Inspection mass rigidity identification effect improvement method based on motion state optimization

Abstract

The invention discloses a method for improving the identification effect of test mass rigidity based on motion state optimization. Comprising the steps of adopting a recursive least square algorithm to identify and test mass rigidity online, designing a fuzzy radial basis function neural network PID controller to realize self-adaptive control, characterizing the motion state of the test mass through multi-frequency sinusoidal signal parameterization, and setting an objective function and constraint conditions of an optimization problem. And carrying out global optimization of the motion state by adopting a dual-stage multi-granularity agent-assisted evolutionary algorithm. According to the invention, the multi-target intelligent optimization algorithm is utilized to realize the optimization of the motion state of the test mass, so that the on-orbit identification effect of the rigidity is effectively improved, and the convergence time is shorter and the convergence precision is higher.

Description

Technical Field

[0001] The present invention relates to the technical field of space gravitational wave detection, and particularly relates to a method for improving the stiffness identification effect of a test mass based on optimizing the motion state. Background Art

[0002] Gravitational waves carry the basic degrees of freedom of gravitational interaction. Detecting and studying gravitational wave physics provides new methods and means for revealing the evolution of the universe, the laws of fundamental physics, and the dynamics of relativistic astrophysics. Space gravitational wave detection uses the laser interferometry method. This method utilizes a three-star formation to detect the picometer-level low-frequency (0.1 mHz - 1 Hz) distance change between freely suspended test masses with a baseline of one hundred thousand to one million kilometers caused by gravitational waves in space, and the detection sensitivity needs to reach 10 -21 order of magnitude, corresponding to achieving a laser interferometry optical path noise better than 10 -12 m / Hz 1 / 2 order of magnitude and a residual acceleration noise of the test mass better than 10 -15 m / s 2 / Hz 1 / 2 order of magnitude. Therefore, it is necessary to use the drag-free control technology to keep the test mass in a freely suspended state and maintain an ultra-low residual acceleration level as the inertial reference for laser interferometry, which is the key to achieving high-precision measurement.

[0003] The stiffness of the test mass and the displacement coupling noise, as an important part of the residual acceleration noise, greatly affect the performance of space gravitational wave detection. It is necessary to identify the stiffness to verify and optimize the control effect and meet the noise suppression requirements. Stiffness refers to the ability of the test mass to resist deformation when subjected to an external force. To overcome this challenge, scientists have proposed the on-orbit stiffness identification technology. Although Document 1 "Method, System, Terminal and Medium for Identifying the On-Orbit Stiffness of a Non-Coaxial Test Mass [P]. Shanghai: CN202410785983.8, 2024-10-18." has derived the on-orbit stiffness identification dynamic model for the non-coaxial test mass layout in space gravitational wave detection, suppressed external disturbances through the double-sensitive-axis decomposition method, and realized the on-orbit identification of stiffness based on the least squares identification algorithm. However, there are still several key problems to be solved:

[0004] 1. Computational resource limitation: The on-board environment has strict limitations on computational resources, and the existing methods may be difficult to meet the real-time requirements in terms of computational efficiency.

[0005] 2. Robustness of the identification algorithm: In a complex space environment, external disturbances and measurement noise may interfere with the accuracy of stiffness identification, and it is necessary to improve the robustness of the algorithm.

[0006] 3. Influence of the motion state on the identification effect: The motion state (displacement, acceleration, etc.) of the test mass directly affects the accuracy of stiffness identification, and this point is not fully considered in the existing methods.

[0007] Content of the invention

[0008] Considering that the stiffness identification effect is affected by the motion state of the test mass, in order to effectively improve the identification effect and overcome the deficiencies of the above-mentioned existing technologies, the present invention provides a method, a system and a space gravitational wave detector for on-orbit stiffness identification of a mass based on motion state optimization.

[0009] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0010] A method for improving the stiffness identification effect based on motion state optimization, which is characterized in that based on the on-orbit stiffness identification dynamic model, the recursive least squares algorithm is used to realize the online identification of the stiffness of the test mass. In order to meet the complex control requirements under different motion states, a fuzzy radial basis neural network PID controller is designed to realize adaptive control. The motion state of the test mass is parametrically characterized by multi-frequency sine signals, and combined with the convergence time and convergence accuracy of parameter identification, the corresponding objective function is set, and the corresponding constraint conditions are given according to the engineering practice. On this basis, a two-stage multi-granularity surrogate-assisted evolutionary algorithm is proposed to globally optimize the motion state parameters of the test mass, and a balance selection strategy for the optimal solution in the Pareto front is given.

[0011] The above method includes the following specific steps:

[0012] S1. Based on the on-orbit stiffness identification dynamic model, the recursive least squares algorithm is used to realize the online identification of the stiffness of the test mass;

[0013] S2. Design a fuzzy radial basis neural network PID controller to realize the adaptive control of the test mass under different motion states;

[0014] S3. The motion state of the test mass is parametrically characterized by multi-frequency sine signals, and combined with the convergence time and convergence accuracy of parameter identification, the corresponding objective function is set, and the corresponding constraint conditions are given according to the engineering practice;

[0015] S4. Based on the two-stage multi-granularity surrogate-assisted evolutionary algorithm, the motion state parameters of the test mass are globally optimized, and a balance selection strategy for the Pareto optimal solution is given.

[0016] The specific content of step S1 includes:

[0017] S1.1 Construct a dynamic model to separate the parameters to be identified and the measured parameters. The dynamics can be expressed as the following linear relationship:

[0018] y = ψ T θ

[0019] wherein, y and ψ T are respectively the output matrix and the weight matrix, which are composed of sensor measurement data and relevant position information, and θ is the parameter to be identified, including the combination term of stiffness and bias disturbance;

[0020] S1.2 adopts the recursive least squares algorithm to realize online parameter estimation: by minimizing the sum of squared residuals and using a forgetting factor to adjust the weights of new and old data, setting the initial value of the covariance matrix and the initial estimated value of the parameter to be identified, and using the update formula of the recursive least squares algorithm to gradually adjust the estimated value of the parameter to be identified until the preset convergence condition or the maximum number of iterations is reached, where the update formula of the recursive least squares algorithm is as follows:

[0021]

[0022] wherein, is the parameter to be identified obtained recursively, λ is the forgetting factor, K is the gain matrix, P is the covariance matrix, and the subscript n is the sampling point (n = 1, 2,..., N).

[0023] The specific steps of S2 include:

[0024] S2.1 The fuzzy radial basis neural network PID controller includes an input layer, a fuzzification layer, a fuzzy inference layer and an output layer. Among them, the input layer directly transmits the input data, and the formula is as follows:

[0025] f 1 (i) = x i

[0026] wherein, i = 1,..., N, and N is the number of input variables x.

[0027] The fuzzification layer adopts the Gaussian function for fuzzification processing, and the formula is as follows:

[0028]

[0029] wherein, j = 1, 2,..., M, c ij and b ij are the center and base width of the membership function.

[0030] The fuzzy inference layer performs fuzzy rule matching. Each neuron is equivalent to a fuzzy rule and performs the and operation, replacing the minimum operation with the product. The formula is as follows:

[0031] f 3 (l) = f 3 (i,j) = f 2 (1,i)·f2 (2, j)

[0032] where \(l = 1, 2, \ldots, M\) N .

[0033] The output layer obtains the tuned incremental PID controller parameters through defuzzification. The formula is as follows:

[0034]

[0035] where \(m = 1, 2, 3\), and \(\omega\) is the connection weight between the fuzzy inference layer and the output layer.

[0036] S2.2 The performance index function of the fuzzy radial basis neural network PID controller is:

[0037]

[0038] where \(r(t)\) and \(y(t)\) are the ideal output and the actual output at time \(t\).

[0039] Minimize \(E(t)\) according to the gradient descent principle, and thus update the relevant parameters in the network. The formula is as follows:

[0040]

[0041] where \(\eta\) is the learning rate and \(\alpha\) is the momentum factor.

[0042] The specific steps of step S3 include:

[0043] S3.1 Generate a multi-frequency sine signal, which is composed of multiple sub-signals. Among them, each sub-signal includes the amplitude \(A\) of the signal i , frequency \(\omega\) i , phase \(\theta\) i and bias \(B\) i . The formula is as follows:

[0044]

[0045] where \(k\) is the number of sub-signals; it is set that the inspection mass is initially located at the center of the nominal position, so that the bias \(B\) i \(=-A\) i \(\sin\theta\) i , thus taking the amplitude \(A\) i , frequency \(\omega\) i , phase \(\theta\) i as the decision variable \(X\) in the optimization;

[0046] S3.2 Set the objective function, including the convergence time \(obj\) 1 and the convergence accuracy \(obj\) 2 where the convergence time \(obj\)1 Denotes the minimum sampling time when the parameter change lasts less than the preset threshold ε, and the convergence accuracy obj 2 It is represented by calculating the root mean square error after convergence. The formula is as follows:

[0047]

[0048] In the formula, t, T 0 , T are the sampling time, the convergence time, and the total sampling time respectively, n is the sampling point, idx is the serial number corresponding to the identification parameter, and ε is the threshold;

[0049] S3.3 According to the given constraints in the engineering practice, including restricting the maximum execution output of the electrostatic force, ensuring that the motion state of the test mass meets the requirements of control effectiveness, and restricting the safe distance between the test mass and the electrode cage. Integrate the decision variables, the objective function, and the constraints into an optimization model. By solving this optimization model, the optimal decision variables are obtained, so as to realize the parametric characterization and optimization of the motion state of the test mass.

[0050] This optimization problem is described as follows:

[0051]

[0052] In the formula, F max is the maximum execution electrostatic force, D is the distance between the test mass and the electrode cage, α 1 , α 2 are adjustment factors to provide a safety margin for other factors.

[0053] The specific steps of S4 include:

[0054] S4.1 Initialize the population and the archive to store possible solutions;

[0055] S4.2 Based on the surrogate model, optimize the population under the condition of only considering the constraint conditions of a single test mass, and calculate the maximum change rate mc of the ideal point in the past gap generations. The formula is as follows:

[0056]

[0057] In the formula, is the i-th of the N target values of the ideal point in the iter-th generation population, and δ is a small positive number to ensure that the denominator is not zero. When the maximum change rate is less than the given threshold, enter the second stage;

[0058] S4.3 Construct a multi-granularity surrogate model based on the distance of the population to the feasible region. Specifically, when the population is far from the feasible region, a coarse-grained model is used for exploration; when the population is at the boundary of the feasible region, a fine-grained model is used to meet the constraint conditions; when the population is within the feasible region, there is no need to construct an additional model. Use the constructed multi-granularity surrogate model to optimize and solve the complete problem, and continuously update the training data to reconstruct the relevant model;

[0059] S4.4 When the preset termination condition is met, stop the optimization process, that is, reach the maximum number of iterations or the population converges. Record the optimal solutions of each objective during the optimization process, and based on this, perform minimum normalization processing on all points in the Pareto front, calculate the distances from all normalized points to the unit point, and select the point with the closest distance as the optimal solution.

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] The present invention enhances the flexibility and environmental adaptability of the system by integrating advanced online identification algorithms and intelligent control strategies. The recursive least squares algorithm is used to realize the online identification of the stiffness of the test mass during orbit inspection. Combined with the fuzzy radial basis neural network PID controller, precise and adaptive control of the test mass in different motion states is achieved. The multi-objective intelligent optimization algorithm is used to globally optimize the motion state of the test mass, which not only optimizes the effect of parameter identification but also achieves faster convergence time and higher convergence accuracy. In addition, the methods and strategies proposed in the present invention also provide new solutions and design references for the identification and control problems of future similar complex systems, and have broad application prospects and important scientific value. Description of the Drawings

[0062] Figure 1 is the structure of the fuzzy radial basis neural network PID controller.

[0063] Figure 2 is the flow chart of the two-stage multi-granularity surrogate-assisted evolutionary algorithm.

[0064] Figure 3 is the overall flow chart of the method of the present invention. Detailed Embodiments

[0065] The technical solutions of the present invention will be described in detail below in conjunction with the drawings and embodiments, but the protection scope of the present invention should not be limited thereby.

[0066] Space gravitational wave detection has extremely high requirements for system noise indicators. Among them, the coupling noise between the stiffness and displacement of the test mass, as an important part of the residual acceleration noise, greatly affects the system detection performance. It is necessary to identify the stiffness to verify and optimize the control effect and meet the noise suppression requirements. Considering the requirements of real-time, effectiveness, stability, etc. for on-orbit identification, the present invention proposes a method for improving the stiffness identification effect based on optimizing the motion state. The following is the specific implementation manner of this method.

[0067] Step 1: Based on the on-orbit stiffness identification dynamic model, use the recursive least squares algorithm to achieve online identification of the test mass stiffness.

[0068] Based on the on-orbit stiffness identification dynamics of the test mass, separate the parameters to be identified and the measurement parameters. The dynamics can be expressed as the following linear relationship:

[0069] y = ψ T θ

[0070] In the formula, y and ψ T are the output matrix and the weight matrix respectively, which are composed of sensor measurement data and relevant position information. θ is the parameter to be identified, including the combination term of stiffness and bias perturbation, and the focus is on the stiffness.

[0071] Use the recursive least squares algorithm to achieve online estimation of the parameters. Its basic principle is to minimize the sum of squared residuals and adjust the weights of new and old data through a forgetting factor. The specific algorithm update formula is as follows:

[0072]

[0073] In the formula, is the parameter to be identified obtained recursively, λ is the forgetting factor, K is the gain matrix, P is the covariance matrix, and the subscript is the sampling point (n = 1, 2,..., N). When the algorithm is initialized, the corresponding P 0 、 value is given.

[0074] Step 2: To meet the complex control requirements under different motion states, design a fuzzy radial basis neural network PID controller to achieve adaptive control.

[0075] The controller structure is as Figure 1 shown. The inputs of the controller are the displacement error e and the error change rate ec of the sensitive axis of the test mass. Through the processing of the fuzzy radial basis neural network, the output result is used to adjust the incremental PID controller in real time. Among them, the fuzzy radial basis neural network includes an input layer, a fuzzification layer, a fuzzy inference layer, and an output layer. The relevant calculation formulas are as follows:

[0076] Input layer: Without processing, directly pass the input data to the next layer,

[0077] f1 (i) = x i

[0078] where i = 1, …, N, and N is the number of input variables x.

[0079] Fuzzification layer: Select the Gaussian function as the membership function to fuzzify the data.

[0080]

[0081] where j = 1, 2, …, M, c ij , b ij are the center and base width of the membership function.

[0082] Fuzzy inference layer: Perform fuzzy rule matching. Each neuron is equivalent to a fuzzy rule, and the and operation is executed, replacing the minimum operation with the product.

[0083] f 3 (l) = f 3 (i, j) = f 2 (1, i) · f 2 (2, j)

[0084] where l = 1, 2, …, M N .

[0085] Output layer: Defuzzify to obtain the tuned incremental PID controller parameters K p , K i , K d ,

[0086]

[0087] where m = 1, 2, 3, and ω is the connection weight between the fuzzy inference layer and the output layer.

[0088] The performance index function considering the fuzzy radial basis neural network is

[0089]

[0090] where r(t) and y(t) are the ideal output and actual output at time t.

[0091] Minimize E(t) according to the gradient descent principle. The update formulas for the network-related parameters are as follows:

[0092]

[0093] where η is the learning rate and α is the momentum factor.

[0094] Step 3: Parametrically characterize the motion state of the inspection mass through multi-frequency sine signals, set the corresponding objective function in combination with the convergence time and convergence accuracy of parameter identification, and given the corresponding constraint conditions according to the actual engineering situation.

[0095] The multi-frequency sine signal is expressed as follows:

[0096]

[0097] In the formula, A i , ω i , θ i and B i are the amplitude, frequency, phase and bias of the sub-signal respectively, and k is the number of sub-signals. It is assumed that the inspection mass is initially located at the center of the nominal position, that is, the initial value is zero, then the bias B i = -A i sinθ i . Therefore, for the motion state, in fact, only A i , ω i and θ i are used as decision variables in the optimization, denoted as X.

[0098] Considering the real-time performance and accuracy guarantee of parameter identification, the convergence time and convergence accuracy are defined as the objective function, and the specific calculation is shown in the following formula:

[0099]

[0100] In the formula, obj 1 is the convergence time, which represents the minimum sampling time when the parameter change is continuously less than the threshold ε. obj 2 is the convergence accuracy, which is expressed by calculating the root mean square error after convergence. t, T 0 , T are the sampling time, convergence time and total sampling time respectively, the subscript n is the sampling point, idx is the serial number corresponding to the identified parameter, and ε is the threshold.

[0101] Regarding the constraint conditions, to ensure the electrostatic force control accuracy and prevent the risk brought by excessive applied electrostatic force, the maximum execution output of the electrostatic force is restricted. The corresponding motion state of the inspection mass should also meet the corresponding constraint conditions to ensure the effectiveness of the control. In addition, the safety distance between the inspection mass and the electrode cage needs to be considered.

[0102] Then this optimization problem can be described as follows:

[0103]

[0104] In the formula, F max is the maximum execution electrostatic force, D is the distance between the inspection mass and the electrode cage, α 1 , α2 As a regulating factor to provide a safety margin for other factors.

[0105] Since the motion states of two test masses are involved in the stiffness identification dynamics, different optimization schemes can be selected according to different configurations of decision variables and objective functions. For example, the motion states of TM1 and TM2 can be optimized simultaneously to improve the stiffness identification effect of the sensitive axis of TM1. In this case, it is a bi-objective optimization with 2×3×k decision variables.

[0106] Step 4: Globally optimize the motion state parameters of the test mass based on the two-stage multi-granularity surrogate-assisted evolutionary algorithm, and give the equilibrium selection strategy for the optimal solution in the Pareto front.

[0107] The stiffness identification optimization involves factors such as dynamic models, noise disturbances, and time series simulations, with a large amount of calculation and long running time. To effectively solve this multi-objective optimization problem with expensive objectives and constraints, a two-stage multi-granularity surrogate-assisted evolutionary algorithm is proposed. In the first stage of this algorithm, only partial constraint conditions are considered for optimization, and in the second stage, the complete optimization problem is solved based on the multi-granularity surrogate model. In the present invention, the selection of constraint conditions is divided by the test mass as an individual, that is, the constraint conditions of a single test mass are considered first. Figure 2 Shows the overall process of the algorithm.

[0108] First, initialize the population and archive to store possible solutions. Then, in the first stage, solve based on the surrogate model while only considering the constraints of a single test mass, and calculate the stage switching function to determine whether to switch to the next stage. Select the maximum change rate mc of the ideal point in the past gap generations as the state switching function, and the calculation is as follows:

[0109]

[0110] In the formula, is the i-th of the N objective values of the ideal point in the iter-th generation population, and δ is a small positive number to ensure that the denominator is not zero.

[0111] When the maximum change rate is less than the given threshold, it enters the second stage of optimization. A multi-granularity surrogate model is constructed based on the distance of the population to the feasible region. The idea is to balance the approximation accuracy and training cost of the surrogate model when solving multi-objective optimization problems with expensive objectives and constraints. The motivation is that when the population is far from the feasible region, the surrogate model should strengthen the exploration of the search space, and a coarse-grained model is sufficient; when the population is on the boundary of the feasible region, every unfulfilled constraint needs to be considered, and a fine-grained model is constructed; when the population is within the feasible region, there is no need to construct additional models. The corresponding management strategies for models with different granularities are also different. The coarse-grained model selects the solutions that survive to the next generation according to the principle of constraint dominance, while the fine-grained model assigns the same priority to objective optimization and constraint satisfaction through multi-objective optimization methods.

[0112] Use the constructed multi-granularity surrogate model to optimize and solve the complete problem, and update the training data to reconstruct the relevant models. Finally, until the termination condition is met, the optimal solution in the archive is output as the result.

[0113] The two-stage multi-granularity surrogate-assisted evolutionary algorithm is used to solve the multi-objective optimization problem and finally obtain the Pareto front rather than a single solution. Therefore, the following strategy is set to select the optimal solution from the Pareto front. Record the optimal solutions (i.e., minimum values) of each objective during the optimization process and normalize all points in the Pareto front based on this. Calculate the distances of all points to the unit point, and determine the optimal solution according to the principle of the closest distance.

[0114] The two-stage multi-granularity surrogate-assisted evolutionary algorithm only considers part of the constraints in the early stage of the search, i.e., stage one, reduces the constraint complexity, lowers the computational cost, and at the same time ensures the feasibility of the optimization solution under some key constraints, which helps to accelerate convergence and promote the diversity of the population. In stage two, a multi-granularity surrogate model is generated based on the position of the population to prevent the population from falling into local optima, and it can effectively solve the optimization problem with expensive objectives and constraints.

[0115] The method proposed in the present invention integrates the online identification algorithm, intelligent control strategy, and intelligent optimization algorithm, and improves the parameter identification effect based on the optimization of the motion state, including faster convergence time and higher convergence accuracy, providing new ideas and design references for subsequent related identification and control.

Claims

1. A method for improving the identification effect of inspection mass stiffness based on motion state optimization, characterized in that: The following steps are involved: S1. Based on the on-track stiffness identification dynamics model, the recursive least squares algorithm is used to realize the online identification of the test mass stiffness; S2. Design a fuzzy radial basis function neural network PID controller to achieve adaptive control of the inspection mass under different motion states; S3. The motion state of the inspection mass is parameterized by multi-frequency sinusoidal signals, and the corresponding objective function is set in combination with the convergence time and convergence accuracy of parameter identification, and corresponding constraints are given according to the actual engineering practice; S4. Based on the two-stage multi-granularity agent-assisted evolutionary algorithm, the motion state parameters of the inspection quality are globally optimized, and a balanced selection strategy for the Pareto optimal solution is given.

2. The method according to claim 1, characterized in that: The step S1 specifically includes: S1.1 Construct a kinetic model to separate the parameters to be identified and the measured parameters. The kinetics can be expressed as the following linear relationship: y=ψ T i Where y and ψT are the output matrix and weight matrix respectively, which are composed of sensor measurement data and related position information, and θ is the parameter to be identified, including the stiffness and bias disturbance combination terms; S1.2 uses a recursive least squares algorithm to achieve online parameter estimation: by minimizing the residual sum of squares and using the forgetting factor to adjust the weights of new and old data, setting the initial value of the covariance matrix and the initial estimated value of the parameter to be identified, and using the update formula of the recursive least squares algorithm to gradually adjust the estimated value of the parameter to be identified until the preset convergence condition or the maximum number of iterations is reached, wherein the update formula of the recursive least squares algorithm is as follows: In the formula, is the recursively obtained parameter to be identified, λ is the forgetting factor, K is the gain matrix, P is the covariance matrix, and subscript n is the sampling point (n=1,2,…,N).

3. The method according to claim 1, characterized in that The step S2 specifically includes: S2.1 Fuzzy radial basis neural network PID controller, including input layer, fuzzification layer, fuzzy reasoning layer and output layer, wherein the input layer directly transmits input data, the formula is as follows: f1(i)=x i In the formula, i=1,…,N, where N is the number of input variables x. The fuzzification layer uses Gaussian basis function for fuzzification processing, and the formula is as follows: Wherein, j = 1, 2, ..., M, cij, bij are the center and base width of the membership function. The fuzzy reasoning layer performs fuzzy rule matching. Each neuron is equivalent to a fuzzy rule. It performs the AND operation and replaces the smaller operation with the product. The formula is as follows: f3(l)=f3(i,j)=f2(1,i)·f2(2,j) In the formula, l = 1, 2,…, MN. The output layer obtains the adjusted incremental PID controller parameters through defuzzification, and the formula is as follows: Where m = 1, 2, 3, and ω is the connection weight between the fuzzy reasoning layer and the output layer. The performance index function of S2.2 fuzzy radial basis neural network PID controller is: Where r(t) and y(t) are the ideal output and actual output at time t. According to the principle of gradient descent, E(t) is minimized to update the relevant parameters in the network. The formula is as follows: Where η is the learning rate and α is the momentum factor.

4. The method according to claim 1, characterized in that: The step S3 specifically includes: S3.1 generates a multi-frequency sinusoidal signal, which is composed of multiple sub-signals, where each sub-signal includes the signal amplitude Ai, frequency ωi, phase θi and offset Bi, and the formula is as follows: Where k is the number of sub-signals; the inspection mass is initially set at the center of the nominal position so that the bias Bi = -Aisinθi, and the amplitude Ai, frequency ωi, and phase θi are used as the decision variables X in the optimization; S3.2 sets the objective function, including the convergence time obj1 and the convergence accuracy obj2, wherein the convergence time obj1 represents the minimum sampling time for the parameter change to be continuously less than the preset threshold ε, and the convergence accuracy obj2 is represented by calculating the root mean square error after convergence, and the formula is as follows: Where t, T0, T are the sampling time, convergence time and total sampling time respectively, n is the sampling point, idx is the serial number corresponding to the identification parameter, and ε is the threshold; S3.3 is based on the actual given constraints of the project, including limiting the maximum execution output of the electrostatic force, ensuring that the motion state of the inspection mass meets the control effectiveness requirements, and limiting the safe distance between the inspection mass and the electrode cage. The decision variables, objective function and constraints are integrated into an optimization model, and the optimal decision variables are obtained by solving the optimization model, thereby realizing the parametric characterization and optimization of the motion state of the inspection mass. The optimization problem is described as follows: Where Fmax is the maximum electrostatic force, D is the distance between the test mass and the electrode cage, and α1 and α2 are adjustment factors to provide safety margins for other factors.

5. The method according to claim 1, characterized in that The step S4 specifically includes: S4.1 Initialize the population and archive to store possible solutions; S4.2 is based on the agent model, and the population is optimized under the condition of only considering a single inspection quality constraint, and the maximum change rate mc of the ideal point in the past gap algebra is calculated. The formula is as follows: In the formula, is the i-th target value of the ideal point N in the iter generation population, and δ is a small positive number to ensure that the denominator is not zero. When the maximum rate of change is less than the given threshold, it enters the second stage; S4.3 Construct a multi-granularity proxy model based on the distance from the population to the feasible region. When the population is far from the feasible region, a coarse-grained model is used for exploration. When the population is at the boundary of the feasible region, a fine-grained model is used to meet the constraints. When the population is within the feasible region, no additional model needs to be constructed. Use the constructed multi-granularity proxy model to optimize and solve the complete problem, and continuously update the training data to reconstruct the relevant model. S4.4 When the preset termination condition is met, the optimization process is stopped, that is, the maximum number of iterations is reached or the population converges. The optimal solution of each objective in the optimization process is recorded, and based on this, all points in the Pareto front are normalized to the minimum value, the distance from all normalized points to the unit point is calculated, and the point with the closest distance is selected as the optimal solution.

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