A surface displacement-based structural contact state detection method and system

Abstract

This invention relates to a method and system for detecting the contact state of a structure based on surface displacement, comprising: step S1, acquiring surface displacement or surface shape response information of the clamped structure as the target response; step S2, establishing a finite element analysis model of the clamped structure; step S3, constructing a Robin boundary equivalent model of the contact interface; step S4, introducing density-based design variables to describe the contact state; step S5, constructing an objective function based on surface displacement error; step S6, calculating the sensitivity of the objective function to the density-based design variables based on the adjoint sensitivity method, and performing optimization iterations to update the density-based design variables so that the calculated displacement approximates the target response of step S1; and step S7, determining the contact area based on the equivalent contact stiffness field or the density-based design variable field. Compared with the prior art, this invention not only improves the accuracy and robustness of structural health monitoring, but also greatly simplifies the detection process and reduces the requirements for sensor arrangement density.

Description

Technical Field

[0001] This invention relates to structural contact state detection technology, and in particular to a method and system for structural contact state detection based on surface displacement. Background Technology

[0002] In engineering applications such as semiconductor manufacturing, precision assembly, precision clamping, and thin-plate structure support, the actual contact state between the structure and its supports, clamps, or positioning components directly affects the stress distribution, deformation response, and final assembly accuracy. For example, during the clamping of thin-plate structures, due to factors such as machining errors, assembly errors, differences in support height, surface roughness, and variations in external loads, the theoretically designed contact area often does not perfectly match the actual contact area. Local areas may exhibit no contact, partial detachment, or insufficient contact stiffness. If the actual contact state at the bottom of the structure or the clamping interface cannot be accurately obtained, it will be difficult to accurately predict structural deformation, impacting subsequent error compensation, clamping optimization, and structural performance evaluation.

[0003] In existing technologies, the acquisition of structural contact states typically relies on direct contact measurement methods, finite element contact analysis methods, and numerical inversion methods based on structural response.

[0004] First, direct contact measurement methods typically acquire local contact pressure or force information by placing pressure sensors, thin-film sensors, or other detection elements at the contact interface. While these methods can reflect the stress state of a portion of the contact area, their application is usually limited by sensor size, installation method, and placement. For high-precision clamping structures, the introduction of sensors may alter the original contact boundary conditions, affecting the actual contact state. Furthermore, due to the limited number and placement of sensor measurement points, especially when the actual contact area is distributed in a dotted pattern, the limited number of measurement points cannot fully characterize the location, extent, and boundary morphology of the contact area. Therefore, direct contact measurement methods are insufficient to meet the needs of identifying the contact state of complex, discrete clamping areas.

[0005] Secondly, finite element contact analysis is a commonly used numerical method for studying structural contact problems. This method typically requires pre-establishing contact pairs between the structure and the support, and then solving the contact constraint problem using methods such as the penalty function method, the Lagrange multiplier method, or the augmented Lagrange method. Finite element contact analysis can simulate the structural response under given contact conditions, but it usually relies on relatively accurate geometric models, contact pair definitions, support heights, boundary conditions, and material parameters. In actual clamped structures, the location, number, extent, and morphology of the contact area are often unknown and change with variations in support height error, assembly state, and external loads. When the actual contact state is unknown, it is difficult to accurately determine the actual contact area using only traditional forward contact analysis. Furthermore, contact nonlinearity increases computational complexity and convergence difficulty, hindering rapid detection and engineering applications.

[0006] Furthermore, numerical inversion methods based on structural response information offer a new approach to identifying the state of unmeasurable regions. These methods typically utilize externally measurable responses, such as displacement, strain, or vibration information, to establish a mapping relationship between the structural response and internal states, material parameters, or boundary conditions, thereby achieving the inversion identification of unknown parameters. In existing research, neural network methods, physical information neural network methods, finite element inverse solving methods, and topology optimization methods have all been used for structural defect identification, material parameter identification, and boundary condition identification.

[0007] Purely data-driven methods typically rely on a large number of training samples, and their recognition accuracy and generalization ability are significantly affected by the coverage of the training data. When the clamping configuration, load type, or contact state changes, the model may struggle to maintain stable recognition accuracy. Physical information neural network methods, by introducing mechanical equation constraints into the data-driven model, can reduce the dependence on the scale of training data to some extent. However, when dealing with complex discrete clamping contact problems, since the location, number, and shape of the contact area are uncertain, these methods still struggle to directly achieve automatic identification of unknown discrete contact areas. Furthermore, these methods are usually highly dependent on full-field response data, while in practical engineering, only displacement and surface shape information of a limited area or local surface is often available.

[0008] Finite element inversion methods can establish unknown parameter identification models based on the responses of a finite number of measurement points, reducing reliance on large amounts of training data to some extent. However, existing finite element inversion methods typically require pre-assuming the location of the boundary to be identified, the range of the contact area, or the form of parameter distribution, focusing more on the identification of boundary stiffness, contact force, or material parameters in the known region. For actual clamping structures, when the contact area itself is unknown, the structural boundary conditions and local constraint states will dynamically change with the change of the contact area. Traditional inversion frameworks based on the assumption of fixed boundaries and known contact areas are difficult to apply directly.

[0009] Since the location, number, extent, and morphology of the contact area may all be unknown, this problem further manifests as the spatial distribution identification of unknown areas. The key to achieving complex discrete contact state detection lies in effectively describing and updating the spatial distribution of the contact area without pre-determining its location.

[0010] In topology optimization, both the level set method and the density basis method possess certain geometric boundary description capabilities, providing a reference technical approach for such problems. The level set method has advantages in geometric boundary characterization, but its identification results are often sensitive to the initial field distribution. When the actual contact area cannot be estimated in advance, it is difficult to provide a suitable initial boundary. In contrast, the density basis method is relatively less dependent on the initial field and has strong adaptability in identification problems with unknown boundaries, complex regional morphology, or uncertain spatial distribution. However, existing inversion methods based on topological representations are mostly used for material distribution, damaged regions, or structural geometry reconstruction. For complex discrete contact problems caused by local normal constraints, such as clamping contact states, a unified mechanical characterization and identification method is still lacking.

[0011] In summary, existing technologies have the following shortcomings in structural contact state detection, especially in the identification of complex discrete clamping regions: First, direct experimental detection and sensor measurement methods are greatly affected by the contact interface space, structural enclosure, and measurement interference, making it difficult to obtain the true contact area without changing the original contact state.

[0012] Second, contact force or pressure measurement methods usually rely on a limited number of measurement points, making it difficult to obtain the complete location, range, and boundary morphology of complex discrete contact areas.

[0013] Third, traditional finite element contact analysis usually requires pre-defined contact pairs, support geometry, and contact conditions. When the actual contact state is unknown, it is difficult to determine the true contact area through forward analysis.

[0014] Fourth, existing inversion methods based on structural response are mostly based on known boundary locations or preset parameter distributions, making it difficult to handle complex discrete clamping problems where the number, location, shape, and distribution of contact areas are unknown.

[0015] Fifth, data-driven inversion methods typically require a high level of training samples and data coverage, while the amount of data available in actual clamping structures is limited, resulting in insufficient model generalization ability and engineering applicability.

[0016] Sixth, existing methods have not yet fully established a unified mechanical description between discrete contact states, local normal constraints, and spatial region distribution, making it difficult to automatically identify unknown contact states based on surface shape or surface displacement response.

[0017] A search of Chinese Patent Publication No. CN121072013A reveals a method for inverting the displacement field of a thick-walled solid structure based on virtual plying, relating to the field of displacement monitoring and inversion technology for thick-walled solid structures. The steps include: embedding a geometrically attached and mechanically isolated virtual ply on the outer surface of the thick-walled solid structure; collecting surface strain as virtual ply membrane strain by arranging measuring points on one side of the virtual ply neutral plane; constructing a weighted least squares functional containing a membrane strain fitting term and bending and shear strain regularization terms; performing variational decomposition of the functional to obtain the virtual ply node displacements; and mapping the virtual ply translational displacements to the corresponding nodes of the solid structure to achieve displacement field inversion. This existing patent solves the problem of high-precision displacement inversion of thick-walled solid structures with single-sided point arrangement without interfering with structural stress, improves the numerical stability of the inversion, adapts to solid element models, is suitable for structures such as pressure vessels, and can be used for structural health assessment. The existing patent uses virtual plying as the calculation medium for displacement inversion, without involving equivalent treatment of contact constraints. It also uses the inverse finite element method to solve the nodal displacements, without involving the reconstruction of the contact stiffness field, density-based design variables, or topology optimization techniques.

[0018] Therefore, how to automatically identify the spatial distribution of unknown discrete contact areas based on the displacement response of the structural surface when the contact interface cannot be directly observed and the location, quantity, and shape of the contact area are unknown, thus providing technical support for fault diagnosis, clamping optimization, and operational status evaluation of precision clamping structures, has become a technical problem that needs to be solved. Summary of the Invention

[0019] The purpose of this invention is to overcome the defects of the prior art by providing a method and system for detecting structural contact state based on surface displacement.

[0020] The objective of this invention can be achieved through the following technical solutions: According to a first aspect of the present invention, a method for detecting the structural contact state based on surface displacement is provided, the method comprising: Step S1: Obtain the surface displacement or surface shape response information of the clamped structure as the target response; Step S2: Establish a finite element analysis model of the clamped structure; Step S3: Construct the Robin boundary equivalent model of the contact interface, wherein an equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the equivalent contact stiffness field is used to characterize the local contact constraint. Step S4: Introduce density-based design variables to describe the contact state. The density-based design variables are used to characterize the local contact state of the possible contact area. The density-based design variables are correlated with the equivalent contact stiffness through the SIMP nonlinear interpolation function, and the contact state identification problem is transformed into a spatial distribution reconstruction problem of design variables and interface stiffness. Step S5: Construct an objective function based on surface displacement error. The objective function is used to measure the difference between the surface displacement calculated by the finite element model and the target response of step S1. Step S6: Calculate the sensitivity of the objective function to the density-based design variables based on the adjoint sensitivity method, and perform optimization iteration to update the density-based design variables so that the calculated displacement approximates the target response of step S1; Step S7: Determine the contact area based on the equivalent contact stiffness field or the density-based design variable field.

[0021] As a preferred technical solution, in step S1, the surface displacement or surface shape response information of the clamped structure surface is obtained through experimental measurement, online detection or high-precision simulation, and used as the target response.

[0022] As a preferred technical solution, in step S3, constructing the Robin boundary equivalent model of the contact interface specifically involves: An equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the local contact constraint is represented as a spatially varying spring support or Robin boundary condition. The region where the contact stiffness is greater than the set threshold corresponds to the actual contact region, and the region where the contact stiffness is less than the set threshold corresponds to the non-contact region or the region where the contact is detached. The contact stiffness is expressed as: in k s This represents the equivalent contact stiffness at the interface location. E s The elastic modulus of the equivalent spring layer. d s This is the equivalent spring layer thickness; In the normal direction, the Robin boundary condition is expressed as: Where, σ( u Let be the structural stress, and n be the outward normal vector. u For structural displacement, u 0 represents the initial displacement.

[0023] As a preferred technical solution, in step S4, the density-based design variables are specifically: Define density-based design variables i The value range is from 0 to 1, where the density base design variable corresponds to the contact area when it is close to 1 and to the non-contact area when it is close to 0; The density-based design variables are correlated with the equivalent contact stiffness using the SIMP nonlinear interpolation function, specifically as follows: in, E s The elastic modulus of the equivalent spring layer. E max E represents the maximum equivalent elastic modulus corresponding to the contact area. min This represents the minimum equivalent elastic modulus corresponding to the non-contact region. Let q be the projected design variable, and q be the penalty factor.

[0024] As a preferred technical solution, in step S5, constructing the objective function based on surface displacement error specifically involves: The objective function is constructed using the least squares method. Where J is the objective function, Γ m For the measured surface, u is the displacement calculated by the identification model. m The vertical displacement obtained for measurement or reference.

[0025] As a preferred technical solution, the optimization iteration in step S6 specifically includes: The density-based design variables are spatially filtered to suppress numerical noise; The filtered design variables are projected to move closer to 0 or 1 in order to obtain clear contact and non-contact boundaries.

[0026] As a preferred technical solution, step S7, determining the contact region based on the equivalent contact stiffness field or the density-based design variable field, includes: Regions in the equivalent contact stiffness field or the density-based design variable field that are greater than the set threshold are identified as contact regions, and regions that are less than the threshold are identified as non-contact regions.

[0027] According to a second aspect of the present invention, a structural contact state detection system based on surface displacement is provided, comprising: The response acquisition module is used to acquire the surface displacement or surface shape response information of the clamped structure as the target response. The model building module is used to build a finite element analysis model of the clamped structure. An equivalent model construction module is used to construct a Robin boundary equivalent model of the contact interface, wherein an equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the equivalent contact stiffness field is used to characterize local contact constraints. The design variable module is used to introduce density-based design variables to describe the contact state, wherein the density-based design variables are used to characterize the local contact state of the possible contact area. The correlation module is used to establish a correlation between the density-based design variables and the equivalent contact stiffness through the SIMP nonlinear interpolation function, transforming the contact state identification problem into a spatial distribution reconstruction problem of design variables and interface stiffness. The objective function module is used to construct an objective function based on surface displacement error, which measures the difference between the surface displacement calculated by the finite element model and the target response; An optimization module is used to calculate the sensitivity of the objective function to the density-based design variables based on the adjoint sensitivity method, and to perform optimization iterations to update the density-based design variables so that the calculated displacement approximates the target response; The region determination module is used to determine the contact region based on the equivalent contact stiffness field or the density-based design variable field.

[0028] According to a third aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described thereon.

[0029] According to a fourth aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0030] Compared with the prior art, the present invention has the following advantages: 1) This invention successfully transforms the discrete and unknown contact state problem into a continuous design variable and interface stiffness space distribution reconstruction problem by constructing a Robin boundary equivalent model of the contact interface and setting an equivalent contact stiffness field in the interface region where contact may occur. 2) This invention introduces density-based design variables and uses the SIMP nonlinear interpolation function to achieve a refined characterization of the local contact state of the contact area. This makes contact identification no longer dependent on predefined contact pairs or complex discrete contact search algorithms, thus effectively overcoming the shortcomings of traditional forward numerical simulation that cannot be applied due to unknown contact parameters, and traditional direct measurement that is difficult to obtain continuous distribution information due to limited installation space. 3) This invention utilizes the adjoint sensitivity method combined with an optimization iteration strategy. It can efficiently invert and calculate the spatial distribution of the equivalent contact stiffness field using only a small amount of surface displacement or surface response data as the target response, which significantly improves the efficiency and stability of state identification of complex structures in the case of completely unknown discrete contact areas. 4) By setting up spatial filtering and projection processing steps, this invention effectively suppresses numerical noise and drives design variables to converge toward extreme values, thereby obtaining clearly defined contact and non-contact regions and avoiding the problem of blurred contact boundaries in traditional methods. 5) Based on a set threshold, this invention determines the equivalent contact stiffness field or density-based design variable field, which can accurately reconstruct the contact position, quantity and morphology, and realize automated and high-precision detection of the contact state of the structure. 6) This invention not only improves the accuracy and robustness of structural health monitoring, but also greatly simplifies the detection process and reduces the requirements for sensor density, thus having broad application prospects and significant engineering practical value. Attached Figure Description

[0031] Figure 1 This is an overall flowchart of the structural contact state detection method based on surface displacement of the present invention; Figure 2 This is a schematic diagram of the Robin boundary equivalent model of the contact interface of the present invention; Figure 3 This is a schematic diagram illustrating the identification process and results of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0033] Example 1 This invention proposes a structural contact state detection method based on surface displacement. This method identifies the contact state of unknown clamping regions by inverting the displacement or surface shape response of the clamped structure's surface when the contact interface cannot be directly observed. The method equates the local normal contact constraint of the clamping interface to a spatially variable stiffness boundary under Robin boundary conditions, and transforms the identification problem of unknown discrete contact regions into a spatial distribution reconstruction problem of the interface contact stiffness field. By introducing density-based design variables, sensitivity analysis, filtering, and projection processing, the method achieves automatic identification of the contact region's location, extent, and morphology.

[0034] like Figure 1As shown, the method of the present invention specifically includes the following steps: Step 1: Obtain the surface displacement or shape response information of the clamped structure: Obtain the vertical displacement or shape data of the surface of the clamped structure through experimental measurement, online detection, or high-precision simulation, and use it as the target response. The surface displacement or shape response can be the full-field displacement data of the upper surface of the structure, or it can be the displacement data of a limited number of measuring points, a local area, or a specific path. In complex precision instruments, the vertical displacement of the upper surface of the clamped structure can be used as the inversion target.

[0035] Step 2: Establish the finite element analysis model of the clamped structure: Establish a finite element model based on the geometric dimensions, material parameters, external loads, and boundary conditions of the clamped structure. The clamped structure can be a thin plate, sheet, mask, wafer, lens, or other precision support structure. Material parameters include elastic modulus, Poisson's ratio, and density, while external loads include normal pressure, gravity, vacuum suction force, clamping force, or other operating loads.

[0036] Step 3: Construct an equivalent Robin boundary model of the contact interface: An equivalent contact stiffness field is set in the interface region where the clamped structures may make contact, representing local contact constraints as spatially varying spring supports or Robin boundary conditions. Regions with higher contact stiffness correspond to the actual contact area, while regions with lower contact stiffness correspond to non-contact or de-contact areas. Contact stiffness can be expressed as… (1) in, k s E represents the equivalent contact stiffness at the interface location. s d is the elastic modulus of the equivalent spring layer. s This is the equivalent spring layer thickness.

[0037] In the normal direction, the Robin boundary condition can be expressed as: (2) Where, σ( u Let be the structural stress, and n be the outward normal vector. u For structural displacement, u 0 represents the initial displacement. This expression indicates that the normal constraint force at the contact interface is proportional to the local displacement deviation, thus allowing for control over the spatially varying contact stiffness. k s (x) represents the contact state at different locations. Step 4: Introduce density-based design variables to describe the contact state: Define continuous design variables within the potential contact area. i This is used to characterize the local contact state. The range of values ​​for the design variables is... (3) in, i A value close to 1 indicates that the position is approaching a contact state. i A value close to 0 indicates that the position is approaching a non-contact state.

[0038] The design variables are correlated with the equivalent contact stiffness or equivalent elastic modulus using the SIMP nonlinear interpolation function. (4) in, E max This represents the maximum equivalent elastic modulus corresponding to the contact area. E min This represents the minimum equivalent elastic modulus corresponding to the non-contact region. Let be the projected design variables, and q be the penalty factor. It is worth noting that... E max The actual material properties of the clamping structure material can be selected. E min To avoid numerical instability, a minimum value close to zero is usually chosen. The penalty factor can be selected according to the problem type, typically 1, 3, or 5. The contact state identification problem can be transformed into design variables using equations (1)-(4). i and interface stiffness k s The problem of spatial distribution reconstruction.

[0039] Step 5, Construct the objective function based on surface displacement error: Compare the surface displacement calculated by the finite element model with the measured target surface displacement to construct the displacement error objective function. The objective function is constructed using the least squares method: (5) in, J Let Γ be the objective function. m For measuring the surface, u To identify the displacements calculated by the model, u m The vertical displacement is measured or referenced. The objective function measures the difference between the structural response corresponding to the current contact stiffness field and the actual measured response.

[0040] Step 6: Perform sensitivity analysis and update design variables: Based on the finite element equilibrium equations and the objective function, the adjoint sensitivity method is used to calculate the sensitivity of the objective function to the design variables. The gradient information of the design variables across the entire field is obtained through a single adjoint solution. The sensitivity can be expressed as: (6) Where, dJ / d i Describe the objective function J For design variables i The rate of change. Subsequently, a gradient optimization algorithm is used to update the design variables, so that the calculated displacement gradually approximates the measured displacement.

[0041] Step 7: Filter and project the design variables: To suppress checkerboard patterns, local oscillations, and numerical noise, spatial filtering is performed on the design variables or sensitivities. The filtering radius can be determined based on the grid size, typically 1-3 times the grid size. The filtered design variables can be expressed as: (7) in, i f The filtered design variables are represented by Filter[ ], which denotes the spatial filtering operator. Furthermore, a projection function is used to drive the design variables towards 0 (non-contact) or 1 (contact), thereby obtaining clear contact and non-contact boundaries.

[0042] The projected design variables can be expressed as: (8) in, i p The projection is the design variable after projection, and Projection[] represents the projection operator.

[0043] The projection slope in the projection function can be gradually increased, for example, from 1 to 6, 12 or higher, to improve the binarization of the contact area recognition results.

[0044] Step 8: Determine convergence and output the contact state identification result: Stop the optimization iteration when the change in the objective function, the change in the design variables, or the iterative residual meets the preset convergence condition. The convergence condition can be set as the maximum change in the design variables being less than 10. -3 Up to 10 -6 The contact area is ultimately determined based on the interface stiffness field or design variable field. Areas with higher design variables or equivalent stiffness are identified as contact areas, while areas with lower design variables or equivalent stiffness are identified as non-contact areas. The contact area boundary can be extracted by setting a threshold, for example, using the median value of the final design variable (0.5) as the threshold; values ​​greater than 0.5 are considered contact areas, and values ​​less than 0.5 are considered non-contact areas.

[0045] Through the above steps, the present invention can obtain the equivalent contact stiffness distribution of an unknown clamping region by utilizing the measurable displacement or surface response of the structural surface without directly measuring the contact interface, and further identify the location, range and morphology of the contact region, thereby realizing the automatic detection of complex discrete contact states.

[0046] The present invention achieves the following technical effects through the above technical solution: 1. No direct measurement of the contact interface is required, making it suitable for clamping structures that are enclosed, confined, and difficult to arrange sensors: This invention utilizes measurable displacement or surface shape response information from the surface of the clamped structure to invert and identify the contact state, eliminating the need to place pressure sensors, thin-film sensors, or other detection elements at the contact interface. Therefore, this method avoids interference from sensor installation on the original contact state and is suitable for engineering scenarios such as semiconductor equipment and precision clamping devices where the contact interface is invisible, inaccessible, or where measurement space is limited.

[0047] 2. It can automatically identify unknown discrete contact regions without relying on pre-defined contact locations, quantities, and shapes: This invention transforms the unknown contact state into a spatial distribution reconstruction problem of the interface stiffness field, and describes the spatial distribution of the contact region through density-based design variables. Compared with traditional finite element contact analysis or boundary condition inversion methods, this invention does not require pre-defining the location, quantity, and boundary shape of the actual contact region. It can automatically obtain the location, extent, and morphology of the contact region based on the surface displacement response, making it suitable for contact state detection in complex discrete clamping regions.

[0048] 3. This invention transforms the complex contact identification problem into a continuous stiffness field inversion problem, improving computational stability and engineering feasibility: It characterizes local contact constraints using Robin boundary conditions and an equivalent spring model, representing the contact region as a high-stiffness interface region and the non-contact region as a low-stiffness interface region, thus avoiding the direct solution of complex contact nonlinear problems. This method can be optimized and updated by combining filtering, projection, and adjoint sensitivity analysis, improving identification efficiency while obtaining clear contact / non-contact determination results, demonstrating good computational stability and engineering application value.

[0049] Example 2 This embodiment is only used to explain the technical solution of the present invention and is not intended to limit the scope of protection of the present invention. For structures with clamping or supporting contact interfaces, the same or similar methods can be used for contact state detection.

[0050] In this embodiment, the clamped structure is a rectangular thin plate. Several potential contact support areas exist on the bottom of this thin plate, but the actual location, number, and extent of these contact areas are unknown. Since the contact interface is located at the bottom of the thin plate and the support structure is densely distributed, it is difficult to directly place sensors to obtain the contact state. Therefore, the method described in this invention is used to identify the bottom contact state by inverting the vertical displacement or surface response of the upper surface of the thin plate.

[0051] First, the displacement or surface response data of the clamped structure surface is acquired. This data can be obtained through interferometry, displacement sensors, online detection systems, or high-precision simulation. In this embodiment, the vertical displacement of the upper surface of the thin plate is preferably used as the target response to characterize the structural deformation under actual clamping conditions.

[0052] Secondly, a finite element analysis model is established based on the geometric dimensions, material parameters, external loads, and boundary conditions of the clamped structure. In the finite element model, the clamped structure adopts a linear elastic material model, and the material parameters include the elastic modulus and Poisson's ratio. The external loads can be surface pressure, vacuum suction force, gravity, clamping force, or other actual working condition loads.

[0053] Then, equivalent contact boundaries are established in the areas where contact may occur at the bottom of the clamped structure. The local contact constraints at the bottom are equated to Robin boundary conditions or equivalent spring layer models, such as... Figure 2 As shown, areas with higher equivalent contact stiffness represent actual contact areas, while areas with lower equivalent contact stiffness represent non-contact or non-contact areas.

[0054] Set continuous design variables in the potential contact area i Its value range is 0 ≤ θ ≤ 1. When i When it approaches 1, the position tends to be in a contact state; when i When the value approaches 0, the location tends to be in a non-contact state. By using the interpolation relationship between design variables and equivalent elastic modulus or equivalent contact stiffness, the contact state identification problem is transformed into a spatial distribution reconstruction problem of the interface stiffness field.

[0055] In this embodiment, the equivalent contact stiffness can be described using the following relationship: in, k s This represents the equivalent contact stiffness at the interface location. E s The elastic modulus of the equivalent spring layer. d s This is the equivalent spring layer thickness.

[0056] The following interpolation relationship can be used between the design variables and the equivalent elastic modulus: in, E max This represents the maximum equivalent elastic modulus corresponding to the contact area. E min Let q be the minimum equivalent elastic modulus corresponding to the non-contact region, and q be the penalty factor.

[0057] Furthermore, an objective function based on surface displacement error is constructed. The surface vertical displacement calculated by the finite element model is compared with the measured surface vertical displacement to minimize the error between the two. in, J Let be the objective function. u z The calculated vertical displacement, u zr The measured vertical displacement. Γ m The measurable surface area is the upper surface in this case.

[0058] Subsequently, sensitivity analysis is used to calculate the sensitivity of the objective function to the design variables, and the design variables are updated based on the sensitivity information. Preferably, adjoint sensitivity analysis is used to obtain the gradient information of the objective function with respect to all design variables through a single adjoint solution. The design variable updates can employ the Moving Asymptote Method (MMA), the Snopt algorithm, or other constrained optimization algorithms.

[0059] During the optimization process, to suppress local oscillations and checkerboard patterns in the design variable field, spatial filtering can be applied to the design variables or sensitivities. The filtered design variables can be expressed as: in, i h For the filtered design variables, i 0 is the initial design variable.

[0060] To further clarify the contact and non-contact boundaries, the filtered design variables can be projected. The projected design variables can be expressed as: in, i p For the projected design variables, i h For the filtered design variables, β The projection slope, i β Let be the projection point. β A gradual increase can be used to push the design variables closer to 0 or 1.

[0061] The optimization iteration stops when the change in the objective function, the change in design variables, or the iterative residual meets the preset convergence condition. Finally, the contact region is extracted based on the projected design variable field or the equivalent contact stiffness field. For example, when... i p ≥ ith When, the area is determined to be the contact area; when i p < i th At that time, the area is determined to be a non-contact area. Among them, i th The contact determination threshold is preferably set to 0.5.

[0062] Through the above steps, the location, extent, and boundary morphology of the unknown contact area at the bottom of the clamped structure can be obtained. For areas that are actually in contact, the inverted design variables or interface stiffness are higher; for areas that are actually out of contact or not in contact, the inverted design variables or interface stiffness are lower, such as... Figure 3 As shown. Therefore, this embodiment can identify the contact state of an unknown discrete clamping region by utilizing only the surface displacement or surface shape response of the clamped structure without directly measuring the contact interface.

[0063] Example 3 This invention relates to a structural contact state detection system based on surface displacement, comprising: The response acquisition module is used to acquire the surface displacement or surface shape response information of the clamped structure as the target response. The model building module is used to build a finite element analysis model of the clamped structure. An equivalent model construction module is used to construct a Robin boundary equivalent model of the contact interface, wherein an equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the equivalent contact stiffness field is used to characterize local contact constraints. The design variable module is used to introduce density-based design variables to describe the contact state, wherein the density-based design variables are used to characterize the local contact state of the possible contact area. The correlation module is used to establish a correlation between the density-based design variables and the equivalent contact stiffness through the SIMP nonlinear interpolation function, transforming the contact state identification problem into a spatial distribution reconstruction problem of design variables and interface stiffness. The objective function module is used to construct an objective function based on surface displacement error, which measures the difference between the surface displacement calculated by the finite element model and the target response; An optimization module is used to calculate the sensitivity of the objective function to the density-based design variables based on the adjoint sensitivity method, and to perform optimization iterations to update the density-based design variables so that the calculated displacement approximates the target response; The region determination module is used to determine the contact region based on the equivalent contact stiffness field or the density-based design variable field.

[0064] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0065] Example 4 This invention also provides an electronic device including a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or loaded from a storage unit into a random access memory (RAM). The RAM may also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0066] Multiple components in the device are connected to the I / O interface, including: input units such as keyboards and mice; output units such as various types of displays and speakers; storage units such as disks and optical discs; and communication units such as network interface cards (NICs), modems, and wireless transceivers. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0067] The processing unit performs the various methods and processes described above, such as the methods of the present invention. For example, in some embodiments, the methods of the present invention may be implemented as computer software programs tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of the methods of the present invention described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute the methods of the present invention by any other suitable means (e.g., by means of firmware).

[0068] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0069] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0070] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0071] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for detecting the structural contact state based on surface displacement, characterized in that, The method includes: Step S1: Obtain the surface displacement or surface shape response information of the clamped structure as the target response; Step S2: Establish a finite element analysis model of the clamped structure; Step S3: Construct the Robin boundary equivalent model of the contact interface, wherein an equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the equivalent contact stiffness field is used to characterize the local contact constraint. Step S4: Introduce density-based design variables to describe the contact state. The density-based design variables are used to characterize the local contact state of the possible contact area. The density-based design variables are correlated with the equivalent contact stiffness through the SIMP nonlinear interpolation function, and the contact state identification problem is transformed into a spatial distribution reconstruction problem of design variables and interface stiffness. Step S5: Construct an objective function based on surface displacement error. The objective function is used to measure the difference between the surface displacement calculated by the finite element model and the target response of step S1. Step S6: Calculate the sensitivity of the objective function to the density-based design variables based on the adjoint sensitivity method, and perform optimization iteration to update the density-based design variables so that the calculated displacement approximates the target response of step S1; Step S7: Determine the contact area based on the equivalent contact stiffness field or the density-based design variable field.

2. The structural contact state detection method based on surface displacement according to claim 1, characterized in that, In step S1, the surface displacement or surface shape response information of the clamped structure surface is obtained through experimental measurement, online detection or high-precision simulation, and used as the target response.

3. The structural contact state detection method based on surface displacement according to claim 1, characterized in that, In step S3, constructing the Robin boundary equivalent model of the contact interface specifically involves: An equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the local contact constraint is represented as a spatially varying spring support or Robin boundary condition. The region where the contact stiffness is greater than the set threshold corresponds to the actual contact region, and the region where the contact stiffness is less than the set threshold corresponds to the non-contact region or the region where the contact is detached. The contact stiffness is expressed as: in k s This represents the equivalent contact stiffness at the interface location. E s The elastic modulus of the equivalent spring layer. d s This is the equivalent spring layer thickness; In the normal direction, the Robin boundary condition is expressed as: Where, σ( u Let be the structural stress, and n be the outward normal vector. u For structural displacement, u 0 represents the initial displacement.

4. The structural contact state detection method based on surface displacement according to claim 1, characterized in that, In step S4, the density-based design variables are specifically: Define density-based design variables θ The value range is from 0 to 1, where the density base design variable corresponds to the contact area when it is close to 1 and to the non-contact area when it is close to 0; The density-based design variables are correlated with the equivalent contact stiffness using the SIMP nonlinear interpolation function, specifically as follows: in, E s The elastic modulus of the equivalent spring layer. E max This represents the maximum equivalent elastic modulus corresponding to the contact area. E min This represents the minimum equivalent elastic modulus corresponding to the non-contact region. Let q be the projected design variable, and q be the penalty factor.

5. The structural contact state detection method based on surface displacement according to claim 1, characterized in that, In step S5, the objective function based on surface displacement error is constructed as follows: The objective function is constructed using the least squares method. in, J Let Γ be the objective function. m For measuring the surface, u To identify the displacements calculated by the model, u m The vertical displacement obtained for measurement or reference.

6. The structural contact state detection method based on surface displacement according to claim 1, characterized in that, In step S6, the optimization iteration specifically includes: The density-based design variables are spatially filtered to suppress numerical noise; The filtered design variables are projected to move closer to 0 or 1 in order to obtain clear contact and non-contact boundaries.

7. The method for detecting structural contact state based on surface displacement according to claim 1, characterized in that, In step S7, determining the contact region based on the equivalent contact stiffness field or the density-based design variable field includes: Regions in the equivalent contact stiffness field or the density-based design variable field that are greater than the set threshold are identified as contact regions, and regions that are less than the threshold are identified as non-contact regions.

8. A structural contact state detection system based on surface displacement, characterized in that, include: The response acquisition module is used to acquire the surface displacement or surface shape response information of the clamped structure as the target response. The model building module is used to build a finite element analysis model of the clamped structure. An equivalent model construction module is used to construct a Robin boundary equivalent model of the contact interface, wherein an equivalent contact stiffness field is set in the interface region where the clamped structure may make contact, and the equivalent contact stiffness field is used to characterize local contact constraints. The design variable module is used to introduce density-based design variables to describe the contact state, wherein the density-based design variables are used to characterize the local contact state of the possible contact area. The correlation module is used to establish a correlation between the density-based design variables and the equivalent contact stiffness through the SIMP nonlinear interpolation function, transforming the contact state identification problem into a spatial distribution reconstruction problem of design variables and interface stiffness. The objective function module is used to construct an objective function based on surface displacement error, which measures the difference between the surface displacement calculated by the finite element model and the target response; An optimization module is used to calculate the sensitivity of the objective function to the density-based design variables based on the adjoint sensitivity method, and to perform optimization iterations to update the density-based design variables so that the calculated displacement approximates the target response; The region determination module is used to determine the contact region based on the equivalent contact stiffness field or the density-based design variable field.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 7.

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