy of John Bandler," IEEE Transactions on Microwave Theory and Techniques, early access, 2024.

[0011] [3]J.W.Bandler,S.Ye,R.Biernacki,S.Chen,and D.Swanson,“Minimaxmicrostrip filterdesign using direct EMfield simulation,”1993IEEE MTT-SInternational MicrowaveSymposium Digest,vol.2,pp.889–892,1993.

[0012] [4]L.Ma,J.Jin,X.Li,W.Liu,K.Ma,and Q.-J.Zhang,“Advanced surrogate-basedEMoptimization using complex frequency domain EMsimulation-based neuro-TFmodel formicrowave components,”IEEE Transactions on Microwave Theory andTechniques,pp.1–11,2024.

[0014] [5]M.Swaminathan,H.M.Torun,H.Yu,J.A.Hejase and W.D.Becker,“Demystifying MachineLearning for Signal and Power Integrity Problems inPackaging,”in IEEE Transactions onComponents,Packaging and ManufacturingTechnology,vol.10,no.8,pp.1276-1295,Aug.2020.

[0016] [6]H.Kabir,Y.Wang,M.Yu,and Q.-J.Zhang,“Neural network inversemodeling andapplications to microwave filter design,”IEEE Transactions onMicrowave Theory andTechniques,vol.56,no.4,pp.867–879,2008.

[0017] [7]J.Jin,C.Zhang,F.Feng,W.Na,J.Ma,and Q.-J.Zhang,“Deep neural networktechnique forhigh-dimensional microwave modeling and applications toparameter extraction ofmicrowave filters,”IEEE Transactions on MicrowaveTheory and Techniques,vol.67,no.10,pp.4140–4155,2019.

[0019] [8]D.Gorissen,L.Zhang,Q.-J.Zhang,and T.Dhaene,“Evolutionary neuro-space mappingtechnique for modeling of nonlinear microwave devices,”IEEETransactions on MicrowaveTheory and Techniques,vol.59,no.2,pp.213–229,2011.

[0020] [9]J.W.Bandler,M.A.Ismail,J.E.Rayas-Sánchez,and Q.-J.Zhang,“Neuromodeling ofmicrowave circuits exploiting space-mapping technology,”IEEETransactions on MicrowaveTheory and Techniques,vol.47,no.12,pp.2417–2427,1999.

[0021]

[10] M.Bakr,J.W.Bandler,M.A.Ismail,J.E.Rayas-Sánchez,and Q.-J.Zhang,“Neural space-mapping optimization for EM-based design,”IEEE Transactions onMicrowave Theory andTechniques,vol.48,no.12,pp.23072315,2000.

[0022]

[11] JW Bandler, MAIsmail, JERayas-Sánchez, and Q.-J. Zhang, “Neuralinverse spacemapping EM-optimization,” 2001IEEE MTT-S International Microwave Symposium Digest, vol.2, pp.1007–1010, 2001.

[0024]

[12] JWBandler, MAIsmail, JERayas-Sánchez, and Q.-J.Zhang, "Neuralinverse spacemapping (NISM) optimization for EM-based microwave design," Int.J.RF and MicrowaveCAE, vol.13, no.2, pp.136–147, 2003. Summary of the invention

[0025] The present invention proposes a microwave filter design method based on a neural space mapping (NSM) inverse model. This method applies NSM technology to the inverse modeling of microwave filters for the first time, and combines the fast Fourier transform (FFT) to reduce the input dimension of the model, making it suitable for the inverse modeling and design of various microwave filters. The main innovations of the present invention include the following aspects:

[0026] (1) Inverse model structure based on NSM: The present invention proposes an NSM inverse model structure with a dimensionality reduction module. The amount of data required for model training is significantly reduced through the neural network space mapping technology, and the input S parameter curve is converted into a Fourier low-frequency spectrum with concentrated energy by using FFT, thereby compressing the input dimension of the model.

[0027] (2) Inverse model training algorithm: The present invention develops an inverse model training algorithm based on NSM and proposes a microwave filter design method based on the inverse model. ;

[0028] The specific implementation steps of the present invention are:

[0029] Step 1: Use the orthogonal distribution design of experiment (DOE) sampling method to simulate the equivalent circuit of the microwave filter (related to the specific filter structure) and generate the rough data of the microwave filter (x c,y c ). c Expressed as the input geometric parameters of the filter equivalent circuit, y c The filter scattering parameter S 21 Or reflection coefficient S 11 .

[0030] Step 2: Construct the training structure of the coarse inverse model. Multilayer Perceptron (MLP) is used to develop the coarse inverse model. c ,like Figure 1 (a) shown.

[0031] Step 3: Train the coarse inverse model. First, swap the input and output of the coarse data to make it the inverse data (y c ,x c ). Then, the rough data y is transformed into c The S parameter curve is converted into a compressed Fourier low-frequency spectrum as the input of the rough inverse model And x c As output. The modeling example of the present invention proposes to achieve dimensionality reduction by reducing the number of input frequency points, reducing the number of 201 input frequency points to 60, which is nearly 1 / 3 less than before dimensionality reduction. Then, the MLP is trained using the dimensionality-reduced inverse data to construct a rough inverse model.

[0032] Step 4: Generate detailed data of the microwave filter through fine-grid electromagnetic simulation, and similarly exchange the input and output to form an inverse data set.

[0033] Step 5: Construct the Input Mapping ANN of the refined model i ) and Output Mapping ANN:f o ). The IDR module, input mapping ANN, rough inverse model and output mapping ANN are combined into a complete NSM-based inverse model, such as Figure 1 (b) As shown in the figure, the present invention adopts an input mapping ANN and an output mapping ANN of a three-layer MLP structure, and the number of hidden neurons can be set to 12 and 32 respectively.

[0034] Step 6: Train the entire NSM-based inverse model. During this process, keep the weights of the coarse inverse model fixed. Evaluate the model performance by the root mean square error (RMSE), and use the model structure adjustment algorithm to optimize the structure of the input-output mapping ANN until the target accuracy is achieved.

[0035] Step 7: Use the trained NSM inverse model to design microwave filters. First, convert the design indicators into several key feature points of the S parameter curve, such as Figure 2 As shown in (a), these feature points are then connected into a broken line as the input of the NSM inverse model, and the required filter geometric parameter x value is predicted by the NSM inverse model.

[0036] The invention is different from the prior art in that:

[0037] 1. NSM technology reduces the amount of data required for neural network reverse modeling and improves the efficiency of reverse modeling.

[0038] Traditional neural network inverse modeling requires a large amount of training data and has a high model input dimension due to the highly nonlinear relationship between the input S parameters and the output geometric parameters, which leads to a complex model structure and difficulty in training. Figure 1 (b) shows the NSM inverse model structure and two-stage training algorithm to develop the NSM-based inverse model, the mathematical expression of which is

[0039]

[0040] Among them, w i and w o are the weights of the input and output mapping ANN respectively. The input fine S parameter data is mapped through the input mapping f i The geometric parameters of the rough inverse model output are converted into the input of the rough inverse model through the output mapping f o The final result is obtained. By using the existing equivalent circuit inverse model f c As a coarse model (prior knowledge), inverse modeling combined with NSM significantly reduces the amount of data required for inverse modeling of microwave filters and improves the efficiency of inverse modeling.

[0041] 2. An IDR module for input dimensionality reduction operation is added to the NSM inverse model.

[0042] In the process of inverse modeling, a high input dimension will lead to a rapid increase in the amount of data required for modeling, which will greatly extend the calculation time and occupy a large amount of storage space. In the IDR module in steps 3 and 5 of the present invention, the low-frequency characteristics of the S parameter performance are extracted by FFT, thereby effectively reducing the input dimension of the model. Specifically, the input y of the inverse model is first converted into a Fourier spectrum vector Y, that is, Y = [Y1 Y2…Y n ], n is the input dimension of the IDR module. The jth element of Y is defined as

[0043]

[0044] where \(y_i\) represents the \(i\)-th element in \(y\), and \((w n ) (i-1)(j-1) is the Fourier transform basis. To extract the low-frequency components of the Fourier spectrum, a vector \(e = [e_1\ e_2 \ldots e n ) T is defined, and the \(i\)-th element is

[0045]

[0046] where \(l\) is half of the number of low-frequency components to be retained in the Fourier spectrum (\(2l < n\)). Then, \(Y\) is multiplied by \(e\) to obtain an \(n\times n\) matrix \(A\), that is

[0047] A = Y\cdot e T (4)

[0048] The non-zero diagonal elements in \(A\) are extracted as the low-frequency components of the Fourier spectrum, that is

[0049]

[0050] where \(A kk are the non-zero diagonal elements in \(A\). To determine the value of \(l\), it is required to define \(R\) as the ratio of the energy contained in the retained \(2l\) low-frequency components to the total energy of the Fourier series, that is

[0051]

[0052] To ensure that the \(2l\) low-frequency components can retain sufficient S-parameter curve information, based on experience, it is recommended to select the value of \(l\) such that \(R > 90\%\). In this way, after the IDR module, the input dimension of the inverse model is reduced from \(n\) to \(2l\), effectively retaining the main characteristic information of the S-parameter curve and facilitating subsequent model development.

[0053] 3. Directly predict the optimal design parameter values based on the design specifications.

[0054] The purpose of establishing an inverse model is to use it to design microwave filters. Usually, the design indicators of the filter are defined by parameters such as passband, cutoff band, and return loss. The traditional microwave filter inverse model that relies on S parameters as input is often difficult to generate an S parameter curve that can accurately match the design indicators and simulation results, so it cannot be used to directly design microwave filters. The method proposed in the present invention converts the design indicators of the microwave filter into several key feature points of the S parameter curve through the prediction ability of the inverse model based on NSM, and then connects these feature points into a broken line and inputs them into the IDR module. After being processed by the IDR module, the low-frequency Fourier leaf space provides an approximate S parameter curve, which can be used to predict the design parameters (geometric parameters) x values ​​of the filter. In this way, the microwave filter inverse model based on NSM can directly obtain the geometric parameter values ​​according to the design indicators without the need for a specific S parameter curve as a model input.

[0055] Figure 2 (b) is an example of using the NSM-based inverse model to design a band-stop filter. The proposed algorithm is required to generate several characteristic points (blue triangles) according to the specified design indicators, namely the starting point, end point and turning point of the passband and stopband. These characteristic points are connected to form a broken line and provided to the NSM inverse model. After model processing, the geometric parameter x value can be directly obtained. It can be seen that the S parameter curve (pink star line) obtained by simulation based on the predicted x successfully meets the given design indicators.

[0056] In summary, the present invention proposes a microwave filter design method based on a neural network space mapping (NSM) inverse model. This method has significant advantages: first, the present invention combines NSM technology so that the inverse model has both the high computational efficiency of a coarse model and the high simulation accuracy of a fine model. Compared with the traditional inverse modeling method, the inverse modeling based on NSM significantly reduces the required amount of training data and training time. Secondly, the low-frequency part of the S-parameter spectrum where the energy is concentrated is extracted by fast Fourier transform (FFT), thereby effectively reducing the input dimension of the inverse model, while retaining the key feature information of the S-parameter curve, reducing the complexity of the model. In addition, the trained NSM inverse model can quickly and accurately predict the design parameter (i.e., geometric parameter) value of the microwave filter according to the given design indicators, greatly improving the design efficiency. The present invention not only simplifies the design process of microwave filters, but also significantly shortens the development cycle, providing an innovative solution for efficient and accurate microwave filter design. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 (a) is a structural diagram for training a rough inverse model proposed in the present invention;

[0058] Figure 1(b) is a structural diagram of the reverse model based on NSM proposed by the present invention;

[0059] Figure 2 (a) is a flow chart of the model application proposed by the present invention;

[0060] Figure 2 (b) is an application example of the present invention using the inverse model based on NSM in the design of a band-stop filter;

[0061] Figure 3 It is a device structure of an example (microstrip band-stop filter) of the present invention;

[0062] Figure 4 It is the equivalent circuit structure of the example (microstrip band-stop filter) of the present invention;

[0063] Figure 5 (a) is an example of the present invention (microstrip band-stop filter) at x = [0.17, 0.26, 2.70, 3.00, 2.90] T At mm, the reverse modeling results based on NSM;

[0064] Figure 5 (b) is the application result of the inverse model based on NSM in the example of the present invention (microstrip band-stop filter) with only design indicators. DETAILED DESCRIPTION

[0065] In order to more clearly demonstrate the objectives, modeling process and significant achievements of the present invention, the application of the NSM-based inverse design method in a microstrip band-stop filter design example will be described in detail below in conjunction with the accompanying drawings.

[0066] like Figure 3 As shown, the present invention performs inverse modeling of the microstrip band-stop filter structure based on NSM. The input of the inverse model is |S 21 |. Parameter S 21 It is the microwave filter scattering parameter, which is used to measure the power transmission efficiency from port 2 to port 1. The design parameters of this filter are geometric parameters, that is, x = [W1, W2, L0, L1, L2] T , where W1 and W2 are the widths of the open stubs on both sides and the middle open stub, L0 is the length of the transmission line between the two open branches, and L1 and L2 are the lengths of the open stubs, respectively.

[0067] In order to reduce the input dimension, the input dimension is reduced from 201 to 60 by setting l = 30. The modeling target of the inverse model is that the test error is less than 1%. In the inverse model of NSM, the data of the coarse model is generated by the equivalent circuit of the filter, such as Figure 4As shown, the detailed data is generated by full-wave electromagnetic simulation using CST. The sampling range of parameter x is [0.15, 0.23, 2.54, 2.54, 2.54] T mm to [0.19,0.27,3.35,3.35,3.35] T The training data includes 1728 sets of coarse data and 361 sets of fine data. The number of hidden neurons of the input mapping ANN is set to 12, and the number of hidden neurons of the output mapping ANN is set to 32.

[0068] Figure 5 (a) shows the inverse modeling results of the microstrip band-stop filter based on NSM. The trained coarse model |S 21 |There is a certain deviation from the expected value, but after further training with fine data, |S 21 |The curve is almost completely consistent with the expected value. The final test error of the inverse model based on NSM is 0.84%, which meets the design requirement of less than 1% error standard. As shown in Table 1, the generation time of fine data is 20.6 hours, the generation time of coarse data is only 5 minutes, and the total modeling time is 21.4 hours.

[0069] In order to verify the advantages of the NSM reverse modeling method in saving training time and data volume, it is compared with the traditional direct reverse modeling method. As shown in Table 1, the direct modeling method needs 112.5 hours to generate 2025 sets of fine data for training, plus the model training time of 113.4 hours in total, and the final model test error is 0.89%, which meets the design accuracy requirements. The comparison shows that the reverse modeling method based on NSM is significantly superior to the traditional method in terms of data volume and time consumption, greatly improving the reverse modeling efficiency of the filter.

[0070] Figure 5 (a) shows that the inverse modeling method based on NSM successfully realizes the inverse modeling of a microstrip band-stop filter with a -3dB bandwidth of 8.15 to 11.7 GHz. In addition, in order to verify the ability of the present invention to simplify the microwave filter design process, the design indicators are converted into several key feature points, and these points are connected into a broken line. This broken line is directly provided as input y to the trained NSM inverse model. Figure 5 (b) shows that the inverse model can directly and accurately predict the geometric parameter values ​​of the filter based on the design indicators, completing the design of the microstrip band-stop filter.

[0071] In summary, the NSM-based inverse design method proposed in the present invention not only greatly improves the efficiency of reverse modeling, but also significantly simplifies the design process of microwave filters, providing an innovative solution for efficient and accurate filter design.

[0072] Table 1 Comparison of modeling results of the present invention example (microstrip band-stop filter) and direct inverse modeling method

[0073]

Claims

1. A microwave filter design method based on a neural network space mapping inverse model, characterized in that: Including the following steps: Step 1: Use the orthogonal distribution experimental design sampling method to simulate the equivalent circuit of the microwave filter and generate the rough data (x c ,y c ); x c Expressed as the input geometric parameters of the filter equivalent circuit, y c is the filter scattering parameter S 21 Or reflection coefficient S 11 ; Step 2: Construct the training structure of the coarse inverse model; use multi-layer perceptron MLP to develop the coarse inverse model f c ; Step 3: Train the coarse inverse model; first swap the input and output of the coarse data to make it the inverse data (y c ,x c ); Then, the rough data y is transformed into c The S parameter curve is converted into a compressed Fourier low-frequency spectrum as the input of the rough inverse model And x c as output; then use the reduced-dimensional inverse data to train the MLP and build a rough inverse model; Step 4: Generate fine data of the microwave filter through fine-grid electromagnetic simulation, and also exchange the input and output to form an inverse dataset; Step 5: Build the Input Mapping ANN of the refined model: i Output Mapping ANN:f o ; The IDR module, input mapping ANN, rough inverse model and output mapping ANN are combined into a complete NSM-based inverse model, and the input mapping ANN and output mapping ANN of the three-layer MLP structure are adopted; Step 6: Train the entire NSM-based inverse model; during this process, keep the weights of the coarse inverse model fixed; evaluate the model performance through the root mean square error RMSE, and use the model structure adjustment algorithm to optimize the structure of the input-output mapping ANN until the target accuracy is achieved; Step 7: Use the trained NSM inverse model for microwave filter design; first, convert the design specifications into several key feature points of the S-parameter curve, and then connect these feature points into a polyline as the input of the NSM inverse model. After prediction by the NSM inverse model, the required filter geometric parameter x value is obtained.

2. The method according to claim 1, characterized in that: Based on the NSM-based inverse model, the mathematical expression of this model is Among them, w i and w o are the weights of the input and output mapping ANN respectively; the input fine S parameter data is mapped through the input i The geometric parameters of the rough inverse model output are converted into the input of the rough inverse model through the output mapping f o Get the final result.

3. The method according to claim 1, characterized in that: First, the input y of the inverse model is converted into a Fourier spectrum vector Y, that is, Y = [Y1 Y2…Y n ], n is the input dimension of the IDR module; the jth element of Y is defined as Where yi represents the i-th element in y, (w n ) (i-1)(j-1) is the Fourier transform basis; in order to extract the low-frequency components of the Fourier spectrum, a vector e = [e1 e2…e n ] T , the i-th element is where l is half of the number of low-frequency components to be retained in the Fourier spectrum, i.e., 2l < n; then multiply Y by e to obtain an n×n matrix A, i.e., A=Y·e T (4) Extract the non-zero diagonal elements in A as y of the low-frequency components of the Fourier spectrum, i.e., Among them A kk are the non-zero diagonal elements in A; in order to determine the value of l, it is required to define R as the ratio of the energy contained in the retained 2l low-frequency components to the total energy of the Fourier series, that is, Select the value of l such that R > 90%; after the IDR module, the input dimension of the inverse model is reduced from n to 2l.

4. The method according to claim 1, characterized in that: Step 7: Convert the design specifications of the microwave filter into several key feature points of the S-parameter curve, and then connect these feature points into a polyline and input it into the IDR module. After being processed by the IDR module, the low-frequency Fourier subspace provides an approximate S-parameter curve, which can be used to predict the geometric parameter x value of the filter.

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