Design of Nonlinear Active Disturbance Rejection Controller Based on the Adaptive Particle Swarm Optimization Algorithm for the Maglev Train Traction Control System

Hu, Lingfeng; Fan, Kuangang; Wei, Libing; Tan, Wengang

doi:https://doi.org/10.1155/2023/6627429

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Research Article | Open Access

Volume 2023 | Article ID 6627429 | https://doi.org/10.1155/2023/6627429

Design of Nonlinear Active Disturbance Rejection Controller Based on the Adaptive Particle Swarm Optimization Algorithm for the Maglev Train Traction Control System

Lingfeng Hu,^1,2Kuangang Fan ,^1,2,3,4Libing Wei,^1,2and Wengang Tan⁵

Academic Editor: Sangsoon Lim

Received28 Nov 2022

Revised03 Mar 2023

Accepted18 Mar 2023

Published14 Apr 2023

Abstract

This paper focuses on speed tracking control of the maglev train operation system. Given the complexity and instability of the maglev train operation system, traditional speed-tracking control algorithms demonstrate poor tracking accuracy and large tracking errors. The maglev train is easily affected by external interference, increasing train energy consumption and reducing passengers’ riding comfort. This study proposes a control algorithm called APSO-NLADRC to address the deficiencies of the automatic train operation control algorithms. The APSO-NLADRC is based on adaptive particle swarm optimization (APSO) algorithm parameter optimization nonlinear active disturbance rejection controller (NLADRC). The method of population comparison, linear update of learning factors, and adaptive updating of inertia weight values addresses the premature convergence phenomenon that occurs during the parameter optimization of the traditional particle swarm algorithm. The APSO algorithm solves the problem that the parameters of the NLADRC are difficult to adjust. Compared with PID, NLADRC, and NLADRC based on traditional particle swarm optimization algorithms, the proposed control algorithm has higher tracking accuracy and more robust anti-interference capability and provides better comfort.

1. Introduction

With the development of intelligent optimization algorithms, increasing attention is being paid to the research on automatic train operation (ATO) algorithms. The research focuses on train operation models [1] and control algorithms [2–6]. The key to the ATO algorithm of the maglev train is the speed curve track, which focuses on controlling the traction and braking force to track the target speed curve accurately [7, 8]. Accurate tracking of the target speed curve can improve the train’s parking accuracy and achieve energy saving [9–11]. The current train speed curve tracking control methods can be roughly divided into the following categories: classical, adaptive, intelligent, and integrated intelligent control methods. Classical control methods are widely used due to their simple structure, for example, the PID control algorithm, fuzzy control algorithm, and sliding mode control algorithm [12–17]. Some scholars have also conducted extensive research to optimise controller parameters. Izci et al. used the novel augmented hunger game search algorithm based on a logarithmic spiral learning technique to tune a fractional order proportional-integral-derivative controller [18]. Ekinci et al. proposed the manta ray foraging optimization algorithm with the generalized opposition-based learning technique and Nelder–Mead simplex search method and successfully verified the optimized performance of the developed algorithm [19]. However, due to the instability and uncertain interference of the maglev train operation system, the PID controller presents deficiencies in control performance and tracking accuracy. To solve the shortcomings of the PID controller, Han formally proposed the active disturbance rejection control (ADRC) [20] in 1998 and described in [21] the specific measures to resolve the weaknesses of the PID control algorithm. ADRC is achieved by introducing a nonlinear state error feedback method for error feedback and an extended state observer for estimating and suppressing total disturbances. As a result, performance and practicality advantages are obtained and widely used. In [22], Long et al. adopted the dynamic model of the maglev train as the control object, and the target speed curve was tracked through the ADRC to achieve tracking accuracy and passenger comfort. Li et al. [23] combined the high-speed train traction calculation model with the traction/braking system model, and a train control model with delay was established. This study also proposed a speed curve tracking algorithm based on sliding mode and the ADRC. An extended state observer was added to estimate and compensate for system disturbances and achieve tracking of the target speed curve of high-speed trains. Given the complexity and instability of the electric traction freight train operation system, Wang et al. [24] proposed a train speed-tracking control system based on nonlinear ADRC, which solves the large train speed-tracking error caused by unknown disturbances and parameter changes in the traditional PID controller. The nonlinear ADRC has good tracking performance because of its less dependence on the controlled object model. However, the nonlinear ADRC parameters are numerous and difficult to adjust, and intelligent optimization algorithms are required to optimize the parameters. Some scholars have conducted extensive research on these problems. [24] used the artificial bee colony algorithm to optimize the parameters of an ADRC. [25] utilized the genetic algorithm to adjust the parameters of the ADRC, improved the algorithm, and evaluated the control effect by establishing an evaluation function. Although these intelligent optimization algorithms play a certain role in parameter tuning, they often have problems such as slow convergence and low search accuracy.

In summary, the operation system of the maglev train is more complex than other medium and high-speed trains. We consider the three following aspects: train model, control method, and parameter optimization algorithm. The analysis is carried out from the train’s force situation, and the maglev train’s single mass model is established. This study adopts the nonlinear active disturbance rejection controller (NLADRC) and designs a speed-tracking system based on NLADRC to achieve high-accuracy tracking of the target speed curve and enhance the anti-interference performance of the system. According to the above analysis, the main improvements are as follows: (1)To solve the premature convergence of the traditional particle swarm algorithm during parameter optimization, an adaptive particle swarm optimization (APSO) algorithm is proposed. Specifically, the main improvement points are the population comparison method, linear update of learning factors, and adaptive update of inertia weights. The particle swarm’s local and global search capabilities can be adaptively changed to prevent the algorithm from falling into the local optimum(2)To solve the problem of the NLADRC’s parameters being difficult to adjust, the APSO algorithm is used in parameter optimization, and the adaptability and tracking performance of the controller on the maglev train is improved

The rest of this paper is summarized as follows. In Section 2, we establish a single-mass model of the maglev train through a force analysis. In Section 3, we introduce the NLADRC for the speed-tracking control system of the maglev train and the parameter optimization of NLADRC based on APSO. In Section 4, the tracking performance of the proposed APSO-NLADRC is analysed and compared with that of PID, NLADRC, and PSO-NLADRC under the same experimental conditions. The full text is summarized in Section 5.

In this paper, the main abbreviations and their full forms are shown in Table 1, and the main symbols and their meanings are shown in Table 2.

2. Establishment of the Maglev Train Model

2.1. Dynamic Model

The operation of maglev trains is more complicated than other medium and high-speed trains, and the operating system could be more unstable. Focusing on the characteristic that the nonlinear active disturbance rejection controller has a relatively small dependence on the system model, this study adopts a single-mass train model, and its force model is shown in Figure 1. is the traction force of the maglev train, is the braking force of the maglev train, is the basic resistance of the maglev train, and is the additional resistance of the maglev train.

In accordance with Newton’s second law, the single-mass model of the maglev train can be established as follows: where is the distance traveled by the maglev train, is the speed at which the maglev train travels, is the acceleration of the maglev train, and is the resultant force of the maglev train. The train operates in four modes: traction, coasting, braking, and cruising. The forces under different modes of operation are shown in Table 3.

2.2. Dynamic Model

2.2.1. Traction Force and Braking Force Calculation

The traction force of the maglev train mainly originates from the linear induction motor, and the magnitude of the traction force is affected by various factors. With constant changes in speed, the maglev train’s traction and braking force change correspondingly. The relationship between force and speed is shown in Figure 2.

2.2.2. Basic Resistance Calculation

The basic resistance of the maglev train in operation can be divided into air resistance and electromagnetic resistance. In accordance with the maglev train resistance formula used by Japan’s high-speed surface transport, the calculation formulas for basic resistance are shown below. (1)Air resistance: (2)Electromagnetic resistance: (3)Basic resistance: where is the speed of the maglev train relative to the airflow, is the total mass of the maglev train, and is the acceleration of gravity.

2.2.3. Additional Resistance Calculation

In the operation process, the maglev train is also affected by additional external resistance, such as extra resistance on ramps and curves. The calculation formulas for additional resistance are shown below. (1)Additional ramp resistance: (2)Additional curve resistance: (3)Additional resistance:

In the above formulas, is the total mass of the maglev train, is the acceleration due to gravity, is the angle of the ramp, and is the radius of the curve.

3. Design of Speed-Tracking Controller

3.1. NLADRC

Because of the instability of the speed-tracking control system of the maglev train and various uncertain factors in the operation process, this paper adopts NLADRC as the controller of the maglev train speed-tracking system. The structure of NLADRC is shown in Figure 3.

The NLADRC consists of the tracking differentiator (TD), nonlinear state error feedback (NLSEF), and nonlinear extended state observer (NLESO). Its simulation model is shown in Figure 4.

3.1.1. Design of TD

The function of the TD module can be expressed as follows: the maglev train’s target speed curve data can be transformed into two output signals, and , by the tracking differentiator module. represents the tracking value of and takes it as the actual target speed. is the signal obtained by differentiating . The derivation formula of the tracking differentiator is as follows: where represents optimal control synthesis function, and its calculation formula is as follows: where , , , and .

In the above formula, is the speed tracking factor, is the integral step, and is the filtering factor. The value of is related to the tracking speed; the larger the value, the faster the tracking speed; however, when the value is greater than a certain value, the effect is not obvious.

3.1.2. Design of NLESO

ESO is the key part of ADRC for active disturbance rejection. Although LESO improves the control performance of the system, it is slightly lacking in tracking accuracy and disturbance rejection capability. Meanwhile, NLESO is better than ESO and NLESO in tracking accuracy and disturbance rejection. Therefore, third-order NLESO is adopted in this paper to deal with the unknown disturbances in the speed-tracking system of the maglev train. The derivation formula of the third-order NLESO is as follows: where is a nonlinear function defined as

In the formula above, is the output error of the system, and are the observed values of the system output, is the observed value of the total system disturbance, and is the actual tracking speed of the output. , , and are the key gain parameters of NLESO, is the compensation factor, and is the control system output.

3.1.3. Design of NLSEF

This paper uses a nonlinear PD controller instead of the linear combination of traditional PID controllers. The error signal is converted into a nonlinear function for the error to obtain a more effective error feedback control rate, thus achieving the effect of “large gain with small error and small gain with large error.” The derivation formula of NLSEF is as follows: where is a nonlinear function defined as where and represent system gains, which are parameters that need to be optimized through intelligent algorithms, and is a compensation factor.

For the uncertain parameters , , , , , and , the general methods include the empirical parameter adjustment method and the intelligent algorithm optimization method. Although the traditional empirical tuning method is very obvious to the controlled object, it does not regulate the controlled object in real time, so this paper uses an adaptive particle swarm. Therefore, this paper adopts the adaptive particle swarm optimization algorithm to adjust the parameters of NLADRC.

3.2. Parameter Optimization of NLADRC Based on APSO

PSO algorithm is an intelligent optimization algorithm proposed by Kennedy and Eberhart [26, 27], which has more straightforward rules, more accessible programming, and more robustness compared to other intelligent optimization algorithms. The PSO algorithm is used to find the optimal solution by iteration, and the fitness value evaluates the quality of the solution.

In the PSO algorithm, the whole particle population consists of particles, and each particle searches in the -dimensional space with a certain velocity. For the parameters to be optimized in this paper, each particle represents a potentially feasible solution, and its moving distance and forward direction are determined by its velocity. In the process of continuous iteration of particles, the current optimal individual is selected by comparing the fitness value of each particle, and the current population extremum is selected by comparing the fitness values of each particle swarm.

The phenomenon of premature convergence occurs in the traditional particle swarm algorithm when optimizing the NLADRC parameters due to the rapid distribution of particles in the feasible solution region, thus causing the algorithm to fall into a local optimum. An adaptive particle swarm optimization algorithm is proposed in this paper to solve this problem, which solves the problems of the traditional PSO algorithm by improving the initial population, linear update of learning factors, and adaptively updating the inertial weight value.

As indicated in the previous section, six parameters need to be optimized in the NLADRC: , , , , , and . The third-order ESO can set the parameters , , and through the “bandwidth method.” To deal with the influence of sampling step size and noise during parameter setting, the corresponding problem can be solved by introducing the parameter observer bandwidth . The setting formula can be given in [28]:

Therefore, the parameters to be optimized for NLADRC can be obtained as , , , and . The NLADRC parameter adjustment diagram based on the APSO algorithm is shown in Figure 5.

The process of optimizing the NLADRC parameters by the APSO algorithm is as follows.

Step 1. Population initialization.
In the APSO algorithm, each particle represents a solution of parameters , , , and in NLADRC, and the quality of the solution is evaluated by comparing the fitness values of each solution. The randomness of population initialization in the traditional PSO algorithm often affects the convergence of the final solution of the algorithm. The population comparison method is proposed in this paper to solve the difference between random initial populations. The first population is generated and the fitness value is calculated. where is the particle population size; is the dimension; and and are the upper and lower bounds of the particle search space location, respectively.
The second population generated by Equation (16) is used in this paper, and the fitness value is calculated. The fitness values of the first and second populations are compared, and the population with an excellent fitness value is retained and adopted as the final initial population of the APSO algorithm. The second population formula can be given in [29]: The specific steps of population initialization in the APSO algorithm are as follows. First, the population size , the number of iterations , the dimension is the number of optimization parameters , and the particle velocity is initialized. Second, the first population is randomly generated for preservation, and its fitness value is calculated. Third, the second population is generated based on reverse learning, and its fitness value is calculated. Finally, the fitness values of the two populations are compared, and the superior one is retained. The entire process is shown in Algorithm 1.

1: Setting Algorithm Parameters: , , , ,
.
2: for I =1 : S.
.
end.
3: for I =1 : S.
.
end.
4: The Fitness Values of the Two Populations Are Compared, and the Excellent One Has Been Selected as the Initial Population of the Algorithm

Step 2. The individual and global optimal values are updated by calculating the fitness value of each particle position, and the current optimal value is recorded. The fitness function is expressed as follows: where is actual tracking speed and is the target speed.

Step 3. Linear update of learning factors.
The values of learning factors and are related to the search performance. A larger value of will make the particles search too much in the local area, while a larger value of will make the particles converge to the local optimum too early. Therefore, a larger value of and a smaller value of are used at the beginning of the algorithm search to increase the particle’s searchability. As the number of iterations increases, decreases linearly and increases linearly, thus enhancing the ability of the particle to search for the global optimum. The learning factors linear update formula is as follows: where and are learning factors; and represent the initial and termination values of , respectively, and , ; and represent the initial and termination values of , respectively, and , .

Step 4. Adaptive updating of inertial weight values.
In each iteration of the APSO algorithm, the inertial weight value of the particle is updated adaptively by comparing the current particle position fitness value with the average fitness value. When the current particle fitness value is less than the average, the inertia weight is reduced to strengthen the local search capability. When the current particle fitness value exceeds the average fitness value, the inertial weight is increased to enhance global search capability. The improved inertia weight value update formula is as follows: The specific steps in the adaptive updating of the inertial weight values are shown in Algorithm 2:

1: Set the maximum inertia weight and minimum inertia weight .
2: In each iteration of the algorithm, the fitness value of the particle is randomly extracted.

3: Calculate the Minimum Fitness Value in the Current Iteration and save It

4: Calculate the Average Fitness of the Current Population and save It

5: Make a Comparison
if :

else:

end.

Step 5. The inertial weight value is updated in Step 4, and the velocity and position of the particles are updated using where is the individual optimum value of the current particle and is the global optimum value of the current particle swarm.

Step 6. The fitness value of each particle is calculated to update the optimal position of the particle and particle swarm. If the position of the particle is better than the current optimal position of the particle, will be updated. If the particle’s position is not better than the optimal position , will not be updated. Afterwards, is compared with the optimal position found by the current population; if it is better than , will be updated; otherwise, no change will be made.

Step 7. Record the optimal position of the current particle, namely, the optimal solution of the four parameters of NLADRC. Determine whether the algorithm reaches the termination condition: if the algorithm reaches the maximum number of iterations, the optimization is finished; if the algorithm does not reach the stopping condition, return to Step 2 to continue the cycle.

To further verify the robustness of the algorithm, the performance of the APSO algorithm is simulated and verified, and the comparison of the performance of different algorithms is shown in Figure 6.

From Figure 6, it can be seen that the traditional PSO algorithm finds the optimal value in about 13 generations, while the APSO finds the optimal solution in 3 iterations. From the simulation results, it can be seen that the APSO algorithm has a faster convergence speed and a higher convergence accuracy.

4. Simulation Result Analysis

This paper conducts simulation experiments from many aspects to verify the control performance of the APSO algorithm. First, the speed-tracking control system simulation model is designed by combining various parameters of the maglev train with the actual track line data. Each parameter of the train is shown in Table 4. Second, the speed-time data of the maglev train’s target speed curve are adopted as the input signal of the speed-tracking control system simulation model. The simulation speed data are designed using the actual speed data. The target speed curve of the train is shown in Figure 7, and its input signals are simple target speed for horizontal straight lines; complex target speed containing ramps and curves.

(a) Simple target speed

(b) Complex target speed

This section compares APSO-NLADRC with PID, ADRC, and PSO-ADRC under the same experimental conditions. The tracking accuracy and anti-interference performance of the speed tracking system are verified. The simulation environment is based on MATLAB2019a.

4.1. Control Performance Analysis of APSO-NLADRC

As we know from Subsection 3.1, the NLADRC has many parameters. A part of them can be obtained by collating the determined parameters of each module as follows: TD, , , and ; NLESO, , , and ; and NLSEF, , , and . The other part is the uncertain parameters , , , and .

The uncertain parameters , , , and of the NLADRC are optimized according to the APSO algorithm in Subsection 3.2. In continuous iteration, the APSO algorithm reduces the fitness value of the objective function by looking for the individual and global optimum. In the simulation model of the speed-tracking control system with no external interference, the best control performance is obtained when the NLADRC parameters are , , , and . The tracking results for simple target speed curves are shown in Figure 8. The tracking results for complex target speed curves are shown in Figure 9.

(a) Speed-tracking curve

(b) Velocity error

(a) Speed-tracking curve

(b) Velocity error

The following conclusions can be obtained from the above two sets of experimental simulation figures: (1)From the magnified effect on the left side of Figures 8(a) and 9(a), it can be seen that the tracking speed curve under the APSO-NLADRC can almost completely fit the target speed curve, the overshoot of the control system is small, and the adjustment time of the control system is short. From the magnified effect on the right side of Figure 9(a), it can be seen that the APSO-NLADRC has a good control effect at the time point where the velocity change rate is large, and it can also recover to a steady state quickly. Therefore, the nonlinear active disturbance rejection controller based on the adaptive particle swarm optimization algorithm can accurately track the target speed curve with high tracking accuracy(2)As can be seen from Figure 8(b), the range of tracking speed error in the simple target speed curve is to , which fully satisfies the speed error range specified by the train ATO system. As can be seen from Figure 9(b), the range of tracking speed error in the case of a complex target speed curve is - to , and the time points with large speed error changes are the transition points of operating conditions. In the cruising operation stage of the train, the speed error tends to 0 m/s infinitely, which indicates that the APSO-NLADRC has a better speed-tracking effect

4.2. Comparative Analysis of Multicontroller Control Performance

In order to verify the effectiveness of the APSO-NLADRC control algorithm for speed tracking control of the maglev train, this subsection compares and analyzes the APSO-NLADRC control algorithm with the PID, NLADRC, and PSO-NLADRC control algorithms under complex speed limiting conditions. A comparison of complex target speed tracking is shown in Figure 10.

As shown in the magnification effect on the left side of Figure 10, the PID and NLADRC control algorithms have greater overshoot, the PSO-NLADRC reduces the system overshoot but increases the system error, and the APSO-NLADRC has the smallest overshoot as well as the smallest system error. The magnification effect on the middle side of Figure 10 shows that the PID, NLADRC, and PSO-NLADRC control algorithms have the weakest tracking effect and a large adjustment time at the position with speed changes greatly. The APSO-NLADRC control algorithm has the best tracking effect and the shortest system adjustment time. In the magnification effect on the right side of Figure 10, the tracking accuracy of APSO-NLADRC is better than that of PID, NLADRC, and PSO-NLADRC control algorithms. In summary, APSO-NLADRC has obvious advantages in speed tracking accuracy over PID, NLADRC, and PSO-NLADRC.

The comparison data of different controllers in terms of error indices (IAE, ITAE, ISE, and ITSE) and the energy of the control signal are shown in Table 5.

The comparison data in Table 5 shows that APSO-NLADRC has the smallest value in different error indices and control signal energy, which indicates the better performance of the APSO-NLADRC.

The velocity error comparison curves are shown in Figure 11, the distance error comparison curves are shown in Figure 12, and the acceleration error comparison curves are shown in Figure 13.

In Figure 11, the velocity error of the APSO-NLADRC control algorithm is significantly smaller than the other three control algorithms, and the range of variation is −0.005 m/s to 0.005 m/s. The velocity error comparison data indicates that the tracking speed curve almost completely conforms to the target speed curve, and the APSO-NLADRC control algorithm has better tracking accuracy. As shown in Figure 12, the displacement error of APSO-NLADRC is the smallest, and the range of variation is relatively smaller than the other three controllers, which indicates that the train speed-tracking system in this controller has a small stopping error and a good tracking effect. As can be seen from Figure 13, the PID and NLADRC control algorithms switching frequency is faster and have a large acceleration error. Although the switching frequency of PSO-NLADRC is reduced a lot, it still has a large acceleration error. The switching frequency of the APSO-NLADRC control algorithm is the smallest, and the acceleration error is also the smallest. A comparison of the above data indicates that the APSO-NLADRC control algorithm helps to improve the passengers’ riding comfort.

A comparison of the maximum value of velocity error, the maximum value of displacement error and the maximum value of acceleration error under the four controllers are shown in Table 6.

As shown in Table 6, compared with the other three control algorithms, the velocity error, displacement error, and acceleration error are the smallest under the APSO-NLADRC control algorithm. Compared with the PSO-NLADRC control algorithm, the maximum value of velocity error is reduced by 91.67%, the maximum value of displacement error is reduced by 55.07%, and the maximum value of acceleration error is reduced by 21.54% for the APSO-NLADRC control algorithm. These show that the speed tracking system with the APSO-NLADRC control algorithm has higher tracking accuracy, higher stopping accuracy, and better passenger ridings comfort.

To further demonstrate the performance of the APSO-NLADRC control algorithm, the control algorithm proposed in this paper is compared with the control algorithm in the existing results. The comparison results are shown in Figure 14.

As can be seen from Figure 14, the control algorithm proposed in this paper has a smaller overshoot and shorter adjustment time, and the tracking of the target velocity curve is better than the controller of the existing results.

4.3. Robustness Research and Analysis

The simulation experiment analysis shows that APSO-NLADRC can accurately track the preset speed curve regardless of whether the target speed tracking is under the simple or complex speed limit. To further verify the performance of APSO-NLADRC, we conduct a disturbance rejection experiment on the controller. We introduce step signals with amplitudes of 0.1 and −0.1 as unknown external disturbances at time points of 500 s and 1150 s, respectively, to simulate the uncertain factors encountered during the operation of the maglev train, such as weather conditions and equipment problems. A comparison of PID, NLADRC, PSO-NLADRC, and APSO-NLADRC in the face of unknown disturbances to recover to the steady state is shown in Figure 15.

As shown in Figure 15, the PID and NLADRCs can deal with unknown disturbances, but they exhibit large fluctuations and take too long to recover to a steady state. Although the amplitude of the PSO-NLADRC is significantly reduced, the oscillations still exist. Compared with the other three controllers, the APSO-NLADRC presents smaller fluctuations, and the time required to return to the steady state is shorter when dealing with unknown disturbances. The simulation experiment shows that the APSO-NLADRC has better control performance and disturbance rejection than the other controllers.

5. Conclusions

This paper proposes a speed-tracking system based on the APSO-NLADRC control algorithm to solve the instability and uncertainty interference problems in the speed-tracking system of maglev trains. Specifically, the proposed APSO-NLADRC speed-tracking controller includes two aspects: improve the PSO algorithm and the APSO algorithm optimizes the parameters of NLADRC. The improvements of the APSO algorithm are population comparison, learning factor update, and adaptive update of the inertia weight method. The algorithm avoided falling into the local optimum, and the convergence speed of the system was improved. The simulation experiment results under the MATLAB/Simulink simulation platform show that compared with the traditional speed-tracking control algorithm based on PID, NLADRC, and PSO-NLADRC, the maglev train operation by the APSO-NLADRC control algorithm results in a reduced maximum value of velocity errors by up to 91.67%, the maximum value of distance error is reduced by 55.07%. The acceleration error is smaller, which improves the passengers’ riding comfort. This study also conducts simulation experiments with different speed limits and uncertain disturbances of the maglev train. The results show that the APSO-NLADRC control algorithm proposed in this paper has better control effects and robustness.

Data Availability

Data are only available upon request due to restrictions regarding, e.g., privacy and ethics. The data presented in this study are available from the corresponding author upon request. The data are not publicly available due to their relation to another ongoing research.

Conflicts of Interest

The authors declare no conflict of interest.

Acknowledgments

This work was supported by the Central Guided Local Science and Technology Funding Project of the Science and Technology Department of Jiangxi Province (Cross-Regional Cooperation, 20221ZDH04052), the 03 Special Project and 5G Program of the Science and Technology Department of Jiangxi Province (No. 20193ABC03A058), the Program of Qingjiang Excellent Young Talents in Jiangxi University of Science and Technology (JXUSTQJBJ2019004), the China Scholarship Council (CSC, No. 201708360150), the Research Projects of Ganjiang Innovation Academy, Chinese Academy of Sciences (No. E255J001), the Key Research and Development Plan of Ganzhou (Industrial Field)([2019]60), and the Cultivation Project of the State Key Laboratory of Green Development and High-Value Utilization of Ionic Rare-Earth Resources in Jiangxi Province (20194AFD44003).

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Copyright © 2023 Lingfeng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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