A flexible sensor design method and system based on topology optimization

Abstract

The present invention relates to the field of sensor design and analysis technology, and specifically to a flexible sensor design method and system based on topological optimization, including the following steps: establishing coupling equations for flexible sensors under the action of mechanical, electrical and thermal multi-physical fields, simulating stress, potential and temperature distribution in different regions of the design space based on material parameters; dividing the design space into high stress regions, transition regions and low stress regions according to stress, potential and temperature distribution, and defining performance targets for each region; and dynamically adjusting the state of unit materials, and adaptively adjusting the connectivity constraints of the topological structure according to the distribution changes of the materials during the iteration process. The present invention effectively improves the sensitivity of the potential response, enables the sensor to have efficient signal detection capabilities in stress concentration areas, and reduces unnecessary material redundancy.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor design and analysis, and in particular to a flexible sensor design method and system based on topology optimization. Background Art

[0002] As an emerging sensing technology, flexible sensors have been widely used in wearable devices, medical health monitoring, industrial automation, and intelligent robots due to their light weight, flexibility, and high conformity to complex surfaces. Traditional flexible sensor design usually relies on empirical rules and simple structural optimization, but in a working environment with complex multi-physical fields (such as mechanics, electricity, and heat) interacting, the sensor performance is often difficult to meet the comprehensive requirements of high sensitivity, high flexibility, and thermal stability, especially in terms of material utilization efficiency and structural reliability.

[0003] In the existing technology, some studies have begun to use topology optimization methods to design flexible sensors, and achieve local performance improvements by optimizing material distribution and structural shape. However, these methods still have the following limitations:

[0004] Incomplete multi-physics modeling: Most optimization designs only consider a single physical field (such as mechanical field or electrical field), which cannot accurately describe the multi-physics coupling behavior of flexible sensors in complex environments, resulting in deviations between the optimization results and actual usage conditions.

[0005] Rough division of functional areas: Existing methods usually perform global optimization based on simple stress or potential thresholds, ignoring the differential contributions of different regions in the design space (such as high stress regions and low stress regions) to sensor performance, resulting in the optimization results being difficult to improve sensitivity, flexibility or thermal stability in a targeted manner.

[0006] Single topology optimization target: The optimization process mainly focuses on a single performance target (such as sensitivity or material utilization rate), fails to comprehensively consider the balance of sensitivity, flexibility and thermal stability, and is difficult to meet the needs of multi-performance coordinated optimization in practical applications. Summary of the invention

[0007] The present invention provides a flexible sensor design method and system based on topology optimization.

[0008] A flexible sensor design method based on topology optimization includes the following steps:

[0009] S1, multi-physics coupling model modeling: establish the coupling equations of the flexible sensor under the action of mechanical, electrical and thermal multi-physics fields, and simulate the stress, potential and temperature distribution in different areas of the design space based on material parameters as optimization input;

[0010] S2, dynamic design space partitioning: according to the stress, potential and temperature distribution, the design space is divided into high stress area, transition area and low stress area, and the performance target is defined for each area, including the sensitivity of the high stress area, the flexibility of the transition area and the thermal stability of the low stress area;

[0011] S3, construction of topology optimization framework: taking the material distribution and structural connectivity in the design space as topological variables, constructing an objective function based on multi-objective weights, comprehensively considering the sensitivity target, flexibility target and thermal stability target, using the topological sensitivity analysis method, calculating the contribution of each unit to the objective function, and dynamically adjusting the unit material state. In the iterative process, according to the changes in material distribution, the connectivity constraints of the topological structure are adaptively adjusted. Through the results generated by topology optimization, the key functional areas, microstructural features and redundant material removal strategies retained in the design space are clarified to form the final topology optimization solution.

[0012] Optionally, the S1 specifically includes:

[0013] S11, Establishment of mechanical, electrical and thermal multi-physics field coupling model: Based on the structural characteristics of the flexible sensor, a multi-physics field coupling model based on the design space is constructed, including mechanical field equations, electrical field equations and thermal field equations;

[0014] S12, calculation of regional response characteristics based on material parameters: the equations of mechanical field, electrical field and thermal field are coupled through the shared parameters of the flexible sensor, including the dielectric constant , thermal conductivity of materials , as the input variable of the model, the design space is discretized by the finite element analysis method and divided into multiple units. The stress, potential and temperature distribution in the unit are numerically solved by the equations of the multi-physics field coupling model mentioned above, and the mechanical, electrical and thermal response characteristics are simulated by combining the material properties of different regions;

[0015] S13, output of multi-physics field distribution data: output the stress distribution, potential distribution and temperature distribution data obtained by numerical solution as optimization input.

[0016] Optionally, the establishment of the mechanical field equations: adopting a large deformation nonlinear mechanical model to describe the stress and strain distribution in the design space under the action of external force loads, specifically expressed as: ,in, is the stress distribution, For external force load.

[0017] Optionally, the electrical field equation is established by adopting a force-electric coupling model to describe the potential distribution of the flexible sensor material under mechanical deformation, which is expressed as: ,in, is the dielectric constant of the material, is the electric potential distribution, is the charge density.

[0018] Optionally, the thermal field equation is established based on the heat conduction equation to describe the distribution and transfer of heat in the material, which is specifically expressed as: ,in, is the thermal conductivity of the material, T is the temperature distribution, q is the heat source intensity, p is the density, is the specific heat capacity, It represents the rate of change of temperature with time.

[0019] Optionally, S2 includes design space region division: stress distribution obtained by solving the multi-physics field integration model , potential distribution And the temperature distribution T, the design space is divided into high stress area, transition area and low stress area, where:

[0020] High stress area: According to stress distribution distribution, identify and divide the areas with large stress concentration, and use the maximum stress value Screening is performed to define high stress areas as ,in, is the stress threshold, for composite materials, ;

[0021] Low stress areas: By identifying areas with low stress distribution, i.e. , identify low stress areas, ;

[0022] Transition Region: The transition region is defined as .

[0023] Optionally, the S3 specifically includes:

[0024] S31, topological variable definition: material distribution in the design space and structural connectivity is the topology optimization variable, material distribution Represents the material density of each unit, and its value range is [0,1], where Indicates that the material exists completely, Indicates complete material removal and structural connectivity Indicates the connectivity status between units, with a value range of [0,1], defined as a Boolean variable, a value of 1 indicates that the unit is connected, and a value of 0 indicates that the unit is isolated;

[0025] S32, Objective function construction: Construct comprehensive optimization objective function , combined with the sensitivity target, flexibility target and thermal stability target, is defined as:

[0026] ,in, is the weight coefficient of the objective function, indicating the priority of sensitivity, flexibility and thermal stability objectives, is the sensitivity objective function, is the flexibility objective function, is the thermal stability objective function;

[0027] S33, Topological sensitivity analysis: Calculate the objective function by topological sensitivity analysis method For each element material density Sensitivity: ;

[0028] Based on the sensitivity results, the material state of each unit is dynamically adjusted: ,in, and are the material densities of element i in the current iteration and the next iteration, respectively. is the step size factor, which controls the convergence speed of the optimization process;

[0029] Connectivity constraint adaptive adjustment: During the optimization iteration process, the structural connectivity is adjusted according to the changes in unit material density , ensuring that key areas are connected and isolated areas are removed;

[0030] Define connectivity constraints: ,in, is the connectivity threshold of the key area;

[0031] S34, topology optimization result generation:

[0032] Based on the material distribution and connectivity after iterative optimization, an optimization plan is generated to clarify the key functional areas to be retained in the design space, the microstructural features to enhance sensitivity, and the removal strategy of redundant materials.

[0033] Optionally, the sensitivity objective function The optimized stress-induced potential response is defined as:

[0034] ,in is the electric potential distribution, is the stress distribution, is the differential volume in integral notation, represents the sensitivity of electric potential to stress, and V is the volume of the design space;

[0035] The flexibility objective function Optimize the material's deformation capacity, defined as:

[0036] ,in is the displacement, is the external load, Indicates the sensitivity of displacement to external force load;

[0037] The thermal stability objective function Optimize the uniformity of temperature distribution, defined as:

[0038] , where T is the temperature distribution, q is the heat source intensity, Indicates the sensitivity of temperature to the intensity of the heat source.

[0039] A flexible sensor design system based on topology optimization is used to implement the above-mentioned flexible sensor design method based on topology optimization, and includes the following modules:

[0040] Multi-physics modeling module: used to establish a coupling model of flexible sensors under the action of mechanical, electrical and thermal multi-physics fields, collect and analyze material parameters, and generate distribution data of stress, potential and temperature in the design space;

[0041] Dynamic design space partitioning module: Based on the output data of the multi-physics modeling module, the design space is divided into high stress area, transition area and low stress area, and the performance target is defined for each area;

[0042] Topology optimization module: Based on material distribution and structural connectivity as topological variables, a multi-objective weighted optimization function that comprehensively considers sensitivity, flexibility and thermal stability is constructed. The contribution of each unit to the optimization target is calculated using the topological sensitivity analysis method, and the unit material state is dynamically adjusted and the connectivity constraints are adaptively adjusted.

[0043] Result output module: used to generate the final design scheme of the flexible sensor based on the optimization results of the topology optimization module, and to clarify the key functional areas, microstructure features and redundant material removal strategies retained in the design space.

[0044] Beneficial effects of the present invention:

[0045] The present invention establishes a mechanical, electrical and thermal multi-physics field coupling model to comprehensively simulate the physical response of flexible sensors in complex environments, ensure the physical accuracy of the optimization solution, introduce a design space division method, and divide the design space into high stress area, transition area and low stress area according to the distribution of multiple physical fields. Specific performance goals are defined for each area, thereby achieving precise optimization of key functional areas. Microstructure features are introduced into high stress areas to effectively improve the sensitivity of potential response, so that the sensor has efficient signal detection capabilities in stress concentration areas, while reducing unnecessary material redundancy.

[0046] The present invention, in a topological optimization framework, comprehensively constructs three objective functions of sensitivity, flexibility and thermal stability, meets the optimization requirements of different application scenarios by adjusting weights, ensures the balance of performance such as sensitivity and flexibility, introduces a topological sensitivity analysis method, dynamically adjusts the distribution of unit materials and structural connectivity, and significantly reduces the use of redundant materials while ensuring the connectivity of key areas. It optimizes the gradual distribution of materials in the transition area to form a smooth stress transition zone, avoids the risk of failure caused by stress concentration, and enhances the overall flexibility and durability of the sensor, making it adaptable to scenarios with high deformation requirements such as wearable devices.

[0047] The present invention, in response to working requirements in a thermal environment, combines multi-physics field modeling with a thermal stability optimization objective function to balance the heat transfer path, significantly reduce the risk of performance drift caused by local heat accumulation, improve the stability of the sensor in a high temperature environment, dynamically adjust the material connectivity threshold, ensure that the optimized structure has a complete heat conduction path, and at the same time remove unnecessary materials in low stress areas, significantly improving material utilization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are only for the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0049] Figure 1 A schematic diagram of a design method flow chart of an embodiment of the present invention;

[0050] Figure 2 Schematic diagram of system function modules according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. At the same time, it is explained here that in order to make the embodiments more detailed, the following embodiments are the best and preferred embodiments, and those skilled in the art may also adopt other alternatives to implement some known technologies; and the accompanying drawings are only for more specific description of the embodiments, and are not intended to specifically limit the present invention.

[0052] It should be noted that the references to "one embodiment", "embodiment", "exemplary embodiments", "some embodiments" and the like in the specification indicate that the embodiments described may include specific features, structures or characteristics, but not every embodiment may include the specific features, structures or characteristics. In addition, when a specific feature, structure or characteristic is described in conjunction with an embodiment, it should be within the knowledge of a person skilled in the art to implement such feature, structure or characteristic in conjunction with other embodiments (whether or not explicitly described).

[0053] In general, a term can be understood, at least in part, from its use in context. For example, depending, at least in part, on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in the singular sense, or can be used to describe a combination of features, structures, or characteristics in the plural sense. Additionally, the term "based on" can be understood as not necessarily intended to convey an exclusive set of factors, but can instead, depending, at least in part, on the context, allow for the presence of other factors that are not necessarily explicitly described.

[0054] like Figure 1 As shown, a flexible sensor design method based on topology optimization includes the following steps:

[0055] S1, multi-physics coupling model modeling: establish the coupling equations of flexible sensors under the action of mechanical, electrical and thermal multi-physics fields, and simulate the stress, potential and temperature distribution in different regions of the design space based on material parameters (such as dielectric constant and material thermal conductivity) as optimization input;

[0056] S2, dynamic design space division: according to the stress, potential and temperature distribution, the design space is divided into high stress area, transition area and low stress area, and performance targets are defined for each area, including the sensitivity of the high stress area, the flexibility of the transition area and the thermal stability of the low stress area. Thermal stability is a key indicator for the continuous operation of flexible sensors in high temperature environments. By optimizing the heat conduction path in the low stress area, local heat accumulation can be effectively reduced and the uniformity of the overall temperature distribution can be improved. The material utilization rate in the low stress area can be appropriately reduced, but the key heat conduction function needs to be retained to ensure the signal stability and structural reliability of the sensor under different ambient temperatures.

[0057] S3, construction of topology optimization framework: taking the material distribution and structural connectivity in the design space as topological variables, constructing an objective function based on multi-objective weights, comprehensively considering the sensitivity target, flexibility target and thermal stability target, using the topological sensitivity analysis method, calculating the contribution of each unit to the objective function, and dynamically adjusting the unit material state (retention, removal or gradual distribution). In the iterative process, according to the changes in material distribution, the connectivity constraints of the topological structure are adaptively adjusted to ensure the stability and functionality of the overall structure in the force, electricity and heat multi-physical fields. Through the results generated by topology optimization, the key functional areas, microstructural features and redundant material removal strategies retained in the design space are clarified to form the final topology optimization solution.

[0058] S1 specifically includes:

[0059] S11, Establishment of mechanical, electrical and thermal multi-physics field coupling model: Based on the structural characteristics of the flexible sensor, a multi-physics field coupling model based on the design space is constructed, including mechanical field equations, electrical field equations and thermal field equations;

[0060] S12, calculation of regional response characteristics based on material parameters: the equations of mechanical field, electrical field and thermal field are coupled through the shared parameters of the flexible sensor, including the dielectric constant , thermal conductivity of materials , as the input variable of the model, the design space is discretized by the finite element analysis method and divided into multiple units. The stress, potential and temperature distribution in the unit are numerically solved by the equations of the multi-physics field coupling model mentioned above, and the mechanical, electrical and thermal response characteristics are simulated by combining the material properties of different regions;

[0061] S13, output of multi-physics field distribution data: output the stress distribution, potential distribution and temperature distribution data obtained by numerical solution as optimization input, which serves as the basis for dynamic design space partition and topology optimization.

[0062] Establishment of mechanical field equations: A large deformation nonlinear mechanical model is used to describe the stress and strain distribution in the design space under the action of external force loads. The specific expression is: ,in, is the stress distribution, For external force load.

[0063] Establishment of electrical field equation: The electromechanical coupling model is used to describe the potential distribution of the flexible sensor material under mechanical deformation, which is expressed as: ,in, is the dielectric constant of the material, is the electric potential distribution, is the charge density.

[0064] Establishment of thermal field equation: Based on the heat conduction equation, it describes the distribution and transfer of heat in the material, which is specifically expressed as: ,in, is the thermal conductivity of the material, is the temperature distribution, is the intensity of the heat source, is the density, is the specific heat capacity, It represents the rate of change of temperature with time.

[0065] S2 includes the design space area division: stress distribution obtained by solving the multi-physics field integration model , potential distribution And the temperature distribution T, the design space is divided into high stress area, transition area and low stress area, where:

[0066] High stress area: According to the stress field distribution, identify and divide the areas with large stress concentration, and use the maximum stress value Screening is performed to define high stress areas as ,in, is the stress threshold, for composite materials, ;

[0067] Low stress areas: By identifying areas with low stress distribution, i.e. , identify low stress areas,

[0068] ;

[0069] Transition Region: The transition region is defined as .

[0070] S3 specifically includes:

[0071] S31, topological variable definition: material distribution in the design space and structural connectivity is the topology optimization variable, material distribution Represents the material density of each unit, and its value range is [0,1], where Indicates that the material exists completely, Indicates complete material removal and structural connectivity Indicates the connectivity status between units, with a value range of [0,1], defined as a Boolean variable, a value of 1 indicates that the unit is connected, and a value of 0 indicates that the unit is isolated;

[0072] S32, Objective function construction: Construct comprehensive optimization objective function , combined with the sensitivity target, flexibility target and thermal stability target, is defined as:

[0073] ,in, is the weight coefficient of the objective function,

[0074] , indicating the priority of sensitivity, flexibility and thermal stability targets, is the sensitivity objective function, is the flexibility objective function, is the thermal stability objective function;

[0075] S33, Topological sensitivity analysis: Calculate the objective function by topological sensitivity analysis method For each element material density Sensitivity: ;

[0076] Based on the sensitivity results, the material state of each unit is dynamically adjusted: ,in, and are the material densities of element i in the current iteration and the next iteration, respectively. is the step size factor, which controls the convergence speed of the optimization process;

[0077] Connectivity constraint adaptive adjustment: During the optimization iteration process, the structural connectivity is adjusted according to the changes in unit material density , ensuring that key areas are connected and isolated areas are removed;

[0078] Define connectivity constraints: ,in, is the connectivity threshold of the key area, Take 0.95;

[0079] Dynamically modify connectivity after each iteration to ensure the physical integrity and functionality of the topology;

[0080] S34, topology optimization result generation:

[0081] Based on the material distribution and connectivity after iterative optimization, an optimization scheme is generated to clarify the key functional areas to be retained in the design space, the microstructure features to enhance sensitivity, and the removal strategy of redundant materials; the details are as follows:

[0082] 1. Analyze iterative optimization results:

[0083] Material distribution analysis: Analyze each unit in the design space, and judge its functionality and necessity based on the value of the optimized material density (e.g., close to 1 means that the material is completely retained, and close to 0 means that the material is completely removed). Focus on the area where the material density is close to 1 and mark it as a potential key functional area.

[0084] Connectivity assessment: Check the physical connectivity of each unit in the design space with adjacent units to ensure that there are complete structural connections between functional areas, identify isolated units or areas, and determine whether they are redundant materials.

[0085] 2. Identify key functional areas: According to the optimization objectives and the response of multi-physics fields, the following key functional areas are determined:

[0086] High stress areas: Through the superposition analysis of material distribution and stress distribution, the areas of stress concentration are located and marked as key functional areas. These areas are critical to structural performance and need to be retained as a priority.

[0087] Transition areas: Combine stress gradient and connectivity analysis to identify areas with gentle stress changes but high functionality. These areas require optimized material flexibility to smooth transitions and avoid stress concentrations.

[0088] Low stress areas: Identify areas with less stress and lower contribution to performance. These areas can be used as the focus for redundant material removal, while ensuring the connectivity and thermal stability of the overall structure.

[0089] 3. Microstructural features that enhance sensitivity:

[0090] High stress areas: In these areas, sophisticated microstructure designs (such as micropore arrays or corrugated features) are introduced to increase the sensitivity of the potential response. These microstructure features can optimize the matching of surface area and stress distribution, thereby improving the overall performance.

[0091] Transition zone: In areas where stress changes slowly, the distribution of materials is adjusted to form a flexible gradient structure. The gradient design can reduce local stress concentration and improve the durability and deformation capacity of the structure.

[0092] Low stress areas: These areas are designed to be simplified, using less material but retaining the necessary structural support, ensuring that they still contribute to overall heat transfer and stability while minimizing overall mass.

[0093] 4. Remove redundant materials:

[0094] Isolated area removal: Check the material units in the optimization results that have no connectivity with the main functional areas and mark them as redundant materials for removal.

[0095] Non-functional unit removal: Units with lower density in the optimization are further evaluated and removed if they do not contribute significantly to sensitivity, flexibility, or thermal stability.

[0096] Ensure the stability and functionality of the optimization scheme under the multi-physical fields of force, electricity, and heat, and output the final topology optimization results as the basis for flexible sensor design.

[0097] Sensitivity objective function The optimized stress-induced potential response is defined as:

[0098] ,in is the electric potential distribution, is the stress distribution, is the differential volume in integral notation, It represents the sensitivity of electric potential to stress, V is the volume of the design space, which represents an infinitesimal volume unit in the design space. It is a volume element used to describe a tiny area in three-dimensional space.

[0099] Flexibility objective function Optimize the material's deformation capacity, defined as:

[0100] ,in is the displacement, is the external load, Indicates the sensitivity of displacement to external force load;

[0101] Thermal stability objective function Optimize the uniformity of temperature distribution, defined as:

[0102] , where T is the temperature distribution, q is the heat source intensity, Indicates the sensitivity of temperature to the intensity of the heat source.

[0103] like Figure 2 As shown, a flexible sensor design system based on topology optimization is used to implement the above-mentioned flexible sensor design method based on topology optimization, and includes the following modules:

[0104] Multi-physics modeling module: used to establish a coupling model of flexible sensors under the action of mechanical, electrical and thermal multi-physics fields, collect and analyze material parameters, and generate distribution data of stress, potential and temperature in the design space;

[0105] Dynamic design space partitioning module: Based on the output data of the multi-physics modeling module, the design space is divided into high stress area, transition area and low stress area, and the performance target is defined for each area;

[0106] Topology optimization module: Based on material distribution and structural connectivity as topological variables, a multi-objective weighted optimization function that comprehensively considers sensitivity, flexibility and thermal stability is constructed. The contribution of each unit to the optimization target is calculated using the topological sensitivity analysis method, and the unit material state is dynamically adjusted and the connectivity constraints are adaptively adjusted.

[0107] Result output module: used to generate the final design scheme of the flexible sensor based on the optimization results of the topology optimization module, and to clarify the key functional areas, microstructure features and redundant material removal strategies retained in the design space.

[0108] The present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention. In order to make the public have a thorough understanding of the present invention, specific details are described in detail in the following preferred embodiments of the present invention, but those skilled in the art can fully understand the present invention without the description of these details. In addition, in order to avoid unnecessary confusion about the essence of the present invention, well-known methods, processes, procedures, components and circuits are not described in detail.

[0109] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A flexible sensor design method based on topology optimization, characterized in that: The following steps are involved: S1, multi-physics coupling model modeling: establish the coupling equations of flexible sensors under the action of mechanical, electrical and thermal multi-physics fields, and simulate the stress, potential and temperature distribution in different regions in the design space based on material parameters as optimization input; S2, dynamic design space partitioning: according to the stress, potential and temperature distribution, the design space is divided into high stress area, transition area and low stress area, and the performance target is defined for each area, including the sensitivity of the high stress area, the flexibility of the transition area and the thermal stability of the low stress area; S3, construction of topology optimization framework: taking the material distribution and structural connectivity in the design space as topological variables, constructing an objective function based on multi-objective weights, comprehensively considering the sensitivity target, flexibility target and thermal stability target, using the topological sensitivity analysis method, calculating the contribution of each unit to the objective function, and dynamically adjusting the unit material state. In the iterative process, according to the changes in material distribution, the connectivity constraints of the topological structure are adaptively adjusted. Through the results generated by topology optimization, the key functional areas, microstructural features and redundant material removal strategies retained in the design space are clarified to form the final topology optimization solution.

2. According to claim 1, a flexible sensor design method based on topology optimization is characterized in that: The S1 specifically includes: S11, Establishment of mechanical, electrical and thermal multi-physics field coupling model: Based on the structural characteristics of the flexible sensor, a multi-physics field coupling model based on the design space is constructed, including mechanical field equations, electrical field equations and thermal field equations; S12, calculation of regional response characteristics based on material parameters: the equations of mechanical field, electrical field and thermal field are coupled through the shared parameters of the flexible sensor, including the dielectric constant , thermal conductivity of materials , as the input variables of the model, the design space is discretized by the finite element analysis method and divided into multiple units. The stress, potential and temperature distribution in the unit are numerically solved by the equations of the multi-physics field coupling model, and the mechanical, electrical and thermal response characteristics are simulated by combining the material properties of different regions; S13, output of multi-physics field distribution data: output the stress distribution, potential distribution and temperature distribution data obtained by numerical solution as optimization input.

3. The flexible sensor design method based on topology optimization according to claim 2 is characterized in that: The establishment of the mechanical field equation: a large deformation nonlinear mechanical model is used to describe the stress and strain distribution in the design space under the action of external force loads, which is specifically expressed as: ,in, is the stress distribution, For external force load.

4. The flexible sensor design method based on topology optimization according to claim 3 is characterized in that: The establishment of the electrical field equation: The electromechanical coupling model is used to describe the potential distribution of the flexible sensor material under mechanical deformation, which is expressed as: ,in, is the dielectric constant of the material, is the electric potential distribution, is the charge density.

5. The flexible sensor design method based on topology optimization according to claim 4 is characterized in that: The establishment of the thermal field equation is based on the heat conduction equation, which describes the distribution and transfer of heat in the material. The specific expression is: ,in, is the thermal conductivity of the material, is the temperature distribution, is the intensity of the heat source, is the density, is the specific heat capacity, Represents the rate of change of temperature with time.

6. The flexible sensor design method based on topology optimization according to claim 5 is characterized in that: S2 includes the design space area division: stress distribution obtained by solving the multi-physics field integration model , potential distribution And temperature distribution , the design space is divided into high stress area, transition area and low stress area, where: High stress area: According to stress distribution distribution, identify and divide the areas with large stress concentration, and use the maximum stress value Screening is performed to define high stress areas as ,in, is the stress threshold; Low stress areas: By identifying areas with low stress distribution, i.e. , identify low stress areas; Transition Region: The transition region is defined as .

7. The flexible sensor design method based on topology optimization according to claim 1 is characterized in that: The S3 specifically includes: S31, topological variable definition: material distribution in the design space and structural connectivity is the topology optimization variable, material distribution Represents the material density of each unit, and its value range is [0,1], where Indicates that the material exists completely, Indicates that the material is completely removed and the structure is connected Indicates the connectivity status between units, with a value range of [0,1], defined as a Boolean variable, a value of 1 indicates that the unit is connected, and a value of 0 indicates that the unit is isolated; S32, Objective function construction: Construct comprehensive optimization objective function , combined with the sensitivity target, flexibility target and thermal stability target, is defined as: ,in, is the weight coefficient of the objective function, indicating the priority of sensitivity, flexibility and thermal stability objectives, is the sensitivity objective function, is the flexibility objective function, is the thermal stability objective function; S33, Topological sensitivity analysis: Calculate the objective function by topological sensitivity analysis method For each element material density Sensitivity: ; Based on the sensitivity results, the material state of each unit is dynamically adjusted: ,in, and are the material densities of element i in the current iteration and the next iteration, respectively. is the step size factor, which controls the convergence speed of the optimization process; Connectivity constraint adaptive adjustment: During the optimization iteration process, the structural connectivity is adjusted according to the changes in unit material density , ensuring that key areas are connected and isolated areas are removed; Define connectivity constraints: ,in, is the connectivity threshold of the key area; S34, topology optimization result generation: Based on the material distribution and connectivity after iterative optimization, an optimization plan is generated to clarify the key functional areas to be retained in the design space, the microstructural features to enhance sensitivity, and the removal strategy of redundant materials.

8. The flexible sensor design method based on topology optimization according to claim 7 is characterized in that: The sensitivity objective function The optimized stress-induced potential response is defined as: ,in is the electric potential distribution, is the stress distribution, is the differential volume in integral notation, represents the sensitivity of electric potential to stress, and V is the volume of the design space; The flexibility objective function Optimize the material's deformation capacity, defined as: ,in is the displacement, is the external load, Indicates the sensitivity of displacement to external force load; The thermal stability objective function Optimize the uniformity of temperature distribution, defined as: , where T is the temperature distribution, q is the heat source intensity, Indicates the sensitivity of temperature to the intensity of the heat source.

9. A flexible sensor design system based on topology optimization, used to implement a flexible sensor design method based on topology optimization as claimed in any one of claims 1 to 8, characterized in that: Includes the following modules: Multi-physics modeling module: used to establish a coupling model of flexible sensors under the action of mechanical, electrical and thermal multi-physics fields, collect and analyze material parameters, and generate distribution data of stress, potential and temperature in the design space; Dynamic design space partitioning module: Based on the output data of the multi-physics modeling module, the design space is divided into high stress area, transition area and low stress area, and the performance target is defined for each area; Topology optimization module: Based on material distribution and structural connectivity as topological variables, a multi-objective weighted optimization function that comprehensively considers sensitivity, flexibility and thermal stability is constructed. The contribution of each unit to the optimization target is calculated using the topological sensitivity analysis method, and the unit material state is dynamically adjusted and the connectivity constraints are adaptively adjusted. Result output module: used to generate the final design scheme of the flexible sensor based on the optimization results of the topology optimization module, and to clarify the key functional areas, microstructure features and redundant material removal strategies retained in the design space.

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