Multi-level deep neural network, relativistic backward wave tube based on multi-level deep neural network and optimization method of relativistic backward wave tube

Abstract

The invention relates to a multi-level deep neural network, a relativistic backward wave tube based on the multi-level deep neural network and an optimization method of the relativistic backward wave tube, belongs to the technical field of vacuum electronic device design, and solves the technical problems that device design time is long and calculation resource consumption of relativistic backward wave tube optimization is large. Comprising the steps that a multi-layer deep neural network is constructed, a low-layer deep neural network learns a nonlinear relation between an input signal and an output signal in a low-dimensional training data set, and a high-layer deep neural network approximates a function relation between a high-dimensional input signal and a relativistic backward wave tube working characteristic parameter; and optimizing the to-be-optimized parameters of the relativistic backward wave tube. The multi-layer deep neural network comprises a low-layer deep neural network and a high-layer deep neural network which are interconnected in a layered manner. The relativistic backward wave tube is of an axisymmetric structure and comprises a high-voltage diode, a resonant reflector, a high-frequency interaction area and an external guide magnetic field generation device.

Description

Technical Field

[0001] The present invention belongs to the technical field of vacuum electronic device design, and specifically relates to a multi-level deep neural network, a relativistic backward wave tube based on the multi-level deep neural network, and an optimization method thereof. Background Art

[0002] The relativistic backward wave tube is a vacuum electronic device that can generate high-power microwave output. This type of device generates a strong current relativistic electron beam through a high-voltage diode. Under the action of an external guiding magnetic field, the electron beam interacts with a high-frequency interaction structure, converting the kinetic energy of the electron beam into the energy of an electromagnetic wave. According to the working characteristics of the relativistic backward wave tube, the transmission direction of the generated electromagnetic wave is opposite to the movement direction of the electron beam. Structures such as resonant reflectors are used to change the propagation direction of the electromagnetic wave. Finally, the generated electromagnetic wave is output along the waveguide port of the relativistic backward wave tube, and is in the same direction as the movement direction of the electron beam. The structure of the relativistic backward wave tube is very complex, including electron guns, high-frequency systems, focusing systems, electron beam collectors, and input and output components. In the development process of the relativistic backward wave tube, there are many adjustable parameters. Designing a device with excellent performance requires a lot of theoretical research, numerical simulation and experimental research. Compared with experimental research, numerical simulation methods have the advantages of low cost and short cycle, and have become an indispensable means in the design process of relativistic backward wave tubes.

[0003] The full electromagnetic particle simulation method obtains the motion trajectory of charged particles by solving the Newton-Lorentz force equation. The current generated by the motion of charged particles is used as the source term of the electromagnetic field. The Maxwell equations with source terms are solved to obtain the change process of the electromagnetic field over time. This method can accurately simulate the nonlinear interaction between the relativistic electron beam and the electromagnetic field in various vacuum electronic devices, and is widely used in the optimization design of relativistic backward wave tubes. When using this method to simulate relativistic backward wave tubes, in order to reduce numerical noise and improve calculation accuracy, it is necessary to perform a relatively fine grid division on the device structure, and at the same time, it is necessary to track the motion process of a large number of charged particles, resulting in the method requiring a lot of computing resources. In particular, when performing three-dimensional numerical simulation of the device structure, it is necessary to calculate the distribution of the electromagnetic field on millions of grid units and the motion equations of macro particles. For relativistic backward wave tubes with higher operating frequencies and more complex device structures, even if hundreds of processes are used for parallel numerical simulation, it usually takes dozens of hours.

[0004] When optimizing the design of a relativistic backward wave tube, it is necessary to conduct a large number of regularity studies on the effects of changes in device parameters on the working characteristics, and then select a set of optimal parameters according to the optimization goal. Since the working characteristics of a relativistic backward wave tube are very sensitive to parameters, a numerical simulation needs to be carried out again each time the parameters are changed, resulting in a large number of numerical simulation studies being required in the design process of the relativistic backward wave tube. In order to improve the optimization design speed of vacuum electronic devices, Chen Zaigao et al. proposed a high-power microwave source optimization design method based on particle simulation and parallel genetic algorithm for relativistic backward wave tubes. Wang Huihui et al. combined the particle swarm optimization algorithm with particle simulation technology to achieve the optimization design of relativistic backward wave tubes. Sun Huifang et al. used genetic algorithms for the automatic optimization design of magnetically insulated wire oscillators. These design methods have improved the optimization design of devices to a certain extent. On this basis, Chen Zaigao et al. proposed combining small signal theory with full electromagnetic particle simulation to achieve the automatic design of relativistic backward wave tubes. In addition, Chen Zaigao et al. proposed a vacuum electronic device optimization method based on deep learning and parallel genetic algorithm. This method constructs a fully connected neural network to learn the laws in the data generated by full electromagnetic particle simulation, further improving the optimization design speed of vacuum electronic devices. Since this method does not fully utilize the learning function of deep neural network for nonlinear data, it still needs to carry out a large number of full electromagnetic particle simulations to provide training data for deep neural network, resulting in the required computing resources are still very large. However, in the process of device optimization, device designers hope to learn the laws in device design, and then use a small amount of high-precision simulation data to optimize the device parameters. Summary of the invention

[0005] In order to shorten the design time of the device and reduce the consumption of computing resources for the optimization of the relativistic backward wave tube, the present invention proposes a multi-level deep neural network, a relativistic backward wave tube based on the multi-level deep neural network and an optimization method thereof.

[0006] The technical solution adopted by the present invention to solve the technical problem is:

[0007] A relativistic backward wave tube optimization method based on a multi-level deep neural network comprises the following steps:

[0008] Step 1: construct a multi-level deep neural network, which includes a low-level deep neural network and a high-level deep neural network.

[0009] Step 2: The low-level deep neural network uses the parameters to be optimized in the low-dimensional training data set as input signals and the working characteristic parameters of the relativistic backward wave tube as output signals to learn the nonlinear relationship between the input signal and the output signal in the low-dimensional training data set.

[0010] Step 3: The high-level deep neural network takes the learning rules of the low-level deep neural network and the parameters to be optimized in the high-dimensional training data set as input signals to approximate the functional relationship between the high-dimensional input signal and the working characteristic parameters of the relativistic backward wave tube.

[0011] Step 4, based on the multi-level deep neural network to describe the functional relationship between the parameters to be optimized and the working characteristic parameters, optimize the parameters to be optimized of the relativistic backward wave tube, and realize the optimization of the parameters to be optimized of the relativistic backward wave tube.

[0012] In the above relativistic backward wave tube optimization method, step 3 further comprises:

[0013] The high-level deep neural network includes a linear deep neural network and a nonlinear deep neural network.

[0014] Linear deep neural networks learn the linear relationship between the parameters to be optimized in the high-dimensional training dataset and the working characteristic parameters in the low-dimensional training dataset.

[0015] Nonlinear deep neural networks learn the nonlinear relationship between the parameters to be optimized in the high-dimensional training data set and the working characteristic parameters in the low-dimensional training data set.

[0016] The two learning results of the linear deep neural network and the nonlinear deep neural network are superimposed to approximate the functional relationship between the parameters to be optimized and the working characteristic parameters in the high-dimensional data set.

[0017] The input of the high-level deep neural network consists of the parameters to be optimized of the high-dimensional training data set and the output of the low-level deep neural network.

[0018] In the above-mentioned relativistic backward wave tube optimization method, the input signal of the low-level deep neural network is the parameters to be optimized of the relativistic backward wave tube, which include geometric parameters and electrical parameters, and the output signal is the working characteristic parameters of the relativistic backward wave tube calculated by the full electromagnetic particle simulation program, which include output power, electron beam energy conversion efficiency, and operating frequency. During the training process, the output signal of the training data set used is the calculation result of the full electromagnetic particle simulation software, the low-level deep neural network contains an input layer, a hidden layer, and an output layer, and the layers are connected in a fully connected layer manner. The optimization algorithm adopts the stochastic gradient descent algorithm, and the loss value is measured by MSE.

[0019] In the above relativistic backward wave tube optimization method, in step 2, in the low-dimensional training data set, when there are multiple parameters to be optimized, only one of the parameters can be changed, and the other parameters are fixed. Then, the value of the parameter is changed, and the working characteristic parameters of the relativistic backward wave tube are calculated using the full electromagnetic particle simulation method, and the parameter to be optimized and the working characteristic parameters are combined as the low-dimensional training data set.

[0020] In step 3, in the high-dimensional training data set, when there are multiple parameters to be optimized, only one of the parameters can be changed, and the other parameters are fixed. Then, the value of the parameter is changed, and the working characteristic parameters of the relativistic backward wave tube are calculated using the full electromagnetic particle simulation method. The parameter to be optimized and the working characteristic parameters are combined as the high-dimensional training data set.

[0021] A multi-layer deep neural network includes a low-layer deep neural network and a high-layer deep neural network.

[0022] The low-level deep neural network and the high-level deep neural network are hierarchically interconnected.

[0023] The low-level deep neural network is used to learn the implicit nonlinear laws between the parameters to be optimized and the working characteristic parameters in the low-dimensional data set;

[0024] The high-level deep neural network includes a linear deep neural network and a nonlinear deep neural network. The linear deep neural network is used to learn the linear relationship between the high-dimensional training data set and the low-dimensional training data set, and the nonlinear deep neural network is used to learn the nonlinear relationship between the high-dimensional training data set and the low-dimensional training data set.

[0025] The above-mentioned multi-level deep neural network, the low-level deep neural network is used to learn the nonlinear relationship between the input signal and the output signal in the low-dimensional training data set, and the high-level deep neural network is used to learn the functional relationship between the input signal in the high-dimensional training data set, the output signal in the low-dimensional training data set and the output signal in the high-dimensional training data set.

[0026] The output signals between the linear deep neural network and the nonlinear deep neural network are linearly superimposed to form the output signal of the multi-level deep neural network.

[0027] The above-mentioned multi-level deep neural network, the low-level deep neural network is composed of 4 layers of fully connected deep neural networks, the input layer of the low-level deep neural network has two input signals, which are the values ​​of L1 and L2 respectively, each hidden layer has 10 neurons, and the activation function used is the hyperbolic tangent function; the output layer has 1 output signal, which is the working characteristic parameter, namely the average output power.

[0028] The high-level deep neural network is composed of two deep neural networks. The linear deep neural network is a 6-layer deep neural network, wherein the input layer has 3 input signals, which correspond to the values ​​of L1 and L2 in the high-dimensional training data set and the output signal of the low-level deep neural network respectively, and the number of neurons in each of the 4 hidden layers is 20. There is no activation function between the layers of the linear deep neural network, and the output layer has 1 output signal, which is the working characteristic parameter of the relativistic backward wave tube, namely the average output power; the nonlinear deep neural network is also a 6-layer deep neural network, wherein the input layer has 3 input signals, which correspond to the values ​​of L1 and L2 in the high-dimensional training data set and the output signal of the low-level deep neural network respectively, and the number of neurons in each of the 4 hidden layers is 20. The output layer has 1 output signal, and the activation function between the layers of the nonlinear deep neural network is a hyperbolic tangent function; the outputs of the nonlinear neural network and the linear neural network are algebraically averaged to obtain the output of the entire multi-level deep neural network.

[0029] A relativistic backward wave tube based on a multi-level deep neural network has an axisymmetric structure and includes a high-voltage diode, a resonant reflector, a high-frequency interaction region, and an external guided magnetic field generating device.

[0030] The high voltage diode comprises a cathode and an anode. The cathode is cylindrical, with its opening facing the Z direction and located inside the anode; the anode is tubular and located outside the cathode.

[0031] The anode, the resonant reflector, and the high-frequency interaction zone are connected in sequence along the Z direction, and the external guide magnetic field generating device is located outside the resonant reflector and the high-frequency interaction zone.

[0032] The above relativistic backward wave tube optimizes the parameters to be optimized of the resonant reflector so that the average output power of the relativistic backward wave tube reaches the maximum value.

[0033] In the above relativistic backward wave tube, the parameters to be optimized of the resonant reflector are L1 and L2. L1 is the top height of the resonant reflector, that is, the distance from the top to the central axis. L2 is the distance from the bottom of the resonant reflector to the inflection point P and along the z-axis. Among them, L1 is preferably 0.023 meters, and L2 is preferably 0.026 meters.

[0034] The beneficial effects of the present invention are:

[0035] A relativistic backward wave tube optimization method based on a multi-level deep neural network adopts a multi-level deep neural network. The method requires a limited number of samples in the training data set. When learning the nonlinear law between the parameters to be optimized and the working characteristic parameters in the low-dimensional training sample set, sufficient data is needed for training to obtain the law. When learning the nonlinear law between the parameters to be optimized and the working characteristic parameters in the high-dimensional training sample set, only a small amount of sample data is needed, and there is no need to carry out a large number of full electromagnetic particle simulations. Therefore, the design time of the device can be greatly shortened and the consumption of computing resources for the optimization of vacuum electronic devices can be reduced.

[0036] A relativistic backward wave tube optimization method based on a multi-level deep neural network uses a low-level deep neural network to learn the nonlinear law between the parameters to be optimized and the working characteristic parameters in the low-dimensional training data set. When preparing the low-dimensional training data set, simulation results with relatively low accuracy can be used, so the number of grids and macro particles in the full electromagnetic particle simulation program can be greatly reduced, further reducing the computing resources required to prepare the training data set and significantly reducing the simulation time.

[0037] A multi-level deep neural network uses a high-level deep neural network to learn the nonlinear relationship between the parameters to be optimized and the working characteristic parameters in low-dimensional training data. The numerical simulation results show that when this method predicts the optimal solution of the working characteristic parameters, the prediction results are consistent with the calculation results of the traditional full electromagnetic particle simulation method, indicating that the multi-level deep neural network proposed in the present invention has high prediction accuracy.

[0038] A relativistic backward wave tube based on a multi-level deep neural network fully utilizes the advantages of deep neural networks in generating physical laws during learning and simulation. It is expected to explore non-traditional structural parameters that researchers cannot imagine based on experience, and break through the typical structure and working principle of existing vacuum electronic devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic cross-sectional view of a relativistic backward wave tube according to a second embodiment of the present invention;

[0040] Figure 2 This is a schematic diagram of the structure of a resonant reflector according to a second embodiment of the present invention;

[0041] Figure 3 When the low-dimensional training data set with L1=0.02 meters is used in the second embodiment of the present invention, the output power changes with L2 curve;

[0042] Figure 4 When the low-dimensional training data set with L1=0.023 meters is used for the second embodiment of the present invention, the output power changes with L2 curve;

[0043] Figure 5When the high-dimensional training data set with L2=0.018 meters is used in the second embodiment of the present invention, the output power changes with L1 curve;

[0044] Figure 6 This is the full electromagnetic particle simulation result when L1=0.032 meters in Example 2 of the present invention;

[0045] Figure 7 This is a comparison between the full electromagnetic particle simulation results and the multi-level deep neural network prediction results when L1=0.032 meters used in Example 2 of the present invention.

[0046] Figure numerals: 1. cathode, 2. anode, 3. resonant reflector, 4. relativistic electron beam, 5. high-frequency interaction region, 6. symmetry axis, 7. external guided magnetic field generating device. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] Embodiment 1

[0049] A relativistic backward wave tube optimization method based on a multi-level deep neural network comprises the following steps:

[0050] 1. First, a multi-level deep neural network is constructed, where the multi-level deep neural network consists of two parts of deep neural networks, one of which is a low-level deep neural network and the other is a high-level deep neural network. The low-level deep neural network is used to learn the nonlinear laws implicit in the parameters to be optimized and the working characteristic parameters in the low-dimensional data set, and the high-level deep neural network contains two deep neural networks, namely a linear neural network and a nonlinear deep neural network, which are used to learn the linear and nonlinear relationships between the high-dimensional training data set and the low-dimensional training data set, respectively. The output of the low-level deep neural network and the parameters to be optimized of the high-dimensional training data set are used as input. The nonlinear laws between the parameters to be optimized and the working characteristic parameters in the low-dimensional data set and a small amount of high-dimensional data sets are used to learn the physical laws implicit in the high-dimensional data set.

[0051] 2. Prepare a training data set for the deep neural network. Generate a set of numerical values ​​of parameters to be optimized. At the same time, the parameters to be optimized are combined with other parameters of the relativistic backward wave tube to construct a relativistic backward wave tube model. The generated relativistic backward wave tube model is numerically simulated using full electromagnetic particle simulation software to obtain the working characteristic parameter values ​​of the relativistic backward wave tube, such as output power and electron beam energy conversion efficiency. The parameter values ​​to be optimized and the working characteristic parameter values ​​as optimization targets are the training data sets required for multi-level deep neural network training.

[0052] 3. The training data set consists of two parts. One part is a relatively complete low-dimensional training data set. By fixing other parameters to be optimized and keeping only one parameter value variable, a low-dimensional training data set is obtained by simulating the change of the working characteristic parameter of the relativistic backward wave tube with the value of the parameter to be optimized. The low-level deep neural network of the multi-level deep neural network can learn the nonlinear law between the working characteristic parameter value and the parameter value in the low-dimensional training data set. The other part of the training data set is a high-dimensional training data set. The sample size of these training data sets is small. These small amounts of data are combined with the nonlinear laws learned previously to train the high-level deep neural networks in the multi-level deep neural network.

[0053] 4. The parameter values ​​to be optimized in the low-dimensional training data set are used as the input signals of the low-level deep neural network, and the working characteristic parameter values ​​of the device in the data set are used as the output signals. The output signals of the low-level neural network and the parameters to be optimized in the high-dimensional training data set are used as the input signals of the high-level deep neural network, and the numerical values ​​representing the working characteristic parameters of the device in the high-dimensional training data set are used as the output signals. By continuously training the multi-level deep neural network, the nonlinear relationship between the working characteristic parameters and the parameters to be optimized in the case of high-dimensional training data sets can be obtained, and then the values ​​of the parameters to be optimized under the optimal working characteristic parameters can be obtained.

[0054] Embodiment 2

[0055] The following is an example of the optimization of the relativistic backward wave tube resonant reflector:

[0056] 1. This embodiment optimizes the resonant reflector structure of the X-band relativistic backward wave tube, wherein the relativistic backward wave tube is an axisymmetric structure, and the cross section of the relativistic backward wave tube can be divided into two identical parts along the axis of symmetry. The schematic diagram of one half of the cross section structure is as follows: Figure 1 As shown, Figure 1 The part marked with 1 is the cathode of the high-voltage diode in the relativistic backward wave tube, the part marked with 2 is the anode of the high-voltage diode in the relativistic backward wave tube, the part marked with 3 is the resonant reflector of the relativistic backward wave tube, the part marked with 4 is the relativistic electron beam generated by the high-voltage diode, the part marked with 5 is the high-frequency interaction area of ​​the relativistic backward wave tube, the part marked with 6 is the symmetry axis, and the part marked with 7 is the external guided magnetic field generating device. The relativistic backward wave tube generates a relativistic electron beam through the cathode of the high-voltage diode, and moves along the z-axis under the guidance of the strong magnetic field generated by the external guided magnetic field generating device. The relativistic backward wave tube converts the kinetic energy of the electron beam into the energy of the electromagnetic wave. Since the group velocity of the generated electromagnetic wave is in the opposite direction of the z-axis, the energy of the electromagnetic wave is reflected by the resonant reflector and transmitted along the positive direction of the z-axis.

[0057] 2. The position and height of the resonant reflector have a great influence on the working characteristic parameters of the relativistic backward wave tube. In this application, the height L1 of the top of the resonant reflector along the R direction and the distance L2 from the bottom of the resonant reflector to the inflection point P and along the z-axis direction are the parameters to be optimized, such as Figure 2 As shown. And taking the working characteristic parameter of the device, namely the average output power, as the optimization target, by optimizing the values ​​of the parameters to be optimized L1 and L2 of the resonant reflector, the working characteristic parameter of the relativistic backward wave tube, namely the average output power, is maximized.

[0058] 3. Build a multi-level deep neural network MFNN, where the low-level deep neural network LFNN in the multi-level deep neural network consists of a 4-layer fully connected deep neural network. The input layer of the deep neural network has two input signals, which are the values ​​of L1 and L2 respectively. Each hidden layer has 10 neurons, and the activation function used is the hyperbolic tangent function; the output layer has 1 output signal, which is the working characteristic parameter, namely the average output power; the high-level deep neural network HFNN of the multi-level deep neural network MFNN consists of two deep neural networks, one of which is a linear deep neural network LHFNN, which is used to learn the linear relationship between the high-dimensional training data set and the low-dimensional training data set. It is a 6-layer deep neural network, where the input layer has 3 input signals, which correspond to the values ​​of L1 and L2 in the high-dimensional training data set and the output signal of the low-level deep neural network LFNN, and the 4 hidden layers have 10 neurons. The number of neurons in each hidden layer in the layer is 20. There is no activation function between the layers of the linear deep neural network LHFNN. The output layer has 1 output signal, which is the working characteristic parameter of the device, namely the average output power; the other deep neural network is the nonlinear deep neural network NLHFNN, which is used to learn the nonlinear relationship between the high-dimensional training data set and the low-dimensional data training set. It is also a 6-layer deep neural network, in which the input layer has 3 input signals, which correspond to the values ​​of L1 and L2 in the high-dimensional training data set and the output signal of the low-layer deep neural network, the number of neurons in each hidden layer of the 4 hidden layers is 20, the output layer has 1 output signal, and the activation function between the layers of the nonlinear deep neural network is the hyperbolic tangent function; the outputs of the nonlinear neural network NLHFNN and the linear neural network LHFNN are algebraically averaged to obtain the output of the entire multi-level deep neural network.

[0059] 4. Prepare a low-dimensional training data set for the multi-level deep neural network MFNN. Fix L1 to 0.02 meters, the value range of L2 is 0 meters to 0.033 meters, and the interval is set to 0.001 meters. L1 and each L2 value constitute a set of data, which can generate 34 sets of data. These 34 sets of data and other structural parameters and electrical parameters of the relativistic backward wave tube are used to generate 34 model files of the relativistic backward wave tube. The full electromagnetic particle simulation software is used to simulate these 34 model files to obtain the average output power of the relativistic backward wave tube. The output power changes with the change of L2 as shown in Figure 3 As shown, each set of L1 and L2 values ​​and the corresponding average output power constitute a training data, in which L1 and L2 are the input signals of the low-layer deep neural network LFNN, and the average output power is the output signal of the low-layer deep neural network LFNN.

[0060] 5. Prepare a high-dimensional training data set for the multi-level deep neural network MFNN. Fix L1 to 0.023 meters, and select L2 only at 0.0 meters, 0.01 meters, 0.02 meters, 0.025 meters, 0.028 meters, 0.03 meters, and 0.033 meters. L1 and each L2 value constitute a set of data. These 7 sets of data and other structural parameters and electrical parameters of the relativistic backward wave tube are used to generate 7 model files of the relativistic backward wave tube. The full electromagnetic particle simulation software UNIPIC is used to simulate these 7 model files to obtain the average output power of the relativistic backward wave tube. The average output power changes with the change of L2 as shown in the figure. Figure 4 As shown in the figure, each set of L1 and L2 values ​​and the corresponding average output power constitute a training data. In addition, L2 is fixed to 0.018 meters, and the value range of L1 is 0.018 meters, 0.02 meters, 0.022 meters, and 0.024 meters. L2 and each L1 value constitute a set of data, generating 4 sets of data. These 4 sets of data and other structural parameters and electrical parameters of the relativistic backward wave tube are used to generate 4 model files of the relativistic backward wave tube. The full electromagnetic particle simulation software UNIPIC is used to simulate these 4 model files, and the average output power of the relativistic backward wave tube can be obtained. The average output power changes with the change of L1 as shown in the figure. Figure 5 As shown, each set of L1, L2 values ​​and the corresponding average output power constitute a training data.

[0061] 6. The multi-level deep neural network MFNN is trained using low-dimensional training data sets and high-dimensional training data sets. The optimization strategy used is the stochastic gradient descent algorithm. After all samples have been trained 20,000 times, L1 is fixed to 0.023 meters, and the value range of L2 is 0 meters to 0.033 meters, with an interval of 0.001 meters. The output signal of the multi-level neural network changes with L2 as shown in the figure. Figure 6 The output of the multi-layer neural network is compared with the full electromagnetic particle simulation results. Figure 7As shown, it can be seen from the figure that when L2 is equal to 0.026, the output signal of the multi-level deep neural network reaches a maximum of 780 MW; using full electromagnetic particle simulation, when L2 is equal to 0.026 meters, the power generated by the device also reaches a maximum of 793 MW. It can be seen from the figure that the relative difference between the output signal of the multi-level deep neural network and the full electromagnetic particle simulation result is less than 2%, and the calculation results of the two are in good agreement. It should also be pointed out that in the high-dimensional training data set, sample data when L2 is equal to 0.026 meters is not provided, but the relativistic backward wave tube optimization method based on the data-driven deep neural network model provided by this application can still accurately predict that L2 is equal to 0.026 meters, and the average output power of the relativistic backward wave tube reaches the maximum value.

[0062] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0063] Those skilled in the art will appreciate that the embodiments described herein are intended to help practitioners in the field understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Practitioners in the field can make various optimizations of other structural parameters and electrical parameters of the relativistic backward wave tube that do not deviate from the essence of the present invention based on the technical inspirations disclosed by the present invention, such as high-frequency structure, high-voltage diode structure, injection wave waveform, etc. In addition, the use of multi-level deep neural networks with different structures can also achieve the optimization effect demonstrated by the present invention. These different parameters to be optimized and multi-level deep neural network models and parameters with different structures are still within the scope of protection of the present invention.

Claims

1. A relativistic backward wave tube optimization method based on a multi-level deep neural network, characterized in that: The following steps are involved: Step 1, constructing a multi-level deep neural network, which includes a low-level deep neural network and a high-level deep neural network; Step 2: The low-level deep neural network uses the parameters to be optimized in the low-dimensional training data set as input signals and the working characteristic parameters of the relativistic backward wave tube as output signals to learn the nonlinear relationship between the input signal and the output signal in the low-dimensional training data set; Step 3: The high-level deep neural network takes the learning rules of the low-level deep neural network and the parameters to be optimized in the high-dimensional training data set as input signals to approximate the functional relationship between the high-dimensional input signal and the working characteristic parameters of the relativistic backward wave tube; Step 4, based on the multi-level deep neural network to describe the functional relationship between the parameters to be optimized and the working characteristic parameters, optimize the parameters to be optimized of the relativistic backward wave tube, and realize the optimization of the parameters to be optimized of the relativistic backward wave tube.

2. The relativistic backward wave tube optimization method according to claim 1, characterized in that: The step 3 further comprises: The high-level deep neural network includes a linear deep neural network and a nonlinear deep neural network; Linear deep neural networks learn the linear relationship between the parameters to be optimized in the high-dimensional training data set and the working characteristic parameters in the low-dimensional training data set; The nonlinear deep neural network learns the nonlinear relationship between the parameters to be optimized in the high-dimensional training data set and the working characteristic parameters in the low-dimensional training data set; The two learning results of the linear deep neural network and the nonlinear deep neural network are superimposed to approximate the functional relationship between the parameters to be optimized and the working characteristic parameters in the high-dimensional data set; The input of the high-level deep neural network consists of the parameters to be optimized of the high-dimensional training data set and the output of the low-level deep neural network.

3. The relativistic backward wave tube optimization method according to claim 1, characterized in that: The input signal of the low-level deep neural network is the parameters to be optimized of the relativistic backward wave tube, which include geometric parameters and electrical parameters. The output signal is the working characteristic parameters of the relativistic backward wave tube calculated by the full electromagnetic particle simulation program, which include output power, electron beam energy conversion efficiency, and operating frequency. During the training process, the output signal of the training data set used is the calculation result of the full electromagnetic particle simulation software. The low-level deep neural network contains an input layer, a hidden layer, and an output layer. The layers are connected in a fully connected layer manner. The optimization algorithm uses a stochastic gradient descent algorithm, and the loss value is measured using MSE.

4. The relativistic backward wave tube optimization method according to claim 1, characterized in that: In step 2, when there are multiple parameters to be optimized in the low-dimensional training data set, only one of the parameters can be changed, and the other parameters are fixed; then the value of the parameter is changed, and the full electromagnetic particle simulation method is used. The working characteristic parameters of the relativistic backward wave tube are calculated, and the parameters to be optimized are combined with the working characteristic parameters as a low-dimensional training data set; In step 3, when there are multiple parameters to be optimized in the high-dimensional training data set, only one of the parameters can be changed, and the other parameters are fixed; then the value of the parameter is changed, and the full electromagnetic particle simulation method is used. The working characteristic parameters of the relativistic backward wave tube are calculated, and the parameters to be optimized are combined with the working characteristic parameters as a high-dimensional training data set; In step 4, the parameters to be optimized of the relativistic backward wave tube are the high-frequency structure, the high-voltage diode structure, and the injection wave shape.

5. A multi-layer deep neural network, characterized in that: Including low-level deep neural networks and high-level deep neural networks; The low-level deep neural network and the high-level deep neural network are hierarchically interconnected; The low-level deep neural network is used to learn the implicit nonlinear laws between the parameters to be optimized and the working characteristic parameters in the low-dimensional data set; The high-level deep neural network includes a linear deep neural network and a nonlinear deep neural network; Linear deep neural networks are used to learn the linear relationship between high-dimensional training data sets and low-dimensional training data sets, and nonlinear deep neural networks are used to learn the nonlinear relationship between high-dimensional training data sets and low-dimensional training data sets.

6. The multi-level deep neural network according to claim 5, characterized in that: The low-level deep neural network is used to learn the nonlinear relationship between the input signal and the output signal in the low-dimensional training data set, and the high-level deep neural network is used to learn the functional relationship between the input signal in the high-dimensional training data set, the output signal in the low-dimensional training data set, and the output signal in the high-dimensional training data set; The output signals between the linear deep neural network and the nonlinear deep neural network are linearly superimposed to form the output signal of the multi-level deep neural network.

7. The multi-level deep neural network according to claim 5, characterized in that: The low-level deep neural network is composed of 4 layers of fully connected deep neural networks. The input layer of the low-level deep neural network has two input signals, which are the values ​​of L1 and L2 respectively. Each hidden layer has 10 neurons, and the activation function used is the hyperbolic tangent function; the output layer has 1 output signal, which is the working characteristic parameter, namely the average output power; the high-level deep neural network is composed of two deep neural networks. The linear deep neural network is a 6-layer deep neural network, in which the input layer has 3 input signals, which correspond to the values ​​of L1 and L2 in the high-dimensional training data set and the output signal of the low-level deep neural network respectively. The number of neurons in each of the 4 hidden layers is 20, and the linear deep neural network has a 6-layer deep neural network. There is no activation function between the layers of the linear deep neural network, and the output layer has 1 output signal, which is the working characteristic parameter of the relativistic backward wave tube, namely the average output power; the nonlinear deep neural network is also a 6-layer deep neural network, in which the input layer has 3 input signals, which correspond to the values ​​of L1 and L2 in the high-dimensional training data set and the output signal of the low-level deep neural network, the number of neurons in each hidden layer of the 4 hidden layers is 20, and the output layer has 1 output signal. The activation function between the layers of the nonlinear deep neural network is the hyperbolic tangent function; the outputs of the nonlinear neural network and the linear neural network are algebraically averaged to obtain the output of the entire multi-level deep neural network.

8. A relativistic backward wave tube based on a multi-level deep neural network, characterized in that: The invention is an axisymmetric structure, comprising a high-voltage diode, a resonant reflector (3), a high-frequency interaction region (5), and an external guided magnetic field generating device (7); the high-voltage diode comprises a cathode (1) and an anode (2); the cathode (1) is cylindrical, with an opening facing the Z direction, and is located on the inner side of the anode (2); the anode (2) is a circular tube, and is located on the outer side of the cathode (1); The anode (2), the resonant reflector (3), and the high-frequency interaction zone (5) are connected in sequence along the Z direction, and the external guide magnetic field generating device (7) is located outside the resonant reflector (3) and the high-frequency interaction zone (5).

9. The relativistic backward wave tube according to claim 8, characterized in that: By optimizing the parameters to be optimized of the resonant reflector (3), the average output power of the relativistic backward wave tube reaches a maximum value.

10. The relativistic backward wave tube according to claim 9, characterized in that: The parameters to be optimized of the resonant reflector (3) are L1 and L2; L1 is the top height of the resonant reflector (3), that is, the distance from the top to the central axis; L2 is the distance from the bottom of the resonant reflector (3) to the inflection point P and along the z-axis direction; L1=0.023m, L2=0.026m.

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