A method and system for rapid correction of system models for high-precision control

Abstract

This invention discloses a method and system for rapid correction of system models for high-precision control, belonging to the fields of high-precision motion control, intelligent system modeling and online compensation technology. The method includes the following steps: obtaining a mechanistic model of the ideal state of a real physical dynamic system to generate low-fidelity data, and collecting small samples of high-fidelity experimental data from real physical dynamic systems with performance deviations to form a dataset; constructing a hierarchical kriging model using the predicted output of the mechanistic model of the ideal state of the real physical dynamic system as the global trend term; training the hierarchical kriging model by maximizing the marginal likelihood function; and correcting the real physical dynamic system to obtain a corrected mechanistic model of the real physical dynamic system, which is used to more accurately describe the real dynamic system. This method can significantly improve the closed-loop control accuracy and trajectory tracking performance of systems with model deviations.

Description

Technical Field

[0001] This invention belongs to the fields of high-precision motion control, intelligent system modeling and online compensation technology, and specifically relates to a method and system for quickly correcting system model deviations to meet high-precision control requirements. Background Technology

[0002] High-precision dynamic systems, such as precision electromechanical actuators, flexible robotic joints, and aerospace intelligent structures, rely heavily on accurate mathematical models for their advanced control strategies. These models are typically based on first-principles physics or system identification methods. However, in practical engineering applications, due to unavoidable manufacturing tolerances, assembly stresses, material property dispersion, and time-varying degradation effects such as wear, fatigue, and aging caused by long-term operation, the dynamic characteristics of actual systems often gradually deviate from their initial calibration or theoretically derived models. This performance deviation between the model and the actual system, known as model mismatch, directly leads to a significant degradation in the performance of high-precision controllers designed based on the model. This manifests as increased tracking errors, reduced steady-state accuracy, and dynamic response distortion, severely impacting the equipment's execution accuracy and mission performance.

[0003] This problem is particularly pronounced in the field of smart materials and structures. Taking piezoelectric drive systems as an example, their high precision and fast response speed have led to their widespread application in active vibration control, shape adjustment, and precision actuation. However, the inherent hysteresis and creep nonlinearity of piezoelectric materials, along with the performance evolution of the bonding interface between the drive unit and the main structure, result in initial model errors during the manufacturing and assembly stages. Furthermore, long-term service performance degrades due to factors such as material polarization decay and interface fatigue. The coupling of these factors causes a significant deviation between the measured input-output relationship of the system and the model obtained based on ideal parameters or initial identification, severely limiting the effectiveness of high-precision strategies such as model-based feedforward compensation or predictive control.

[0004] To address the aforementioned model mismatch problem, existing technologies primarily focus on three directions. The first approach aims to establish more accurate and complex mechanistic models. Researchers introduce more refined nonlinear operators to describe physical phenomena such as hysteresis and creep. While this approach can improve model accuracy under specific conditions, its modeling process is complex, computationally burdensome, and heavily reliant on accurate prior knowledge of the system's nonlinear mechanisms. When the system exhibits multi-physics coupling or unknown time-varying degradation, model complexity increases dramatically, limiting its practicality. The second approach focuses on modeling degradation mechanisms at the material or component level. This method studies the performance degradation laws of specific components, such as piezoelectric ceramics, from a microscopic or macroscopic perspective. This research is scientifically valuable for understanding local failure mechanisms, but it typically targets single failure modes and struggles to describe the system-wide comprehensive performance degradation caused by the coupling of multiple factors. Furthermore, its application often relies on specific physical assumptions. The third approach employs a purely data-driven modeling strategy, such as using neural networks to directly learn the system's input-output mapping relationship. This approach shows potential in characterizing complex nonlinearities, but its success depends entirely on a large amount of high-quality training data covering the entire operating domain of the system. For many high-end equipment or long-running systems, acquiring sufficient data is extremely costly and time-consuming, and the extrapolation and generalization capabilities with a small number of data samples are often insufficient.

[0005] Therefore, developing a general method that can effectively integrate known physical mechanisms with a very small amount of online measured data to quickly and robustly correct system-level model deviations and directly serve high-precision control is of great significance for improving the reliability and performance maintenance capabilities of intelligent systems throughout their entire life cycle. Summary of the Invention

[0006] To address the technical problems existing in the prior art, the technical solution adopted in this invention is: a method for rapid correction of system models for high-precision control, comprising the following steps:

[0007] S1. Obtain a mechanism model of the ideal state of a real physical dynamic system to generate low-fidelity data and collect a small sample of high-fidelity experimental data from a real physical dynamic system with performance deviations to form a dataset; S2: Based on the training set in the dataset, a hierarchical kriging model is constructed using the predicted output of the mechanism model of the ideal state of the actual physical dynamic system as the global trend term. S3: Using small-sample high-fidelity experimental data, the hierarchical kriging model is trained by maximizing the marginal likelihood function, the hyperparameters of the hierarchical kriging model are optimized, and the trained hierarchical kriging model is obtained, which outputs an estimate of the performance deviation of the actual physical dynamic system. S4: Based on the estimation of the actual physical dynamic system performance deviation of the output of the trained hierarchical kriging model, the actual physical dynamic system is corrected, and the mechanism model of the corrected actual physical dynamic system is obtained, which is used to more accurately describe the actual dynamic system.

[0008] Furthermore, the actual physical dynamic system is a flexible electromechanical system containing a smart material actuator, and the performance deviation of the flexible electromechanical system is caused by the long-term aging and degradation of the smart material actuator or the structure body, or by initial manufacturing and assembly errors.

[0009] Furthermore, the low-fidelity data covers the expected input operating range of the mechanism model, which is the range of variation of the input signal of the actual physical dynamic system when it is working normally.

[0010] Furthermore, in step S1, the number of samples in the small sample high-fidelity experimental data is less than the number of samples in the low-fidelity dataset.

[0011] Furthermore, the number of samples in the small-sample high-fidelity experimental data is 15 to 25 groups.

[0012] Furthermore, the high-fidelity response of the actual physical dynamic system The hierarchical kriging model can be expressed as follows:

[0013] in, This is the input vector of the actual physical dynamic system. For the mechanism model, the input The predicted output, This is the scaling factor. A zero-mean Gaussian process is used to model the performance deviation.

[0014] Furthermore, the mechanistic model of the modified actual physical dynamic system is expressed as follows:

[0015] in, This is the original prediction output of the mechanistic model. The performance deviation estimate learned in step S2.

[0016] Furthermore, the performance deviation includes at least one of manufacturing tolerance, assembly error, material aging, or interface degradation.

[0017] A controller employs any of the aforementioned methods for rapid correction of system models for high-precision control to perform feedforward prediction of dynamic systems.

[0018] A system for rapid correction of system models for high-precision control, used to implement any of the methods described above, includes: Acquisition module: used to acquire low-fidelity data from the mechanism model of the ideal state of a real physical dynamic system and to collect small samples of high-fidelity experimental data from real physical dynamic systems with performance deviations, forming a dataset; Building Module: Used to construct a hierarchical kriging model based on the training set in the dataset, using the predicted output of the mechanism model of the ideal state of the actual physical dynamic system as the global trend term; Training module: Used to train the hierarchical kriging model by maximizing the marginal likelihood function using small sample high-fidelity experimental data, optimize the hyperparameters of the hierarchical kriging model, obtain the trained hierarchical kriging model, and output an estimate of the performance deviation of the actual physical dynamic system. Correction module: Based on the estimation of the performance deviation of the actual physical dynamic system from the output of the trained hierarchical kriging model, the module corrects the actual physical dynamic system and obtains the mechanistic model of the corrected actual physical dynamic system, which is used to more accurately describe the actual dynamic system.

[0019] This invention provides a method for rapid correction of system models for high-precision control, and the benefits brought by this invention are significant and multifaceted.

[0020] First, this method can significantly improve the closed-loop control accuracy and trajectory tracking performance of real systems with deviations in the mechanism model due to long-term degradation or manufacturing errors.

[0021] Secondly, it has excellent data efficiency, typically requiring only a few dozen sets of key experimental data to achieve high-precision model correction, which greatly reduces the testing cost and time cycle for model maintenance.

[0022] Furthermore, this method demonstrates a powerful ability to learn complex biases, specifically through the Gaussian process term in the hierarchical Kriging model. By probabilistically modeling residual nonlinear biases that cannot be described by explicit formulas, we can effectively compensate for system-level performance degradation caused by the coupling of multiple physical mechanisms, which is difficult to describe by explicit formulas. In addition, the obtained modified model has both good extrapolation robustness and environmental adaptability, overcoming the inherent defect of pure data-driven models that are unstable outside the training domain.

[0023] Finally, the proposed solution is highly practical in engineering. The modified hybrid model can be used as a plug-and-play high-precision feedforward module, which can be seamlessly integrated into the existing control architecture, quickly and significantly improving the closed-loop control performance of the system, such as trajectory tracking. It provides a general and efficient technical approach to solving the problem of maintaining long-term accuracy in intelligent systems of high-end equipment.

[0024] This invention is particularly applicable to flexible electromechanical systems that incorporate actuators made of smart materials such as piezoelectric and shape memory alloys, including precision actuators, robot joints, and smart structures. It is used to correct model deviations caused by time-varying degradation or manufacturing variations, and directly improves control accuracy. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the overall process of the model-data hybrid-driven fast correction method provided in the embodiments of the present invention; Figure 2 This is a schematic diagram of the MFC-driven flexible cantilever beam structure used in this embodiment of the invention; Figure 3 This is a schematic diagram of the verification platform for the hybrid drive correction method according to an embodiment of the present invention; Figure 4 This is a comparison chart of the predicted and actual displacement values ​​under the test voltage sequence in an embodiment of the present invention; Figure 5 This is a graph showing the relationship between the root mean square error of prediction and the number of training samples in an embodiment of the present invention. Figure 6 This is a comparison diagram of trajectory tracking performance when using a model modified by the method of this invention for feedforward control in an embodiment of the present invention. Figure 7 This is a comparison chart of system trajectory tracking errors when using different feedforward models in embodiments of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] The method of the present invention is particularly suitable for piezoelectrically driven flexible structures as described in the embodiments, and can also be applied to other flexible electromechanical systems that include smart material actuators and have similar performance deviations.

[0029] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0030] A method for rapid correction of system models for high-precision control includes the following steps: S1. Obtain the mechanism model of the ideal state or the mechanism simulation model of the nominal state of the actual physical dynamic system, generate low-fidelity data and collect a high-fidelity experimental data containing a small number of samples from the actual physical dynamic system with performance deviations, and form a dataset. S2: Based on the training set in the dataset, a hierarchical kriging model is constructed using the predicted output of the mechanism model of the ideal state of the actual physical dynamic system as the global trend term. S3: Using small-sample high-fidelity experimental data, the hierarchical kriging model is trained by maximizing the marginal likelihood function, the hyperparameters of the hierarchical kriging model are optimized, and the trained hierarchical kriging model is obtained, which outputs an estimate of the performance deviation of the actual physical dynamic system. S4: Based on the estimation of the actual physical dynamic system performance deviation of the output of the trained hierarchical Kriging model, the actual physical dynamic system is corrected to obtain the mechanism model of the corrected actual physical dynamic system, which is used to more accurately describe the actual dynamic system. The mechanism model of the corrected actual physical dynamic system is also used to perform feedforward prediction of the dynamic system or to integrate it into the controller to improve control accuracy.

[0031] The steps S1 / S2 / S3 / S4 are executed sequentially; Furthermore, the low-fidelity data includes the expected input operating range, used to characterize the response characteristics of the mechanistic model within this range. The actual physical dynamic system, such as a piezoelectrically driven flexible structure, has a planned operating range for its actuator in practical applications.

[0032] Furthermore, in step S1, the number of samples in the small sample high-fidelity experimental data is less than the number of samples in the low-fidelity dataset.

[0033] Furthermore, the low-fidelity dataset is generated by sampling according to the design within the system's expected operating range, and the number of samples is significantly greater than that of the high-fidelity experimental data.

[0034] The sample size of the small-sample high-fidelity experimental data is 15 to 25 groups.

[0035] Furthermore, the hierarchical Kriging model will provide a high-fidelity response. The expression is as follows:

[0036] in, Represents the system's input vector. The mechanism model represents the input Low-fidelity prediction output; It is a learnable scaling factor used to characterize the global linear correlation between high-fidelity and low-fidelity responses. It is a Gaussian random process with zero mean, whose covariance is determined by a specified kernel function, used to probabilistically model the residual, unmodeled local nonlinear deviations after global trend correction.

[0037] By maximizing the marginal likelihood function, the model hyperparameters are analyzed using the obtained high-fidelity experimental data. and Perform optimization estimation, where This is the process variance, thus completing the assessment of system performance deviations. Through learning, its best estimate is obtained. .

[0038] Furthermore, the trained hierarchical Kriging model is encapsulated into a directly usable hybrid correction model. The mechanistic model of the corrected real-world physical dynamic system is expressed as follows:

[0039] in, This is the original prediction output of the mechanistic model. This represents the performance bias estimate learned in step S2. This hybrid correction model fully preserves the physical laws and generalization framework inherent in the mechanistic model, while also incorporating data-driven bias terms. It accurately compensates for the actual performance deviation of the system.

[0040] Furthermore, the performance deviation includes at least one of manufacturing tolerance, assembly error, material aging, or interface degradation.

[0041] Furthermore, maximizing the marginal likelihood function specifically involves optimizing the hyperparameters of the hierarchical Kriging model. and process variance To maximize the observed high-fidelity experimental data Marginal probability distribution Its negative logarithmic form, used as the objective function, is expressed as:

[0042] in, For high-fidelity input sample matrix, This represents the number of samples. The covariance matrix of the hierarchical Kriging model has the following matrix elements. Calculated by the following formula:

[0043] In the formula, and These are the kernel functions selected for the low-fidelity trend term and the bias term, respectively. Let Kronecker function be the objective function. Minimize the objective function using the gradient descent algorithm. The optimal hyperparameter estimate can then be obtained.

[0044] A controller employs any of the aforementioned methods for rapid correction of system models for high-precision control to perform feedforward prediction of dynamic systems.

[0045] A system for rapid correction of system models for high-precision control, used to implement any of the methods described above, includes: Acquisition module: used to acquire low-fidelity data from the mechanism model of the ideal state of a real physical dynamic system and to collect small samples of high-fidelity experimental data from real physical dynamic systems with performance deviations, forming a dataset; Building Module: Used to construct a hierarchical kriging model based on the training set in the dataset, using the predicted output of the mechanism model of the ideal state of the actual physical dynamic system as the global trend term; Training module: Used to train the hierarchical kriging model by maximizing the marginal likelihood function using small sample high-fidelity experimental data, optimize the hyperparameters of the hierarchical kriging model, obtain the trained hierarchical kriging model, and output an estimate of the performance deviation of the actual physical dynamic system. Correction module: Based on the estimation of the performance deviation of the actual physical dynamic system from the output of the trained hierarchical kriging model, the module corrects the actual physical dynamic system and obtains the mechanistic model of the corrected actual physical dynamic system, which is used to more accurately describe the actual dynamic system.

[0046] Example 1: To clearly demonstrate the specific implementation process and effects of the method of the present invention, the following example, a piezoelectric-driven cantilever beam, a smart material-driven flexible electromechanical system particularly applicable to the present invention, will be used to illustrate the invention in detail. This case aims to simulate the model mismatch problem commonly encountered in high-end equipment due to material aging or interface degradation, and to verify the improvement in system control accuracy after correcting the model using the method of the present invention. The implementation steps will be described in detail based on the application verification process of this method in such systems.

[0047] 1. Problem and System Description The test object in this embodiment is as follows: Figure 2As shown, this represents a typical piezoelectric-driven flexible structure system. The substrate is a 1060 aluminum cantilever beam structure with a free end length of 500 mm, a width of 35 mm, and a thickness of 1 mm. An M-8528-P1 type MFC piezoelectric actuator is firmly attached to the surface near the root of the beam. After long-term use, the actuator exhibits performance degradation, manifested in a significantly lower steady-state deformation of the structure under the same driving voltage excitation compared to its new state. This phenomenon is a typical system performance deviation, leading to a decrease in the accuracy of the control strategy based on the initial calibration model. The objective of this embodiment is to apply the method of the present invention to quickly correct the system model using a very small amount of online experimental data, thereby improving its prediction and control accuracy.

[0048] 2. Specific Implementation Steps The implementation of this embodiment strictly follows... Figure 1 The process is shown below, with the specific steps as follows: S1: Multifidelity data preparation.

[0049] First, based on the design parameters of the cantilever beam and the novel MFC actuator, an ideal mechanistic simulation model is established as the ideal physical model. Using this model, within its operating voltage range... Within the dataset, 200 input-output data pairs were generated using the Latin hypercube sampling method, denoted as the low-fidelity dataset. .

[0050] Secondly, from Figure 3 The actual physical system shown acquires high-fidelity experimental data. Within the same voltage range, 25 input points are selected, resulting in 25 sets of high-fidelity data pairs. The dataset is randomly divided into a training set containing 15 data sets and a test set containing 10 data sets. The number of training samples can be adjusted adaptively based on the accuracy and cost requirements of actual engineering projects; the above number is merely a preferred example.

[0051] S2: Construction of a hierarchical kriging mixture model; The 15 sets of high-fidelity training data obtained in step S1 and their corresponding ideal model simulation values Based on this, a hierarchical kriging model is constructed.

[0052] S3: Train the hierarchical kriging mixture model; By maximizing the marginal likelihood function to optimize the model hyperparameters, an estimate of the system performance deviation can be learned. .

[0053] S4: Correct model generation and application verification.

[0054] Generate the final hybrid correction model: This model will be used for subsequent prediction accuracy evaluation and control performance verification.

[0055] 3. Implementation Results and Analysis (1) Comparison of model prediction accuracy To verify the effectiveness of the method of this invention, an uncorrected ideal mechanism model was compared with the hybrid corrected model of this invention. For example... Figure 4 As shown, under a set of test voltage sequences, the prediction of the ideal model exhibits significant systematic bias; however, the prediction curve of the hybrid correction model of this invention closely matches the actual value. Quantitative test results show that after correction by the method of this invention, the root mean square error of the model prediction is reduced from approximately 4.71 mm to approximately 0.82 mm, a reduction of over 82%, demonstrating the effectiveness of the method of this invention in improving the absolute accuracy of the model.

[0056] (2) Data efficiency analysis The advantages of the method of this invention in terms of data utilization efficiency are achieved through Figure 5 Verification is required. Figure 5 The prediction error trends of the hybrid correction model, the pure data-driven model, and the uncorrected baseline model as the number of training samples increases were compared. As shown in the figure, the hybrid correction model exhibits the best data efficiency under different training sample numbers. In particular, even under the extreme condition of only 3 training samples, the hybrid correction model still maintains a low prediction error, significantly outperforming the pure data-driven model under the same conditions. As the number of training samples increases to 15, the prediction error of the hybrid correction model can be reduced to an extremely low level. In contrast, the error curve of the pure data-driven model fluctuates more, making it difficult to obtain a stable and reliable model under small sample conditions.

[0057] (3) Verification of the effect of improving control accuracy To demonstrate the practical engineering value of the modified model, it was integrated into the control loop as a feedforward compensator to perform a sinusoidal trajectory tracking task. The control results are as follows: Figure 6 and Figure 7 As shown. Figure 6 The tracking performance was compared using different feedforward models. When using an uncorrected ideal model feedforward, the tracking output exhibited significant amplitude attenuation due to inaccurate model gain. However, when using the hybrid corrected model feedforward provided by this invention, the system output closely followed the desired trajectory. Figure 7 The tracking errors of the two cases were quantitatively compared. When using the ideal model feedforward, the maximum tracking error reached 8.3 mm; while after using the modified model feedforward of this invention, the maximum tracking error was reduced to 1.5 mm, and the control accuracy was improved by about 82%.

[0058] This embodiment fully demonstrates and verifies the method of the present invention through a typical piezoelectric-driven flexible structure system. The results show that this method can efficiently correct the model of a system with degraded performance using very little online measurement data, thereby significantly improving control accuracy. It provides a fast and practical solution for solving model mismatch problems in engineering systems.

[0059] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for rapid correction of system models for high-precision control, characterized in that, Includes the following steps: S1. Obtain a mechanism model of the ideal state of a real physical dynamic system to generate low-fidelity data and collect a small sample of high-fidelity experimental data from a real physical dynamic system with performance deviations to form a dataset; S2: Based on the training set in the dataset, a hierarchical kriging model is constructed using the predicted output of the mechanism model of the ideal state of the actual physical dynamic system as the global trend term. S3: Using small-sample high-fidelity experimental data, the hierarchical kriging model is trained by maximizing the marginal likelihood function, the hyperparameters of the hierarchical kriging model are optimized, and the trained hierarchical kriging model is obtained, which outputs an estimate of the performance deviation of the actual physical dynamic system. S4: Based on the estimation of the actual physical dynamic system performance deviation of the output of the trained hierarchical kriging model, the actual physical dynamic system is corrected, and the mechanism model of the corrected actual physical dynamic system is obtained, which is used to more accurately describe the actual dynamic system.

2. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, The actual physical dynamic system is a flexible electromechanical system containing a smart material actuator. The performance deviation of the flexible electromechanical system is caused by the long-term aging and degradation of the smart material actuator or the structure itself, or by initial manufacturing and assembly errors.

3. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, The low-fidelity data covers the expected input operating range of the mechanism model, which is the range of variation of the input signal of the actual physical dynamic system when it is working normally.

4. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, In step S1, the number of samples in the small sample high-fidelity experimental data is less than the number of samples in the low-fidelity dataset.

5. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, The sample size of the small-sample high-fidelity experimental data is 15 to 25 groups.

6. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, High-fidelity response of the actual physical dynamic system The hierarchical kriging model can be expressed as follows: in, This is the input vector of the actual physical dynamic system. For the mechanism model to input The predicted output, This is the scaling factor. A zero-mean Gaussian process is used to model the performance deviation.

7. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, The modified mechanistic model of the actual physical dynamic system is described as follows: in, This is the original prediction output of the mechanistic model. The performance deviation estimate learned in step S2.

8. The method for rapid correction of system models for high-precision control according to claim 1, characterized in that, The performance deviations include at least one of the following: manufacturing tolerances, assembly errors, material aging, or interface degradation.

9. A controller, characterized in that, The system model fast correction method for high-precision control described in any one of claims 1-8 is used for feedforward prediction of dynamic systems.

10. A system for rapid correction of system models for high-precision control, characterized in that, For implementing the method as described in any one of claims 1-8, comprising: Acquisition module: used to acquire low-fidelity data from the mechanism model of the ideal state of a real physical dynamic system and to collect small samples of high-fidelity experimental data from real physical dynamic systems with performance deviations, forming a dataset; Building Module: Used to construct a hierarchical kriging model based on the training set in the dataset, using the predicted output of the mechanism model of the ideal state of the actual physical dynamic system as the global trend term; Training module: Used to train the hierarchical kriging model by maximizing the marginal likelihood function using small sample high-fidelity experimental data, optimize the hyperparameters of the hierarchical kriging model, obtain the trained hierarchical kriging model, and output an estimate of the performance deviation of the actual physical dynamic system. Correction module: Based on the estimation of the performance deviation of the actual physical dynamic system from the output of the trained hierarchical kriging model, the module corrects the actual physical dynamic system and obtains the mechanistic model of the corrected actual physical dynamic system, which is used to more accurately describe the actual dynamic system.

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