Harmonic balance method, device and medium based on neural network

Abstract

This invention discloses a harmonic balancing method, device, and medium based on a neural network, belonging to the field of nonlinear circuit simulation analysis. The method includes the following steps: S1, establishing the node voltage equations of the nonlinear circuit; S2, constructing a neural network and an error function: constructing a three-layer BP neural network, where the input layer is a discrete time sequence of a complete cycle; the hidden layer includes a set of trigonometric functions of harmonic components or mixed frequency components; the output layer is the steady-state solution of the node voltage equations of the nonlinear circuit; the error function is constructed based on the node voltage equations of the nonlinear circuit; S3, training the constructed neural network to obtain the steady-state solution satisfying the node voltage equations of the nonlinear circuit. This invention avoids the frequent time-frequency transformations in the wave balancing method during iteration and is applicable to single-tone and multi-tone excitation. Simultaneously, it has high accuracy and good convergence, and is a method independent of initial values, making it very suitable for the periodic response analysis of nonlinear circuits.

Description

Technical Field

[0001] This invention relates to the field of nonlinear circuit simulation and analysis, and more specifically, to a harmonic balancing method, device, and medium based on neural networks. Background Technology

[0002] Harmonic balance (HB) techniques are widely used in the periodic response analysis of nonlinear circuits, approximating the steady-state solution of the circuit using a set of trigonometric polynomials. Currently, a widely applied technique is Piecewise Harmonic Balance (PHB), proposed by MSNakhla and J. Vlach et al. This technique decomposes the nonlinear network into linear and nonlinear components, analyzing the linear component in the frequency domain and the nonlinear component in the time domain, thus significantly reducing the solution size and effectively improving computational efficiency. Piecewise harmonic balance technology has laid the foundation for subsequent research and commercial software applications.

[0003] However, a drawback of piecewise harmonic balancing techniques is that time-frequency transformation and its inverse transformation are required at each step of the iterative calculation. For single-tone excitation circuits, the Discrete Fourier Transform (DFT) is typically used to perform the time-frequency domain transformation. For multi-tone excitation circuits such as mixers and modulators, the time-frequency transformation becomes more complex. Although scholars have proposed some methods to solve the time-frequency transformation problem under multi-tone excitation, researching a method that does not require time-frequency transformation remains of great significance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a harmonic balancing method, device, and medium based on neural networks. This avoids the frequent time-frequency changes in the iterative process of the propagation balancing method and is applicable to both single-tone and multi-tone excitation. Furthermore, it exhibits high accuracy and good convergence, and is an initial value-independent method, making it highly suitable for the periodic response analysis of nonlinear circuits.

[0005] The objective of this invention is achieved through the following approach:

[0006] A harmonic balancing method based on neural networks includes the following steps:

[0007] S1, establish the node voltage equations for the nonlinear circuit;

[0008] S2, construct the following neural network and error function: Construct a three-layer BP neural network, whose input layer is a discrete time sequence of a complete cycle; its hidden layer includes a set of trigonometric functions of harmonic components or mixed frequency components; its output layer is the steady-state solution of the voltage equation of the nonlinear circuit node; the error function is constructed based on the voltage equation of the nonlinear circuit node.

[0009] S3, train the constructed neural network to obtain the steady-state solution that satisfies the voltage equation of the nonlinear circuit node.

[0010] Furthermore, in step S2, the activation function of the hidden layer is a set of trigonometric functions containing harmonic frequencies when the excitation is single-tone; when the excitation is multi-tone, the activation function is a trigonometric function containing mixed frequencies.

[0011] Furthermore, in step S2, the weight matrix of the input layer is a constant vector; the hidden layer does not contain a bias term, and the elements of the weight matrix of the hidden layer are the coefficients in the steady-state solution of the nonlinear circuit node voltage equation; the bias vector of the output layer is composed of the DC shunt of the nonlinear circuit node voltage equation.

[0012] Furthermore, the elements of the weight matrix of the hidden layer are coefficients in the steady-state solution of the voltage equation of the nonlinear circuit node, specifically: Fourier coefficients when single-tone excitation, and coefficients of the trigonometric function of the mixed frequency when multi-tone excitation.

[0013] Furthermore, in step S2, during the error backpropagation process, without the need for training samples, the error function of the neural network is directly reconstructed using the voltage equations of the nonlinear circuit nodes.

[0014] Further, in step S2, the error function of the reconstructed neural network includes the following sub-steps: using the gradient descent algorithm to update the weights and biases of the neural network, thereby minimizing the error function; and obtaining the gradients of the error function with respect to the weight matrix of the hidden layer and the bias vector of the output layer based on the topology and components of the specific circuit, and then updating the weight matrix of the hidden layer and the bias vector of the output layer respectively.

[0015] Furthermore, in step S3, during the neural network training process, the initial value, learning rate, and expected error are first set; then the training algorithm is selected; finally, the forward calculation process and the error backpropagation process are alternately iterated, and the weight matrix of the hidden layer and the bias vector of the output layer are updated until convergence to the expected error.

[0016] Furthermore, in step S3, the training algorithm includes gradient descent; the learning rate is dynamically adjusted according to the network's error value.

[0017] A computer device comprising a processor and a memory, the memory storing a computer program which, when loaded by the processor, executes the method as described in any of the preceding claims.

[0018] A computer-readable storage medium storing a computer program therein, the computer program being loaded by a processor and executing the method as described in any of the preceding claims.

[0019] The beneficial effects of this invention include:

[0020] This invention proposes a harmonic balance method based on neural networks, which is named NNHB (Neural Network based Harmonic Balance, abbreviated as NNHB) and can be used for the analysis of the periodic response of nonlinear circuits.

[0021] This invention constructs a back propagation (BP) neural network with a special structure, and then trains it to obtain a steady-state solution that satisfies the nonlinear circuit equations. The NNHB method avoids the frequent time-frequency changes during iteration in traditional harmonic balance methods and is applicable to both single-tone and multi-tone excitations. Furthermore, the NNHB method exhibits high accuracy and good convergence, and is an initial value-independent method. This invention is highly suitable for the periodic response analysis of nonlinear circuits. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the NNHB neural network structure constructed in this invention;

[0024] Figure 2 This is a schematic diagram of the power supply circuit involved in the embodiments of the present invention;

[0025] Figure 3a This is a time-domain waveform diagram of node voltage 1 in an embodiment of the present invention;

[0026] Figure 3b This is the amplitude spectrum diagram of node voltage 1 in an embodiment of the present invention;

[0027] Figure 3c This is a time-domain waveform diagram of node voltage 2 in an embodiment of the present invention;

[0028] Figure 3d This is the amplitude spectrum of node voltage 2 in an embodiment of the present invention;

[0029] Figure 3e This is a time-domain waveform diagram of node voltage 3 in an embodiment of the present invention;

[0030] Figure 3f This is the amplitude spectrum of node voltage 3 in an embodiment of the present invention;

[0031] Figure 4a This is the deviation curve between the simulation results of node voltage 1NNHB and PHB in the embodiment of the present invention;

[0032] Figure 4b This is the deviation curve between the simulation results of the node voltage 2NNHB and PHB in the embodiment of the present invention;

[0033] Figure 4c The figure shows the deviation curve between the node voltage 3NNHB and the simulation results of PHB in the embodiment of the present invention. Detailed Implementation

[0034] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.

[0035] To address the technical problems mentioned in the background, embodiments of the present invention provide a harmonic balance method based on neural networks in the periodic response analysis of nonlinear circuits, comprising:

[0036] Step 1: Establish the circuit node voltage equations

[0037] For the nonlinear circuit to be analyzed, its node voltage equations are established according to circuit theory: arbitrarily select a node in the circuit as the reference node, and the other nodes as independent nodes. The voltages between these nodes and the reference node are called node voltages. Then, the current of each branch is expressed by the node voltages. The resulting set of independent equations is called the node voltage equations.

[0038] Based on the number of frequencies contained in the circuit's excitation source, circuits can be classified into single-tone excitation and multi-tone excitation. According to circuit analysis theory, the steady-state solution of a nonlinear circuit with single-tone excitation is in the following Fourier series form.

[0039]

[0040] That is, it consists of a set of trigonometric functions containing harmonic frequencies. The steady-state solution of the multi-tone excitation circuit, on the other hand, consists of a set of mixed frequency components and no longer contains harmonic frequencies.

[0041] It should be noted that the steps of the NNHB method in analyzing single-tone and multi-tone excitations are roughly the same. Therefore, the following text will take single-tone excitation as an example and only explain the differences when there are differences with multi-tone excitation.

[0042] Step 2: Constructing the neural network in NNHB

[0043] Backpropagation (BP) neural networks are a widely used type of neural network that can achieve nonlinear mapping. The BP neural network method includes two processes: forward computation and backward propagation. The activation values ​​are obtained through forward computation, and the network weight matrix and bias vector are adjusted through backpropagation of the error.

[0044] This invention constructs a special three-layer BP neural network, which, through training, allows the network's output to satisfy the voltage equations at circuit nodes. The specific construction process is as follows:

[0045] (1) Neural network structure

[0046] The neural network constructed in NNHB is a three-layer BP neural network (e.g. Figure 1 As shown in the figure, its input layer is a discrete time sequence of a complete cycle; its hidden layer consists of a set of trigonometric functions of harmonic components or mixed frequency components; and its output layer is the steady-state solution of the circuit node voltage equation.

[0047] Unlike traditional BP neural networks, Figure 1 The activation function of the hidden layer is a set of trigonometric functions containing harmonic frequencies. For multi-tone excitation, the activation function is a trigonometric function containing mixed frequencies.

[0048] Figure 1 The weight matrix of the input layer is U = [1,1,…,1]. 2N×1 It is a constant vector. The hidden layer does not contain a bias term; the elements of its weight matrix W are the Fourier coefficients in equation (1), i.e.

[0049]

[0050] The bias vector C of the output layer is formed by the DC shunt of equation (1), i.e., C = [c1 … c i … c M ] T .

[0051] (2) Forward computation

[0052] Another difference between NNHB and traditional BP neural networks is that NNHB does not require additional training samples because its error function is constructed from the circuit equations. The steady-state solution of the circuit is V = [V1, V2, ..., V...]. M ] T It is periodic, i.e., V i (t)=V i (t+nT), therefore we only need to consider one complete period.

[0053] Dividing the time interval [0, T] into X equal parts yields the discretized time series [t0, t1, ..., tt].X Let X be the number of samples in the neural network. Therefore, the forward computation is to calculate the value of V at each time point, and the neural network at time t... j The output at time t is

[0054]

[0055] (3) Backpropagation

[0056] In the training process of a traditional backpropagation (BP) neural network, the error function is constructed based on the deviation between the network's actual output and the training samples. In NNHB, since there are no training samples, we need to reconstruct the neural network's error function based on circuit equations.

[0057] The error function here is constructed as follows:

[0058]

[0059] Among them, E equ1 E equ2 E equ3 These are the values ​​on the right side of the equation in circuit equation (1).

[0060] In practice, the training method can use gradient descent (GD) (but is not limited to this) to update the weights and biases of the neural network, thereby minimizing the error function (4).

[0061] Based on the specific circuit topology and components, the gradients of the error function with respect to the weight matrix W and the bias vector C are obtained. Then, the weight matrix W and the bias vector C can be updated using the GD method (but not limited to it) as follows:

[0062]

[0063] Where ε represents the learning rate, and its value ranges from (0,1).

[0064] Step 3: Training the neural network

[0065] In the neural network training process, the initial values, learning rate, and expected error are first set; then, gradient descent (but not limited to this method) is selected as the training method; finally, the forward computation process and the backpropagation process are alternately iterated, and the weight matrix W and the bias vector are updated until convergence to the expected error. To accelerate the convergence process, the learning rate can be dynamically adjusted according to the network's error value.

[0066] To address the shortcomings of piecewise harmonic balancing techniques, this invention proposes a Neural Network based Harmonic Balance (NNHB) method. NNHB constructs a specially structured back propagation (BP) neural network, which is then trained to obtain a steady-state solution satisfying the nonlinear circuit equations. The proposed NNHB method has the following advantages: First, NNHB avoids frequent time-frequency changes during iteration and is applicable to circuit analysis with single-tone and multi-tone excitations; second, NNHB exhibits good convergence, independent of initial conditions, and can converge from random initial conditions to a steady-state solution; third, NNHB has high simulation accuracy. The NNHB method provides an effective approach for analyzing the periodic response of nonlinear circuits.

[0067] This invention uses a power supply circuit as an example to illustrate and verify the NNHB method of this invention.

[0068] Figure 2 The diagram shows a power supply circuit schematic. Because the diodes in the circuit are nonlinear components, harmonic components exist in the circuit. Therefore, the NNHB method of this invention can be used for harmonic balance analysis. The NNHB method for analyzing this power supply circuit includes the following steps:

[0069] Step 1: Establish the circuit node voltage equations

[0070] Figure 2 The parameters of each component in the circuit shown are V in =10sin(120πt), R1=5Ω, C1 = 10 -6 F, L1 = 0.1H, C2 = 10 -3 F, C3 = 10 -3 F, R2 = 1KΩ. Therefore, this power supply circuit is a single-tone excitation.

[0071] Based on circuit theory, the node voltage equations of the circuit can be written as follows:

[0072]

[0073] Where V1, V2, and V3 are the node voltages to be solved, and the voltage across the diode is V. d =V1-V2, and These represent the current flowing through each capacitor and inductor, respectively.

[0074] Step 2: Constructing the neural network in NNHB

[0075] (1) Neural network structure

[0076] The neural network structure parameters are determined based on the number of node voltages in the circuit being analyzed and the harmonic orders to be considered. For Figure 2 The power supply circuit shown, and the neural network constructed by NNHB are as follows: Figure 1 As shown, this considers the highest 7th harmonic and the circuit contains only 3 node voltages, therefore Figure 1 The network parameters are set to M=3 and N=3 respectively.

[0077] (2) Forward computation

[0078] Selecting a sample size X = 100, the time interval [0, T] is divided into X equal parts, resulting in a discretized time series [t0, t1, ..., tt]. X Then, using equation (3), V at each time point t is calculated. j The value of .

[0079] (3) Backpropagation

[0080] For the power supply circuit in this embodiment, the error function is as shown in equation (4), and the error function with respect to the weight matrix W is...

[0081]

[0082] Among them, E equ1 E equ2 E equ3 These are the values ​​on the right side of the equation in circuit equation (6).

[0083] Considering Figure 2 From the topological relationships and parameter values ​​of each component, we can obtain

[0084]

[0085]

[0086]

[0087] Considering equations (1) and (2), we can obtain the partial differentials of V, dV / dt, and ∫Vdt with respect to the weight matrix as follows:

[0088]

[0089]

[0090]

[0091] Substituting equations (8) to (13) into equation (7) yields the gradient of the error function with respect to the weight matrix W. Similarly, the gradient of the error function with respect to the bias vector C can be obtained. Finally, the weight matrix and bias vector are updated according to equation (5).

[0092] Step 3: Training the neural network

[0093] For the power supply circuit in this embodiment, NNHB starts from a random initial value W = 0.01 × [-O M×2N +2×R M×2N ] and C = 0.01 × [O M×1 -R M×1 Start calculating, O m×n R is an m×n matrix of all 1s. m×n The network is an m×n random matrix whose elements take random values ​​between 0 and 1, with a learning rate of ε = 0.05. Gradient descent is used to train the network, and when the error reaches the expected accuracy, the output of the neural network is the steady-state solution of the power supply circuit.

[0094] The simulation results of the NNHB method are compared with those of the traditional piecewise harmonic balance PHB method. Figure 3a , Figure 3b , Figure 3c , Figure 3d , Figure 3e , Figure 3f As can be seen from the time-domain waveform and amplitude spectrum of the node voltage shown, the simulation results of the NNHB method and PHB have a good agreement. Figure 4a , Figure 4b and Figure 4c The deviation curves shown also demonstrate the high accuracy of the NNHB method. Simulation results show that the NNHB method proposed in this invention maintains high accuracy while avoiding the problem of frequent time-frequency transformations required by traditional harmonic balance methods.

[0095] Example 1

[0096] A harmonic balancing method based on neural networks includes the following steps:

[0097] S1, establish the node voltage equations for the nonlinear circuit;

[0098] S2, construct the following neural network and error function: Construct a three-layer BP neural network, whose input layer is a discrete time sequence of a complete cycle; its hidden layer includes a set of trigonometric functions of harmonic components or mixed frequency components; its output layer is the steady-state solution of the voltage equation of the nonlinear circuit node; the error function is constructed based on the voltage equation of the nonlinear circuit node.

[0099] S3, train the constructed neural network to obtain the steady-state solution that satisfies the voltage equation of the nonlinear circuit node.

[0100] Example 2

[0101] Based on Example 1, in step S2, the activation function of the hidden layer is a set of trigonometric functions containing harmonic frequencies when the excitation is single-tone; when the excitation is multi-tone, the activation function is a trigonometric function containing mixed frequencies.

[0102] Example 3

[0103] Based on Example 1, in step S2, the weight matrix of the input layer is a constant vector; the hidden layer does not contain a bias term, and the elements of the weight matrix of the hidden layer are the coefficients in the steady-state solution of the voltage equation of the nonlinear circuit node; the bias vector of the output layer is composed of the DC shunt of the voltage equation of the nonlinear circuit node.

[0104] Example 4

[0105] Based on Example 3, the elements of the weight matrix of the hidden layer are the coefficients in the steady-state solution of the voltage equation of the nonlinear circuit node, specifically: Fourier coefficients when there is single-tone excitation, and coefficients of the mixed frequency trigonometric function when there is multi-tone excitation.

[0106] Example 5

[0107] Based on Example 1, in step S2, during the error backpropagation process, without training samples, the error function of the neural network is directly reconstructed using the voltage equation of the nonlinear circuit node.

[0108] Example 6

[0109] Based on Example 5, in step S2, the error function of the reconstructed neural network includes the following sub-steps: using the gradient descent algorithm to update the weights and biases of the neural network, thereby minimizing the error function; and obtaining the gradients of the error function with respect to the weight matrix of the hidden layer and the bias vector of the output layer according to the topology and components of the specific circuit, and then updating the weight matrix of the hidden layer and the bias vector of the output layer respectively.

[0110] Example 7

[0111] Based on Example 1, in step S3, during the neural network training process, the initial value, learning rate, and expected error are first set; then the training algorithm is selected; finally, the forward calculation process and the error backpropagation process are alternately iterated, and the weight matrix of the hidden layer and the bias vector of the output layer are updated until convergence to the expected error.

[0112] Example 8

[0113] Based on Example 7, in step S3, the training algorithm includes gradient descent; the learning rate is dynamically adjusted according to the network error value.

[0114] Example 9

[0115] A computer device includes a processor and a memory, wherein the memory stores a computer program that is loaded by the processor and executed as described in any one of Embodiments 1 to 8.

[0116] Example 10

[0117] A computer-readable storage medium is characterized in that a computer program is stored in the readable storage medium, the computer program being loaded by a processor and executed as described in any one of Embodiments 1 to 8.

[0118] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0119] According to one aspect of this application, a computer program product or computer program is provided, comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the methods provided in the various alternative implementations described above.

[0120] In another aspect, this application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.

[0121] All parts not covered in this invention are the same as or can be implemented using existing technologies.

[0122] The above technical solution is only one embodiment 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 above specific embodiments of the present invention. Therefore, the methods described above are only preferred and are not restrictive.

[0123] In addition to the examples above, other embodiments may be obtained by those skilled in the art based on the above disclosure or by making modifications using knowledge or technology in related fields. The features of each embodiment may be interchanged or replaced. Modifications and changes made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A harmonic balancing method based on neural networks, characterized in that, Including the following steps: S1, establish the node voltage equations for the nonlinear circuit; based on the number of frequencies contained in the circuit's excitation source, classify the circuit into single-tone excitation and multi-tone excitation; the steady-state solution of the nonlinear circuit with single-tone excitation is in the following Fourier series form: The steady-state solution of the multi-tone excitation circuit consists of a set of mixed frequency components; S2, construct the following neural network and error function: Construct a three-layer BP neural network, whose input layer is a discrete time sequence of a complete cycle; its hidden layer includes a set of trigonometric functions of harmonic components or mixed frequency components; its output layer is the steady-state solution of the voltage equation of the nonlinear circuit node; The error function is constructed based on the node voltage equations of the nonlinear circuit; The hidden layer activation function is a set of trigonometric functions containing harmonic frequencies for single-tone excitation; for multi-tone excitation, the activation function is a trigonometric function containing mixed frequencies. The input layer weight matrix is ​​a constant vector. The hidden layer does not contain a bias term. The elements of the hidden layer weight matrix are coefficients in the steady-state solution of the nonlinear circuit node voltage equation: Fourier coefficients for single-tone excitation and coefficients of the mixed-frequency trigonometric functions for multi-tone excitation. The output layer bias vector is composed of the DC shunt of the nonlinear circuit node voltage equation. The error function is constructed as follows: ； in, , , These are the values ​​on the right side of the equal signs in circuit equation 1); S3, train the constructed neural network to obtain the steady-state solution that satisfies the voltage equation of the nonlinear circuit node.

2. The harmonic balance method based on neural networks according to claim 1, characterized in that, In step S2, during the error backpropagation process, without the need for training samples, the error function of the neural network is directly reconstructed using the voltage equations of the nonlinear circuit nodes.

3. The harmonic balance method based on neural networks according to claim 2, characterized in that, In step S2, the error function of the reconstructed neural network includes the following sub-steps: using the gradient descent algorithm to update the weights and biases of the neural network to minimize the error function; and obtaining the gradients of the error function with respect to the weight matrix of the hidden layer and the bias vector of the output layer based on the topology and components of the specific circuit, and then updating the weight matrix of the hidden layer and the bias vector of the output layer respectively.

4. The harmonic balance method based on neural networks according to claim 1, characterized in that, In step S3, during the neural network training process, the initial value, learning rate, and expected error are first set; then the training algorithm is selected; finally, the forward calculation process and the backpropagation process are alternately iterated, and the weight matrix of the hidden layer and the bias vector of the output layer are updated until convergence to the expected error.

5. The harmonic balancing method based on a neural network according to claim 4, characterized in that, In step S3, the training algorithm includes gradient descent; the learning rate is dynamically adjusted according to the network's error value.

6. A computer device, characterized in that, The computer device includes a processor and a memory, the memory storing a computer program that is loaded by the processor and executed according to any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that, A computer program is stored in a readable storage medium, the computer program being loaded by a processor and executing the method as described in any one of claims 1 to 5.

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