A wideband frequency response extrapolation system and method

Abstract

A wideband frequency response extrapolation system and method are disclosed. This method employs a long-short memory recurrent neural network to address the correlated characteristic responses between high and low frequencies, uses Hilbert transform to solve the complex impedance extrapolation problem, and employs a variational inference-based Bayesian method to evaluate the uncertainty of the prediction in the extrapolation space. This method can estimate the frequency response over a wide range without requiring additional measurements, while overcoming the limitations of traditional methods in terms of the frequency band and the number of sampling points, as well as the inability to accurately predict non-smooth responses.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic compatibility of spacecraft, and in particular to a method for analyzing responses outside a frequency band based on the response within the test or analysis frequency band. Background Technology

[0002] Electromagnetic compatibility (EMC) is a crucial aspect of spacecraft reliability design, especially for microwave-loaded spacecraft. The complex electromagnetic environment necessitates EMC control. Traditional methods of addressing issues based on later testing results are unsuitable for microwave-loaded spacecraft EMC work. This is because the electromagnetic environment of microwave-loaded spacecraft is complex, and EMC design requirements are stringent. During the spacecraft verification phase, the design and development are largely finalized, leaving limited options for addressing EMC issues at their root. Therefore, it is essential to conduct EMC analysis during the individual device design phase to proactively implement EMC design and ensure the EMC of the spacecraft system from the outset.

[0003] Current electromagnetic compatibility (EMC) design and EMC control for spacecraft primarily focus on the frequency domain, controlling the electromagnetic response within the required frequency band. For microwave payload spacecraft, the system operates over a wider frequency band, requiring EMC control and design to be conducted across this broad band. The wide-band EMC requirements of spacecraft systems present a challenge for EMC assessment during the design phase: firstly, in the early design stages, comprehensive EMC testing of the equipment is often lacking, making it impossible to obtain wide-band test data; secondly, within the wide band, the parasitic parameters and high-frequency responses of components and circuits vary significantly, making it difficult to obtain the responses of different components and circuits across the entire band. Therefore, directly performing wide-band frequency response analysis is challenging and even impractical.

[0004] To address the aforementioned issues, this invention proposes a method for cross-band out-of-band response analysis based on finite frequency band response data. This method aims to enable the evaluation of wide-band electromagnetic response under spacecraft system-level electromagnetic compatibility requirements, based on finite frequency band analysis and test data during the initial design phase of equipment design.

[0005] A common method for extrapolating frequency domain data is the Cauchy method, where the frequency response is modeled as the ratio of two polynomials whose coefficients are determined using singular value decomposition (SVD). The estimated response is then analyzed for extrapolation. This method is only applicable to the extrapolation of smooth frequency responses and is not suitable for non-smooth responses. If the sampled data misses poles or zero frequencies, the extrapolation may be incorrect. An extrapolation method is presented in "Extrapolation of time and frequency responses of resonant antennas using damped sinusoids and orthogonal polynomials," which represents the frequency response as the sum of orthogonal polynomials and uses a genetic algorithm to extract the necessary extrapolation parameters. It uses a fixed analysis function to describe the response and cannot generalize to multiple frequency responses. "Direct extrapolation of a causal signal using low-frequency and early-time data based on matrix equations" uses a conjugate gradient descent iterative scheme to solve the integral equations, inferring low-frequency and early-time responses, but has limitations in inferring high-frequency and broadband responses. Summary of the Invention

[0006] This disclosure overcomes the shortcomings of the prior art and provides a system and method for analyzing responses outside a frequency band based on the response within the test or analysis frequency band in the field of spacecraft electromagnetic compatibility. It can extrapolate wide-band responses and is applicable to non-smooth phenomena in frequency responses.

[0007] The wideband frequency response extrapolation system disclosed herein is implemented using a machine learning architecture. This architecture comprises four units:

[0008] Unit 1: In-band input signal processing network, used to decompose the input signal into two data sequences, real part and imaginary part. The real part sequence is input to Units 2 and 4, and the imaginary part sequence is input to Unit 4.

[0009] The second unit is a long short-term memory recurrent neural network, which is used to extrapolate the signal input from the first unit based on the loss calculation results of the fourth unit, and obtain the predicted values ​​of the in-band and out-of-band real parts.

[0010] The third unit: Hilbert transform network, used to perform frequency response analysis on the signal obtained in the second unit and obtain the predicted value of the imaginary part;

[0011] The fourth unit is the loss calculation network, which is used to calculate the loss based on the difference between the actual and predicted values ​​of the in-band signal. The calculation results are then output to the second unit for network training and optimization.

[0012] Furthermore, the Long Short-Term Memory Recurrent Neural Network uses a probability-based quantification method to predict uncertainty for the hidden layers.

[0013] Furthermore, the loss calculation network performs loss calculation based on the actual values ​​of the real and imaginary parts of the in-band signal, as well as the difference between the predicted values ​​of the real and imaginary parts of the in-band signal.

[0014] This disclosure provides a broadband frequency response extrapolation method, comprising the following steps:

[0015] Step S1, In-band signal processing: Decompose the acquired frequency response signal into real and imaginary parts, establish data sequences for each part, and divide them into multiple intervals;

[0016] Step S2: For each interval, based on the long short-term memory recurrent neural network, the real part sequence is extrapolated to obtain the predicted values ​​of the real part in and out of the band.

[0017] Step S3: Perform Hilbert transform on the predicted signal obtained in step S2 to obtain the predicted values ​​of the in-band and out-of-band imaginary parts;

[0018] Step S4: Calculate the loss function based on the difference between the predicted signal and the actual signal, and use it for training and optimization of the long short-term memory recurrent neural network;

[0019] Step S5: Repeat steps S2 to S4 until the data calculation rounds for all intervals are completed, and obtain the out-of-band frequency response.

[0020] Furthermore, step S1 specifically includes:

[0021] The in-band response Z in-band (f) divided into y r =Re[Z in-band (f)] and y imag =Im[Z in-band (f)];

[0022] y r It is divided into W intervals, each interval including P peaks or extremes, the values ​​of which are determined according to the designer's needs;

[0023] In each interval, data scaling is performed to limit the originally dynamically large data to the range [0,1]. Methods include:

[0024]

[0025] In the formula, Zω (f i ) represents the frequency point f in each interval. i of y r Value, Z' ω (f i The values ​​are scaled values, and max(·) and min(·) represent the maximum and minimum values ​​in the current interval, respectively; i = 1, 2, 3, ..., N, where N is the total number of frequency samples, forming the dataset.

[0026] Z' ω (f i Forming data sequences: Each data sequence consists of S sampled data. The first sequence in the data sequence is a sample from frequency exponent 0 to S-1, the second sequence is a sample from frequency exponent 1 to S, the third sequence is a sample from frequency exponent 2 to S+1, and so on. For a total of N samples, there are N-S+1 sequences.

[0027] Establish a feature sequence set and a target sequence set. The feature sequence set is the set of data sequences obtained from the input signal, and the target sequence set is the set of data sequences that need to be obtained by extrapolation.

[0028] Furthermore, step S2 specifically includes:

[0029] The parameters of the deep learning hidden layer network are determined. For each feature sequence set, the batch number of the deep learning is determined. For each batch of input, the long short-term memory recurrent neural network generates future values ​​of samples at a certain scale.

[0030] Sample the standard Gaussian distribution ε ~ N(0,1) and calculate ω = μ + ε × σ to form a new known probability distribution q(ω), where ω is the probability distribution parameter; μ is the mean; and σ is the standard deviation.

[0031] The probability distribution p(θ|D) is formed from the dataset D;

[0032] θ represents the parameters to be optimized. A set of optimal parameters θ is selected. opt By minimizing the KL divergence, the parameter θ is calculated. opt :

[0033]

[0034] Where KL[·] represents the calculation of KL divergence;

[0035] Use parameter θ opt The feature sequence is input into the long short-term memory recurrent neural network to predict the target sequence for all batches, thereby deriving the output.

[0036] Furthermore, in step S2, each sequence set contains 700 sequences for training and 301 sequences for testing, for a total of 10 batches.

[0037] Furthermore, step S3 specifically includes:

[0038] Flip the input signal: Where y real (-f) indicates that the real part characteristic y of the original signal is transformed. real (f) The new signal characteristics obtained by flipping the frequency f;

[0039] Forming a two-sided signal:

[0040] For y DS Perform a discrete Fourier transform: Y DS =DFT(y DS );

[0041] Forming a one-sided signal: Y single sided =2Y DS ;

[0042] Perform a Hilbert transform to obtain the imaginary part.

[0043]

[0044] Where K represents the number of sampling points, and m represents each sampling point, with values ​​ranging from 0 to K-1.

[0045] Furthermore, step S4 specifically includes:

[0046] The loss L1 between the actual and predicted values ​​of the real part within the band is calculated as follows:

[0047]

[0048] Where p(y r )and These represent the probability distributions of the actual value and the predicted value, respectively.

[0049] The loss L2 between the in-band actual value and the predicted value of the imaginary part is calculated as follows:

[0050]

[0051] Among them, y imag and These represent the actual and predicted values ​​of the imaginary part, respectively.

[0052] Calculate the overall loss L:

[0053] L=α×L1+β×L2

[0054] Here, α is chosen to optimize the network performance, and the network is affected by α. 2 +β 2 =1 and constraints of α>0, β>0;

[0055] Calculate the loss gradient g:

[0056]

[0057] make:

[0058]

[0059]

[0060] Where ξ is the learning rate;

[0061] The obtained μ and σ are used to train and optimize the long short-term recurrent neural network.

[0062] Further out-of-band calculation results:

[0063]

[0064] The frequency response extrapolation method disclosed herein employs a long-short memory recurrent neural network to address the correlation characteristic response between high and low frequencies, a Hilbert transform to solve the complex impedance extrapolation problem, and a variational inference-based Bayesian method to evaluate the uncertainty of the prediction in the extrapolation space. This method can estimate the frequency response over a wide range without requiring additional measurements, while overcoming the limitations of traditional methods in terms of the frequency band and number of sampling points, and the inability to accurately predict non-smooth responses.

[0065] Compared with the prior art, the beneficial effects of this disclosure are:

[0066] 1) Based on data from a limited frequency band, wide-band frequency response analysis can be performed, effectively solving the problem of insufficient frequency band data when conducting electromagnetic compatibility analysis and evaluation in the early stages of microwave payload spacecraft electronic equipment design.

[0067] 2) Long-short memory recurrent neural networks are used to solve the problem of correlation feature response between high and low frequencies, and to realize cross-band frequency response data extrapolation.

[0068] 3) For long short memory recurrent neural networks, this invention proposes a probability-based quantitative prediction uncertainty method for the hidden layer, which solves the problem that traditional error-based training methods cannot eliminate the uncertainty involved in prediction.

[0069] 4) A frequency response analysis method based on Hilbert transform is proposed, which is applicable to the signal characteristics of actual electromagnetic environments, while reducing the complexity of prediction analysis and mathematical calculation.

[0070] 5) The proposed comprehensive loss function calculation method makes full use of the information from known and predicted data, and considers the uncertainty of prediction, to ensure that the training of machine learning networks is more sufficient and accurate, and to make full use of known information to ensure the applicability of machine learning networks. Attached Figure Description

[0071] The above and other objects, features and advantages of this disclosure will become more apparent from the more detailed description of exemplary embodiments of this disclosure taken in conjunction with the accompanying drawings, in which the same reference numerals generally represent the same components.

[0072] Figure 1 This diagram shows the system architecture for wideband frequency response extrapolation according to this disclosure;

[0073] Figure 2 Input data for an exemplary embodiment;

[0074] Figure 3 Scaling processing result for an exemplary embodiment;

[0075] Figure 4 Analysis results for an exemplary embodiment. Detailed Implementation

[0076] Preferred embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art.

[0077] In the printed circuit board design of equipment, the power distribution network design directly relates to the power integrity of the equipment, thus significantly impacting its electromagnetic compatibility (EMC). Therefore, it is necessary to conduct a comprehensive analysis of the impedance characteristics of the power distribution network during the equipment design phase. The EMC design of equipment addresses the EMC requirements of the system, which typically require a wide frequency band. During the equipment design phase, due to limitations imposed by the equipment's state and the unknown nature of distributed parameters and parasitic parameters across a wide frequency band, only a limited bandwidth frequency response can often be obtained. This embodiment focuses on a power distribution network, predicting the wideband frequency response from the narrowband frequency response.

[0078] As attached Figure 1As shown, this disclosure employs a machine learning architecture to achieve wideband frequency response extrapolation. This architecture comprises four parts: the first part is an in-band input signal processing network; the second part is a long short-term memory recurrent neural network; the third part is a Hilbert transform network; and the fourth part is a loss calculation network.

[0079] The main functions and connections of the four parts are as follows:

[0080] 1. In the first part of the in-band input signal processing network, the input signal is decomposed into real and imaginary parts to form a data sequence. The real part sequence is input to the second and fourth parts. The imaginary part sequence is input to the fourth part.

[0081] 2. The second part is a Long Short-Term Memory Recurrent Neural Network. Based on the input signal from the first part and the loss function from the fourth part, the network is trained, and the output is the predicted in-band and out-of-band real parts. This output is then fed into the third part.

[0082] 3. The third part is a Hilbert transform network, which transforms the in-band and out-of-band real part predictions from the second part into imaginary part predictions. These real and imaginary part predictions are then passed to the fourth part. After the second part's long short-term memory recurrent neural network is trained, the third part outputs the real and imaginary part predictions, forming the out-of-band calculation result.

[0083] 4. The fourth part is the loss calculation network, which receives the actual values ​​of the real and imaginary parts of the in-band signal from the first part, as well as the predicted values ​​of the real and imaginary parts of the in-band signal from the third part, performs loss calculation, and outputs the calculation results to the second part for network training and optimization.

[0084] The specific calculation steps include:

[0085] 1. The in-band response Z in-band (f) divided into y r =Re[Z in-band (f)] and y imag =Im[Z in-band (f)].

[0086] 2. As attached Figure 2 As shown, y r It is divided into 5 intervals, each of which includes 3 peaks or extremes, and the values ​​are determined according to the designer's needs.

[0087] 3. Within each interval, data scaling is performed to limit the range of the data, confining the originally highly dynamic data to the range [0,1]. This processed data, used as input for subsequent deep learning, allows the neural network to converge faster and with smaller errors. The preferred method is:

[0088]

[0089] In the formula, Z ω (f i ) represents the frequency f in each interval i point y r Value, Z' ω (f i The values ​​are scaled values. `max(·)` and `min(·)` represent the maximum and minimum values ​​within the current interval, respectively. `i` = 1, 2, 3, ..., N, where N is the total number of frequency samples; in this example, it is 2000. The results are attached. Figure 3 As shown. This forms a dataset.

[0090] 4. Place Z' ω (f i The data sequences are formed. Each data sequence consists of 1000 sampled data points. The first sequence contains samples from frequency exponent 0 to S-1, the second sequence contains samples from frequency exponent 1 to S, the third sequence contains samples from frequency exponent 2 to S+1, and so on. For a total of N samples, there are 1001 sequences. The data is divided into different sequences, and the neural network is trained using these sequences.

[0091] 5. Establish feature and target sequence sets, as shown in the table below:

[0092] Feature sequence target sequence Sequence 0 Sequence 1 Sequence 1 Sequence 2 …… …… Sequence i-1 Sequence i …… …… Sequence N-S+1 Predicted sequence

[0093] 6. Determine the parameters of the deep learning hidden layer network, and determine the number of batches B for each sequence set G. The network receives 700 sequences sequentially for training and 301 sequences for testing, for a total of 10 batches. For each batch of input, the Long Short-Term Memory recurrent network layer generates future values ​​at a scale of F samples.

[0094] 7. Sample the standard Gaussian distribution ε ~ N(0,1) to form a new known probability distribution q. θ (ω), and calculate ω=μ+ε×σ.

[0095] 8. The probability distribution p(θ|D) is formed from D. A set of optimal parameters θ was chosen. opt By minimizing the KL divergence, the parameter θ is calculated. opt :

[0096]

[0097] Where KL[·] represents the calculation of KL divergence.

[0098] 9. Using parameter θ optThe feature input sequence is fed into an LSTM-RNN to predict the target sequence for all batches, thus yielding the output y. r .

[0099] 10. Calculate the loss L1 between the actual and predicted values ​​within the band. The calculation method is as follows:

[0100]

[0101] Where p(y r )and Let Z and θ represent the probability distributions of the actual and predicted values, respectively, and p(Z|θ,D) refer to the likelihood value.

[0102] 11. Calculate the Hilbert transform and obtain the imaginary part. The process is as follows:

[0103] 1) Flip the input signal:

[0104] 2) Forming a two-sided signal:

[0105] 3) For y DS Perform a discrete Fourier transform: Y DS =DFT(y DS )

[0106] 4) Forming a one-sided signal: Y single sided =2Y DS

[0107] 5) Perform a Hilbert transform to obtain the imaginary part.

[0108]

[0109] 12. Calculate the loss L2 between the actual value and the predicted value. The calculation method is as follows:

[0110]

[0111] Among them, y imag and These represent the actual value and the predicted value of the imaginary part, respectively.

[0112] 13. Calculate the overall loss L:

[0113] L=α×L1+β×L2

[0114] Here, α is chosen to optimize the network performance, and the network is affected by α. 2 +β 2 =1 and α>0, β>0 constraints, here we take α=0.8, β=0.6.

[0115] 14. Calculate the loss gradient g:

[0116]

[0117] 15. Order:

[0118]

[0119]

[0120] Where ξ = 0.05.

[0121] 16. Repeat steps 6 to 14 until all data calculation rounds are completed.

[0122] 17. As attached Figure 4 As shown, the out-of-band calculation results are obtained:

[0123]

[0124] The above technical solutions are merely exemplary embodiments of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the methods described in the specific embodiments of the present invention. Therefore, the methods described above are merely preferred and not restrictive.

Claims

1. A broadband frequency response extrapolation method, comprising the following steps: Step S1, in-band signal processing: decompose the obtained frequency response signal into real and imaginary parts, respectively establish data sequences, and divide them into multiple intervals; Step S2, for each interval, based on a long short-term memory recurrent neural network, the real part sequence is extrapolated to obtain in-band and out-of-band real part prediction values; Step S3, performing Hilbert transform on the prediction signal obtained in step S2 to obtain in-band and out-of-band imaginary part prediction values; Step S4, based on the difference between the prediction signal and the actual signal, a loss function is calculated for training and optimization of the long short-term memory recurrent neural network; Step S5, repeat steps S2-S4 until the data calculation round of all intervals is completed to obtain the out-of-band frequency response; The step S1 specifically comprises: in-band response split into and ; Will be divided into intervals, each interval includes peaks or poles, the value of which is determined according to the needs of the designer; ​ In each interval, the data is scaled to limit the originally larger dynamic data to between [0, 1], the method comprising: wherein, denotes the value of the frequency sample at the frequency point of the interval, is the scaled value, and denote the maximum and minimum values in the current interval, respectively; , is the total number of frequency samples forming the data set ;​ Forming data sequences: determine that each data sequence includes samples of data, the first sequence in the data sequence having samples from frequency index 0 to the second sequence having samples from frequency index 1 to the third sequence having samples from frequency index 2 to and so on, for a total of samples, there are sequences;​ Establishing a feature sequence set and a target sequence set, the feature sequence set being a set of data sequences obtained from the input signal, and the target sequence set being a set of data sequences that need to be obtained by extrapolation.

2. The method of claim 1, wherein, The step S2 specifically comprises: Determine the deep learning hidden layer network parameters, for each feature sequence set, determine the number of batches of deep learning, and for each batch input, the long short-term memory recurrent neural network generates a certain scale of future values of samples; Sampling from a standard Gaussian distribution and computing forms a new known probability distribution where ω is a probability distribution parameter; μ is the mean; σ is the standard deviation; from the dataset forming a probability distribution ; Θ are parameters to be optimized and solved, select a set of optimal parameters , by minimizing the KL divergence, calculate the parameters : wherein, denotes the computation of the KL divergence; Usage parameters inputting the sequence of features into the long short-term memory recurrent neural network to predict the sequence of targets for all batches, thereby resulting in an output .

3. The method of claim 2, wherein, In the step S2, each sequence set contains 700 sequences for training and 301 sequences for testing, and a total of 10 batches are received.

4. The method of claim 2, wherein, The step S3 specifically comprises: The input signal is flipped: wherein represents the original signal real part characteristics are frequency flipped to obtain new signal characteristics; forming a bilateral signal: ; To do the discrete Fourier transform: ;​ forming a single side signal: ; Performing a Hilbert transform to obtain the imaginary part : Wherein, K represents the number of sampling points, and m represents each sampling point, the value of which is from 0 to K-1.

5. The method of claim 3, wherein, The step S4 specifically comprises: loss between the in-band actual value and the predicted value of the real part is calculated the calculation method is: wherein, and respectively denote the probability distribution of the actual and predicted values; loss between the in-band actual value and the predicted value of the imaginary part is calculated the calculation method is: wherein and Im and Im, respectively, denote the actual and predicted values of the imaginary part; Computing the overall loss : wherein the selection to optimize the performance of a network subject to and , constraints. Computing loss gradients : Let: wherein, is a parameter learning rate; Use the obtained μ and σ to train and optimize the long short-term memory recurrent neural network.

6. The method of claim 4, wherein, Out-of-band calculation result: 。

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