Simulation parameter iterative calibration method based on super-computing platform, electronic device and storage medium

Abstract

This invention provides a simulation parameter iterative calibration method, electronic device, and storage medium based on a supercomputing platform. The method includes: acquiring a geometric model of the structure to be analyzed, containing a hydraulic actuator; establishing a compressible fluid cavity model to replace actual hydraulic oil in driving a piston rod; configuring the physical parameters and state equations of the model; constructing a parameter estimation algorithm, where the state variable is the internal gas pressure of the model, and the observed value is the measured thrust of the piston rod in actual experiments; and iteratively correcting the undetermined parameters in the state equations using the difference between the simulated thrust value and the measured thrust value, until the error between the simulated thrust value and the measured thrust value meets a preset convergence condition. This invention simulates hydraulic oil drive using a compressible fluid cavity model and combines it with a parameter estimation algorithm to perform closed-loop calibration of the state equation parameters based on experimental data, improving simulation accuracy while avoiding complex fluid-structure interaction calculations.

Description

Technical Field

[0001] This invention relates to the field of mechanical structure simulation analysis, and in particular to a simulation parameter iterative calibration method, electronic device, and storage medium based on a supercomputing platform. Background Technology

[0002] In the field of mechanical structure simulation analysis, especially for the analysis of motion mechanisms with hydraulic cylinders as driving components, existing technologies mainly adopt the following two approaches: The first approach simplifies the hydraulic cylinder as a rigid body. In this approach, engineers typically apply a forced displacement or concentrated force in a predetermined direction directly to the end of the piston rod to drive the connected structural components to move. The drawbacks of this method are twofold: first, the cylinder itself is treated as a rigid body that does not deform, making it impossible to assess the stress distribution and structural strength of the cylinder body (such as the cylinder barrel and piston rod) during the simulation process; second, because the driving force acts directly on the piston rod, it is impossible to realistically simulate the reverse force generated on the cylinder wall at the bottom of the cylinder when the hydraulic oil pushes the piston in actual working conditions, thus making it impossible to effectively verify the strength of key load-bearing components such as the base and trunnion connected to the cylinder.

[0003] The second approach is to use fluid-structure interaction (FSI) analysis. This approach defines the hydraulic oil region as a fluid domain and the cylinder body, piston, and connecting mechanism as solid domains, and simulates the process of hydraulic oil flow driving the mechanism's motion by setting up a FSI interface. However, this method has inherent drawbacks: First, the dynamic boundary treatment between the fluid and solid is extremely complex, and the fluid mesh is prone to penetrating the solid mesh, leading to calculation divergence or distorted results; second, the physical properties (such as viscosity and compressibility) of different grades of hydraulic oil vary significantly, making it difficult to accurately represent in the model; finally, the FSI problem involves a large number of nonlinear iterative calculations, resulting in huge computational costs and low efficiency, making it difficult to apply to large-scale or high-precision engineering analysis.

[0004] Therefore, how to provide a simulation method that can accurately simulate the transmission path of hydraulic oil driving force while taking into account both computational efficiency and structural strength analysis accuracy has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows: According to a first aspect of the present invention, a method for iterative calibration of simulation parameters based on a supercomputing platform is provided, the method comprising the following steps: Obtain the geometric model of the structure to be analyzed, which includes the hydraulic actuator, and perform mesh discretization on the hydraulic actuator.

[0006] A compressible fluid cavity model is established in the internal chamber of the hydraulic actuator. The compressible fluid cavity model is used to replace the actual hydraulic oil to drive the piston rod.

[0007] Configure the physical parameters of the compressible fluid cavity model and the state equation describing the internal gas pressure change of the compressible fluid cavity model, the state equation containing at least one undetermined parameter.

[0008] A parameter estimation algorithm is constructed, wherein the state variable of the parameter estimation algorithm is the internal gas pressure of the compressible fluid cavity model, and the observed value is the measured thrust of the piston rod in the actual test.

[0009] The simulation calculation task is submitted to the supercomputing platform for execution. The difference between the simulated thrust value and the measured thrust value is used to iteratively correct the undetermined parameters in the state equation until the error between the simulated thrust value and the measured thrust value meets the preset convergence condition. The values ​​of the undetermined parameters determined in the last iteration and the corresponding simulation analysis results are then output.

[0010] According to a second aspect of the present invention, an electronic device is provided, including a processor and a memory; the processor executes the steps of the method described in the first aspect of the present invention by invoking a program or instructions stored in the memory.

[0011] According to a third aspect of the present invention, a computer-readable storage medium is provided that stores a program or instructions that cause a computer to perform the steps of the method described in the first aspect of the present invention.

[0012] The present invention has at least the following beneficial effects: First, addressing the problem that existing rigid body simplification methods cannot simulate the reaction force of hydraulic oil on the cylinder wall of a hydraulic actuator, resulting in a lack of strength verification for the hydraulic actuator base, this invention uses a compressible fluid cavity model to replace the actual hydraulic oil. By setting the contact relationship between the compressible fluid cavity grid and the inner wall of the cylinder, the internal pressure of the compressible fluid cavity can be directly transmitted to the cylinder wall. This accurately simulates the reaction force generated by the hydraulic oil pushing the piston on the bottom or top cylinder wall of the hydraulic actuator while driving the piston rod. Therefore, mechanism motion analysis and hydraulic actuator base structural strength assessment can be completed simultaneously in the same simulation model.

[0013] Secondly, in view of the shortcomings of existing fluid-structure interaction methods, such as fluid mesh penetration, difficulty in accurately characterizing different hydraulic oil parameters, and huge computational load, this invention adopts a compressible fluid cavity model based on the assumption of uniform pressure. It does not require the establishment of complex fluid-structure interaction boundaries, avoids the mesh penetration problem, and significantly reduces computational overhead. It can support large-scale, long-term dynamic simulations and improve the feasibility of engineering applications.

[0014] Furthermore, to address the issue of insufficient simulation accuracy caused by the difference in physical properties (gas compressibility versus liquid near-incompressibility) between the compressible fluid cavity model and actual hydraulic oil, this invention introduces parameter estimation algorithms (such as Kalman filters, extended Kalman filters, unscented Kalman filters, or ensemble Kalman filters). Using the internal pressure of the compressible fluid cavity as the state variable and the measured piston rod thrust as the observation variable, the difference between the simulated and measured values ​​is used to iteratively correct the undetermined parameters in the state equation. This closed-loop calibration method enables the simulation results to approximate experimental data, significantly improving analytical accuracy while avoiding the inefficiency of manual trial-and-error parameter tuning.

[0015] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0017] Figure 1 A flowchart illustrating the simulation parameter iterative calibration method based on a supercomputing platform provided in the first embodiment of the present invention; Figure 2 Schematic diagram of a compressible fluid cavity setup; Figure 3 A schematic diagram illustrating the placement of the foldable compressible fluid cavity; Figure 4 This is a schematic diagram of a compressible fluid cavity. Figure 5 This is a schematic diagram illustrating the working principle of the simulation model. Detailed Implementation

[0018] 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.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0020] It should be noted that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of these steps can be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the steps can be rearranged. A process can be terminated when its operation is complete, but it may also have additional steps not included in the figures. A process can correspond to a method, function, procedure, subroutine, subroutine, etc.

[0021] First Embodiment This embodiment provides a simulation parameter iterative calibration method based on a supercomputing platform.

[0022] It should be noted that the hydraulic actuator described in this embodiment and its variants refers to an actuating element that uses hydraulic oil as its working medium; specifically, the hydraulic actuator is a hydraulic cylinder. For ease of description, the hydraulic cylinder will be used directly in some places in the following description.

[0023] Before describing the specific steps, let's first briefly explain the actual working process of the hydraulic cylinder.

[0024] The hydraulic cylinder described in this embodiment has a rodless chamber and a rod chamber. The rodless chamber corresponds to the bottom of the cylinder, and the rod chamber corresponds to the top of the cylinder. The piston rod is fixedly connected to the piston and extends out of the cylinder. When the hydraulic cylinder acts as a power device to drive the movement of an external structure, its actual working process is as follows: When the piston rod extends outward, hydraulic oil flows into the rodless chamber of the hydraulic cylinder through the inlet of the rodless chamber. The hydraulic oil pushes the piston away from the bottom of the cylinder, and at the same time, the hydraulic oil generates a reaction force on the cylinder wall at the bottom of the cylinder. When the piston rod retracts inward, hydraulic oil flows into the rod chamber of the hydraulic cylinder through the rod chamber inlet. The hydraulic oil pushes the piston towards the bottom of the cylinder, while at the same time the hydraulic oil generates a reaction force on the top wall of the cylinder.

[0025] The aforementioned reaction force is a key load for verifying the strength of the cylinder base and connecting components. Existing rigid body simplification methods, which directly apply forced displacement or concentrated force to the piston rod, cannot simulate this reaction force; while fluid-structure interaction methods can simulate it, the computational burden is enormous. Therefore, this embodiment provides a simulation parameter iterative calibration method based on a supercomputing platform. Figure 1As shown, the method includes the following steps: S100: Obtain the geometric model of the structure to be analyzed, which includes the hydraulic actuator, and perform mesh discretization on the hydraulic actuator.

[0026] Specifically, S100 includes: First, import the geometric model of the structure to be analyzed, which includes the hydraulic actuator, into finite element preprocessing software (such as HyperMesh, Ansa, or Abaqus / CAE). The structure to be analyzed includes at least the cylinder, piston rod, piston, and external mechanical components driven by the hydraulic actuator.

[0027] Then, the imported geometric model is discretized into a mesh. Specifically, the cylinder, piston rod, and piston of the hydraulic actuator are meshed separately. To improve computational accuracy and efficiency, the cylinder, piston rod, and piston are discretized using either tetrahedral or hexahedral meshes. Tetrahedral meshes are suitable for complex geometric features, while hexahedral meshes can achieve higher computational accuracy in regular regions. Those skilled in the art can choose the appropriate element type based on the specific geometric features and computational resources. Other external mechanical components can be meshed according to conventional finite element analysis requirements, which will not be elaborated here.

[0028] Through the above mesh discretization process, a finite element model foundation for subsequent simulations was established.

[0029] S110, a compressible fluid cavity model is established in the internal chamber of the hydraulic actuator, the compressible fluid cavity model being used to replace the actual hydraulic oil to drive the piston rod.

[0030] A compressible fluid cavity model is a simulation model that uses compressible gas as the working medium and drives piston movement through gas pressure changes. In finite element simulation, this model controls internal pressure changes by inputting the mass flow rate of the gas, thereby driving the piston and piston rod to move, replacing the function of actual hydraulic oil.

[0031] In this embodiment, the model is specifically implemented as an airbag model. This step first establishes a compressible fluid cavity model in the corresponding chamber area according to the actual working mode of the hydraulic actuator.

[0032] It should be noted that those skilled in the art will understand that in other embodiments, the compressible fluid cavity model can also be implemented in other forms, for example: Inflatable cavity model: Directly defines a closed inflatable space that matches the volume of the cavity, without the need for virtual folding steps, and is suitable for working conditions where the piston is already filled with gas at the initial position; Pressure chamber model: A simplified model using the pressure equalization assumption is adopted, which only calculates the pressure changes of the gas in the chamber without building a solid mesh, which can further reduce the computational cost; Multi-chamber gas model: The cavity is divided into multiple interconnected sub-chambers, which is suitable for simulating the non-uniform distribution of gas in complex chambers.

[0033] All the above-mentioned alternative implementations fall within the protection scope of this invention. The following uses an airbag model as an example to describe in detail the process of establishing a compressible fluid cavity model, specifically including the following steps: S1101, Determine the location of the compressible fluid cavity model according to the working mode. The operating mode of the hydraulic actuator determines the area where the compressible fluid cavity model is set. If the hydraulic actuator's operating mode is to only drive the piston rod to extend outward (i.e., the push-out condition), then a single compressible fluid cavity model is established in the first region corresponding to the rodless cavity of the hydraulic actuator, such as... Figure 2 Region 1 in the model corresponds to the cavity where hydraulic oil actually flows in to push the piston outward. If the hydraulic actuator operates by only driving the piston rod inward (i.e., inward pull condition), then a single compressible fluid cavity model is established in the second region corresponding to the rod cavity of the hydraulic actuator. It should be noted that the rod cavity in the 3D model actually includes two sub-regions on both sides of the piston rod (e.g.,...). Figure 2 Regions 2 and 3 in the model are interconnected under gas pressure and can be considered as the same region, so only one compressible fluid cavity model needs to be established. If the working mode of the hydraulic actuator is to alternately drive the piston rod to extend outward and retract inward (i.e., to push outward and pull inward simultaneously), then two independent compressible fluid cavity models are established in the first region and the second region respectively to control the pushing outward and pulling inward actions.

[0034] S1102, Calculate the spatial volume of the initial state and the final state. After determining the area for setting up the compressible fluid cavity model, the first volume of the internal chamber is calculated when the piston rod is in its initial position, and the second volume is calculated when the piston rod reaches its end position. These two volume parameters depend on the inner diameter of the hydraulic actuator and the piston's stroke. Specifically, the first volume corresponds to the initial volume of gas that can be contained within the chamber before the piston rod has moved, and the second volume corresponds to the maximum volume of gas that can be contained within the chamber when the piston rod reaches its limit position.

[0035] S1103, Create a compressible fluid cavity unfolded mesh model A shell mesh is used to create a compressible fluid cavity deployment mesh model that matches the volume of the second space. Specifically, based on the volume of the second space and the inner diameter of the hydraulic actuator, the geometric dimensions of the compressible fluid cavity when deployed are determined, where the diameter of the compressible fluid cavity is equal to the inner diameter of the hydraulic actuator, and the length of the compressible fluid cavity is equal to the volume of the second space divided by the cross-sectional area of ​​the hydraulic actuator. Based on the determined geometric dimensions, a three-dimensional geometric model representing the fully deployed state of the compressible fluid cavity is constructed. Then, shell elements are used to mesh this three-dimensional geometric model to obtain the compressible fluid cavity deployment mesh model. This compressible fluid cavity deployment mesh model represents the geometry of the compressible fluid cavity when it is completely filled with the chamber. Figure 3 This is a schematic diagram of a compressible fluid cavity in operation, where S1 represents the fully deployed compressible fluid cavity, and 1 represents the piston at the working end. Figure 3 As shown, when the compressible fluid cavity is fully expanded, its volume exactly fills the chamber space when the piston moves to the end position.

[0036] S1104, Virtual folding of the unfolded mesh model of the compressible fluid cavity. Since the compressible fluid cavity model should occupy a small volume matching the chamber volume at the piston's initial position when uninflated, it is necessary to virtually fold the unfolded compressible fluid cavity mesh model. Specifically, the unfolded compressible fluid cavity mesh model is virtually folded along its length, causing its volume to shrink until the difference between the unfolded mesh model and the first spatial volume is less than a preset value (e.g., volume error less than 5%). Folding is performed only along the length direction, without changing the radial dimensions, to ensure that the compressible fluid cavity still conforms to the cylinder wall shape after folding. This virtual folding can be implemented using a known airbag mesh folding method.

[0037] S1105, Placement of the folded compressible fluid cavity mesh model The folded compressible fluid cavity mesh model is moved and placed at the initial position of the internal chamber to obtain the compressible fluid cavity model. After placement, the compressible fluid cavity model is in a state of being ready to be inflated. The initial volume of the compressible fluid cavity model is basically the same as the chamber space volume when the piston is in its initial position, thus avoiding the problem of the piston failing to start or the initial motion being distorted due to an excessively large initial volume. Figure 4 This is a schematic diagram showing the placement of the folded compressible fluid cavity, where S2 represents the folded compressible fluid cavity, 2 represents the hydraulic actuator wall, and 3 represents the piston rod. Figure 4 As shown, the folded compressible fluid cavity is placed in the initial position of the internal chamber of the hydraulic actuator, and its volume matches the chamber space when the piston is in the initial position, with the piston rod in the initial state before it extends.

[0038] S1106, Set contact relationship After establishing the compressible fluid cavity model, the contact relationship between the mesh of the compressible fluid cavity model and the mesh of the inner wall of the cylinder of the hydraulic actuator needs to be set. This contact relationship is used to prevent the compressible fluid cavity mesh from penetrating the cylinder mesh during expansion, while transferring the pressure load to the cylinder wall, thereby achieving accurate simulation of the reaction force of the hydraulic actuator base. Specifically, in this embodiment, the CONTACT AUTOMATIC SURFACE TO SURFACE type is used to define this contact relationship. In this contact definition, the shell element mesh of the compressible fluid cavity model is set as the slave face, and the mesh of the inner wall of the cylinder is set as the master face. Through this contact definition, the software will detect whether the slave face node penetrates the master face segment at each time step of the simulation calculation. Once penetration is detected, a contact force proportional to the penetration depth will be applied according to the penalty function algorithm to prevent further penetration, and the contact force will be transferred to the mesh node of the inner wall of the cylinder, thereby simulating the reaction force of the hydraulic oil. As an example, the friction coefficient is set to 0.1 in this embodiment to simulate the friction between hydraulic oil and the cylinder wall. Those skilled in the art can adjust the friction coefficient according to actual working conditions. Through the above steps, the establishment and initialization of the compressible fluid cavity model are completed, laying the foundation for subsequent simulation calculations and parameter calibration.

[0039] In the existing technology, there are two main paths for the simulation analysis of hydraulic actuators as power components: one is to simplify the hydraulic actuator as a rigid body and directly apply forced displacement to the piston rod end. This method cannot simulate the reaction force of hydraulic oil on the cylinder wall, resulting in the lack of strength verification of the hydraulic actuator base; the other is to use the fluid-structure interaction method to set the hydraulic oil as a fluid domain. However, this method has inherent defects such as fluid mesh penetration, difficulty in characterizing different hydraulic oil parameters, and huge computational load.

[0040] This embodiment uses a compressible fluid cavity model instead of actual hydraulic oil, which has the following improvements: 1. Preserve the reaction force transmission path. The compressible fluid cavity model, by establishing its contact relationship with the inner wall of the cylinder, allows the internal gas pressure to act directly on the cylinder wall during inflation and expansion. This accurately simulates the reaction force generated on the bottom or top cylinder wall of the hydraulic actuator when actual hydraulic oil pushes the piston. This enables simulation analysis not only to drive the piston rod but also to simultaneously verify the structural strength of the hydraulic actuator base and connecting components, overcoming the inherent limitations of the rigid body simplification method.

[0041] 2. Avoid the complexity and instability of fluid-structure interaction. The compressible fluid cavity model uses the finite volume method based on the assumption of uniform pressure to describe gas behavior. It eliminates the need to establish coupling boundaries between the fluid and solid meshes, thus completely avoiding problems such as fluid infiltration and mesh distortion. At the same time, the computational cost of the compressible fluid cavity model is much lower than that of fluid-structure interaction analysis, enabling it to support large-scale, long-term dynamic simulations.

[0042] 3. Achieving initial volume matching through virtual folding technology. In a real hydraulic actuator, the chamber is already filled with hydraulic oil when the piston is in its initial position, with no gaps. This embodiment virtually folds the compressible fluid cavity's unfolded mesh model along its length, shrinking its initial volume to match the chamber space volume when the piston is in its initial position. This process allows the compressible fluid cavity to generate effective pressure in the initial inflation phase, avoiding problems such as the piston failing to start or initial motion distortion due to an excessively large initial volume. The folding only occurs along the length direction, without changing the radial dimension, ensuring consistent contact between the compressible fluid cavity and the cylinder wall during unfolding.

[0043] 4. Supports multiple working modes Depending on the hydraulic actuator's push-out, pull-in, or alternating operating mode, independent compressible fluid cavity models can be flexibly established in the rodless cavity, rod cavity, or both cavities simultaneously. This modular approach allows the same simulation method to adapt to different driving requirements without altering the underlying algorithm.

[0044] In summary, the compressible fluid cavity model establishment method proposed in this embodiment significantly reduces computational complexity and improves simulation stability and engineering applicability while preserving the hydraulic oil reaction force transmission characteristics.

[0045] S120, Configure the physical parameters of the compressible fluid cavity model and the state equation describing the internal gas pressure change of the compressible fluid cavity model, the state equation containing at least one undetermined parameter.

[0046] After establishing and placing the compressible fluid cavity model, this step further configures the physical parameters of the compressible fluid cavity model and the state equation describing the changes in internal gas pressure.

[0047] S1201, Configure the physical parameters of the compressible fluid cavity model. First, set the basic physical parameters of the compressible fluid cavity model, including: Gas density ρ0: represents the initial density of the gas inside the input compressible fluid cavity; Constant volumetric specific heat capacity (CV): used to describe the heat capacity per unit mass of a gas when its volume remains constant; Specific heat capacity at constant pressure (CP): used to describe the heat capacity per unit mass of a gas when the pressure remains constant. Input gas temperature T: Usually set to room temperature to simulate the actual working environment of hydraulic oil; Curve of input mass flow rate: This curve defines the mass flow rate of the gas input into the compressible fluid cavity at different times, and is the power input that drives the expansion of the compressible fluid cavity.

[0048] Among the above parameters, the gas density ρ0, specific heat capacity CV, and CP can be determined according to the selected gas type (such as air, nitrogen, etc.), the input gas temperature T is set according to the environmental conditions, and the input gas mass flow rate curve is calibrated according to the actual hydraulic oil pump's oil supply characteristics.

[0049] S1202 defines the equation of state describing the pressure change of gas inside a compressible fluid cavity. To accurately describe the relationship between internal gas pressure and volume / density changes during the inflation process of a compressible fluid cavity, the following equation of state is used in this embodiment: P=ρ0×C 2 ×u+(γ+A×u)×E0.

[0050] Where P is the internal gas pressure of the compressible fluid cavity model, ρ0 is the initial gas density, i.e. the gas density in the aforementioned physical parameters; u=(ρ / ρ0)-1, ρ is the gas density inside the compressible fluid cavity at the current moment, C and γ are constants of the equation of state, A is the first-order volume correction coefficient, and E0 is the initial internal energy.

[0051] In the above equation of state, C, γ, A, E0, and the initial relative volume V0 are all undetermined parameters. The theoretical values ​​of these parameters deviate from actual gas behavior. Directly using empirical or theoretical values ​​will lead to discrepancies between the simulation results and real-world conditions. Therefore, these undetermined parameters need to be iteratively optimized in subsequent steps using parameter estimation algorithms (such as ensemble Kalman filtering) to ensure that the simulation results (especially the piston rod thrust) closely match the actual experimental data, thereby achieving high simulation accuracy.

[0052] S130, Construct a parameter estimation algorithm, wherein the state variable of the parameter estimation algorithm is the internal gas pressure of the compressible fluid cavity model, and the observed value is the measured thrust of the piston rod in the actual test.

[0053] In order to accurately calibrate the undetermined parameters in the equation of state, this embodiment introduces a parameter estimation algorithm and uses the piston rod thrust data measured in actual experiments to perform closed-loop correction on the simulation model. Figure 5 This is a schematic diagram illustrating the working principle of the simulation model in this embodiment, showing the data flow between the compressible fluid cavity input, Kalman filter iterative correction, and thrust output. Figure 5In this context, M represents the input to the compressible fluid cavity, and F represents the thrust at the top of the piston rod.

[0054] (a) Selection of parameter estimation algorithm type The parameter estimation algorithm can employ any one of the following: Kalman filter, extended Kalman filter, unscented Kalman filter, or ensemble Kalman filter. All of these algorithms are applicable to state estimation and parameter identification of dynamic systems. Their core idea is to recursively correct the state estimate using observations through two steps: prediction and update.

[0055] (II) Definitions of State Variables, Observed Variables, and Input Variables In this embodiment, the variables of the parameter estimation algorithm are defined as follows: State variable: Internal gas pressure P in the compressible fluid cavity model. This variable directly reflects the thermodynamic state inside the compressible fluid cavity and is a key factor determining the piston rod thrust.

[0056] Observed variable: The measured thrust F of the piston rod in the actual test. test This value was obtained through actual experiments and serves as the basis for calibrating the simulation model.

[0057] Input variable: The mass flow rate of the gas inside the compressible fluid cavity model at a certain moment. This variable is provided by the aforementioned input gas mass flow rate curve.

[0058] (III) Prediction and Update Steps of Ensemble Kalman Filtering In a preferred embodiment of this invention, an ensemble Kalman filter is used to iteratively correct the undetermined parameters in the state equation. The ensemble Kalman filter characterizes the probability distribution of state variables using a set of states, making it suitable for parameter estimation of nonlinear systems. Its iterative process includes a prediction step and an update step. Prediction Steps: Based on the posterior state estimate from the previous time step (k-1) (i.e., the compressible fluid cavity internal pressure value corrected by measured values ​​from the previous time step), and the input gas mass flow rate at the current time step (k), predict the prior state estimate and its covariance matrix for the current time step. The prior state estimate refers to the compressible fluid cavity internal pressure estimate predicted solely based on historical information and the current input before correction using the measured thrust value at the current time step. The posterior state estimate refers to the final estimate of the compressible fluid cavity internal pressure obtained after fusing and correcting the prior state estimate with the measured thrust value at the current time step.

[0059] Specifically, the predicted state set is obtained by forward propagation through the state transition function for each set member, and the covariance matrix of the predicted states is calculated. This step can be expressed as: x e k|k-1 =f(x e k-1|k-1 ,u k )+w k P k|k-1 =F k ·P k-1|k-1 ·F T k +Q k Among them, x e k|k-1 For the prior state estimate at time k, x e k-1|k-1 The state posterior estimate is given by the previous time step, f is the system state function at time k, and u k Let w be the input variable (mass flow rate) at time k. k P represents the process noise at time k. k|k-1 Let F be the covariance matrix of the prior state estimate at time k. k Let P be the state transition matrix. k-1|k-1 Q is the covariance matrix of the posterior state estimate at time k-1. k It is the process noise covariance matrix.

[0060] Update steps: Calculate the Kalman gain using the measured thrust value at the current moment, and correct the state prior estimate and its covariance matrix to obtain the state posterior estimate at the current moment.

[0061] Specifically, the difference (innovation) between the observed and predicted values ​​is first calculated. Then, the prior estimate is weighted and corrected according to the Kalman gain, and the covariance matrix is ​​updated. This step can be expressed as: x e k|k =x e k|k-1 +K k ·(z k -H·x e k|k-1 ), P k|k =(IK k H)P k-1|k-1 Among them, x e k|k For the posterior estimate of the state at the current time, z k Let K be the measured thrust value at time k. k For Kalman gain, K k =P k|k-1 H T (HP) k|k-1 H T+R) -1 H is the observation matrix, used to map the state variable (pressure inside the compressible fluid cavity) to the estimated value of the observed variable (piston rod thrust), and P... k|k Let I be the covariance matrix of the state posterior estimate at time k, where I is the identity matrix and R is the measurement noise covariance matrix.

[0062] Through iterative execution of the above prediction and update steps, the undetermined parameters in the simulation model will gradually converge to the optimal value that makes the simulated thrust highly consistent with the experimental thrust.

[0063] (iv) Iteration Termination Condition When the error between the simulated thrust value and the measured thrust value obtained from the simulation meets the preset convergence condition (e.g., the relative error is less than or equal to 5%), the iteration stops, and the value of the undetermined parameter determined by the last iteration is output as the final calibration result.

[0064] This embodiment combines a compressible fluid cavity model with a parameter estimation algorithm (such as ensemble Kalman filtering), which has the following advantages: (1) Retain the reaction force transmission path to realize the strength verification of the hydraulic actuator base. Traditional rigid body simplification methods treat hydraulic actuators as rigid bodies and directly apply forced displacement to the piston rod end, failing to simulate the reaction force of hydraulic oil on the cylinder wall. This results in a lack of strength verification for the hydraulic actuator base and connecting components. This embodiment uses a compressible fluid cavity model to replace the actual hydraulic oil. By setting the contact relationship between the compressible fluid cavity mesh and the inner wall of the cylinder, the pressure inside the compressible fluid cavity can be transmitted to the cylinder wall, thus simulating the reaction force generated by the hydraulic oil pushing the piston on the bottom or top cylinder wall of the hydraulic actuator. Based on this, the mechanism motion analysis and the hydraulic actuator base structural strength analysis can be completed simultaneously in the same simulation model.

[0065] (2) Avoid the complexity and instability of fluid-structure interaction and reduce computational cost. While existing fluid-structure interaction (FSI) methods can simulate hydraulic oil actuation, they suffer from challenges such as difficult boundary treatment between fluid and solid meshes, fluid penetration, and difficulty in accurately characterizing different hydraulic oil parameters, as well as high computational costs. This embodiment employs a compressible fluid cavity model based on the assumption of uniform pressure, eliminating the need for fluid-structure interaction boundaries, avoiding mesh penetration, reducing computational overhead, supporting large-scale, long-term dynamic simulations, and improving the feasibility of engineering applications.

[0066] (3) Automatic model calibration is achieved through parameter estimation algorithms to improve simulation accuracy. There are inherent differences between the compressible fluid cavity model and real hydraulic oil (e.g., the difference between the compressibility of gases and the near incompressibility of liquids), and directly using theoretical parameters may lead to insufficient simulation accuracy. This embodiment introduces a parameter estimation algorithm (e.g., ensemble Kalman filtering), using the internal pressure of the compressible fluid cavity as the state variable and the measured value of the piston rod thrust as the observation variable, and iteratively corrects the parameters to be determined using prediction and update steps. This closed-loop calibration method enables the simulation results to approximate experimental data, improves the accuracy of analysis, and avoids the inefficiency of manual trial and error parameter tuning.

[0067] (4) Synergistic effect between compressible fluid cavity model and parameter estimation algorithm There is a synergistic effect between the compressible fluid cavity model and the parameter estimation algorithm: on the one hand, the compressible fluid cavity model provides an efficient way to simulate driving forces, offering a stable positive simulation environment for parameter calibration; on the other hand, the parameter estimation algorithm compensates for the accuracy loss caused by the physical approximation of the compressible fluid cavity model (compressible gas replacing incompressible liquid). The two complement each other, overcoming the difficulty of balancing computational efficiency and simulation accuracy in existing technologies, achieving an overall technical effect that cannot be achieved by a single technical approach.

[0068] S140, the simulation calculation task is submitted to the supercomputing platform for execution. The difference between the simulated thrust value and the measured thrust value is used to iteratively correct the undetermined parameters in the state equation until the error between the simulated thrust value and the measured thrust value meets the preset convergence condition. The values ​​of the undetermined parameters determined in the last iteration and the corresponding simulation analysis results are then output.

[0069] Specifically, the iterative correction process is executed according to the following procedure: S1401, Initialization and First Simulation Initial values ​​are assigned to the undetermined parameters (C, γ, A, E0, V0) in the equation of state based on empirical or theoretical values ​​(e.g., C is an approximation of the air adiabatic index, γ is 1.4, A is 0, E0 is the default value, and V0 is 1). These initial parameters are then substituted into the compressible fluid cavity model, which is then submitted to a supercomputing platform for the first simulation calculation, yielding the simulated thrust F at the piston rod tip. sim .

[0070] S1402, Calculate Differences and Update Parameters The thrust simulation value F sim The measured thrust F obtained through testing under the same operating conditions testThe two are compared, and the difference (information) between them is calculated. A parameter estimation algorithm (such as ensemble Kalman filtering) calculates the Kalman gain based on this difference, combined with the current state variables (pressure inside the compressible fluid cavity) and the observation matrix, and corrects the undetermined parameters in the state equation according to the prediction and update steps. The corrected parameters will be used in the next round of simulation.

[0071] S1403, Iterative convergence judgment The process of "submitting to the supercomputing platform for simulation calculation → difference calculation → parameter correction" is repeated. After each iteration, the corrected parameters are re-submitted into the compressible fluid cavity model, submitted to the supercomputing platform for solution, and the difference between the new simulated thrust value and the measured thrust value is calculated.

[0072] This embodiment submits the simulation calculation task to a supercomputing platform for execution, utilizing its parallel computing technology to accelerate the solution of large-scale or high-precision models during multiple iterations. Compared to traditional single-machine or small cluster computing environments, the supercomputing platform can significantly shorten the computation time required for multiple iterations, making the closed-loop calibration method based on parameter estimation algorithms practical for engineering applications, especially suitable for scenarios involving the construction of digital twin models with high timeliness requirements.

[0073] After each iteration, it is determined whether the relative error between the simulated thrust value and the measured thrust value meets a preset convergence condition. As an example, the convergence condition can be set to a relative error of less than or equal to 5%. If the condition is met, the iteration stops; if not, the next round of correction continues.

[0074] S1404, Output calibration results Once the iteration converges, the value of the undetermined parameter (C) determined in the last iteration is taken. opt γ opt A opt E 0opt V 0opt The final calibration result is output, and this set of parameters can be used for subsequent final simulation analysis (such as evaluating the structural strength of the hydraulic actuator and the load-bearing capacity of the base).

[0075] Through the iterative correction process performed on the supercomputing platform, the behavior of the compressible fluid cavity in the simulation model can approximate the real hydraulic oil drive characteristics to the greatest extent. At the same time, the high-performance computing power of the supercomputing platform can be used to significantly shorten the iteration cycle, thereby improving the analysis efficiency while ensuring the calculation accuracy.

[0076] Furthermore, the method also includes: updating the compressible fluid cavity model using the values ​​of the undetermined parameters determined in the last iteration, performing the final simulation calculation, and generating the stress distribution and deformation results of the hydraulic actuator and the connecting base of the hydraulic actuator in a complete working cycle.

[0077] After completing the above iterative correction and obtaining the optimal values ​​of the undetermined parameters, the method further includes updating the compressible fluid cavity model using the set of parameters and performing the final simulation calculation to evaluate the structural mechanical performance of the hydraulic actuator and its connecting base under actual working loads.

[0078] Specifically, the optimal parameter values ​​determined in the last iteration are substituted into the state equation of the compressible fluid cavity model, replacing the original initial empirical values. Keeping other modeling conditions (mesh model, contact definition, boundary conditions, input gas mass flow rate curve, etc.) unchanged, a complete simulation model is established for the final analysis.

[0079] The compressible fluid cavity model is then submitted to a simulation solver (which can be run on a supercomputing platform to improve computational efficiency) to simulate the dynamic response of the hydraulic actuator during a complete working cycle (including piston rod extension, retraction, and possible alternating movements). After solving, the following simulation results are extracted using a post-processing module: The stress distribution and deformation results of the hydraulic actuator body include the equivalent stress (von Mises stress) of the cylinder wall, the axial stress and bending stress of the piston rod, and the pressure distribution at the contact surface between the piston and the cylinder. These are used to verify whether the hydraulic actuator meets the strength design requirements under different working conditions.

[0080] Stress distribution and deformation results of the connecting base: Extract the support reaction force and local stress concentration areas at the connection between the hydraulic actuator and the connecting base (such as trunnion, pin hole, flange face) to evaluate the load-bearing capacity and fatigue life of the base structure under the action of hydraulic oil reaction force.

[0081] Based on the above simulation results, stress-time curves and deformation cloud maps of key nodes can be further plotted and compared with design indicators such as material yield strength and fatigue limit, thereby quantitatively judging the structural safety of the hydraulic actuator and its connecting base.

[0082] Through the above final simulation analysis, this method can not only accurately simulate the kinematic behavior of hydraulic actuators driving external mechanisms, but also simultaneously complete the structural strength verification of the hydraulic actuator body and base, providing a reliable simulation basis for engineering design.

[0083] Second Embodiment This embodiment provides another simulation parameter iterative calibration method based on a supercomputing platform. The difference from the first embodiment is the addition of a virtual vent. This embodiment adds a virtual vent to the compressible fluid cavity model to simulate the minute leakage or overflow characteristics of hydraulic oil under pressure, and jointly calibrates the vent area and state equation parameters, making the simulation closer to the non-ideal characteristics of a real hydraulic system. Specifically, it includes the following steps: S200, obtain the geometric model and mesh it.

[0084] Same as the first embodiment S100, and will not be described again here.

[0085] S210, Establish a compressible fluid cavity model with a virtual exhaust port.

[0086] A compressible fluid cavity model is established within the internal chamber of the hydraulic actuator. This model replaces the actual hydraulic oil to drive the piston rod. Unlike the first embodiment, this embodiment sets at least one virtual vent hole at a predetermined location on the compressible fluid cavity model (e.g., the sidewall or end face of the model). The virtual vent hole simulates the loss of working medium in an actual hydraulic system due to minor leakage from seals or the opening of an overflow valve. The initial geometric parameters of the virtual vent hole are configured, including the number of vent holes, their diameter, and their location distribution.

[0087] S220, configured with physical parameters, exhaust characteristic curves and state equations.

[0088] Configure the physical parameters of the compressible fluid cavity model (gas density ρ0, constant volumetric specific heat capacity CV, constant pressure specific heat capacity CP, input gas temperature T, input gas mass flow rate curve) and the exhaust characteristic curve of the virtual exhaust port. The exhaust characteristic curve describes the relationship between the gas mass flow rate at the exhaust port and the internal pressure of the compressible fluid cavity and the external ambient pressure.

[0089] As an example, the orifice outflow formula can be used: q out =Cd·S·(2ΔP / ρ) 1 / 2 .

[0090] Where, q out ΔP is the mass flow rate through the vent (the mass of gas discharged per unit time); Cd is the flow coefficient, which depends on the geometry of the vent and the flow state (the value range is usually 0.6~1.0); S is the effective flow area of ​​the vent; ΔP is the difference between the internal pressure of the compressible fluid cavity and the external ambient pressure. When the internal pressure is higher than the external pressure, the gas is discharged outward.

[0091] The exhaust characteristic curve described above includes at least one second undetermined parameter. As an example, the second undetermined parameter could be a flow coefficient, an exhaust orifice area, or a correction factor for the exhaust orifice area.

[0092] Simultaneously, a state equation describing the gas pressure change inside the compressible fluid cavity model is configured, which includes at least one first undetermined parameter (C, γ, A, E0, V0). The expression of the state equation is the same as in the first embodiment.

[0093] S230, Construct a parameter estimation algorithm.

[0094] A parameter estimation algorithm (such as ensemble Kalman filtering) is constructed. The state variables of this algorithm include the internal gas pressure of the compressible fluid cavity model and the exhaust flow rate of the virtual exhaust port, while the observed values ​​are the measured thrust of the piston rod in actual experiments. The state vector can be extended to [P, q]. out ] T Where P is the internal pressure of the compressible fluid cavity model, and q out This refers to the exhaust flow rate.

[0095] S240, joint iterative correction and convergence.

[0096] By utilizing the difference between the simulated thrust value and the measured thrust value obtained from simulation calculations, a joint iterative correction is performed on the first undetermined parameter (state equation parameter) and the second undetermined parameter (exhaust characteristic curve parameter). In each iteration, the current parameters are substituted into the model and submitted to the supercomputing platform for simulation calculation to obtain the simulated thrust value; the difference between the calculated and measured values ​​is then considered; the parameter estimation algorithm updates both types of undetermined parameters simultaneously based on the difference. This process is repeated until the error between the simulated thrust value and the measured thrust value meets the preset convergence condition (as an example, the relative error ≤ 5%). The final output includes all parameter values ​​determined in the last iteration and the corresponding simulation analysis results.

[0097] The beneficial effects of this embodiment are as follows: By setting a virtual vent, it is possible to simulate the unavoidable internal leakage or relief valve pressure relief characteristics in actual hydraulic systems, thus overcoming the shortcomings of traditional impermeable compressible fluid cavity models that are too idealistic. Simultaneously, by jointly calibrating the state equation parameters and the vent parameters, the identification problem of multiple coupled nonlinear factors is solved, enabling the simulation model to more realistically reflect the dynamic response of hydraulic actuators under non-ideal operating conditions.

[0098] Third Embodiment This embodiment provides another simulation parameter iterative calibration method based on a supercomputing platform. The difference from the first embodiment is the use of multi-sensor observation variables. This embodiment not only uses the piston rod thrust as an observation variable, but also simultaneously uses the pressure or strain of the cylinder wall at the bottom of the hydraulic actuator as an additional observation variable. This multi-source data assimilation improves the robustness and uniqueness of parameter calibration. Specifically, it includes the following steps: S300, acquire the geometric model and mesh it.

[0099] Same as the first embodiment S100.

[0100] S310, Establish a compressible fluid cavity model.

[0101] A compressible fluid cavity model is established within the internal chamber of the hydraulic actuator to replace the actual hydraulic oil and drive the piston rod. The specific establishment method (determining the region based on the working mode, calculating the volume, virtual folding, placement, setting contacts, etc.) is the same as in the first embodiment S110.

[0102] S320, configure physical parameters and state equations.

[0103] Same as the first embodiment S120.

[0104] S330, construct a multi-observation variable parameter estimation algorithm.

[0105] A parameter estimation algorithm (such as ensemble Kalman filtering) is constructed, where the state variable of the algorithm is the internal gas pressure of the compressible fluid cavity model. Observations include a first observation and a second observation: the first observation is the measured thrust of the piston rod in the actual test; the second observation is the measured pressure or strain of the cylinder wall of the hydraulic actuator in the actual test. The measured pressure can be obtained by placing pressure sensors at the bottom or top of the cylinder wall of the hydraulic actuator, and the measured strain can be measured using strain gauges.

[0106] The observation matrix H of the parameter estimation algorithm is expanded into a two-dimensional column vector form: H = [h1, h2] T Where h1 is the thrust observation coefficient, used to map the state variable (internal pressure of the compressible fluid cavity model) to the thrust estimate F. e Satisfying F e =h1·P; h2 is the pressure observation coefficient, used to map the state variables to the cylinder wall pressure estimate P. e wall Or strain estimate ε e Satisfying P e wall =h2·P or ε e =h2·P.

[0107] The above mapping relationship can be predetermined based on the geometric parameters and material properties of the hydraulic actuator. As an example, for a piston area of ​​S... p The hydraulic actuator, h1=S p For a thin-walled cylindrical cylinder with an inner diameter of D, a wall thickness of t, and an elastic modulus of E, if the observed value is the circumferential strain of the cylinder wall, then h2 = D / (2tE). If the observed value is the cylinder wall pressure (e.g., the pressure inside the cylinder wall directly measured by a pressure sensor), then h2 = 1.

[0108] S340, joint iterative correction and convergence.

[0109] Using the first difference between the simulated value of the first thrust obtained from the simulation calculation and the first observed value, and the second difference between the simulated value of the cylinder wall pressure (or the simulated value of the strain) obtained from the simulation calculation and the second observed value, the undetermined parameters in the equation of state are jointly iteratively corrected.

[0110] In each iteration, the current parameters are substituted into the model and submitted to the supercomputing platform for simulation calculation, simultaneously obtaining simulated thrust and cylinder wall pressure (or strain) values. The parameter estimation algorithm considers both types of differences and updates the parameters to be determined using an extended Kalman gain matrix (whose dimension is twice the dimension of the state variables). Specifically, this gain matrix calculates the weights of the two observations on the state correction, and then weights and fuses them to obtain the final posterior state estimate.

[0111] Repeat the "Simulation Calculation → Difference Calculation → Parameter Correction" loop until both the first and second differences satisfy their respective preset convergence conditions. As an example, the thrust relative error can be set to ≤5%, and the pressure relative error to ≤3% (or the strain relative error to ≤3%). Output the values ​​of the undetermined parameters determined in the last iteration and the corresponding simulation analysis results.

[0112] The advantages of this embodiment are as follows: Traditional methods calibrate models using only single thrust data, which may result in multiple sets of parameters fitting the same thrust curve, leading to non-unique solutions. This embodiment introduces cylinder wall pressure or strain as additional observations, constraining parameters from different physical dimensions, significantly improving the uniqueness and physical accuracy of the calibration results. Simultaneously, multi-source data assimilation enhances the model's robustness to sensor noise, enabling stable parameter estimates even when some observations have high noise levels.

[0113] Fourth embodiment This embodiment provides another simulation parameter iterative calibration method based on a supercomputing platform. This embodiment combines the virtual exhaust port features of the second embodiment with the multi-sensor observation features of the third embodiment to achieve more comprehensive simulation model calibration. Specifically, it includes the following steps: S400, acquire the geometric model and mesh it.

[0114] Same as the first embodiment S100.

[0115] S410, establish a compressible fluid cavity model with a virtual exhaust port.

[0116] A compressible fluid cavity model is established within the internal chamber of the hydraulic actuator, and at least one virtual vent is set at a preset position on the compressible fluid cavity model, with its initial geometric parameters configured. This is specifically the same as S210 in the second embodiment.

[0117] S420, configured with physical parameters, exhaust characteristic curves and state equations.

[0118] Configure the physical parameters of the compressible fluid cavity model, the exhaust characteristic curve of the virtual exhaust port (including the second undetermined parameter), and the state equation describing the pressure change inside the compressible fluid cavity (including the first undetermined parameter). Same as S220 in the second embodiment.

[0119] S430, construct a multi-observation variable parameter estimation algorithm.

[0120] A parameter estimation algorithm is constructed, wherein the state variables of the algorithm include the internal gas pressure of the compressible fluid cavity model and the exhaust flow rate of the virtual exhaust port. The observations include a first observation (measured piston rod thrust) and a second observation (measured hydraulic actuator cylinder wall pressure or strain). Both the state vector and the observation vector are extended to two-dimensional or three-dimensional.

[0121] S440, Cooperative Iterative Correction and Convergence.

[0122] The parameter estimation algorithm simultaneously uses the exhaust flow rate from the virtual exhaust port as an additional state variable, and the piston rod thrust and hydraulic actuator cylinder wall pressure (or strain) as joint observations to perform coordinated iterative correction on the first undetermined parameter (state equation parameter), the second undetermined parameter (exhaust characteristic curve parameter), and other undetermined parameters in the state equation. In each iteration, the state vector and covariance matrix are updated through a prediction step, and then the Kalman gain is calculated using multidimensional observations through an update step, while simultaneously correcting the state vector and parameters. This process is repeated until the errors of all observations satisfy their respective convergence conditions. The algorithm outputs all parameter values ​​determined in the last iteration and the simulation analysis results.

[0123] The beneficial effects of this embodiment are that it combines the advantages of the second and third embodiments. On the one hand, it simulates the non-ideal characteristics of leakage or overflow in a hydraulic system through a virtual vent; on the other hand, it identifies constraint parameters from multiple physical dimensions through multi-sensor observations. The synergistic effect of these two methods ensures that the calibrated simulation model closely matches the real system in multiple aspects such as driving force transmission, leakage loss, and structural response, making it particularly suitable for high-end hydraulic system digital twin applications where high simulation accuracy is required.

[0124] This invention also provides an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being configured to perform the method described in this invention.

[0125] This invention also provides a computer-readable storage medium storing computer-executable instructions for performing the methods described in this invention.

[0126] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0127] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A simulation parameter iterative calibration method based on a supercomputing platform, characterized in that, The method includes the following steps: Obtain the geometric model of the structure to be analyzed, which includes the hydraulic actuator, and perform mesh discretization on the hydraulic actuator; A compressible fluid cavity model is established in the internal chamber of the hydraulic actuator. The compressible fluid cavity model is used to replace the actual hydraulic oil to drive the piston rod. Configure the physical parameters of the compressible fluid cavity model and the state equation describing the internal gas pressure change of the compressible fluid cavity model, the state equation containing at least one undetermined parameter; A parameter estimation algorithm is constructed, wherein the state variable of the parameter estimation algorithm is the internal gas pressure of the compressible fluid cavity model, and the observed value is the measured thrust of the piston rod in the actual test. The simulation calculation task is submitted to the supercomputing platform for execution. The difference between the simulated thrust value and the measured thrust value is used to iteratively correct the undetermined parameters in the state equation until the error between the simulated thrust value and the measured thrust value meets the preset convergence condition. The values ​​of the undetermined parameters determined in the last iteration and the corresponding simulation analysis results are then output.

2. The method according to claim 1, characterized in that, The process of establishing a compressible fluid cavity model within the internal chamber of the hydraulic actuator specifically includes: If the working mode of the hydraulic actuator is to only drive the piston rod to extend outward, then a single compressible fluid cavity model is established in the first region corresponding to the rodless cavity of the hydraulic actuator. If the working mode of the hydraulic actuator is to drive the piston rod to retract inward only, then a single compressible fluid cavity model is established in the second region corresponding to the rod cavity of the hydraulic actuator. If the hydraulic actuator operates by alternately driving the piston rod to extend outward and retract inward, then two independent compressible fluid cavity models are established in the first region and the second region, respectively.

3. The method according to claim 1, characterized in that, The step of establishing a compressible fluid cavity model in the internal chamber of the hydraulic actuator further includes: Calculate the first spatial volume of the internal chamber when the piston rod is in the initial position, and the second spatial volume when the piston rod moves to the end position; Use a shell mesh to create a compressible fluid cavity unfolded mesh model that matches the volume of the second space; The compressible fluid cavity unfolded mesh model is virtually folded along its length, so that the volume of the compressible fluid cavity unfolded mesh model shrinks to a value less than a preset value compared with the volume of the first space. The folded compressible fluid cavity unfolds into a mesh model, which is then moved and placed at the initial position of the internal chamber to obtain the compressible fluid cavity model.

4. The method according to claim 1, characterized in that, The expression for the state equation is: P = ρ0 × C 2 ×u+(γ+A×u)×E0; where P is the internal gas pressure of the compressible fluid cavity model, ρ0 is the initial gas density, u=(ρ / ρ0)-1, ρ is the gas density at the current moment, C and γ are constants of the equation of state, A is the first-order volume correction coefficient, and E0 is the initial internal energy; the parameters to be determined include C, γ, A, E0 and the initial relative volume V0.

5. The method according to claim 1, characterized in that, The parameter estimation algorithm is any one of the following: Kalman filter, extended Kalman filter, unscented Kalman filter, or ensemble Kalman filter.

6. The method according to claim 1, characterized in that, The process of performing mesh discretization on the hydraulic actuator specifically involves dividing the cylinder, piston rod, and piston of the hydraulic actuator into tetrahedral or hexahedral meshes.

7. The method according to claim 1, characterized in that, After establishing the compressible fluid cavity model, the method further includes setting the contact relationship between the mesh of the compressible fluid cavity model and the mesh of the inner wall of the cylinder of the hydraulic actuator.

8. The method according to claim 1, characterized in that, The method further includes: updating the compressible fluid cavity model using the values ​​of the undetermined parameters determined in the last iteration, performing the final simulation calculation, and generating the stress distribution and deformation results of the hydraulic actuator and the connecting base of the hydraulic actuator in a complete working cycle.

9. An electronic device, characterized in that, Including processor and memory; The processor executes the steps of the method as described in any one of claims 1 to 8 by invoking programs or instructions stored in the memory.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a program or instructions that cause a computer to perform the steps of the method as described in any one of claims 1 to 8.

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