FPGA-based particle accelerator beam position real-time self-calibration system

Abstract

The invention discloses an FPGA-based particle accelerator beam position real-time self-calibration system, which comprises a beam acquisition and conversion module and an FPGA processing module, and is characterized in that the beam acquisition and conversion module is used for acquiring an analog signal of a beam in a particle accelerator pipeline, amplifying the analog signal and outputting the amplified analog signal to the FPGA processing module; the amplified analog signal is converted into a digital signal; the FPGA processing module is used for receiving the digital signals from the beam acquisition and conversion module in real time, performing digital filtering processing on the digital signals of the beam by using an LMS algorithm optimized by a genetic algorithm, then constructing a random forest prediction model, performing analysis and prediction on the filtered digital signals of the beam through the random forest prediction model, and outputting the result. And the current of the magnet and the voltage of the deflection plate are dynamically adjusted according to the analyzed and predicted result, so that the self-adaptive adjustment of the beam position of the particle accelerator is realized. According to the invention, the adaptive capability of the system is enhanced, so that the beam position of the particle accelerator is controlled more accurately and dynamically.

Description

Technical Field

[0001] The present invention belongs to the technical field of beam calibration of particle accelerators, and particularly relates to a real-time self-calibration system for the beam position of a particle accelerator based on FPGA. Background Art

[0002] The overall performance improvement of a particle accelerator requires the coordinated operation of various physical subsystems and involves numerous physical parameters. Taking the accelerator light source as an example, its core requirements include maintaining the stability of the machine state and the flexibility of regulation. The control of these physical parameters is usually not simply determined by a few accelerator control parameters, but rather the interaction of multiple parameters shows complex non-linear characteristics. Precise control of these parameters requires experts to deeply understand the physical connections between them. However, due to the large number of parameters and the complexity of their interrelationships, directly grasping these connections is sometimes challenging. To automate and optimize the regulation of machine performance, many stochastic optimization algorithms suitable for online optimization have been developed internationally. In addition, machine learning techniques have also been applied to further improve the beam performance and the overall performance of the accelerator, especially showing significant effects in aspects such as orbit correction, beam stability, and longitudinal phase space control. Although certain progress has been made in the research related to machine learning in the accelerator field, the overall development level is still in the initial stage and there is still much room for development. Even in the currently well-developed research topics on machine learning applications, the algorithms applied still have a large gap compared with the most advanced and comprehensive machine learning algorithms in the field of artificial intelligence.

[0003] FPGA (Field Programmable Gate Array), that is, a field programmable gate array, is a further developed product based on programmable devices such as PAL, GAL, and CPLD. FPGA has powerful parallel processing capabilities, which enables it to quickly process a large amount of data and is very suitable for computationally intensive tasks. This parallel execution and pipeline design can achieve high-speed operation. At the same time, FPGA can perform real-time pipeline operations, achieving the highest real-time performance, low latency, and high efficiency. Compared with CPU and GPU, FPGA can provide lower latency and higher efficiency. This is because FPGA can achieve very low latency through a pipeline architecture and has the ability of data parallelism and pipeline parallelism. By introducing machine learning algorithms into the beam parameter control system of a particle accelerator in the FPGA manner and giving full play to the advantages of FPGA, the control accuracy, response speed, and system stability can be improved, while reducing power consumption and increasing the flexibility of the system. Summary of the Invention

[0004] The object of the present invention is to provide a real-time self-calibration system for the beam position of a particle accelerator based on FPGA, which makes full use of the high parallel data processing ability of FPGA, optimizes the traditional LMS algorithm according to the characteristics of the beam of the particle accelerator, and constructs a random forest prediction model. Through the prediction ability of the random forest prediction model for the multi-variable non-linear model, the real-time acquisition and algorithm processing of the beam intensity are realized, and the data is fed back to the control device in a timely manner, so as to realize the adaptive adjustment of the beam position of the particle accelerator. The present invention not only improves the response speed of beam control, but also enhances the adaptive ability of the system, making the control of the beam position of the particle accelerator more accurate and dynamic.

[0005] The technical solution adopted by the present invention is a real-time self-calibration system for the beam position of a particle accelerator based on FPGA, which includes a beam acquisition and conversion module and an FPGA processing module, wherein:

[0006] The beam acquisition and conversion module is used to obtain the analog signal of the beam in the particle accelerator pipeline, amplify the analog signal, and convert the amplified analog signal into a digital signal;

[0007] The FPGA processing module is used to receive the digital signal from the beam acquisition and conversion module in real time, perform digital filtering processing on the digital signal of the beam by using the LMS algorithm optimized by the genetic algorithm, then construct a random forest prediction model, analyze and predict the filtered digital signal of the beam through the random forest prediction model, and dynamically adjust the current of the magnet and the voltage of the deflection plate according to the result of the analysis and prediction, so as to realize the adaptive adjustment of the beam position of the particle accelerator.

[0008] Further, the beam acquisition and conversion module includes a beam position detector, a transimpedance amplifier, and an analog-to-digital converter; the beam position detector is used to obtain the analog signal of the beam in the particle accelerator pipeline; the transimpedance amplifier is used to amplify the analog signal obtained by the beam position detector; the analog-to-digital converter is used to accurately convert the amplified analog signal into a digital signal.

[0009] Further, the beam position detector is a quadrant plate.

[0010] Further, the FPGA processing module includes beam signal acquisition, adaptive digital filtering, random forest prediction model analysis and prediction, and beam position adaptive adjustment; the beam signal acquisition is used to receive the digital signal of the beam from the analog-to-digital converter in real time; the adaptive digital filtering is used to perform digital filtering processing on the digital signal of the beam by using the LMS algorithm optimized by the genetic algorithm;

[0011] The random forest prediction model analyzes and predicts the digital signals of the filtered beam current through the random forest prediction model; the beam position adaptive adjustment is used to dynamically adjust the current of the magnet and the voltage of the deflection plate according to the results of the analysis and prediction by the random forest prediction model, so as to realize the adaptive adjustment of the beam position of the particle accelerator.

[0012] Furthermore, the step size factor in the LMS algorithm is optimized by the genetic algorithm to achieve the optimization of the LMS algorithm. The specific optimization steps are as follows:

[0013] Initializing the population: In the genetic algorithm, an initial population is generated, which consists of multiple individuals, and each individual represents a possible value of the step size factor in the LMS algorithm;

[0014] Fitness evaluation: Perform fitness evaluation on each individual, that is, calculate the performance index of each step size factor value and the mean square error of the filter;

[0015] Selection operation: Based on the fitness value, select individuals with better performance as parents for generating the next generation;

[0016] Crossover operation: Combine the genes of different individuals through the crossover operation to generate new individuals;

[0017] Mutation operation: Randomly change some gene values of an individual through the mutation operation to generate new individuals;

[0018] Composition of the new generation population: The individuals after selection, crossover, and mutation operations are composed into a new generation population;

[0019] Iterative evolution: Repeat the above fitness evaluation, selection, crossover, and mutation operations to gradually search for the optimal solution to the problem;

[0020] Output of the optimal solution: When the termination condition is met, select the individual with the highest fitness from the population, that is, the optimal value of the step size factor, as the final optimization result.

[0021] Furthermore, the specific steps for constructing the random forest prediction model are as follows:

[0022] Data collection: Collect data on beam current intensity and corresponding magnet current and deflection plate voltage;

[0023] Data preprocessing: Clean and preprocess the collected data;

[0024] Feature selection: Determine the input features, that is, the average value of beam current intensity, the difference between the left and right beam currents, and the difference between the upper and lower beam currents;

[0025] Model training: Use the preprocessed data to train the random forest prediction model;

[0026] Model validation: Evaluate the performance of the model through cross-validation methods to ensure that the model has good generalization ability;

[0027] Parameter tuning: Adjust the model parameters according to the validation results to improve the prediction accuracy;

[0028] Model testing: Evaluate the performance of the final model on an independent test set.

[0029] Furthermore, in the data preprocessing, cleaning and preprocessing the collected data include removing noise, filling missing values, normalizing or standardizing.

[0030] Furthermore, in the model training, training the random forest prediction model using the preprocessed data includes setting the random forest model parameters, and the parameters include the number of trees, the maximum depth, and the minimum number of samples for splitting.

[0031] Furthermore, the random forest prediction model is:

[0032] (C 磁铁 ,V 偏转 )=f(ΔC 左右 ,ΔC 上下 ,C 平均 )

[0033] where C 磁铁 is the current of the magnet lens; V 偏转 is the voltage of the electrostatic deflection plate; ΔC 左右 is the difference between the left and right beam currents; ΔC 上下 is the difference between the upper and lower beam currents; C 平均 is the average value of the beam intensity.

[0034] Furthermore, the adaptive adjustment of the beam position depends on the difference in the beam intensity measured at the four positions of the beam position detector in the up, down, left, and right directions. By comparing the magnitudes of the beam intensities, it is determined in which direction the beam should move, so that the beam can be centered in the particle accelerator pipe, achieving the maximum efficiency utilization of the beam.

[0035] The beneficial effects of the present invention are as follows:

[0036] The present invention makes full use of the high parallel data processing ability of FPGA, optimizes the traditional LMS algorithm for the characteristics of the particle accelerator beam, and constructs a random forest prediction model. Through the prediction ability of the random forest prediction model for the multi-variable non-linear model, it realizes the real-time acquisition and algorithm processing of the beam intensity, and timely feeds back the data to the control device, realizing the adaptive adjustment of the particle accelerator beam position. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a schematic diagram of the system structure provided by the embodiment of the present invention;

[0038] Figure 2 Schematic diagram of the beam position detector (quadrant plate) provided by the embodiment of the present invention;

[0039] Figure 3 Circuit design diagram of the transimpedance amplifier (ADA4530) provided by the embodiment of the present invention;

[0040] Figure 4 Circuit design diagram of the analog-to-digital converter (ADS1115) provided by the embodiment of the present invention;

[0041] Figure 5 Flowchart of the working principle of the adaptive filtering of the present invention;

[0042] Figure 6 Flowchart of the working process of the random forest prediction model of the present invention. Detailed implementation manners

[0043] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings.

[0044] A real-time self-calibration system for the beam position of a particle accelerator based on FPGA includes a beam acquisition and conversion module and an FPGA processing module.

[0045] Beam acquisition and conversion module

[0046] The beam acquisition and conversion module is used to obtain the analog signal of the beam in the particle accelerator pipeline, amplify the analog signal, and convert the amplified analog signal into a digital signal.

[0047] The beam acquisition and conversion module includes a beam position detector, a transimpedance amplifier and an analog-to-digital converter.

[0048] The beam position detector (BPM) is used to obtain the analog signal of the beam in the particle accelerator pipeline.

[0049] Among them, the beam position detector of the present invention is a quadrant plate.

[0050] The transimpedance amplifier is used to amplify the analog signal obtained by the beam position detector.

[0051] The circuit structure that converts current into voltage by the feedback resistance method is called a transimpedance amplifier, and the present invention uses this principle to measure the beam intensity of the particle accelerator.

[0052] The analog-to-digital converter (ADC) is used to accurately convert the amplified analog signal into a digital signal, providing an accurate data basis for the subsequent FPGA processing module.

[0053] FPGA Processing Module

[0054] The FPGA processing module is used to receive digital signals from the beam current acquisition and conversion module in real time, perform digital filtering on the digital signals of the beam current using the LMS algorithm optimized by the genetic algorithm, then construct a random forest prediction model, analyze and predict the filtered digital signals of the beam current through the random forest prediction model, and dynamically adjust the current of the magnet and the voltage of the deflection plate according to the analysis and prediction results to achieve the adaptive adjustment of the beam current position of the particle accelerator.

[0055] The FPGA processing module includes beam current signal acquisition, adaptive digital filtering, random forest prediction model analysis and prediction, and beam current position adaptive adjustment.

[0056] The beam current signal acquisition is used to receive the digital signals of the beam current from the analog-to-digital converter in real time and provide a continuous beam current data stream for the system.

[0057] The adaptive digital filtering is used to perform digital filtering on the digital signals of the beam current using the LMS algorithm optimized by the genetic algorithm to eliminate noise and interference and improve the quality and reliability of the signals.

[0058] An adaptive filter is a signal processing tool that dynamically adjusts its parameters to adapt to a changing environment and is widely used in fields such as noise cancellation, channel equalization, and system identification. Among them, the LMS (Least Mean Squares) algorithm is widely used because of its simplicity and high computational efficiency and is a classic adaptive filtering algorithm.

[0059] The LMS algorithm continuously adjusts the filter coefficients to minimize the mean square value of the error signal. This process continues until the filter coefficients converge or reach a preset number of iterations. However, for a particle accelerator, the beam current intensity under the current control parameters may fluctuate over time, which may be caused by unstable electromagnetic fields inside the accelerator, non-uniformity of the beam source, or external environmental changes (such as temperature, magnetic field, etc.), resulting in errors in the adaptive filtering algorithm. Therefore, the present invention introduces the genetic algorithm to improve the LMS algorithm. The genetic algorithm is used to optimize the step size factor (μ) in the LMS algorithm to further improve the convergence speed and accuracy of the filter.

[0060] The random forest prediction model analysis and prediction analyzes and predicts the filtered digital signals of the beam current through the random forest prediction model.

[0061] The beam current position adaptive adjustment is used to dynamically adjust the current of the magnet and the voltage of the deflection plate according to the results of the random forest prediction model analysis and prediction to achieve the adaptive adjustment of the beam current position of the particle accelerator.

[0062] The adaptive adjustment of the beam position depends on the differences in beam intensities measured at the four positions (up, down, left, and right) of the quadrant plate. By comparing the magnitudes of the beam intensities, it is determined in which direction the beam should move, enabling the beam to be centered in the particle accelerator pipe and achieving the maximum efficiency utilization of the beam.

[0063] The movement of the beam is determined by the magnet lens and the electrostatic deflection plate. The current C of the magnet lens determines the focusing and divergence degree of the beam, and the voltage V of the electrostatic deflection plate determines the position of the beam in the horizontal or vertical direction. The adaptive adjustment of the beam position is achieved by establishing the relationship among the beam intensities of the quadrant plate, the differences in beam intensities, the current of the magnet lens, and the voltage of the electrostatic deflection plate. The present invention uses the random forest algorithm to map this relationship and deploys the model on the FPGA. The constructed random forest prediction model is:

[0064] (C 磁铁 ,V 偏转 )=f(ΔC 左右 ,ΔC 上下 ,C 平均 )

[0065] Wherein, C 磁铁 is the current of the magnet lens; V 偏转 is the voltage of the electrostatic deflection plate; ΔC 左右 is the difference in beam intensities between the left and right; ΔC 上下 is the difference in beam intensities between the up and down; C 平均 is the average value of the beam intensity.

[0066] Example 1

[0067] The current input of the self-calibration test system uses a BNC interface, and the power supply uses a 9V / 1A linear adapter.

[0068] As Figures 1-6 shown, the beam position detector BMP selected in the system of the embodiment of the present invention is a quadrant plate, the diameter of the central pipe is 25 mm, and the material is stainless steel. It represents the beams in the four directions of up, down, left, and right. The beam intensities in different directions are obtained through the transimpedance amplifier in the beam acquisition and conversion module, and the beam position is calibrated by the differences in beam intensities.

[0069] The operational amplifier of the weak current test system should meet the following conditions: (1) The input bias current Ib of the operational amplifier should be as small as possible, such as less than 10 fA; (2) The offset voltage Vos of the operational amplifier should be as small as possible; (3) The resistance value of the input resistance Ri of the operational amplifier should be sufficiently large, and the input current should flow into the feedback resistance as much as possible, that is, the input resistance should be much larger than the feedback resistance, such as greater than 100 TΩ. Based on the above considerations, ADA4530-1 with good characteristics in terms of input bias current, input offset voltage, and noise level is selected.

[0070] The operational amplifier ADA4530-1 chip with fA-level input bias current is selected as the transimpedance amplifier. The potential of the GRD pin of this amplifier follows the +IN input inside the ADA4530-1 chip to be virtual ground, almost the same as the potential of -IN. The GRD pins are interconnected. When wiring the circuit board, the resistor R1 and the input signal line are surrounded by GRD, which is used as an equipotential shielding protection to prevent the leakage of weak input current to other adjacent pins of this device or other devices. The +IN pin is grounded. C1 is connected in parallel at the -5V power supply terminal to provide a 5V negative voltage for the VEE pin. The IC pin is connected to the -5V power supply. C2 is connected in parallel at the 5V power supply terminal to provide a 5V voltage for the VCC pin. The input signal is input from the Input port and connected to one end of the resistor R1. The other end of the resistor R1 is first connected to one end of the capacitor C2, and the other end is connected to the VOUT port of the ADA4530. At the same time, the output signal is led out from the VOUT port. The other end of the resistor R1 is secondly connected to the other end of the resistor R2. Since the input bias current of this operational amplifier is very small, it is ensured that almost all the current flows into the resistor R1, making the output voltage Vout of the operational amplifier proportional to the input current Iin: Vout = -R * Iin. Thus, the purpose of current-voltage conversion is achieved.

[0071] ADS1115 is selected as the 4-channel 16-bit analog-to-digital converter sampling chip to simultaneously collect the signals of 4 beam position detectors, and the collected data is sent to the FPGA through the I2C protocol.

[0072] The FPGA hardware platform uses Zynq7010. For the programmable logic (PL) part of Zynq7010, the pins of the I2C interface are configured to ensure correct connection with the I2C device. The Vivado development environment is used to configure the connection between the IP core and the AXI bus to utilize the I2C controller of Zynq-7010 for efficient data transmission.

[0073] In the software design stage, a driver program for I2C communication is written, including initializing the I2C controller, setting the correct clock frequency, and implementing the basic operations of the I2C communication protocol, such as the START condition, sending the device address, reading and writing data, and the STOP condition.

[0074] Adaptive Digital Filter Design Based on FPGA

[0075] Initializing filter coefficients: Before the adaptive filter starts working, the filter coefficients are usually initialized to zero or random values.

[0076] Input signal x(n): The input signal sample at the current moment.

[0077] Filter output y(n): The output signal calculated using the current filter coefficients.

[0078] Calculate the error e(n): The difference between the desired signal d(n) and the filter output y(n), which is the error.

[0079] Update the filter coefficients: According to the error e(n) and the input signal x(n), use the LMS algorithm to update the filter coefficients, and at the same time use the genetic algorithm to optimize the step size factor (μ) of the LMS algorithm.

[0080] Check the convergence condition: Determine whether the filter coefficients have converged, that is, whether the error has reached an acceptable level.

[0081] Output the filtering result: If the filter coefficients have converged, output the filtering result.

[0082] The specific steps for optimizing the step size factor (μ) of the LMS algorithm using the genetic algorithm are as follows:

[0083] Initialize the population: In the genetic algorithm, first, an initial population needs to be generated. This population consists of multiple individuals, and each individual represents a possible value of the step size factor (μ) in the LMS algorithm.

[0084] Fitness evaluation: Conduct fitness evaluation for each individual, that is, calculate the performance index of each step size factor (μ) value and the mean square error (MSE) of the filter. Among them, the fitness function is usually proportional to the performance index, and the better the performance, the higher the fitness.

[0085] Selection operation: Based on the fitness values, select individuals with better performance as parents for generating the next generation.

[0086] Crossover operation: Combine the genes (i.e., step size factor values) of different individuals through the crossover operation to generate new individuals. This process simulates the gene recombination process in biological evolution. By exchanging part of the genes of individuals, new combinations are produced, thereby increasing the diversity of the population.

[0087] Mutation operation: Randomly change some gene values of individuals through the mutation operation to also generate new individuals. This process simulates gene mutations in biological inheritance, helps maintain the diversity of the population, and prevents the algorithm from prematurely falling into local optimal solutions.

[0088] Composition of the new generation population: Compose the individuals after selection, crossover, and mutation operations into a new generation population.

[0089] Iterative evolution: Repeat the above fitness evaluation, selection, crossover, and mutation operations to gradually search for the optimal solution to the problem. Each generation of the population will be updated according to the fitness function until the maximum number of iterations N is reached.

[0090] Output the optimal solution: After the termination condition is met, select the individual with the highest fitness from the population, which is the optimal value of the step size factor (μ), as the final optimization result.

[0091] Design of Random Forest Prediction Model

[0092] Data collection: Collect data on beam intensity and corresponding magnet current and deflector plate voltage. This data will be used to train the random forest model.

[0093] Data preprocessing: Clean and preprocess the collected data, including removing noise, filling missing values, normalizing or standardizing, etc.

[0094] Feature selection: Determine the input features, namely the average value of beam intensity, the difference between the left and right beams, and the difference between the upper and lower beams.

[0095] Model training: Use the preprocessed data to train the random forest model, including setting random forest model parameters such as the number of trees, maximum depth, minimum number of samples for splitting, etc.

[0096] Model validation: Evaluate the performance of the model through methods such as cross-validation to ensure that the model has good generalization ability.

[0097] Parameter tuning: Adjust the model parameters according to the validation results to improve the prediction accuracy.

[0098] Model testing: Evaluate the performance of the final model on an independent test set.

[0099] Model deployment: Deploy the trained random forest prediction model to the FPGA, integrate the FPGA with the beam control system, and ensure that the input and output of the random forest prediction model match the actual beam parameters and control signals.

[0100] Real-time model prediction: During actual operation, the FPGA will receive beam intensity data in real time, use the deployed random forest model for prediction, and output control signals for magnet current and deflector plate voltage.

[0101] What is not described in detail in the specification of the present invention belongs to the prior art in the technical field.

Claims

1. A real-time self-calibration system for beam position of a particle accelerator based on FPGA, characterized in that, It includes a beam current acquisition and conversion module and an FPGA processing module, where: The beam current acquisition and conversion module is used to obtain the analog signal of the beam current in the particle accelerator pipeline, amplify the analog signal, and convert the amplified analog signal into a digital signal; The FPGA processing module is used to receive the digital signal from the beam current acquisition and conversion module in real time, perform digital filtering on the digital signal of the beam current by using the LMS algorithm optimized by the genetic algorithm, then construct a random forest prediction model, analyze and predict the filtered digital signal of the beam current through the random forest prediction model, and dynamically adjust the current of the magnet and the voltage of the deflection plate according to the analysis and prediction results, so as to realize the adaptive adjustment of the beam current position of the particle accelerator.

2. The real-time self-calibration system for the beam position of the particle accelerator based on FPGA according to claim 1, characterized in that, The beam current acquisition and conversion module includes a beam position detector, a transimpedance amplifier, and an analog-to-digital converter; the beam position detector is used to obtain the analog signal of the beam current in the particle accelerator pipeline; the transimpedance amplifier is used to amplify the analog signal obtained by the beam position detector; the analog-to-digital converter is used to accurately convert the amplified analog signal into a digital signal.

3. The real-time self-calibration system for the beam position of a particle accelerator based on FPGA according to claim 2, characterized in that, The beam position detector is a quad plate.

4. The real-time self-calibration system for the beam position of the particle accelerator based on FPGA according to claim 2, wherein The FPGA processing module includes beam signal acquisition, adaptive digital filtering, random forest prediction model analysis and prediction, and beam position adaptive adjustment; the beam signal acquisition is used to receive the digital signal of the beam current from the analog-to-digital converter in real time; the adaptive digital filtering is used to perform digital filtering on the digital signal of the beam current by using the LMS algorithm optimized by the genetic algorithm; the random forest prediction model analysis and prediction analyzes and predicts the filtered digital signal of the beam current through the random forest prediction model; the beam position adaptive adjustment is used to dynamically adjust the current of the magnet and the voltage of the deflection plate according to the analysis and prediction results of the random forest prediction model, so as to realize the adaptive adjustment of the beam current position of the particle accelerator.

5. The real-time self-calibration system for the beam position of a particle accelerator based on FPGA according to claim 4, characterized in that, The LMS algorithm is optimized by optimizing the step size factor in the genetic algorithm. The specific optimization steps are as follows: Initializing the population: In the genetic algorithm, an initial population is generated, which consists of multiple individuals, and each individual represents a possible value of the step size factor in the LMS algorithm; Fitness evaluation: Perform fitness evaluation on each individual, that is, calculate the performance index of each step size factor value and the mean square error of the filter; Selection operation: Based on the fitness value, select individuals with better performance as parents for generating the next generation; Crossover operation: Combine the genes of different individuals through the crossover operation to generate new individuals; Mutation operation: Randomly change some gene values of individuals through the mutation operation to generate new individuals; Composition of the new generation population: The individuals after selection, crossover, and mutation operations are combined to form a new generation population; Iterative evolution: Repeat the above fitness evaluation, selection, crossover, and mutation operations to gradually search for the optimal solution to the problem; Output of the optimal solution: When the termination condition is met, select the individual with the highest fitness from the population, that is, the optimal value of the step size factor, as the final optimization result.

6. The real-time self-calibration system for the beam position of a particle accelerator based on FPGA according to claim 4, wherein The specific steps for constructing a random forest prediction model are as follows: Data collection: Collect data on beam intensity and the corresponding magnet current and deflector plate voltage; Data preprocessing: Clean and preprocess the collected data; Feature selection: Determine the input features, namely the average value of the beam intensity, the difference between the left and right beams, and the difference between the upper and lower beams; Model training: Use the preprocessed data to train a random forest prediction model; Model validation: Evaluate the performance of the model through the cross-validation method to ensure that the model has good generalization ability; Parameter tuning: Adjust the model parameters according to the validation results to improve the prediction accuracy; Model testing: Evaluate the performance of the final model on an independent test set.

7. The real-time self-calibration system for the beam position of the particle accelerator based on FPGA according to claim 6, characterized in that, In the data preprocessing, cleaning and preprocessing the collected data includes removing noise, filling missing values, normalizing or standardizing.

8. The real-time self-calibration system for the beam position of the particle accelerator based on FPGA according to claim 6, characterized in that, In the model training, using the preprocessed data to train a random forest prediction model includes setting the random forest model parameters, and the parameters include the number of trees, the maximum depth, and the minimum number of samples for splitting.

9. The real-time self-calibration system for the beam position of the particle accelerator based on FPGA according to claim 4, wherein The random forest prediction model is: (C 磁铁 ,V 偏转 ) = f(ΔC 左右 ,ΔC 上下 ,C 平均 ) Among them, C 磁铁 is the current of the magnet lens; V 偏转 is the voltage of the electrostatic deflection plate; ΔC 左右 is the difference between the left and right beam currents; ΔC 上下 is the difference between the upper and lower beam currents; C 平均 is the average value of the beam current intensity.

10. The real-time self-calibration system for the beam position of the particle accelerator based on FPGA according to claim 1, characterized in that, The adaptive adjustment of the beam position depends on the differences in beam intensity measured at the four positions of up, down, left, and right by the beam position detector. By comparing the magnitudes of the beam intensities, it is determined in which direction the beam should move, so that the beam can be centered in the particle accelerator pipe, achieving the maximum efficiency utilization of the beam.

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