CN-121997736-A - Artificial neural network microwave device wide-range modeling method based on multidimensional space division and dynamic self-adaptive sampling

Abstract

An artificial neural network microwave device wide-range modeling method based on multidimensional space division and dynamic self-adaptive sampling relates to the field of microwave device modeling. The invention provides a boundary smooth splicing method based on a Sigmoid function. And the overlapping unit samples are shared by the adjacent subareas, so that rich data support is provided for the boundary area. On the basis, an adaptive correction function is constructed by utilizing a Sigmoid function, namely, single-side Sigmoid correction is adopted in the boundary partition and double-side correction is adopted in the middle partition according to the positions of the submodels in each dimension. The correction only carries out weighted fusion in the boundary overlapping area, so that the output of the adjacent subareas is smooth and excessive, and the internal precision of each submodel is not affected. And finally, superposing all corrected sub-models to form a global continuous and seamless spliced ANN model, and effectively solving the problem of boundary discontinuity in multi-dimensional and wide-range modeling.

Inventors

• Na Weicong
• Ke Shanchao
• JIN DONGYUE
• XIE HONGYUN
• ZHANG WANRONG

Assignees

• 北京工业大学

Dates

Publication Date

20260508

Application Date

20260123

Claims (2)

1. 1. An artificial neural network microwave device wide-range modeling method based on multidimensional space division and dynamic self-adaptive sampling, Step 1, initializing modeling parameters; Aiming at the modeling problem of an N-dimensional microwave device, a design parameter vector x and a large-range modeling interval thereof are definitely input, and a target model error threshold E d , a division number L i of each dimension and a spatial overlapping coefficient delta are set; step 2, space grid division and overlapping area construction; Dividing the parameter range into L i sections in each dimension equally, constructing mutually exclusive grid subareas, and then expanding the boundaries of all subareas outwards according to an overlapping coefficient delta to construct a training subarea with an overlapping region, so as to provide a structural foundation for the subsequent boundary smoothing; step 3, extracting key points and dividing minimum units; The method comprises the steps of extracting boundary points of all training subareas in each dimension, and forming a key point sequence after sequencing, subdividing a global N-dimensional parameter space into a plurality of mutually exclusive minimum units by utilizing the sequence, and counting the number P c of each minimum unit covered by the training subareas; step4, performing dynamic self-adaptive sampling; For each non-overlapping unit, generating an initial sample by adopting a DOE method, dynamically adjusting the sampling density according to the current error of the sub-model by combining an AMG technology, adaptively increasing sampling points in a key area until the local model converges; step 5, sample distribution and sub-model parallel training; If a certain minimum unit is covered by K c training subregions, namely K c > 1, the samples in the minimum unit are shared by the subregions; collecting all minimum unit samples covered by each training subarea to form a training data set, and training each local sub-model in parallel by adopting a light ANN structure until each sub-model reaches target precision; step 6, integrating sigmoid boundary smoothing with a global model; in order to eliminate the boundary discontinuity of the submodel, a Sigmoid correction function is applied in a self-adaptive mode based on the position of the submodel in the dimension, namely, single-side correction is adopted when the submodel is positioned at the boundary of the dimension, and double-side correction is adopted when the submodel is positioned in the middle; step 7, global verification and iterative adjustment; And (3) evaluating the global model test error E on the independent test set, if E is less than or equal to E d , modeling is successful, otherwise, returning to the step (1), and adjusting the division number L i or the overlapping coefficient delta for re-modeling.
2. 2. The method according to claim 1, wherein: For a wide-range modeling problem of a microwave device, first, a design parameter vector is defined And its corresponding electromagnetic response vector Wherein N represents the number of design parameters and M represents the number of corresponding electromagnetic responses, each (x, y) forming a training data point; Let the range matrix of the modeling space be (1) Wherein X i min and X i max represent the minimum and maximum values, respectively, of the ith geometric parameter, and the range D i of parameter X i is (2) Each dimension x i is equally divided into L i segments, each segment having a length of (3) The sum of the mutually exclusive initial grid sub-regions is the sum of the memory division vector L= [ L 1 , L 2 , …, L N ] T ] (4) To establish the basis of smooth transitions, an overlap coefficient delta is introduced, and the overlap length d 0i of each dimension is calculated, i.e (5) Accordingly, expanding the boundary of each initial sub-region to generate N R training sub-regions with clear overlapping regions, wherein the k (k=1, 2.,. The range of the L i -1) sub-region in the i-th dimension is [ X i min +(k-1)d i , X i min +(k-1)d i +d 0i ], [ X i min +(L i -1)d i , X i min +L i d i ] when k=L i ; Extracting boundary points of all training subareas in each dimension, sequencing to obtain a key point sequence P i , and subdividing a global space into a series of mutually exclusive minimum units by utilizing the key points, wherein each minimum unit is a multidimensional geometrical body between adjacent key points, and the total number is (6) Where M i is the number of keypoints in dimension i; Recording the number of each minimum unit covered by the training subregion, P c , defining as non-overlapping unit when P c =1, defining as overlapping unit when P c >1, multiplexing mechanism is that if one minimum unit is covered by P c training subregions, all sample points in the minimum unit will be shared by the P c subregions, otherwise, the sample points are only used for covering a single subregion of the minimum unit, thus eliminating boundary sample inconsistency fundamentally and reducing the sampling requirement of the overlapping region by about (P c -1)/ P c ; Based on the above-described partitioning, differential sampling is implemented to further improve efficiency: (1) For non-overlapping units, DOE-AMG dynamic self-adaptive sampling is adopted, the process is carried out in a staged mode, and in the kth stage, a horizontal vector l k is defined and used for specifying the division number of each input dimension of a sample space; firstly, g-grade% ) The orthogonal DOE initializes the training sample set P 1 , corresponding to the initial horizontal vector l 1 , and then, for each sub-region R ij , a local interpolation model F (x ij ) is built whose output can be expressed as F (x ij ) =Jh, where J is the coefficient matrix to be solved and h is a set of coefficients comprising Y ij is the output value of the test sample, and each sub-region model error e ij k is estimated by the test sample, i.e (7) If the maximum error E max k =max(e ij k ) is smaller than the preset threshold E t ,E t and less than or equal to 2%, the training sample is enough to represent the input-output relation of the microwave device, and the self-adaptive orthogonal sampling is stopped, otherwise, a level l new is newly added in the center of the sub-region with the maximum error, a new sample x new is generated, and the updated level vector enters the next stage, namely k is updated to k+1; (2) For the overlapping units, performing differential fixed-number sampling according to the geometric volumes thereof; For the i-th dimension, i=1, 2,..n, divided into three types of subintervals: Type A is a long non-overlapping interval, which only appears at the initial end of the dimension, the length is d i , and the number is 1; The type B is an overlapping interval, wherein the overlapping interval appears at the junction of every two adjacent equal segments, the length is d 0i , and the number is (L i -1); Type C, short non-overlapping interval, is that at the end of each equal segment except the initial segment, the length is (d i −d 0i ), and the number is (L i -1); Thus, the total number of subintervals in each dimension is (2L i -1), which includes L i non-overlapping intervals, i.e., 1 class A+ (L i -1) class C, and (L i -1) overlapping intervals, i.e., class B; An N-dimensional overlap minimum unit formed by independently selecting one subinterval or A, B or C for each dimension and satisfying at least one dimension falling on the overlap interval or type B, defining a group of binary selection variables alpha i , β i , γ i E {0, 1} for the ith dimension and satisfying alpha i + β i + γ i =1, respectively, indicating whether the dimension is selected from A, B, C types of intervals, let k A , k B , k C respectively indicate the number of types A, B, C selected in the design parameter number N, namely K A +k B +k C = N is satisfied, and k B is not less than 1; The geometric volume V of the overlapping minimum unit may be given by the product of the lengths of the selected regions of the dimensions: (8) Substituting formula (5), the above volume formula can be simplified as: (9) Given that the overlap factor δ is typically small (δ+.0.1), then δ < 1-2 δ <1- δ < 1; of all overlapping cells, the cell with the smallest volume appears in the case of k B =n, i.e. all dimensions fall within the class B interval, with a volume of ; Setting a basic sampling number m corresponding to the sampling number of the volume minimum unit V min , for any other overlapping unit, first calculating the ratio R of its volume to the minimum volume V min , (10) Then, in combination with the analysis of the volume formula, the ratio R is mainly determined by the number k B of the overlapping dimensions of the unit, and the sampling point number is determined as ; After sampling is completed, each training subarea collects samples in all the minimum units covered by the subarea to form an independent training data set, and as the consistency of boundary samples is solved, each subarea can adopt an ANN with a simple structure, namely a simple MLP structure with a hidden layer of 1 layer or 2 layers to carry out completely independent parallel training, and the training of a t-th submodel is realized by minimizing an error function of the training subarea: (11) Wherein the method comprises the steps of Representing the output of the t-th sub-model, For corresponding real electromagnetic simulation response, N t represents the number of training samples required for training the t-th sub-model, N f represents the number of frequency points, x k represents the k-th training sample, w t represents the ANN internal weight of the t-th sub-model, and f q represents the q-th frequency point; A boundary smoothing method based on Sigmoid function is disclosed, which includes defining an index vector for each sub-model For accurately locating its position in a global grid, i.e (12) Where mod represents the modulo operation, the symbol pair Representing a downward rounding; The adjacent charge condition of the two sub-models is that (13) Wherein t 1 and t 2 represent the numbers of the different sub-models; for the t th sub-model, a correction function is adaptively constructed along each dimension x i according to its index λ i t and the total number of divisions L i : (1) If L i =1, the dimension is not divided =1, No correction is required; (2) If λ i t =1, the partition is started, then only the modified Sigmoid function S i t,u (x i along the boundary in the x i dimension is applied, i.e. (14) (3) If lambda i t =L i is the termination partition, then only the modified Sigmoid function S i t,l (x i along the boundary in the x i dimension is applied, i.e (15) (4) If 1< lambda i t < L i , the middle partition, then bilateral correction is applied to both upper and lower boundaries, i.e (16) For upper boundary correction, the transition center c i t,u is the center point of the boundary of the adjacent subarea, the slope a i t,u =12/d 0i ensures that the correction is strictly limited in the overlapping area with the width d 0i ; The total correction function of the t-th sub-model is the product of all its dimension correction functions, i.e (17) The corrected submodel is output as (18) Finally, by linearly superposing all the corrected sub-models, a global continuous model covering the whole modeling space is obtained, namely (19) The input of the model is the design parameter of the microwave device, and the output is the response of the microwave device.

Description

Artificial neural network microwave device wide-range modeling method based on multidimensional space division and dynamic self-adaptive sampling Technical Field The invention relates to the field of modeling of microwave devices, in particular to a wide-range modeling problem under a multidimensional parameter space. Background In recent years, the rapid development of mobile communication technology continues to push the emergence of new processes, new materials and new structure microwave devices. To address the increasing device design needs, modeling techniques based on artificial neural networks (ARTIFICIAL NEURAL NETWORK, ANN) have been widely used in the microwave device design flow [1]-[5]. ANN simulates the information processing mechanism of the human brain nervous system by a mathematical method, and a well-trained neural network model can rapidly and accurately represent the complex nonlinear relationship between input and output in a modeling space. The microwave device replacement model constructed based on ANN can replace time-consuming full-wave electromagnetic simulation, and realizes rapid optimization design, so that the design efficiency is remarkably improved, and the development period is shortened. However, in the practical design process, in order to meet diversified performance indexes, the geometric parameters of the microwave device often need to be optimally adjusted [6]-[8] in a relatively large range. As the range of parameter variation expands, the nonlinearity between the device response and its geometric parameters increases significantly, which makes the construction of a wide range parameterized model that is both accurate and efficient, a serious challenge. If a single neural network is used to cover the whole parameter space, although the method is feasible in theory, the required training samples and the test samples are huge in quantity, and the time for generating the samples is long, so that the overall modeling efficiency is low. In addition, this approach tends to converge slowly and the final model accuracy is difficult to predict. In order to alleviate the above problems, researchers have proposed parallel decomposition techniques, i.e. dividing a wide-range parameter space into a plurality of sub-regions and respectively establishing sub-models, and then splicing to form an overall model, so as to increase the modeling speed [9]. However, the method still needs to generate a large number of training samples uniformly distributed in the whole modeling space in advance to divide the region, so that the method is still limited by the bottleneck of large sample scale and long sampling time, and the overall modeling efficiency is improved only to a limited extent. Therefore, it has become an urgent need to develop a new method that can efficiently model a wide range of highly nonlinear microwave devices in a parameterized manner. Therefore, the invention provides an artificial neural network modeling method based on multidimensional space division and dynamic self-adaptive sampling, which aims to realize efficient and high-precision modeling of a wide-range parameter space of a microwave device through a systematic space decomposition and intelligent sampling strategy. Reference is made to: [1]H. M. Torun, A. C. Durgun, K. Aygün, and M. Swaminathan, "Causal and passive parameterization of s-parameters using neural networks," IEEE Transactions on Microwave Theory and Techniques, vol. 68, no. 10, pp. 4290–4304, 2020. [2]Feng F, Na W, Jin J, et al. ANNs for Fast Parameterized EM Modeling: The State of the Art in Machine Learning for Design Automation of Passive Microwave Structures[J]. IEEE Microwave Magazine, 2021, 22(10): 37-50. [3]Y. Yu, Z. Zhang, Q. S. Cheng, B. Liu, Y. Wang, C. Guo, and T. T. Ye, "State-of-the-art: AI-assisted surrogate modeling and optimization for microwave filters," IEEE Transactions on Microwave Theory and Techniques, vol. 70, no. 11, pp. 4635–4651, 2022. [4]Liu Z, Hu X, Liu T, et al. Attention-Based Deep Neural Network Behavioral Model for Wideband Wireless Power Amplifiers[J]. IEEE Microwave and Wireless Components Letters, 2020, 30(1): 82-85. [5]F. Feng, W. Na, J. Jin, J. Zhang, W. Zhang, and Q.-J. Zhang, "Artificial neural networks for microwave computer-aided design: The state of the art," IEEE Transactions on Microwave Theory and Techniques, vol. 70, no. 11, pp. 4597–4619, 2022. [6]H. Kabir, V. Shilimkar, L. Zhang and K. Kim, "Large space RFIC spiral inductor parametric modeling technique," 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), Ottawa, ON, Canada, 2015, pp. 1-3. [7]P. Barmuta, G. Avolio, F. Ferranti, A. Lewandowski, L. Knockaert and D. M. M. . -P. Schreurs, "Hybrid Nonlinear Modeling Using Adaptive Sampling," in IEEE Transactions on Microwave Theory and Techniques, vol. 63, no. 12, pp. 4501-4510, Dec. 2015. [8]H. Kabir, L. Zhang and K. Kim, "Automatic para