Nonlinear unknown parameter estimation method for digital twin modeling of hydraulic system
By constructing a physical model and a digital twin model of the hydraulic system, and combining multiple regression analysis and multi-objective optimization algorithms, the problem of insufficient accuracy in estimating unknown parameters in the hydraulic system was solved, achieving efficient and accurate parameter estimation and improving the intelligent operation and maintenance capabilities of the hydraulic system.
Patent Information
- Application Number
- CN202511665445.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-13
- Publication Date
- 2026-02-10
AI Technical Summary
The dynamic characteristics of hydraulic systems are highly dependent on key physical parameters such as the elastic modulus of the hydraulic fluid, gas content, and sealing gap, which are difficult to measure and quantify accurately. This leads to parameter uncertainty, which becomes a bottleneck restricting the accuracy of digital twin models. Existing methods are insufficient in estimating unknown parameters in complex integrated hydraulic systems.
A physical model of the hydraulic system is constructed, basic data is obtained, and a digital twin model is established. Through multiple regression analysis and multi-objective optimization algorithms, combined with response surface surrogate models and comprehensive evaluation methods, the globally optimal parameter combination is screened to achieve efficient and high-precision estimation of unknown parameters.
It enables efficient and high-precision estimation of unknown parameters in complex hydraulic systems, improves the accuracy of digital twin models and the reliability of system operation, and supports intelligent operation and maintenance decision-making.
Smart Images
Figure CN121503053A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of digital twin technology, and in particular to a method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems. Background Technology
[0002] Manufacturing is the leading industry of the national economy, the foundation of a nation, and the cornerstone of a strong country. Hydraulic systems, due to their unique advantages, are widely used in various core areas of manufacturing; therefore, their reliable operation is crucial to the safety and stability of production. In recent years, with the rapid development of new-generation information technologies such as cloud computing and the Internet of Things, hydraulic system operation and maintenance methods are rapidly evolving towards informatization and intelligence. Among these, "digital twin" technology has attracted much attention due to its core advantages, including precise characterization of the physical process of faults, generation of missing data throughout the entire lifecycle, and estimation of unmeasurable state data.
[0003] Since hydraulic systems are typically complex and nonlinear time-varying systems, constructing a high-fidelity digital twin model with good generalization capabilities in the virtual domain is a core support for the intelligent operation and maintenance and health management of industrial hydraulic equipment. However, the dynamic characteristics of hydraulic systems are highly dependent on key physical parameters such as the elastic modulus of the hydraulic fluid, gas content, and sealing clearance. These parameters are often difficult to measure and quantify accurately, and are easily affected by the dynamic coupling of operating conditions such as temperature and pressure. This makes parameter uncertainty a core bottleneck restricting the accuracy of digital twin models. Therefore, in the presence of parameter uncertainty, accurate estimation of unknown parameters is crucial to ensuring the consistency between the digital twin model and the physical entity in dynamic response and performance evolution.
[0004] Digital twin technology has attracted much attention as a cutting-edge technology for improving the intelligent operation and maintenance capabilities of hydraulic systems. However, the dynamic characteristics of hydraulic systems are highly dependent on key physical parameters that are difficult to measure and quantify precisely, such as the elastic modulus of the hydraulic fluid, gas content, and sealing clearance. This makes parameter unknowns one of the core challenges restricting the construction of high-fidelity digital twin models. Most existing methods for estimating unknown parameters in hydraulic systems focus on the overall system model as the optimization object, but their estimation accuracy is significantly limited by the accuracy of the modeling. Furthermore, hierarchical estimation methods for system-level and component-level parameters place high demands on computational resources. In addition, existing methods are all guided by a single objective function. However, as hydraulic systems become increasingly complex and integrated, a single optimization objective is insufficient to accurately represent the overall system state. Therefore, it is necessary to develop multi-objective optimization methods to achieve accurate estimation of unknown parameters. Summary of the Invention
[0005] The purpose of this invention is to provide a method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems, aiming to solve or improve at least one of the above-mentioned technical problems.
[0006] To achieve the above objectives, the present invention provides the following solution: A method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems includes: A physical model of the target hydraulic system was constructed, and relevant basic data were obtained through experiments; the relevant basic data included physical characteristic data, working principle data, and actual working condition data of hydraulic components. A digital twin model is constructed based on the physical model of the hydraulic system; the parameter variables of the digital twin model include deterministic parameters and unknown parameters; the deterministic parameters include the manufacturing parameters and inherent characteristic parameters of the hydraulic components; the unknown parameters are the uncertain parameters of the hydraulic system that need to be estimated. Specifically, for the unknown parameters, the design variable matrix and response objective function are determined based on the relevant basic data, and a response surface surrogate model is established using multiple regression analysis. Then, the Pareto front solution set of the response surface surrogate model is solved using a multi-objective optimization algorithm. Finally, the globally optimal parameter combination is selected by combining a comprehensive evaluation method.
[0007] Optionally, the target hydraulic system physical model specifically includes: a hardware system and a control system and an interaction system connected to the hardware system; The hardware system includes physical hydraulic components, sensors, and a data acquisition card. The sensors include multiple sensors that collect different data, which are respectively installed on the corresponding physical components and connected to the data acquisition card. The physical hydraulic components include a power component, a control component, and a drive component.
[0008] Optionally, the construction process of the digital twin model is as follows: Based on the solid model of the hydraulic system, integrated modeling of the electromechanical-hydraulic coupling system, covering multiple physical components and their interactions and connections, was completed in the AMESim environment using the Mechanical Library, Hydraulic Library, and Hydraulic Component Design Library.
[0009] Optionally, the method for determining the design variable matrix and the response objective function is as follows: Based on the mechanism analysis of hydraulic systems, the key parameters affecting the accuracy of digital twin models are defined as the design variable matrix. ,in n For the parameter dimension, the range of values for each parameter. Determined by the characteristics of the physical system and engineering experience; Based on the digital twin model, a response objective function is constructed according to the output error between the simulation calculation results and the experimentally collected data: ; in, The number of sampling points. Output data for the model. To collect data for the experiment.
[0010] Optionally, the process of establishing the response surface proxy model is as follows: Based on the design variable matrix and the response objective function, a response surface surrogate model is established using multiple regression analysis: ; in, and As an independent variable, in a hydraulic system it specifically refers to unknown parameters (such as gas content, bulk modulus, leakage clearance, etc.). As the dependent variable, in the process of digital twin modeling in hydraulic systems, it specifically refers to the error between the calculation results of the digital twin model and the experimentally collected data under different monitoring variables; For constant terms, The coefficients of the linear term, The coefficient of the quadratic term, The coefficient of the interaction term. This is the residual term.
[0011] Optionally, the step of using a multi-objective optimization algorithm to solve the Pareto front solution set of the established multi-objective optimization mathematical model specifically includes: The Pareto front solution set is obtained by solving the established multi-objective optimization mathematical model using a multi-objective optimization algorithm. ; ; ; in, For the first In the process of digital twin modeling in hydraulic systems, the optimization objective specifically refers to the error between the calculation results of the simulation twin model and the experimentally collected data under different monitoring variables. and These are inequality constraints and equality constraints, respectively. represent 3D solution space The lower bound of the variable. This refers to the upper limit of the variables, specifically the range of the search space for unknown parameters such as gas content, bulk modulus, and leakage gap in the multi-objective optimization process. It is a set of unknown parameter variables such as gas content, bulk modulus, and leakage gap.
[0012] Optionally, the step of using a comprehensive evaluation method to select the globally optimal parameter combination specifically includes: Using the TOPSIS method, the Euclidean distance between each Pareto solution and the ideal and inferior solutions is defined as follows: ; in, and They represent the first The distance between each solution and the ideal and inferior solutions. and These represent the ideal solution and the inferior solution, respectively. Represents each Pareto solution; And calculate the relative similarity of the current solution: ; The combination of parameters with the highest similarity value is determined as the globally optimal combination.
[0013] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems. The method includes constructing a solid model of the target hydraulic system and obtaining relevant basic data through experiments; constructing a digital twin model based on the solid model; the parameter variables of the digital twin model include determined parameters and unknown parameters; for unknown parameters, the design variable matrix and response objective function are determined based on the relevant basic data, and a response surface surrogate model is established using multiple regression analysis. Then, a multi-objective optimization algorithm is used to solve for the Pareto front solution set of the response surface surrogate model, and finally, a comprehensive evaluation method is used to select the globally optimal parameter combination. This invention can achieve efficient and high-precision estimation of unknown parameters in digital twin models of complex hydraulic systems by constructing a mapping relationship model between unknown parameters and simulation-experiment errors, combined with multi-objective optimization algorithms and intelligent decision-making theory. Attached Figure Description
[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0015] Figure 1 This is a flowchart of the nonlinear unknown parameter estimation method in this embodiment; Figure 2 This is a schematic diagram of the hydraulic system physical entity in this embodiment. Figure 3This is a schematic diagram of the Pareto front solution set and the TOPSIS optimal solution in this embodiment; Figure 4 This is a comparison chart of the output results of the digital twin model of system pressure in this embodiment and the experimental data. Figure 5 This is a comparison chart of the digital twin model calculation results of the internal leakage volume in this embodiment and the experimental data results.
[0016] Reference numerals in the attached diagram: 1. Oil tank; 2. Manual pump; 3. Shut-off valve; 4. Pressure sensor; 5. Throttle valve; 6. Hydraulic cylinder under test; 7. Measuring cup. Detailed Implementation
[0017] 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.
[0018] The purpose of this invention is to provide a method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems, aiming to solve or improve at least one of the above-mentioned technical problems.
[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0020] like Figures 1-5 As shown, this invention addresses the shortcomings of commonly used methods for estimating unknown parameters in hydraulic systems by providing a nonlinear unknown parameter estimation method for digital twin modeling of hydraulic systems. This method constructs a mapping relationship model between unknown parameters and simulation-experiment errors, combining multi-objective optimization algorithms and intelligent decision-making theory to achieve efficient and high-precision estimation of unknown parameters in complex hydraulic system digital twin models. Specifically, firstly, the design variables and multi-objective optimization function are defined, and the response values of the objective function are obtained through experimental design. Secondly, a response surface regression surrogate model is constructed, and the statistical significance and predictive reliability of the model are verified using goodness-of-fit and analysis of variance (ANOVA). Finally, the multi-objective optimization mathematical model is solved using a multi-objective optimization algorithm to generate a Pareto front solution set, and the globally optimal parameter combination is selected using a top-optimal comprehensive evaluation method (TOPSIS).
[0021] The specific steps include: A physical model of the target hydraulic system is constructed, and relevant basic data are obtained through experiments; the relevant basic data includes physical characteristic data, working principle data, and actual working condition data of hydraulic components.
[0022] A digital twin model is constructed based on the physical model of the hydraulic system; the parameter variables of the digital twin model include deterministic parameters and unknown parameters; the deterministic parameters include the manufacturing parameters and inherent characteristic parameters of the hydraulic components; the unknown parameters are the uncertain parameters of the hydraulic system that need to be estimated.
[0023] Specifically, for the unknown parameters, the design variable matrix and response objective function are determined based on the relevant basic data, and a response surface surrogate model is established using multiple regression analysis. Then, the Pareto front solution set of the established multi-objective optimization mathematical model is solved using a multi-objective optimization algorithm. Finally, the global optimal parameter combination is selected by combining a comprehensive evaluation method.
[0024] As a further implementation method, the specific processing procedures of each of the above steps will be described in detail.
[0025] For the solid model of the hydraulic system: Build a physical model of the hydraulic system, which includes the hardware system, control system, and interaction system. The hardware system includes the physical entities of each hydraulic component, sensors, data acquisition cards, etc.
[0026] Typically, physical entities include power components, control components, and drive components. Power components are motors and hydraulic pumps, while drive components are valves and hydraulic cylinders. Sensor types in hydraulic systems include pressure sensors, flow sensors, temperature sensors, etc. Data acquisition cards are used to collect monitoring data from various types of sensors and communicate with a host computer via communication cables for visualization.
[0027] For the establishment of digital twin models of hydraulic systems: A digital twin model of the hydraulic system is established based on the physical model of the system and the physical characteristics, working principles, and actual operating conditions of each component. For electromechanical-hydraulic integrated hydraulic control systems, this is typically implemented using AMESim or Matlab / Simulink.
[0028] Specifically, in AMESim, the Mechanical Library, Hydraulic Library, and Hydraulic Component Design Library can be used to complete the integrated modeling of electromechanical-hydraulic coupling systems that cover physical components such as hydraulic pumps, valves, pipelines, and hydraulic cylinders, as well as their interactions and connections.
[0029] The parameters of the digital twin model can be divided into deterministic parameters and unknown parameters. The deterministic parameters are derived from the manufacturing parameters and inherent characteristic parameters of the hydraulic components, while the unknown parameters are the uncertain parameters of the hydraulic system that need to be estimated.
[0030] For response surface methodology: Response surface methodology (RSM) is a comprehensive mathematical modeling, analysis, and optimization method that incorporates various mathematical and statistical theories, including experimental design, model fitting, and analysis of variance. This method uses regression models to describe the functional relationship between design variables and response variables, thereby enabling prediction, optimization, and analysis.
[0031] When conducting RSM analysis, the first step is to determine the response objective and the design variables that affect it, and to clarify the range of values for these design variables. Based on the hydraulic system mechanism analysis, the key parameters affecting the accuracy of the digital twin model are defined as the set of design variables. ,in For the parameter dimension, the range of values for each parameter. It is determined by the characteristics of the physical system and engineering experience.
[0032] According to the definition of a digital twin model, the response objective function can usually be defined as the output error between the simulation and experimental results. Specifically, the root mean square error (RMSE) between the digital twin model output (such as pressure, flow rate, displacement) and the experimental measurement value can be defined as Equation (1).
[0033] (1) in, The number of sampling points. Output data for the twin model. To collect data for the experiment.
[0034] Next, experimental design is required. Common methods include central composite design, Box-Behnken design (BBD), and D-optimal design. In practical applications, the selection should be based on a comprehensive consideration of factors such as the number of factors, constraints, and experimental costs.
[0035] For the fitting and analysis of variance of the multiple linear regression model: Based on the design variable matrix and the output results of the response target established above, a response surface surrogate model is established using multiple regression analysis. The form of the multiple linear regression model is shown in equation (2).
[0036] (2) in, and As an independent variable, in a hydraulic system it specifically refers to unknown parameters (such as gas content, bulk modulus, leakage clearance, etc.). As the dependent variable, in the process of digital twin modeling in hydraulic systems, it specifically refers to the error between the calculation results of the digital twin model and the experimentally collected data under different monitoring variables; For constant terms, The coefficients of the linear term, The coefficient of the quadratic term, The coefficient of the interaction term. This is the residual term.
[0037] Further evaluation of the model fit results is conducted, typically using regression coefficients (R²) and analysis of variance (ANOVA). Statistical significance of the model and each factor is determined using a probability level (P < 0.05).
[0038] For obtaining Pareto front solution sets in multi-objective optimization: As hydraulic systems become increasingly complex and integrated, and the data acquisition processes do not belong to the same error system, it becomes difficult for a single monitoring quantity to accurately characterize the overall state of the system.
[0039] Therefore, the problem of estimating unknown parameters of a hydraulic system can be transformed into a complex mixed-variable nonlinear multi-objective optimization problem. The challenge of multi-objective problems lies in the need to consider multiple evaluation criteria simultaneously during the optimization process, and the system may face the dilemma of choosing between multiple global optimal solutions (i.e., Pareto front solutions).
[0040] Based on the validated response surface surrogate model and the established multi-objective optimization mathematical model, an efficient multi-objective optimization algorithm can be selected for solving the problem. Typically, the multi-objective optimization mathematical model is shown in equations (3) to (5).
[0041] (3) (4) (5) in, For the first The optimization objective, in the process of digital twin modeling in hydraulic systems, specifically refers to the error between the calculation results of the digital twin model and the experimentally collected data under different monitoring variables; and These are inequality constraints and equality constraints, respectively. represent 3D solution space The lower bound of the variable. This refers to the upper limit of the variables, specifically the range of the search space for unknown parameters such as gas content, bulk modulus, and leakage gap in the multi-objective optimization process. It is a set of unknown parameter variables such as gas content, bulk modulus, and leakage gap.
[0042] For the TOPSIS method: After completing the multi-objective optimization process, the optimal solution needs to be identified in the Pareto front solution set. The TOPSIS method is a commonly used comprehensive evaluation method for multi-objective optimization, mainly used to evaluate the overall quality of multiple Pareto solutions.
[0043] The key to the TOPSIS method is to compare each Pareto solution with the ideal solution and the inferior solution. If a solution is both closest to the ideal solution and far from the inferior solution, then that solution is the optimal solution. The Euclidean distance between each Pareto solution and the ideal and inferior solutions is defined by equation (6).
[0044] (6) in, and They represent the first The distance between each solution and the ideal and inferior solutions. and These represent the ideal solution and the inferior solution, respectively. This represents each Pareto solution.
[0045] Furthermore, the relative closeness of the current scheme is calculated using equation (7), and the scheme with the highest closeness is selected as the optimal scheme.
[0046] (7) For verifying the accuracy of parameter estimation: The optimal unknown parameters obtained by the TOPSIS method are used to perform simulation calculations of the digital twin model of the hydraulic system. The output data of the digital twin model of the monitored quantities are compared with the data collected by the sensors of the physical hydraulic system to verify the accuracy of the parameter estimation.
[0047] Based on the above technical solution, the following embodiments are provided.
[0048] This invention provides a method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems. The specific principle of the method is as follows: Figure 1 As shown, it can be divided into a simulation-experiment calculation module, a response surface proxy model construction module, and an optimal parameter combination decision module.
[0049] In this embodiment, a hydraulic cylinder internal leakage test bench was constructed. The following details how to use the proposed method for accurate parameter estimation based on the physical entity of this test bench. Figure 2 The diagram shown is the hydraulic schematic of the hydraulic cylinder internal leakage test bench, which includes: The system consists of an oil tank (1), a manual pump (2), a shut-off valve (3), a pressure sensor (4), a throttle valve (5), the hydraulic cylinder under test (6), and a measuring cup (7). The outlet of the manual pump (2) is connected to the shut-off valve (3). The outlet of the shut-off valve (3) is connected to the inlet of the hydraulic cylinder under test (6) via a pipe connector. It is crucial to ensure that the pipe between the shut-off valve (3) and the hydraulic cylinder under test (6) is as short as possible. Simultaneously, the other two ends of the pipe connector are connected to the pressure sensor (4) and the throttle valve (5), respectively. The pressure sensor (4) should be positioned as close as possible to the outlet of the hydraulic cylinder. The other end of the pressure sensor (4) is connected to a data acquisition system, transmitting data to a host computer for real-time monitoring. A measuring cup (11) is placed below the outlet of the throttle valve (5).
[0050] The manual pump 2 provides hydraulic fluid to the hydraulic component 10 under test during the test.
[0051] When the main oil circuit reaches the specified test pressure, the shut-off valve 4 locks the main oil circuit to achieve the pressure holding test process for the hydraulic component under test.
[0052] Measuring cup 7 is used to collect the volume of hydraulic oil leaking from the simulated hydraulic cylinder of the throttle valve.
[0053] In this embodiment, the NI USB-6343 multi-function data acquisition system is preferred for data acquisition and transmission.
[0054] In this embodiment, the digital twin model of the hydraulic cylinder internal leakage test system is established based on AMESim. In AMESim, the electromechanical-hydraulic coupling system of physical components such as hydraulic pumps, valves, pipelines, and the hydraulic cylinder under test, as well as their interactions and connections, is integrated and modeled using the Mechanical Library, Hydraulic Library, and Hydraulic Component Design Library. The internal leakage of the hydraulic cylinder is simulated by setting a sealing gap.
[0055] When conducting RSM analysis, it is first necessary to determine the response objective and the design variables that affect the objective, and to clarify the range of values for the design variables.
[0056] Based on the working principle of the hydraulic cylinder internal leakage testing system, this embodiment defines the key parameters affecting the accuracy of its digital twin model as the design variable set. ,in The gas content in the oil is expressed as % (%). This is the bulk modulus of the oil, expressed in GPa. Equivalent leakage gap, unit: .
[0057] The range of values for each parameter This is determined by the characteristics of the physical system and engineering experience. In this embodiment, it is determined based on engineering experience and pre-simulation experiments. , , Within this range, the success of the experiment can be ensured with a relatively high probability.
[0058] Based on the definition of the digital twin model and the actual requirements of this embodiment, the response objective function is defined as the error between the simulation results and the experimental results of the two monitoring variables, pressure drop and internal leakage volume, during the pressure holding experiment. Pressure drop is defined as the difference between the initial pressure and the final pressure during the hydraulic cylinder pressure holding process, and internal leakage volume is defined as the volume of oil seeping out through the valve port during the pressure holding process. The mathematical model is shown in equation (8).
[0059] (8) in, The pressure drop value during the pressure holding process of the digital twin model. Similarly, the pressure drop value during the pressure holding process in the experiment, The internal leakage volume during the pressure holding process of the digital twin model. The internal leakage volume during the pressure holding process is the average value of multiple experiments for the two types of monitoring variables during the pressure holding process.
[0060] In this embodiment, the Box-Behnken Design (BBD) experimental design method is preferred because it offers excellent efficiency and flexibility, enabling the acquisition of sufficient information about the influence of factors on the response with a relatively small number of experiments. Table 1 shows the design variable matrix of the BBD experimental method in this embodiment.
[0061] Table 1 Design variable matrix for BBD experimental methods
[0062] Based on the established design variable matrix and the output results of the response objective, a response surface proxy model under a working pressure of 16 MPa was established using multiple regression analysis. and The multiple linear regression model is shown in equation (9).
[0063] (9) The model fitting results were further evaluated, and the goodness of fit was assessed using regression coefficients (R²) and analysis of variance (ANOVA). In this embodiment, the p-values of the two objective function response surface fitting models were both less than 0.0001, and the calculation results of the regression coefficients are shown in Table 2.
[0064] It can be concluded through calculation and correlation coefficient The values are 0.9999 and 0.9992 respectively, indicating that the model has extremely high data fit. Furthermore, the adjusted... and prediction The differences were 0.0002 and 0.0004, respectively, which were significantly lower than the critical value of 0.2, further verifying the high predictive accuracy of the regression model.
[0065] Table 2 Regression coefficients of the target model
[0066] Based on the verified response surface proxy model, a multi-objective optimization mathematical model can be established. In this embodiment, the simulation and experimental results of each output monitoring quantity may have two types of errors: positive and negative solutions. Therefore, in order to simplify the mathematical expression while ensuring high-precision solution calculation, the multi-objective optimization mathematical model shown in equation (10) is constructed.
[0067] (10) The solution is based on the multi-objective optimization mathematical model of Equation (10). Optionally, in this embodiment, the multi-objective artificial hummingbird optimization algorithm is preferred. The effectiveness of this method in engineering parameter optimization design problems has been widely verified.
[0068] Furthermore, the TOPSIS method is used to select the optimal solution in the Pareto front solution set. First, each solution in the Pareto solution set is compared with the ideal solution and the inferior solution. The Euclidean distance between each Pareto solution and the ideal solution and the inferior solution is calculated by Equation (11).
[0069] (11) Next, calculate the relative tracking progress of the current scheme according to equation (12), and select the scheme with the highest tracking degree as the optimal combination of unknown parameters.
[0070] (12) Pareto front solution set and TOPSIS method for selecting optimal solution, such as Figure 3 As shown, the small gray circles represent the Pareto front solution set, and the large black circles represent the TOPSIS optimal solution. The optimal parameter combination corresponding to the optimal solution is... .
[0071] Verification Experiment Example: After determining the working conditions such as pressure level and oil temperature, a pressure holding experiment was carried out. During the experiment, the pressure data of the high-pressure chamber of the hydraulic cylinder and the volume of oil leaking through the valve port were collected. In this example, the working pressure level was determined to be 16MPa and the oil temperature to be 35℃.
[0072] Verification simulation example: Except for the unknown parameters in the digital twin model, which use the optimal parameter combination values calculated above, all other parameters are derived from the physical entity. The working pressure level is determined to be 16 MPa, and the oil temperature is 35℃. In addition, the experimental procedures and data types collected are consistent with those in the experimental example.
[0073] Comparison of results: Figure 4 and Figure 5 The figure shows a comparison between the digital twin model data and the experimental data of pressure drop and internal leakage volume during the pressure holding process. The results show that the optimal combination of unknown parameters estimated by the method proposed in this invention has high accuracy and achieves a high degree of consistency between the output results of the digital twin model and the experimental data.
[0074] Therefore, the response surface proxy model proposed in this invention effectively avoids the core problem of the difficulty in modeling the overall state mechanism of hydraulic systems. It does not rely on complex mechanism derivations and can build a high-precision nonlinear mapping relationship model between unknown parameters and simulation-experiment errors based solely on experimental data, twin data, and operating parameters, providing an efficient modeling method for subsequent parameter estimation.
[0075] Furthermore, the response surface surrogate model-multi-objective optimization-TOPSIS decision theory system involved in this invention overcomes the limitations of traditional single-objective estimation methods in adapting to nonlinear systems, achieving collaborative estimation and optimization of unknown parameters under the coupled effects of multiple monitoring variables. This method not only enriches the methods for estimating unknown parameters in hydraulic / hydraulic systems, but also significantly improves the parameter estimation accuracy of digital twin models of hydraulic / hydraulic systems, providing key technical support for improving system operational reliability and optimizing intelligent operation and maintenance decisions.
[0076] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0077] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems, characterized in that, include: Construct a solid model of the target hydraulic system and obtain relevant basic data through experiments; The relevant basic data includes the physical characteristics, working principle, and actual operating conditions of the hydraulic components. A digital twin model is constructed based on a physical model of the hydraulic system; the parameter variables of the digital twin model include deterministic parameters and unknown parameters; the deterministic parameters include the manufacturing parameters and inherent characteristic parameters of the hydraulic components; the unknown parameters are the uncertain parameters of the hydraulic system that need to be estimated. Specifically, for the unknown parameters, the design variable matrix and response objective function are determined based on the relevant basic data, and a response surface surrogate model is established using multiple regression analysis. Then, the Pareto front solution set of the established multi-objective optimization mathematical model is solved using a multi-objective optimization algorithm. Finally, the global optimal parameter combination is selected by combining a comprehensive evaluation method.
2. The method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems according to claim 1, characterized in that, The target hydraulic system physical model specifically includes: a hardware system and a control system and an interaction system connected to the hardware system; The hardware system includes physical hydraulic components, sensors, and a data acquisition card. The sensors include multiple sensors that collect different data, which are respectively installed on the corresponding physical components and connected to the data acquisition card. The physical hydraulic components include a power component, a control component, and a drive component.
3. The method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems according to claim 1, characterized in that, The construction process of the digital twin model is as follows: Based on the solid model of the hydraulic system, integrated modeling of the electromechanical-hydraulic coupling system, covering multiple physical components and their interactions and connections, was completed in the AMESim environment using the Mechanical Library, Hydraulic Library, and Hydraulic Component Design Library.
4. The method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems according to claim 1, characterized in that, The method for determining the design variable matrix and the response objective function is as follows: Based on the mechanism analysis of hydraulic systems, the key parameters affecting the accuracy of digital twin models are defined as the design variable matrix. ,in n For the parameter dimension, the range of values for each parameter. Determined by the characteristics of the physical system and engineering experience; Based on the digital twin model, a response objective function is constructed according to the output error between the simulation calculation results and the experimentally collected data: ； in, The number of sampling points. Calculate output data for the twin model. To collect data for the experiment.
5. The method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems according to claim 1, characterized in that, The process of establishing the response surface proxy model is as follows: Based on the design variable matrix and the response objective function, a response surface surrogate model is established using multiple regression analysis: ； in, and The independent variables include gas content, bulk modulus, and leakage gap; As the dependent variable, in the process of digital twin modeling in hydraulic systems, it specifically refers to the error between the calculation results of the digital twin model and the experimentally collected data under different monitoring variables; For constant terms, The coefficients of the linear term, The coefficient of the quadratic term, The coefficient of the interaction term. This is the residual term.
6. The method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems according to claim 1, characterized in that, The method of using a multi-objective optimization algorithm to solve the Pareto front solution set of the established multi-objective optimization mathematical model specifically includes: The Pareto front solution set is obtained by solving the established multi-objective optimization mathematical model using a multi-objective optimization algorithm. ； ； ； in, For the first One optimization objective; and These are inequality constraints and equality constraints, respectively. represent 3D solution space; The lower bound of the variable. This refers to the upper limit of the variables, specifically the range of the search space for gas content, bulk modulus, and leakage gap in the multi-objective optimization process. It is a set of variables consisting of gas content, bulk modulus, and leakage gap.
7. The method for estimating nonlinear unknown parameters in digital twin modeling of hydraulic systems according to claim 1, characterized in that, The method of selecting the globally optimal parameter combination using a comprehensive evaluation approach specifically includes: Using the TOPSIS method, the Euclidean distance between each Pareto solution and the ideal and inferior solutions is defined as follows: ； in, and They represent the first The distance between each solution and the ideal and inferior solutions. and These represent the ideal solution and the inferior solution, respectively. Represents each Pareto solution; And calculate the relative similarity of the current solution: ； The combination of parameters with the highest similarity value is determined as the globally optimal combination.