A low-thermal-deformation fluctuation structure optimization method and system based on joint simulation
By constructing a thermal deformation compensation combined structure and utilizing a joint simulation optimization algorithm, the problem of low optimization efficiency of design parameters for low thermal deformation wave structures was solved, achieving efficient optimization of structural thermal stability and meeting the ultra-high precision requirements of space gravitational wave detection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-03-19
- Publication Date
- 2026-06-12
AI Technical Summary
How to efficiently optimize the design parameters of low-thermal-deformation wave structures to meet the ultra-high precision requirements of applications such as space gravitational wave detection.
By using a co-simulation approach and combining materials with different coefficients of thermal expansion, a thermal deformation compensation structure is constructed. Then, by using parametric modeling, multiphysics simulation and optimization algorithms, a multidimensional design space is automatically searched and the design parameters are optimized to minimize thermal deformation fluctuations.
It automates the design of low-thermal-deformation wave structures, improves optimization efficiency, meets the requirements for ultra-high precision thermal stability, and is suitable for scenarios such as space gravitational wave detection.
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Abstract
Description
Technical Field
[0001] This application belongs to the field of design and analysis technology of elastic mechanical structures in solid mechanics, and more specifically, relates to a method and system for optimizing low thermal deformation wave structures based on co-simulation. Background Technology
[0002] In cutting-edge scientific missions such as space gravitational wave detection, scientific payloads form the core of the entire detection system, mainly including inertial reference systems and laser interferometry systems. Key optomechanical units such as telescopes, optical platforms, and inertial sensors are integrated into a unified optomechanical system through an optomechanical support structure. Among these components, the support structure not only constitutes the mechanical framework of the optomechanical system but also serves as the path for the transmission of mechanical forces.
[0003] The on-orbit operating environment is complex, and periodic temperature changes cause deformation of materials and structures, known as thermally induced deformation. When the structure is in a thermal environment with fluctuating temperatures, mechanical components will experience corresponding thermal deformation fluctuations. To ensure the ultra-high accuracy in the mHz frequency band required for space gravitational wave detection, the support structure design must guarantee ultra-high dimensional stability in the on-orbit state, and its own thermally induced deformation stability is one of the key factors determining the system performance.
[0004] Currently, there are two main technical approaches to mitigate heat-induced deformation: one is to develop new materials with higher thermal stability and a coefficient of thermal expansion closer to zero through advancements in materials science; the other is to develop structural design systems with ultra-high stability. Thermal compensation design is one of the key means to achieve structural ultra-stability. Its core idea is to cleverly utilize the difference in the coefficients of thermal expansion between two or more materials, coupling them through welding, bonding, or mechanical connections to form a composite structure.
[0005] When this composite structure is heated, the different materials expand in different directions or with different magnitudes. Through precise structural design, these deformations can be made to cancel each other out at the ends of the structure, thereby significantly reducing or even approaching zero overall thermal expansion. Therefore, this composite structure is also called a low thermal deformation fluctuation structure.
[0006] How to efficiently optimize the design parameters of low thermal deformation fluctuation structures is a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0007] In view of the shortcomings of the prior art, the purpose of this application is to efficiently optimize the design parameters of low thermal deformation fluctuation structures.
[0008] To achieve the above objectives, in a first aspect, this application provides a method for optimizing low-thermal-deformation-fluctuation structures based on co-simulation, the method comprising: A composite structure for thermal deformation compensation is constructed based on a combination of materials with different coefficients of thermal expansion. Based on the geometric characteristics of the thermal deformation compensation composite structure, the initial design parameters are determined. Continue to perform the following design parameter optimization operations until the optimization termination condition is met (the thermal deformation fluctuation amplitude is less than the convergence tolerance or the maximum number of iterations is reached) to obtain the optimal design parameters that minimize the thermal deformation fluctuation amplitude. Design parameter optimization operations include: Based on design parameters, a parametric geometric model is constructed by parametrically modeling and assigning values to the thermal deformation compensation composite structure in 3D CAD (Computer-Aided Design) software. The design parameters used in the first construction of the parametric geometric model are the initial design parameters, and the design parameters used in subsequent constructions of the parametric geometric model are the updated design parameters provided by the optimization algorithm. Based on the simulation boundary conditions set by the parametric geometric model and thermal environment analysis, frequency domain thermal deformation analysis is performed using multiphysics simulation software to obtain the thermal deformation fluctuation amplitude at the compensation end. The end of the thermal deformation compensation combination structure connected to the object to be installed is the compensation end. Based on the objective function, the optimization algorithm determines whether the optimization termination condition is met. If so, the optimal design parameters are determined; otherwise, the design parameters are updated. The objective function is a function that minimizes the amplitude of thermal deformation fluctuation.
[0009] The objective function described above is illustrated here. The objective function value is the amplitude of thermal deformation fluctuation of the compensation end in the target direction, calculated by the simulation module. By minimizing this amplitude as the optimization objective, the net displacement of the installed object in the target direction can be made close to zero, thereby significantly reducing or even approaching zero the overall thermal expansion effect.
[0010] Understandably, this method integrates parametric modeling, multiphysics simulation, and (gradient-free) optimization algorithms to establish a closed-loop optimization process. In each iteration, the optimization algorithm determines the next optimization direction based on the current simulation results and historical simulation data, generates a new set of design parameters, and calls 3D CAD software to update the parametric geometric model. Subsequently, multiphysics simulation software is called to perform frequency domain thermal deformation analysis on the new model (the updated parametric geometric model) to obtain the thermal deformation results. This process is repeated cyclically, automatically searching the multidimensional design space until the thermal deformation amplitude is less than the set convergence tolerance or the maximum number of iterations is reached, thereby automatically determining the optimal combination of structural design parameters to minimize the thermally induced deformation of the structure. This mechanism effectively overcomes the shortcomings of traditional manual iterative design, such as low efficiency and difficulty in achieving optimal performance, and achieves efficient optimization of design parameters for structures with low thermal deformation fluctuations.
[0011] In one possible implementation, the thermal deformation compensation composite structure is constructed by combining a compensated structure and a thermal compensation structure, wherein the coefficient of thermal expansion of the material used in the compensated structure is lower than that of the material used in the thermal compensation structure.
[0012] In one possible implementation, the initial design parameters include and , The length of the structure being compensated in the target direction. is the length of the thermal compensation structure in the target direction, which is the positive expansion direction of the compensated structure.
[0013] In one possible implementation, the optimization termination condition includes: the thermal deformation fluctuation amplitude being less than the convergence tolerance or the maximum number of iterations being reached.
[0014] In one possible implementation, the above frequency domain thermal deformation analysis includes: Based on temperature fluctuation values The amplitude of thermal deformation fluctuation at the compensation end in the target direction can be obtained by simultaneously solving the following formulas. (amplitude) ; ; ; ; in, Indicates thermal deformation fluctuation, Indicates the coefficient of thermal expansion of a material. Represents the stress tensor. This represents the elastic stiffness tensor. This represents the total strain tensor. It is the Hamiltonian operator. Represents the displacement tensor. Indicates the excitation frequency. Indicates the density of the material. External force per unit volume.
[0015] Understandably, based on temperature fluctuation values The resulting thermal expansion effect is expressed by the formula Calculate thermal deformation fluctuations Subsequently, according to the theory of elasticity, the total strain tensor With displacement tensor Satisfy geometric equations stress tensor Then by equation The decision is made; finally, elasticity boundary conditions are introduced to solve the frequency domain form of the structural dynamics equations (i.e., the stress equations). By solving the above system of equations simultaneously, the amplitude of thermal deformation fluctuation at any point on the structure (including the compensation end) in the target direction can be obtained.
[0016] In one possible implementation, the temperature fluctuation value It is determined by the following formula: ; in, This indicates the specific heat capacity of a material under constant pressure. Indicates thermal conductivity, This represents the density fluctuation value of the heat source.
[0017] In one possible implementation, the optimization algorithm is specifically a gradient-free optimization algorithm.
[0018] In one possible implementation, the optimal solution corresponding to the lowest frequency of the preset design frequency band is taken as the global optimal solution.
[0019] Understandably, the thermal response of a structure exhibits typical low-pass filtering characteristics. For applications requiring minimization of thermal deformation across a specific frequency band (e.g., the 0.1 mHz–1 Hz band for space gravitational wave detection) rather than at a single frequency point, the thermal deformation at the lowest frequency is typically the most significant across the entire band. Therefore, using the lowest frequency within this band as the reference frequency for perturbation design optimization, and taking the optimal solution at that lowest frequency as the global optimal solution, can effectively ensure that thermal deformation is suppressed to the greatest extent across the entire band of interest, thereby meeting the requirements for ultra-high dimensional stability.
[0020] Secondly, this application provides a low-thermal-deformation-fluctuation structural optimization system based on co-simulation, the system comprising: The thermal deformation compensation combined structure construction module is used to construct thermal deformation compensation combined structures based on combinations of materials with different thermal expansion coefficients. The initial design parameter determination module is used to determine the initial design parameters based on the geometric features of the thermal deformation compensation composite structure. The optimization scheduling module is used to continuously schedule the three-dimensional parametric model design module, thermal deformation simulation analysis module, and optimization integration module until the optimization termination condition is met, so as to obtain the optimal design parameters that minimize the thermal deformation fluctuation amplitude. The 3D parametric model design module is used to construct a parametric geometric model based on design parameters by parametrically modeling and assigning values to the thermal deformation compensation combination structure in 3D CAD software. The design parameters used for the first construction of the parametric geometric model are the initial design parameters, and the design parameters used for subsequent constructions of the parametric geometric model are the updated design parameters provided by the optimization algorithm. The thermal deformation simulation analysis module is used to perform frequency domain thermal deformation analysis based on the simulation boundary conditions set by the parametric geometric model and thermal environment analysis, and to obtain the thermal deformation fluctuation amplitude of the compensation end. The end of the thermal deformation compensation combination structure connected to the object to be installed is the compensation end. The optimization integration module is used to determine whether the optimization termination condition is met based on the objective function and through the optimization algorithm. If it is met, the optimal design parameters are determined; otherwise, the design parameters are updated. The objective function is a function that minimizes the amplitude of thermal deformation fluctuation.
[0021] Thirdly, this application provides an electronic device, including: a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions; the one or more processors invoke the computer instructions to cause the electronic device to perform the method described in the first aspect or any possible implementation of the first aspect.
[0022] It is understood that the beneficial effects of the second and third aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.
[0023] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) Design automation and efficiency improvement: By integrating parametric modeling, multiphysics simulation and optimization algorithms, a closed-loop automated process from design and analysis to optimization is realized, which effectively improves optimization efficiency.
[0024] (2) Performance optimization and high precision: By using optimization algorithms to automatically search the multi-dimensional design space, the optimal parameter combination that is difficult to find in traditional empirical design can be found, thereby maximizing the thermal stability of the structure and meeting the ultra-high precision requirements of application scenarios such as space gravitational wave detection. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of a thermal deformation compensation composite structure; Figure 2 This is a flowchart illustrating the low thermal deformation fluctuation structure optimization method based on co-simulation provided in the embodiments of this application; Figure 3This is a schematic diagram of the structure of the low thermal deformation fluctuation structure optimization system based on co-simulation provided in the embodiments of this application; Figure 4 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application.
[0026] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 11 is the mounting platform; 12 is the compensation structure; 13 is the thermal compensation structure; 14 is the object to be installed. Detailed Implementation
[0027] To facilitate a clearer understanding of the various embodiments of this application, some relevant background knowledge will be introduced as follows.
[0028] Figure 1 This is a schematic diagram of a thermal deformation compensation composite structure, such as... Figure 1 As shown, a typical thermal deformation compensation assembly mainly includes a compensated structure 12 (e.g., a slender rod made of a material with a low coefficient of thermal expansion) and a thermal compensation structure 13 (e.g., a compensation section made of a material with a high coefficient of thermal expansion). One end of the compensated structure 12 is fixed to the mounting platform 11, and the other end is connected to the thermal compensation structure 13, while the object to be mounted 14 is mounted at the end of the thermal compensation structure 13. When the whole assembly is heated, the compensated structure 12 expands in the positive direction along the X-axis, while the thermal compensation structure 13 is designed to produce a displacement component in the negative direction along the X-axis. The length of the compensated structure 12... And the key dimensions of the thermal compensation structure 13 (such as length) By employing reasonable parametric design, the net displacement of the installed object 14 in the X-axis direction can be made close to zero. To efficiently achieve this precise design, frequency domain thermal deformation simulation analysis of the structure can be combined with modern optimization algorithms to realize automated optimization design of the compensation structure.
[0029] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0030] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.
[0031] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.
[0032] The embodiments of this application are described below with reference to the accompanying drawings.
[0033] In one embodiment, this application provides a method for optimizing low-thermal-deformation-fluctuation structures based on co-simulation, such as... Figure 2 As shown, it includes the following steps one through six.
[0034] Step 1: Structure and Material Definition. Based on the design requirements of the existing structure and combined with the physical properties of the selected materials (including but not limited to specific heat capacity, material density, thermal conductivity, and coefficient of thermal expansion), a thermal deformation compensation composite structure based on a combination of materials with different coefficients of thermal expansion is constructed (constructed by combining the compensated structure and the thermal compensation structure). In this structure, the object 14 to be installed and kept in a stable position is fixed at the compensation end of the thermal compensation structure 13.
[0035] Step 2: Optimize Parameter Initialization. Set key control variables for the optimization process, including the maximum number of optimization iterations, the values of initial design parameters, and convergence tolerance used to determine whether the optimization is complete.
[0036] Step 3: Parametric Modeling. Construct a parametric geometric model of the thermal deformation compensation composite structure in 3D CAD software, incorporating the initial design parameters set in Step 2 (such as...). Figure 1 In , The geometric model is assigned key dimensions (such as scalar dimensions) to generate the corresponding initial geometric model.
[0037] Step 4: Thermal Deformation Simulation Analysis. Based on the on-orbit thermal environment analysis or temperature sensor measurement data, set the thermal boundary conditions for the simulation (e.g., using the temperature data measured by the sensor as the specified temperature boundary condition on a specific surface of the model, or using the measured heat flux data as the heat flux boundary condition). Based on the given elastic boundary conditions of the structure (including displacement, force, or mixed boundary conditions), conduct frequency domain thermal deformation analysis on the geometric model under the current design parameters using multiphysics simulation software. Obtain the thermal deformation fluctuation amplitude at the location of the installed object 14, and store this result in variables as the objective function value of the current design.
[0038] Step 5: Optimization Iteration and Judgment. The thermal deformation fluctuation amplitude obtained in Step 4 is input into the optimization algorithm for evaluation. The optimization algorithm determines whether the current design objective function value meets the preset design target (e.g., less than a certain threshold), or whether the number of iterations has reached the preset maximum value. If the judgment result is "yes", the process ends and proceeds to Step 6; if the judgment result is "no", the optimization algorithm determines the next optimization direction based on the current simulation results and historical simulation data, generates a new set of design parameters, and passes the updated design parameters back to the parameterized geometric model in Step 3, then returns to Step 4 to continue execution, forming a closed-loop iteration.
[0039] Step Six: Output Results. Output the current optimal combination of design parameters and the corresponding minimum thermal deformation fluctuation value, end the iteration process, and obtain the final optimized design.
[0040] The following is based on Figure 1 Taking the structure shown as an example, the specific steps of this method will be illustrated.
[0041] Steps one through three: Parametric modeling and initialization.
[0042] First, create a geometric model of the thermal deformation compensation composite structure in 3D CAD software (such as SOLIDWORKS, UG, or CATIA). Then, define key dimensions, such as... Figure 1 The length of the compensated structure 12 shown and the length of the thermal compensation structure 13 , defined as a parameter that can be driven by an external program. The compensated structure 12 is made of stainless steel, and the thermal compensation structure 13 is made of aluminum alloy.
[0043] Setting optimization parameters: The maximum number of iterations in the optimization process is limited by the simulation calculation time and the number of control variables. To ensure computational efficiency, it is usually set to no more than 300 iterations. The convergence tolerance of the optimization process should match the design machining accuracy; for example, under the International System of Units (SI), if the machining accuracy requirement is at the millimeter level, the optimization convergence tolerance should be at least one order of magnitude lower than the machining accuracy, which can be set to 0.0001m.
[0044] Step 4: Theory and Implementation of Thermal Deformation Simulation.
[0045] Import the parametric model into multiphysics simulation software. Multiphysics simulation software is capable of three-dimensional multiphysics coupled simulation, especially software that simultaneously performs thermal and elasticity simulations, such as COMSOL or ANSYS. The simulation process is based on frequency domain thermo-structural coupling analysis, and its core governing equations are as follows.
[0046] The thermal deformation simulation process is based on frequency domain analysis. The solution... Assumed as static temperature Superimposed with a small harmonic fluctuation: (1); in, It is the instantaneous temperature. It is the static temperature. It is the temperature fluctuation value (which is a complex number). It is the excitation frequency. It is the imaginary unit. It's time.
[0047] Substituting equation (1) into the heat conduction equation and performing a Laplace transform, we get: (1a); in, It is the imaginary unit. It is the density of the material. It is the specific heat capacity of the material under constant pressure. It is thermal conductivity. It is the density of the heat source. It is the density fluctuation value of the heat source. It is the excitation frequency.
[0048] By separating the fluctuation term, we obtain the frequency domain heat conduction equation satisfied by the frequency domain temperature fluctuation and the heat source fluctuation: (2); in, It is the Hamiltonian operator.
[0049] The relationship between deformation fluctuations and temperature fluctuations is as follows: temperature fluctuations It will cause thermal deformation fluctuations : (3); in, It is the coefficient of thermal expansion of the material. It is a thermal deformation fluctuation.
[0050] According to the theory of elasticity, the stress tensor and and The relationship is: (4); in, It is the stress tensor. It is the elastic stiffness tensor, symbol " The '' operator represents the double contraction operator for fourth-order and second-order tensors. This represents the total strain tensor.
[0051] With displacement tensor The relationship is: (5); in, It is the displacement tensor.
[0052] Finally, by introducing elasticity boundary conditions, solving the frequency domain form of the structural dynamics equations (i.e., the stress equations) yields the frequency domain thermal deformation: (6); in, It is the external force per unit volume. By solving the above coupled equations (2)-(6), the thermal deformation fluctuation at any point on the structure can be obtained.
[0053] Steps five and six: Optimize integration and execution.
[0054] The optimization integration module is implemented using a computational and visualization software platform (such as MATLAB). This module connects to simulation and CAD software via an interface program (such as LiveLink for MATLAB). The optimization algorithm is built in MATLAB, and the entire optimization process is controlled. Since thermal deformation simulations typically do not provide analytical gradients for design dimensions, gradient-free optimization algorithms should be selected, including but not limited to genetic algorithms, particle swarm optimization, BobbyQA, and Nelder-Mead algorithms. The input to the optimization algorithm is a vector of design variables (e.g., […]). , The objective function value is the amplitude of thermal deformation fluctuation at the compensation end in the target direction, calculated by the simulation module. The output of the optimization algorithm is a set of updated design variables, which are then sent to the CAD module to update the model.
[0055] In each iteration, MATLAB calls CAD software to update the model, then calls simulation software to calculate the new model, obtain the thermal deformation results, and determines the next set of design parameters based on these results. This process is repeated until the thermal deformation amplitude is less than the set convergence tolerance or the maximum number of iterations is reached, finally outputting the optimal combination of design parameters. , ].
[0056] Regarding the selection of optimization frequency: For applications requiring focus on a specific frequency band (e.g., 0.1 mHz for gravitational wave detection) Instead of minimizing thermal deformation at a single frequency point (e.g., 0.1 MHz), this application proposes using the lowest frequency within this band as the reference frequency for perturbation design optimization. The rationale is that the thermal response of a structure exhibits typical low-pass filtering characteristics. Therefore, in scenarios such as gravitational wave detection where low-frequency stability is critical, the thermal deformation of the structure at the lowest frequency is typically the most significant across the entire frequency band. The optimal solution corresponding to this lowest frequency (e.g., 0.1 MHz) is taken as the global optimal solution.
[0057] In summary, this application designs a thermal deformation compensation composite structure by utilizing the difference in thermal expansion coefficients between different materials; it obtains simulation boundary conditions through thermal environment analysis or sensor temperature data and performs frequency domain thermal deformation simulation to determine the thermal deformation fluctuation value at the compensation end; it constructs a gradient-free optimization algorithm in programming software and uses the interface between the programming software and simulation software to transfer data; it parameterizes the thermal deformation compensation composite structure, selects key dimensions as design variables, and uses minimizing the thermal deformation amplitude at the compensation end as the objective function passed to the optimization algorithm; it runs the entire optimization process, automatically searching for the optimal parameter combination to minimize thermal deformation and obtain the optimal thermal deformation compensation composite structure dimensions. This application automates the design of low thermal deformation fluctuation structures, effectively improving the design efficiency and thermal stability of low thermal deformation fluctuation structures.
[0058] The co-simulation-based low-thermal-deformation-fluctuation structure optimization system provided in this application is described below. The co-simulation-based low-thermal-deformation-fluctuation structure optimization system described below can be referred to in correspondence with the co-simulation-based low-thermal-deformation-fluctuation structure optimization method described above.
[0059] In one embodiment, this application provides a co-simulation-based low thermal deformation fluctuation structure optimization system, such as... Figure 3 As shown, the system includes: a thermal deformation compensation combined structure construction module 21, an initial design parameter determination module 22, an optimization scheduling module 23, a three-dimensional parametric model design module 24, a thermal deformation simulation analysis module 25, and an optimization integration module 26.
[0060] The thermal deformation compensation combined structure construction module 21 is used to construct a thermal deformation compensation combined structure based on the combination of materials with different thermal expansion coefficients. The initial design parameter determination module 22 is used to determine the initial design parameters based on the geometric features of the thermal deformation compensation combined structure. The optimization scheduling module 23 is used to continuously schedule the three-dimensional parametric model design module, thermal deformation simulation analysis module and optimization integration module until the optimization termination condition is met, so as to obtain the optimal design parameters that minimize the thermal deformation fluctuation amplitude. The 3D parametric model design module 24 is used to construct a parametric geometric model based on design parameters by parametrically modeling and assigning values to the thermal deformation compensation combination structure in 3D CAD software. The design parameters used for the first construction of the parametric geometric model are the initial design parameters, and the design parameters used for subsequent constructions of the parametric geometric model are the updated design parameters provided by the optimization algorithm. The thermal deformation simulation analysis module 25 is used to perform frequency domain thermal deformation analysis based on the simulation boundary conditions set by the parametric geometric model and thermal environment analysis, and to obtain the thermal deformation fluctuation amplitude of the compensation end. The end of the thermal deformation compensation combination structure connected to the object to be installed is the compensation end. The optimization integration module 26 is used to determine whether the optimization termination condition is met based on the objective function and through the optimization algorithm. If it is, the optimal design parameters are determined; otherwise, the design parameters are updated. The objective function is a function with the goal of minimizing the amplitude of thermal deformation fluctuation.
[0061] Understandably, the thermal deformation simulation analysis module can perform simulation calculations for each frequency point within the frequency band to obtain the thermal deformation fluctuations at the installation location of the compensated structure or a specified test location. The optimization integration module is used to build optimization algorithms and control the entire optimization process.
[0062] For example, the compensated structure is made of a material with a low coefficient of thermal expansion, such as titanium alloy, stainless steel, or other structures with low overall thermal expansion performance; the thermal compensation structure is made of a material with a high coefficient of thermal expansion, such as aluminum alloy, copper alloy, or other structures with high overall thermal expansion performance.
[0063] For example, the thermal deformation simulation analysis module has the ability to interact and transmit data with the three-dimensional parametric model design module.
[0064] For example, the optimization algorithm is a gradient-free optimization algorithm.
[0065] For example, for minimizing thermal deformation within a frequency band rather than a single frequency point, the lowest frequency within the band is used as the reference frequency for the perturbation design, and the optimal solution corresponding to the lowest frequency of the design band is used as the global optimal solution.
[0066] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.
[0067] It should be understood that the above system is used to execute the methods in the above embodiments. The corresponding program modules in the system are similar in implementation principle and technical effect to those described in the above methods. The working process of the system can be referred to the corresponding process in the above methods, and will not be repeated here.
[0068] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 4 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.
[0069] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.
[0070] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.
[0071] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.
[0072] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.
[0073] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.
[0074] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).
[0075] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.
[0076] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. A method for optimizing low-thermal-deformation-fluctuation structures based on co-simulation, characterized in that, include: A thermal deformation compensation composite structure is constructed based on material combinations with different coefficients of thermal expansion. Based on the geometric characteristics of the thermal deformation compensation composite structure, the initial design parameters are determined. Continue to perform the following design parameter optimization operations until the optimization termination condition is met in order to obtain the optimal design parameters that minimize the amplitude of thermal deformation fluctuation; Design parameter optimization operations include: Based on the design parameters, a parametric geometric model is constructed by parametrically modeling and assigning values to the thermal deformation compensation composite structure in 3D CAD software. The design parameters used in the first construction of the parametric geometric model are the initial design parameters, and the design parameters used in subsequent constructions of the parametric geometric model are the updated design parameters provided by the optimization algorithm. Based on the simulation boundary conditions set by the parametric geometric model and thermal environment analysis, frequency domain thermal deformation analysis is performed using multiphysics simulation software to obtain the thermal deformation fluctuation amplitude at the compensation end. The end of the thermal deformation compensation combination structure connected to the object to be installed is the compensation end. Based on the objective function, the optimization algorithm determines whether the optimization termination condition is met. If so, the optimal design parameters are determined; otherwise, the design parameters are updated. The objective function is a function that minimizes the amplitude of thermal deformation fluctuation.
2. The low-thermal-deformation-fluctuation structure optimization method based on co-simulation according to claim 1, characterized in that, The thermal deformation compensation composite structure is constructed by combining the compensated structure and the thermal compensation structure. The coefficient of thermal expansion of the material used in the compensated structure is lower than that of the material used in the thermal compensation structure.
3. The low-thermal-deformation-fluctuation structure optimization method based on co-simulation according to claim 2, characterized in that, Initial design parameters include and , The length of the structure being compensated in the target direction. is the length of the thermal compensation structure in the target direction, which is the positive expansion direction of the compensated structure.
4. The low thermal deformation fluctuation structure optimization method based on co-simulation according to claim 1, characterized in that, The optimization termination conditions include: the thermal deformation fluctuation amplitude is less than the convergence tolerance or the maximum number of iterations is reached.
5. The low-thermal-deformation-fluctuation structure optimization method based on co-simulation according to claim 1, characterized in that, The frequency domain thermal deformation analysis includes: Based on temperature fluctuation values The amplitude of thermal deformation fluctuation at the compensation end in the target direction can be obtained by simultaneously solving the following formulas: ； ； ； ； in, Indicates thermal deformation fluctuation, Indicates the coefficient of thermal expansion of a material. Represents the stress tensor. This represents the elastic stiffness tensor. This represents the total strain tensor. It is the Hamiltonian operator. Represents the displacement tensor. Indicates the excitation frequency. Indicates the density of the material. External force per unit volume.
6. The low-thermal-deformation-fluctuation structure optimization method based on co-simulation according to claim 5, characterized in that, Temperature fluctuation value It is determined by the following formula: ； in, This indicates the specific heat capacity of a material under constant pressure. Indicates thermal conductivity, This represents the density fluctuation value of the heat source.
7. The low-thermal-deformation-fluctuation structure optimization method based on co-simulation according to claim 1, characterized in that, The optimization algorithm is specifically a gradient-free optimization algorithm.
8. The low-thermal-deformation-fluctuation structure optimization method based on co-simulation according to claim 1, characterized in that, Also includes: The optimal solution corresponding to the lowest frequency of the preset design frequency band is taken as the global optimal solution.
9. A low-thermal-deformation fluctuation structure optimization system based on co-simulation, characterized in that, include: The thermal deformation compensation combined structure construction module is used to construct thermal deformation compensation combined structures based on combinations of materials with different thermal expansion coefficients. The initial design parameter determination module is used to determine the initial design parameters based on the geometric features of the thermal deformation compensation composite structure. The optimization scheduling module is used to continuously schedule the three-dimensional parametric model design module, thermal deformation simulation analysis module, and optimization integration module until the optimization termination condition is met, so as to obtain the optimal design parameters that minimize the thermal deformation fluctuation amplitude. The 3D parametric model design module is used to construct a parametric geometric model based on design parameters by parametrically modeling and assigning values to the thermal deformation compensation combination structure in 3D CAD software. The design parameters used for the first construction of the parametric geometric model are the initial design parameters, and the design parameters used for subsequent constructions of the parametric geometric model are the updated design parameters provided by the optimization algorithm. The thermal deformation simulation analysis module is used to perform frequency domain thermal deformation analysis based on the simulation boundary conditions set by the parametric geometric model and thermal environment analysis, and to obtain the thermal deformation fluctuation amplitude of the compensation end. The end of the thermal deformation compensation combination structure connected to the object to be installed is the compensation end. The optimization integration module is used to determine whether the optimization termination condition is met based on the objective function and through the optimization algorithm. If it is met, the optimal design parameters are determined; otherwise, the design parameters are updated. The objective function is a function that aims to minimize the amplitude of thermal deformation fluctuations.
10. An electronic device, characterized in that, include: Memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-8.