Thermal coupling structure topological optimization method and device capable of dynamically and adaptively aggregating hotspot constraints
By employing the Sigmoid function and chain rule to calculate the dynamic soft weighting factor of sensitivity in thermo-coupled structure optimization, the slow convergence of the traditional P-norm method and the gradient inconsistency problem of the ACS method are solved, achieving efficient and stable hotspot elimination.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-18
- Publication Date
- 2026-03-27
AI Technical Summary
In existing thermally coupled structure optimization, the traditional P-norm method leads to slow convergence and insufficient accuracy, while the ACS method suffers from gradient inconsistency, causing oscillations and making it difficult to effectively eliminate hot spots.
A dynamic soft weighting factor is constructed using the Sigmoid function, and the sensitivity is calculated using the chain rule. The P-norm aggregation constraint is dynamically adjusted, and the thermo-mechanical coupling structure is optimized by combining it with the SIMP material interpolation model.
It improves convergence efficiency and accuracy, enables intelligent focusing on hotspots, avoids oscillations, and enhances the optimization stability and accuracy of the thermo-coupling structure.
Smart Images
Figure CN121747792A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of material structure optimization, and more specifically, relates to a method and device for dynamic adaptive aggregation hotspot constraint-based thermo-coupling structural topology optimization. Background Technology
[0002] Topology optimization is a key technique in structural design that finds the optimal distribution of materials under given constraints. With increasing engineering complexity, topology optimization has been widely applied to multiphysics coupling problems, particularly thermo-coupled systems such as aero-engines and electronic chip heat sinks.
[0003] In these thermo-mechanical coupling problems, in addition to global constraints such as material volume, the design is often limited by a large number of local constraints, such as the stress, displacement, or temperature at any point in the structure not exceeding a certain threshold. Hotspot constraints are a typical challenge. Directly handling thousands of local constraints is computationally infeasible; therefore, aggregation methods are widely used to approximate a large number of local constraints into a single or a few global constraints.
[0004] The P-norm aggregation method is one of the most commonly used techniques. It leverages the property of the P-norm: when the P-value is sufficiently large, the P-norm value approaches the maximum value among all local constraints. However, traditional P-norm methods have inherent flaws. A prominent problem is that the algorithm design aggregates constraints across all regions of the design domain to the same degree. This design leads to the aggregation of numerous small constraint values in non-critical regions during the early stages of optimization, interfering with the optimizer's identification of truly hot spots and resulting in slow convergence. Furthermore, in the later stages of optimization, it may become overly sensitive to all regions close to the threshold, hindering the accurate elimination of the most severe peaks.
[0005] To address this issue, the Adaptive Constraint Scaling P-Norm (ACS) method was proposed. The ACS method calibrates the P-norm value relative to the true maximum value using an external scaling factor, but it neglects the effect of this factor when calculating sensitivity, leading to a theoretical inconsistency between the constraint value and its gradient. This inconsistency can cause oscillations in the optimization process, or even convergence to a suboptimal solution. Summary of the Invention
[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method and apparatus for dynamically and adaptively optimizing the topology of thermo-coupled structures with aggregated hotspot constraints. It aims to solve the problems of slow convergence and insufficient accuracy of existing optimization schemes for thermo-coupled structures.
[0007] To achieve the above objectives, according to one aspect of the present invention, a method for topology optimization of thermo-coupled structures capable of dynamically and adaptively aggregating hotspot constraints is provided, comprising the following steps: Step 1: Based on the thermo-mechanical coupling structure to be optimized, establish the governing equations for thermal conduction analysis and linear elastic thermal expansion analysis. Based on the governing equations, use a material interpolation model to characterize the relationship between unit material properties and design variables. Step 2: Based on the relationship between unit material properties and design variables, construct a topology optimization model with structural flexibility as the objective function and local volume and local temperature hotspots as constraints. Step 3: Use a dynamic soft weighting factor with a sigmoid function. Construct a weighted P-norm aggregation constraint This is used to aggregate multiple local temperature hotspot constraints into a single global constraint; wherein, the dynamic soft weighting factor It is defined based on the local temperature hotspot constraint in the topology optimization model; Step four: Based on the objective function and the P-norm aggregation constraint... The topology optimization model is iteratively optimized relative to the sensitivity of the design variables to obtain the optimal topology; wherein, the dynamic soft weighting factor... The enhancement magnitude of the hotspot weight and the proportion of hotspot threshold increase linearly with the progress of iterative optimization.
[0008] Furthermore, using the SIMP material interpolation model, the elastic modulus of the element is... and thermal conductivity With design variables Related:
[0009] In the formula, The elastic modulus of the element. The thermal conductivity of the unit cell is . For design variables, and As a penalty factor; The elastic modulus of a solid material; The elastic modulus of the pores is used to prevent the stiffness matrix from becoming singular; The thermal conductivity of the solid material; is the thermal conductivity of the pores.
[0010] Furthermore, the mathematical expression of the topology optimization model is:
[0011] In the formula, Let be the objective function. The total integral of the material. It is the total number of local constraints. It is the normalized temperature; It is the displacement vector; Here is the stiffness matrix; It represents the volume fraction of the material. Let this be the initial volume of the design domain; For the first The actual temperature of each node; This is the critical temperature threshold, i.e., the highest permissible temperature.
[0012] Furthermore, the dynamic soft weighting factor The expression is:
[0013] in, The extent to which the weight of hot topics is increased. For the first The normalized temperature of each node, The transition slope of the Sigmoid function. This represents the percentage of hotspot thresholds.
[0014] Furthermore, P-norm aggregation constraints The expression is:
[0015] in, For the P-norm parameter, It is a dynamic soft weighting factor. For the first The normalized temperature of each node, This represents the summation over all relevant nodes; That is, the original A global approximation of a local hotspot constraint.
[0016] Furthermore, the objective function and the P-norm aggregation constraint are calculated using the chain rule. Sensitivity relative to design variables.
[0017] Furthermore, the enhancement of hotspot weights increases linearly from 1 to 5 as the iteration optimization progresses.
[0018] Furthermore, the proportion of hotspot thresholds increased linearly from 0.7 to 0.9 as the iteration optimization progressed.
[0019] The present invention also provides a thermally coupled structure topology optimization system capable of dynamically and adaptively aggregating hotspot constraints. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the thermally coupled structure topology optimization method capable of dynamically and adaptively aggregating hotspot constraints as described above.
[0020] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the thermally coupled structural topology optimization method described above, which can dynamically and adaptively aggregate hotspot constraints.
[0021] In summary, compared with the prior art, the thermally coupled structural topology optimization method and device with dynamic adaptive aggregation hotspot constraints provided by the present invention have the following advantages: 1. This invention employs a dynamic soft weighting factor based on a sigmoid function. Construct a weighted P-norm aggregation constraint The sensitivity calculation adopts the chain rule, which ensures the mathematical consistency between the aggregation constraint function and its gradient, fundamentally avoiding the convergence oscillations and instabilities that may be caused by heuristic methods such as ACS, and improving accuracy and efficiency.
[0022] 2. Through dynamic adjustment and Parameters, this method is used in the early stages of optimization (when they are relatively small) (Value) can broadly identify potential hotspots and achieve pre-processing of potential risks; in the later stages of optimization (higher value) Value and higher The P-norm can precisely focus on the most severe critical hotspots, achieving efficient elimination. This strategy is far superior to the traditional static unified processing method of P-norm, improving convergence efficiency and accuracy, and realizing dynamic intelligent focusing.
[0023] 3. Due to its intelligent focusing strategy and theoretical robustness, this method demonstrates better convergence performance and stronger hotspot elimination ability in numerical examples compared to the standard P-norm and ACS methods, and exhibits better robustness. Attached Figure Description
[0024] Figure 1 This is a flowchart of a thermally coupled structural topology optimization method that can dynamically and adaptively aggregate hotspot constraints, provided by an embodiment of the present invention. Figure 2 This is the dynamic hotspot weighting function of the present invention. Conceptual diagram; Figure 3This is a schematic diagram of the design domain, boundary conditions, and loads of a cantilever beam provided in an embodiment of the present invention; Figure 4 This is the topology diagram and corresponding temperature field distribution diagram obtained after optimization using the DAW-PN method in this embodiment of the invention; Figure 5 This is a comparison chart of the optimized convergence curves (including compliance, maximum temperature, and dynamic parameter changes) of the DAW-PN method with the standard P-Norm and ACS-P-Norm methods in this embodiment of the invention. Detailed Implementation
[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0026] This invention provides a topology optimization method for thermo-mechanically coupled structures that can dynamically and adaptively aggregate hotspot constraints. The topology optimization method solves the problems of slow convergence and insufficient accuracy caused by the traditional P-norm method, which aggregates all regions to the same degree. It also overcomes the gradient inconsistency and convergence oscillation problems that may exist in existing improved methods, and achieves more stable and efficient hotspot elimination and thermo-mechanically coupled topology optimization.
[0027] Please see Figure 1 The topology optimization method mainly includes the following steps: Step 1: Based on the thermo-mechanical coupling structure to be optimized, establish the governing equations for thermal conduction analysis and linear elastic thermal expansion analysis. Based on the governing equations, use a material interpolation model to characterize the relationship between unit material properties and design variables.
[0028] Specifically, firstly, the design domain of the structure to be optimized is meshed. This method involves thermo-mechanical coupling and requires solving two physical fields: Steady-state heat conduction analysis: Establishing the heat balance equation and solving for the nodal temperature field. .
[0029] Linear elastic analysis: Establish the force balance equations, where the load terms include the external mechanical load F and the thermal expansion load caused by the temperature field. .
[0030] The SIMP material interpolation model is used to determine the elastic modulus of the element. and thermal conductivity With design variables Related:
[0031] In the formula, The elastic modulus of the element. The thermal conductivity of the unit cell is . For design variables, and As a penalty factor; The elastic modulus of a solid material; The elastic modulus of the pores is used to prevent the stiffness matrix from becoming singular; The thermal conductivity of the solid material; is the thermal conductivity of the pores.
[0032] Step 2: Based on the relationship between unit material properties and design variables, construct a topology optimization model with structural flexibility as the objective function and local volume and local temperature hotspots as constraints.
[0033] The optimization objective of this implementation is to minimize structural flexibility ( , The constraints include the total material integral. Not exceeding the upper limit and all nodes in the design domain temperature Not exceeding the critical temperature .
[0034] The mathematical expression for the topology optimization model is:
[0035] In the formula, Let be the objective function. The total integral of the material. It is the total number of local constraints. It is the normalized temperature; It is the displacement vector; Here is the stiffness matrix; It represents the volume fraction of the material. Let this be the initial volume of the design domain; For the first The actual temperature of each node; This is the critical temperature threshold, i.e., the highest permissible temperature.
[0036] Step 3: Use a dynamic soft weighting factor with a sigmoid function. Construct a weighted P-norm aggregation constraint This is used to aggregate multiple local temperature hotspot constraints into a single global constraint; wherein, the dynamic soft weighting factor It is defined based on the local temperature hotspot constraint in the topology optimization model.
[0037] The dynamic soft weight factor Normalized temperature of nodes Related. The dynamic soft weighting factor The expression is:
[0038] in, The extent to which the weight of hot topics is increased. For the first The normalized temperature of each node, The transition slope of the Sigmoid function. This represents the percentage of hotspot thresholds.
[0039] P-norm aggregation constraint The expression is:
[0040] in, For the P-norm parameter, It is a dynamic soft weighting factor. For the first The normalized temperature of each node, This represents the summation over all relevant nodes; That is, the original A global approximation of local hotspot constraints is achieved by simultaneously introducing weights into both the numerator and denominator. This achieves the effect of a weighted average. The optimizer minimizes... At that time, those with high weight will be prioritized for reduction. (i.e., hotspot areas) value.
[0041] The Sigmoid function is a smooth S-shaped curve function. It controls the magnitude of hotspot weight enhancement, thus controlling the hotspot (…). The weights of () relative to the baseline weights The degree of improvement. It is the transition slope that determines the weight from Increase to The steepness of the slope at that time; It is the hotspot threshold percentage, which defines the temperature point at which the weight begins to increase significantly.
[0042] Step four: Based on the objective function and the P-norm aggregation constraint... The topology optimization model is iteratively optimized relative to the sensitivity of the design variables to obtain the optimal topology; wherein, the dynamic soft weighting factor... The enhancement magnitude of the hotspot weight and the proportion of hotspot threshold increase linearly with the progress of iterative optimization.
[0043] The dynamic soft weight factor The key parameters include at least the magnitude of the increase in hotspot weight. and hotspot threshold ratio This allows it to change as the optimization iteration progresses. In the early stages of the optimization iteration, a smaller value is set. and lower As the iteration progresses, it gradually increases. And improve .
[0044] The sensitivity calculation employs a chain rule to ensure mathematical consistency between the aggregation constraint function and its gradient. The moving asymptote method is used for iterative optimization of the topology optimization model.
[0045] Dynamic adjustment: from a smaller The value increases linearly to a large value. The value, in this embodiment, increases linearly from 1 to 5.
[0046] Dynamic adjustment: from a smaller The value increases linearly to a large value. The value is linearly increased from 0.7 to 0.9 in this embodiment.
[0047] Please see Figure 2 In the early stages of optimization ( The value is small. (Smaller values), the weight curve (green dashed line) is flat and leans to the left, the optimizer will... We pay attention to a wide range of areas to avoid overlooking potential hotspots in the early stages.
[0048] In the later stages of optimization ( The value is relatively large. (With larger values), the weight curve (blue solid line) is steep and to the right (close to 1.0), indicating that the optimizer focuses most of its attention (on high weights). Precise elimination can be achieved at critical hotspots.
[0049] To use a gradient-based optimizer, it is necessary to compute... For design variables Sensitivity According to the chain rule:
[0050] in Solve using the adjoint method.
[0051] The key lies in the calculation ,make and ,but .
[0052]
[0053] because Only depend on (Right now when (When), the above formula can be simplified:
[0054] in It is the derivative of the Sigmoid weight.
[0055] When calculating this sensitivity, dynamic parameters and They are considered constants in the current iteration (because they only change with each iteration). Changes, rather than directly following design variables (Change). This makes The function and its gradient are completely self-consistent, ensuring mathematical consistency.
[0056] Calculate the objective function Sensitivity Items and aggregation constraints Sensitivity Then, these values are input into the Method of Moving Asymptotes (MMA) optimizer; MMA calculates the new design variables. Then, filtering and projection are performed, and the process proceeds to the next iteration, updating the dynamic parameters. and Continue until the convergence condition is met.
[0057] The present invention will be further described in detail below with reference to specific embodiments.
[0058] like Figure 3 As shown, a thermo-coupled cantilever beam example is used to verify the method provided by the present invention.
[0059] Design domain and parameters: dimensions , The left end is fixed, and a downward mechanical load is applied to the center of the right end. Apply heat flux to the top. .
[0060] Constraint: Upper limit of volume fraction Critical temperature .
[0061] DAW-PN parameter: Weighted P-norm parameter Maximum number of iterations The transition slope of the Sigmoid function Initial value of the increase in the weight of hot topics The final value of the increase in the weight of hot topics Initial value of hotspot threshold percentage The final value of the hotspot threshold percentage .
[0062] Figure 4 The final topology and temperature field optimized using the DAW-PN method of this invention are shown. The structure is clear, the force transmission path is reasonable, and the highest temperature in the temperature field is effectively controlled within a certain range. nearby.
[0063] Figure 5 The convergence comparison of the three methods is shown.
[0064] DAW-PN (this invention): Both the compliance curve and the maximum temperature curve decrease smoothly and eventually converge stably, with the maximum temperature precisely controlled near the critical value.
[0065] ACS-P-Norm: The maximum temperature curve shows significant oscillations in the later stages of optimization, which is consistent with the gradient inconsistency problem analyzed in the background technique.
[0066] Standard P-Norm: Converges slowly and is difficult to accurately eliminate the hottest spots.
[0067] As can be seen from the comparison, the DAW-PN method provided by this invention is superior to the comparative methods in terms of convergence stability, hotspot elimination accuracy, and optimization efficiency.
[0068] The present invention also provides a thermally coupled structure topology optimization system capable of dynamically and adaptively aggregating hotspot constraints. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the thermally coupled structure topology optimization method capable of dynamically and adaptively aggregating hotspot constraints as described above.
[0069] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the thermally coupled structural topology optimization method described above, which can dynamically and adaptively aggregate hotspot constraints.
[0070] This invention also provides a system for implementing the above method, the system comprising: a modeling and definition module for performing finite element mesh generation on the thermo-coupled structure, establishing control equations, and defining the optimization problem; and a dynamic weight definition module for defining weights based on the normalized temperature of the nodes. Calculating dynamic soft weight factors based on the Sigmoid function ; Parameter adaptive module: used to dynamically update the dynamic soft weight factor according to the current optimization iteration progress. and Parameters; Constraint aggregation module: used to employ the dynamic soft weighting factor This aggregates a large number of local hotspot constraints into a single weighted P-norm aggregate constraint. Sensitivity analysis module: used to calculate the objective function and the aggregation constraints. Regarding the gradient of the design variables; Optimization solution module: used to perform iterative solution using optimization algorithms based on the sensitivity information, updating the design variables until convergence.
[0071] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for topology optimization of thermo-coupling structures with dynamic adaptive aggregation hotspot constraints, characterized in that, The steps are as follows: Step 1: Based on the thermo-mechanical coupling structure to be optimized, establish the governing equations for thermal conduction analysis and linear elastic thermal expansion analysis. Based on the governing equations, use a material interpolation model to characterize the relationship between unit material properties and design variables. Step 2: Based on the relationship between unit material properties and design variables, construct a topology optimization model with structural flexibility as the objective function and local volume and local temperature hotspots as constraints. Step 3: Use a dynamic soft weighting factor with a sigmoid function. Construct a weighted P-norm aggregation constraint This is used to aggregate multiple local temperature hotspot constraints into a single global constraint; wherein, the dynamic soft weighting factor It is defined based on the local temperature hotspot constraint in the topology optimization model; Step four: Based on the objective function and the P-norm aggregation constraint... The topology optimization model is iteratively optimized relative to the sensitivity of the design variables to obtain the optimal topology; wherein, the dynamic soft weighting factor... The enhancement magnitude of the hotspot weight and the proportion of hotspot threshold increase linearly with the progress of iterative optimization.
2. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in claim 1, characterized in that: The SIMP material interpolation model is used to determine the elastic modulus of the element. and thermal conductivity With design variables Related: In the formula, The elastic modulus of the element. The thermal conductivity of the unit cell is . For design variables, and As a penalty factor; The elastic modulus of a solid material; The elastic modulus of the pores is used to prevent the stiffness matrix from becoming singular; The thermal conductivity of the solid material; is the thermal conductivity of the pores.
3. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in claim 1, characterized in that: The mathematical expression for the topology optimization model is: In the formula, Let be the objective function. The total integral of the material. It is the total number of local constraints. It is the normalized temperature; It is the displacement vector; Here is the stiffness matrix; It represents the volume fraction of the material. Let this be the initial volume of the design domain; For the first The actual temperature of each node; This is the critical temperature threshold, i.e., the highest permissible temperature.
4. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in claim 1, characterized in that: The dynamic soft weight factor The expression is: in, The extent to which the weight of hot topics is increased. For the first The normalized temperature of each node, The transition slope of the Sigmoid function. This represents the percentage of hotspot thresholds.
5. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in claim 4, characterized in that: P-norm aggregation constraint The expression is: in, For the P-norm parameter, It is a dynamic soft weighting factor. For the first The normalized temperature of each node, This represents the summation over all relevant nodes; That is, the original A global approximation of a local hotspot constraint.
6. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in any one of claims 1-5, characterized in that: The objective function and the P-norm aggregation constraint are calculated using the chain rule. Sensitivity relative to design variables.
7. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in any one of claims 1-5, characterized in that: The enhancement of hotspot weight increases linearly from 1 to 5 as the iteration optimization progresses.
8. The thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in claim 7, characterized in that: The percentage of hotspot thresholds increased linearly from 0.7 to 0.9 as the iteration and optimization progressed.
9. A thermo-coupled structural topology optimization system capable of dynamically and adaptively aggregating hotspot constraints, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the thermally coupled structural topology optimization method with dynamic adaptive aggregation hotspot constraints as described in any one of claims 1-8.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the thermally coupled structural topology optimization method for dynamically adaptive aggregation hotspot constraints as described in any one of claims 1-8.