A large-format closed area internal gap and small displacement high-precision measurement method based on a flexible pressure sensor

Abstract

A large-format closed area internal gap and small displacement high-precision measurement method based on a flexible pressure sensor, comprising: 1) attaching a sensor array between the base layer structure and the skin, collecting the local array signal of the fitting interface between the base layer structure and the skin; 2) constructing a composite material structure mechanics model; 3) inputting the collected local array signal into the composite material structure mechanics model to obtain the gap height of the fitting interface; 4) processing the gap height of the fitting interface by using a spatial interpolation and fitting algorithm to generate a continuous fitting gap atlas. The application has strong flexibility, and the multi-physical quantity collaborative sensing improves the accuracy and anti-interference ability of the fitting state recognition. The application can effectively correct the deviation caused by the thickness shear error and the curvature. The application has strong gap reconstruction capability, realizes quantitative evaluation and visual expression of the fitting quality. The application supports dynamic fitting process and supports software and hardware system integration.

Description

Technical Field

[0001] This invention relates to the field of gap measurement technology, specifically to a high-precision method for measuring the gap and minute displacement inside a large-format enclosed area based on a flexible pressure sensor. Background Technology

[0002] In aerospace and high-end manufacturing, large composite material components (such as skins, beams, and compartments) are often reinforced or functionally integrated (e.g., corrosion protection, electromagnetic shielding) through lamination processes. However, the lamination process can easily create minute gaps that are difficult to detect, potentially leading to problems such as decreased airtightness, interlayer delamination, or electrical performance failure. Therefore, achieving high-precision detection of these minute gaps is of significant engineering importance.

[0003] In existing technologies, some solutions have attempted to monitor the bonding state of composite material structures using capacitive displacement sensors or piezoresistive thin-film structures. These technologies mostly employ rigid parallel plate structures as capacitor units, which are attached to the back of the mold or skin to sense local deformation. However, these structures are typically distributed at single points or a small number of points, lacking flexible array capabilities and making it difficult to adapt to the complex curvature and large-area coverage requirements of actual skin bonding processes. Furthermore, existing capacitive sensors often lack environmental drift compensation or self-calibration capabilities, making them susceptible to changes in temperature and humidity, electromagnetic interference, and other factors, affecting measurement stability and long-term repeatability.

[0004] In terms of modeling and data processing, most existing technologies only provide simplified descriptions of structural responses based on linear thin-plate theory, failing to consider the anisotropic stiffness of composite material laminates, the effects of shear deformation, and the nonlinear large deformation behavior generated during surface bonding. Furthermore, the vast majority of existing methods rely solely on a single physical quantity such as displacement or pressure for bonding evaluation, lacking a complete mechanical inversion model for accurate measurement of bonding gaps. This prevents the continuous reconstruction of the bonding gap field and the establishment of a response mechanism suitable for dynamic bonding processes. Currently available technologies cannot meet the requirements for high-precision, multi-point array, flexible deployment, and dynamically adaptable bonding gap detection, especially in scenarios such as complex composite material structure bonding, automated manufacturing, and quality visualization inspection, where significant technological gaps remain.

[0005] Current composite material bonding condition detection technologies suffer from several technical shortcomings and application bottlenecks, limiting their widespread application in high-performance composite material manufacturing and assembly quality monitoring:

[0006] Existing capacitive or piezoresistive sensors generally suffer from high structural rigidity and poor flexibility, making it difficult to achieve full-coverage measurement of large-sized curved surface bonding areas. During the bonding process, the skin often has complex hypercurvature and continuous curved surface structures, making it impossible for traditional rigid or semi-rigid sensors to stably bond between interfaces, affecting data acquisition accuracy and regional integrity, and lacking the ability to be peeled off and reused. Furthermore, existing technologies mostly use single-point measurements or a small number of distributed points, failing to form continuous area array data support and lacking the basic data density for reconstructing the bonding gap field distribution. At the same time, traditional methods often only collect single physical quantities (such as strain, pressure, or displacement), without constructing a multi-physical quantity collaborative measurement and modeling mechanism, making it difficult to accurately reflect the true deformation state and gap distribution of the bonding interface.

[0007] In terms of theoretical modeling, existing methods are mostly simplified derivations based on ideal plate structures, linear assumptions, and uniform load premises, neglecting the stiffness heterogeneity, shear effects, and nonlinear response characteristics caused by the curved surface morphology of composite laminate structures. Furthermore, they lack the mathematical mapping relationship to invert the actual bonding gap height from measurement signals, making it impossible to achieve direct quantitative calculation and visualization reconstruction of the bonding gap. Currently available solutions generally lack the modeling and adaptability for dynamic bonding processes. In actual automated bonding scenarios (such as vacuum adsorption, flexible roller pressing, and robotic pressing), they cannot perform time-domain tracking and real-time feedback control of the structural response process, nor have they established response prediction models based on dynamic mechanical mechanisms.

[0008] Therefore, existing technologies are not yet able to achieve high-precision, array-based, and reconfigurable gap detection and quality evaluation of composite material structure bonding interfaces on a non-destructive, in-situ, scalable, and dynamically adaptable basis. Breakthroughs are urgently needed in key areas such as sensor structure design, modeling theory, data fusion, and gap inversion. Summary of the Invention

[0009] The purpose of this invention is to provide a high-precision method for measuring the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor, comprising the following steps:

[0010] 1) Attach the sensor array between the base structure and the skin to collect local array signals at the bonding interface between the base structure and the skin.

[0011] 2) Construct a mechanical model of composite material structure.

[0012] 3) Input the collected local array signals into the mechanical model of the composite material structure to obtain the gap height of the bonding interface.

[0013] 4) Spatial interpolation and fitting algorithms are used to process the gap height of the bonding interface to generate a continuous bonding gap map.

[0014] Furthermore, the sensor array includes a distributed capacitive-pressure coupled sensing sensor layer.

[0015] The distributed capacitive-pressure coupled sensing sensor layer includes an integrated flexible bonding structure layer, signal lead-out lines, circuit units, and a flexible substrate layer.

[0016] The integrated flexible bonding structure layer includes several pressure sensors and several capacitive displacement sensors.

[0017] Several pressure sensors are evenly arranged to form a surface array sensor network, which is used to collect local pressure array signals.

[0018] Several capacitive displacement sensors are evenly arranged at preset intervals to form a flexible capacitive displacement sensor array.

[0019] The flexible capacitive displacement sensor array is used to collect load distribution during the bonding process of the base structure and the skin.

[0020] The flexible capacitive displacement sensor array and the area array sensor network are interspersed or integrated in the same layer.

[0021] The signal lead-out line and circuit unit are disposed on one side of the flexible substrate layer.

[0022] The circuit unit is used to receive the local pressure array signal collected by the pressure sensor and to preprocess the received local pressure array signal.

[0023] The circuit unit is used to receive the load distribution collected by the capacitive displacement sensor and to preprocess the received load distribution.

[0024] The preprocessing includes signal amplification, filtering, and level adjustment.

[0025] The signal lead is used to transmit the preprocessed local pressure array signal and load distribution to an external processing chip.

[0026] The external processing chip stores a mechanical model of the composite material structure.

[0027] The flexible substrate layer is used to mount the integrated flexible bonding structure layer.

[0028] Furthermore, when the sensor array is a distributed capacitive-pressure coupled sensing sensor layer, the steps for constructing the mechanical model of the composite material structure are as follows:

[0029] 2.1.1) Construct the stiffness function of the skin structure as follows:

[0030]

[0031] In the formula, D0 represents the total bending stiffness of the skin structure. E M ν represents the equivalent Young's modulus. h represents the total skin thickness. M This represents the equivalent Poisson's ratio.

[0032] 2.1.2) Construct a parallel plate model of a capacitive displacement sensor, and then establish the capacitance-displacement conversion relationship to obtain displacement data.

[0033] The parallel plate model of the capacitive displacement sensor is shown below:

[0034]

[0035] In the formula, a spatial coordinate system is constructed with the lower left corner of the integrated flexible bonding structure layer as the origin, the plane of the integrated flexible bonding structure layer as the xoy plane, and the direction perpendicular to the plane of the integrated flexible bonding structure layer as the z-axis. x and y represent the horizontal and vertical coordinates in the spatial coordinate system, respectively. C(x,y) represents the capacitance value measured by the capacitive displacement sensor at coordinate (x,y). ε r ε0 represents the equivalent dielectric constant of the bonding interface. ε0 represents the vacuum dielectric constant. A represents the effective area of ​​the capacitive displacement sensor. d(x,y) represents the local gap distance at coordinates (x,y).

[0036] The capacitance-displacement conversion relationship is as follows:

[0037]

[0038] In the formula, w(x,y) represents the displacement of the interface in the z-direction at coordinate (x,y). This indicates the conversion formula.

[0039] 2.1.3) Based on the first-order shear deformation plate theory, the displacement field at any point on the bonding interface is described, and the displacement data is optimized based on the displacement field to obtain the optimized displacement data.

[0040] 2.1.4) Introducing the mid-surface deformable shell theory, parametric modeling of the curved surface structure of the mating interface is performed to obtain the curved surface structure adaptation model and determine the mid-surface point location.

[0041] 2.1.5) Establish the transient relationship between structure-load-response, dynamically model the bonding process between the base structure and the skin, obtain the nonlinear vibration response model, and solve the nonlinear vibration response model based on the optimized displacement data to determine the displacement data of the mid-surface point.

[0042] 2.1.6) Construct the load function of the pressure sensor.

[0043] 2.1.7) Based on the stiffness function, displacement data of mid-surface points, and load function, a function for calculating the gap height is constructed as follows:

[0044]

[0045] In the formula, h represents the gap height. a and b represent the lengths of the mating interface in the x and y directions, respectively. Indicates coordinates The displacement of the mating interface in the z-direction. F represents the load value measured by the area array sensor network.

[0046] Furthermore, the displacement field at any point on the bonding interface is shown below:

[0047]

[0048] In the formula, x, y, and z represent the abscissa, ordinate, and ordinate in the spatial coordinate system, respectively. u0(·), v0(·), and w0(·) are all mid-surface displacement functions. φ x (·), φ y (·) represents the transverse shear angle. u(x,y,z), v(x,y,z), and w(x,y,z) represent the displacements of the interface at coordinate (x,y,z) in the x, y, and z directions, respectively.

[0049] Furthermore, the parameters in the parametric modeling of the curved surface structure of the bonding interface include mid-surface points and strain terms.

[0050] The mid-surface points are shown below:

[0051]

[0052] In the formula, x and y represent the horizontal and vertical coordinates in the spatial coordinate system, respectively. Indicates the middle surface in ξ i Covariant basis vectors / tangential basis vectors in direction. ξ i These represent the curvilinear coordinate parameters of the mid-surface deformable shell. i = 1 corresponds to the x-direction. i = 2 corresponds to the y-direction. This represents the position vector of any point on the mid-surface.

[0053] The strain term is as follows:

[0054]

[0055] In the formula, ε1 and ε2 both represent strain terms. A1 and A2 are the basis modulus lengths of the mid-plane. R1 and R2 are the principal radii of curvature. u1, u2, and u3 represent the displacement components along the x, y, and z directions, respectively. a1 and a2 represent the basis components of the mating interface in the x and y directions, respectively. γ 12 This represents shear strain.

[0056] Furthermore, the control variational form of the nonlinear vibration response model is shown below:

[0057]

[0058] In the formula, t2 and t1 represent the upper and lower limits of the fixed time boundary, respectively. t represents time. δU is the virtual strain energy generated by structural deformation. δW is the virtual work done by the applied load.

[0059] The structural inertial-related virtual kinetic energy δK is shown below:

[0060]

[0061] In the formula, x, y, and z represent the horizontal, vertical, and horizontal coordinates in the spatial coordinate system, respectively. h represents the gap height. Ω0 represents the mid-surface region. These represent the velocity components along the x, y, and z directions, respectively. ρ(x,y,z) represents the material density function. These represent the virtual displacement velocity components along the x, y, and z directions, respectively.

[0062] Solving for the variational form of the control equations, we obtain the system response control equations, as shown below:

[0063]

[0064] In the formula, w1 represents the acceleration, velocity, and displacement of the generalized displacement of the first mode, respectively. γ1 represents the equivalent damping coefficient of the first mode. ω1 is the natural angular frequency of the first mode. ζ1 and ζ2 represent the self-nonlinear stiffness coefficient of the first mode and the coupling nonlinear coefficient of the second mode, respectively. ω2 represents the generalized displacement of the second mode. η1 represents the forced participation coefficient of the first mode. f represents the equivalent external load amplitude. Ω1 represents the external harmonic excitation angular frequency.

[0065] Furthermore, the load function of the pressure sensor is as follows:

[0066] F(x,y) = p(x,y)·A s (11)

[0067] In the formula, x and y represent the abscissa and ordinate in the spatial coordinate system, respectively. F(x,y) represents the equivalent applied load at coordinate (x,y). p(x,y) represents the pressure value measured by the pressure sensor at coordinate (x,y). A s This indicates the effective area of ​​a single pressure sensor.

[0068] Furthermore, the sensor array includes a distributed pressure sensor layer.

[0069] The distributed pressure sensor layer includes several pressure sensors, signal leads, circuit units, and a flexible substrate layer.

[0070] Several pressure sensors are evenly arranged to form a surface array sensor network, which is used to collect local pressure array signals.

[0071] The signal lead-out line and circuit unit are disposed on one side of the flexible substrate layer.

[0072] The circuit unit is used to receive the local pressure array signal collected by the pressure sensor and to preprocess the received local pressure array signal.

[0073] The preprocessing includes signal amplification, filtering, and level adjustment.

[0074] The signal lead is used to transmit the preprocessed local pressure array signal to an external processing chip.

[0075] The external processing chip stores a mechanical model of the composite material structure.

[0076] The flexible substrate is used to mount an array-type sensor network.

[0077] Furthermore, when the sensor array is a distributed pressure sensor layer, the steps for constructing a mechanical model of the composite material structure are as follows:

[0078] 2.2.1) Construct the load function as follows:

[0079]

[0080] In the formula, This represents the pressure value measured by the j0th pressure sensor. A s This indicates the effective area of ​​a single pressure sensor. Indicates the j-th o The load value at the pressure sensor.

[0081] 2.2.2) Based on the load function, the displacement field is obtained through pressure distribution inversion, as shown below:

[0082]

[0083] In the formula, Indicates the j-th o The displacement field at each pressure sensor. H represents the compliance matrix. Indicates the j-th o The load value at the pressure sensor.

[0084] 2.2.3) Based on the displacement field, a function for solving the gap height is constructed as follows:

[0085]

[0086] In the formula, h represents the gap height. D0 represents the total bending stiffness of the skin structure. This represents the displacement field. 'a' represents the horizontal side length of the interface. 'F' represents the load value measured by the area array sensor network.

[0087] Furthermore, the spatial interpolation and fitting algorithms include cubic splines, RBF, and polynomial regression.

[0088] The continuous bonding gap pattern is shown below:

[0089] h)x j ,y j )=Interp{h j} (15)

[0090] In the formula, a spatial coordinate system is constructed with the lower left corner of the integrated flexible bonding structure layer as the origin, the plane of the integrated flexible bonding structure layer as the xoy plane, and the direction perpendicular to the plane of the integrated flexible bonding structure layer as the z-axis. x and y represent the horizontal and vertical coordinates in the spatial coordinate system, respectively. j represents the index of a point in the integrated flexible bonding structure layer. (x j ,y j h(x) represents the coordinates of the j-th point. j ,y j ) indicates that at coordinate (x j ,y j The patch gap value at point (). Interp represents the spatial interpolation and fitting algorithm.

[0091] Where, in coordinate (x j ,y j The gap height h at point ) j As shown below:

[0092]

[0093] In the formula, D0 represents the total bending stiffness of the skin structure. j This represents the displacement measured at point j. 'a' represents the horizontal side length of the interface. F j This represents the load value measured at the j-th point.

[0094] The technical effects of this invention are undeniable, and its beneficial effects are as follows:

[0095] 1. High flexibility and adaptability: This invention employs a flexible capacitor and pressure sensor array, which can be fitted to complex curved surfaces to achieve large-area fitting measurement. Compared to traditional rigid sensors, it has better interface adaptability and reusability.

[0096] 2. Multi-physical quantity collaborative sensing: By simultaneously measuring displacement and pressure, a multi-source data coupling model is constructed to improve the accuracy and anti-interference capability of fit state recognition. This differs from single-channel solutions that only collect strain or displacement data.

[0097] 3. High-precision structural modeling, incorporating shear deformation theory and shell modeling methods, better reflects the nonlinear response characteristics of composite materials. It effectively corrects for deviations caused by thickness shearing errors and curvature.

[0098] 4. Strong gap reconstruction capability: This invention establishes a bonding gap inversion model based on multi-point measurement results, which can generate a continuous distribution map. This enables quantitative evaluation and visual representation of bonding quality.

[0099] 5. Supports dynamic bonding processes. By introducing Hamilton's principle to establish a nonlinear dynamic model, it can adapt to dynamic working conditions such as automatic pressing and vacuum adsorption. It has the ability to identify transient bonding states in real time.

[0100] 6. Excellent integration and scalability; the sensor module can be expanded into an array and supports hardware and software system integration. It is easy to deploy in industrial automated bonding systems and is suitable for the entire process of composite material assembly and manufacturing. Attached Figure Description

[0101] Figure 1 This is a flowchart of the present invention;

[0102] Figure 2 A schematic diagram of the overall structure for measuring the micro-gap of a large composite component after molding and application of the mold. Figure 2 (a) is a schematic diagram of the distributed pressure sensor layer structure; Figure 2 (b) is a schematic diagram of the distributed capacitive-pressure coupled sensing sensor layer structure;

[0103] Figure 3 A schematic diagram of pulse injection ranging and waveform reflection; Figure 3 (a) is a schematic diagram of the distributed pressure sensor layer structure; Figure 3 (b) is a schematic diagram of the flexible structure of the distributed pressure sensor layer; Figure 3 (c) is a schematic diagram of the distributed capacitive-pressure coupled sensing sensor layer structure; Figure 3 (d) is a schematic diagram of the flexible structure of the distributed capacitive-pressure coupled sensing sensor layer;

[0104] Figure 4 Schematic diagram for measuring the gap between the front and back molds using micro-gap measurement; Figure 4 (a) is a schematic diagram of the open gap of the positive mold; Figure 4 (b) is a schematic diagram of the closed gap of the positive mold; Figure 4 (c) is a schematic diagram of the closed gap of the reverse mold; Figure 4(d) is a schematic diagram of the open gap of the reverse mold;

[0105] Figure 5 This is a schematic diagram illustrating the stress-strain relationship principle of the shell.

[0106] Figure 6 This is a diagram illustrating the bonding gap detection and map reconstruction process based on a sensor array.

[0107] In the diagram: 1. Skin; 2. Base structure; 3. Distributed pressure sensor layer; 4. Distributed capacitive-pressure coupling sensing sensor layer; 5. Pressure sensor; 6. Capacitive displacement sensor. Detailed Implementation

[0108] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0109] Example 1:

[0110] See Figures 1 to 6 A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor includes the following steps:

[0111] 1) Attach the sensor array between the base structure and the skin to collect local array signals at the bonding interface between the base structure and the skin.

[0112] 2) Construct a mechanical model of composite material structure.

[0113] 3) Input the collected local array signals into the mechanical model of the composite material structure to obtain the gap height of the bonding interface.

[0114] 4) Spatial interpolation and fitting algorithms are used to process the gap height of the bonding interface to generate a continuous bonding gap map.

[0115] Example 2:

[0116] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is described in Example 1. Further, the sensor array includes a distributed capacitive-pressure coupled sensing sensor layer 4.

[0117] The distributed capacitive-pressure coupled sensing sensor layer 4 includes an integrated flexible bonding structure layer, signal lead-out lines, circuit units, and a flexible substrate layer.

[0118] The integrated flexible bonding structure layer includes several pressure sensors 5 and several capacitive displacement sensors 6.

[0119] Several pressure sensors 5 are evenly arranged to form a surface array sensor network, which is used to collect local pressure array signals.

[0120] Several capacitive displacement sensors 6 are evenly arranged at preset intervals to form a flexible capacitive displacement sensor array.

[0121] The flexible capacitive displacement sensor array is used to collect the load distribution during the bonding process between the base structure 2 and the skin 1.

[0122] The flexible capacitive displacement sensor array and the area array sensor network are interspersed or integrated in the same layer.

[0123] The signal lead-out line and circuit unit are disposed on one side of the flexible substrate layer.

[0124] The circuit unit is used to receive the local pressure array signal collected by the pressure sensor 5 and to preprocess the received local pressure array signal.

[0125] The circuit unit is used to receive the load distribution collected by the capacitive displacement sensor 6 and to preprocess the received load distribution.

[0126] The preprocessing includes signal amplification, filtering, and level adjustment.

[0127] The signal lead is used to transmit the preprocessed local pressure array signal and load distribution to an external processing chip.

[0128] The external processing chip stores a mechanical model of the composite material structure.

[0129] The flexible substrate layer is used to mount the integrated flexible bonding structure layer.

[0130] Structure 2: The distributed sensor array consists of, from top to bottom, a flexible substrate layer, an integrated flexible bonding structure layer, and a signal lead-out / circuit unit layer. The integrated flexible bonding structure layer integrates the following units: a flexible capacitive displacement sensor array, each capacitor unit including upper and lower electrode structures, positioned perpendicular to the bonding direction, responding to changes in the bonding spacing; a flexible pressure sensor array, interspersed with or integrated in the same layer as the capacitor array, used to measure load distribution during the bonding process; a dielectric layer disposed between the capacitor electrodes to enhance sensitivity and environmental stability; and a multi-channel data lead-out module, connected to a host controller, enabling synchronous acquisition and joint analysis of pressure and displacement signals.

[0131] Example 3:

[0132] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is disclosed in any one of Examples 1 and 2. Further, when the sensor array is a distributed capacitive-pressure coupled sensing sensor layer 4, the steps for constructing the mechanical model of the composite material structure are as follows:

[0133] 2.1.1) Construct the stiffness function of the skin structure as follows:

[0134]

[0135] In the formula, D0 represents the total bending stiffness of the skin structure. E M ν represents the equivalent Young's modulus. h represents the total skin thickness. M This represents the equivalent Poisson's ratio.

[0136] 2.1.2) Construct a parallel plate model of a capacitive displacement sensor, and then establish the capacitance-displacement conversion relationship to obtain displacement data.

[0137] The parallel plate model of the capacitive displacement sensor is shown below:

[0138]

[0139] In the formula, a spatial coordinate system is constructed with the lower left corner of the integrated flexible bonding structure layer as the origin, the plane of the integrated flexible bonding structure layer as the xoy plane, and the direction perpendicular to the plane of the integrated flexible bonding structure layer as the z-axis. x and y represent the horizontal and vertical coordinates in the spatial coordinate system, respectively. C(x,y) represents the capacitance value measured by the capacitive displacement sensor at coordinate (x,y). ε r ε0 represents the equivalent dielectric constant of the bonding interface. ε0 represents the vacuum dielectric constant. A represents the effective area of ​​the capacitive displacement sensor. d(x,y) represents the local gap distance at coordinates (x,y).

[0140] The capacitance-displacement conversion relationship is as follows:

[0141]

[0142] In the formula, w(x,y) represents the displacement of the interface in the z-direction at coordinate (x,y). This indicates the conversion formula.

[0143] 2.1.3) Based on the first-order shear deformation plate theory, the displacement field at any point on the bonding interface is described, and the displacement data is optimized based on the displacement field to obtain the optimized displacement data.

[0144] 2.1.4) Introducing the mid-surface deformable shell theory, parametric modeling of the curved surface structure of the mating interface is performed to obtain the curved surface structure adaptation model and determine the mid-surface point location.

[0145] 2.1.5) Establish the transient relationship between structure-load-response, dynamically model the bonding process between the base structure and the skin, obtain the nonlinear vibration response model, and solve the nonlinear vibration response model based on the optimized displacement data to determine the displacement data of the mid-surface point.

[0146] The core function of the nonlinear vibration response model is to incorporate transient dynamics into the entire inversion chain: first, a nonlinear vibration response model of "structure-load-response" is established (based on Hamilton's principle of control variation and inertial terms, and then the system response equation), and then the "optimized displacement data" obtained in step 2.1.3) is used to identify, correct and solve the parameters of the model, thereby obtaining the displacement time history of the mid-surface point and extracting the characteristic quantities (such as static equivalent value / steady-state value / peak value, etc.) for subsequent gap solution.

[0147] 2.1.6) Construct the load function of the pressure sensor.

[0148] 2.1.7) Based on the stiffness function, displacement data of mid-surface points, and load function, a function for calculating the gap height is constructed as follows:

[0149]

[0150] In the formula, h represents the gap height. a and b represent the lengths of the mating interface in the x and y directions, respectively. Indicates coordinates The displacement of the mating interface in the z-direction. F represents the load value measured by the area array sensor network.

[0151] Example 4:

[0152] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is disclosed in any one of Embodiments 1 to 3. Further, the displacement field at any point on the bonding interface is shown below:

[0153]

[0154] In the formula, x, y, and z represent the abscissa, ordinate, and ordinate in the spatial coordinate system, respectively. u0(·), v0(·), and w0(·) are all mid-surface displacement functions. φ x (·), φ y (·) represents the transverse shear angle. u(x,y,z), v(x,y,z), and w(x,y,z) represent the displacements of the interface at coordinate (x,y,z) in the x, y, and z directions, respectively.

[0155] Example 5:

[0156] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is provided. The main technical contents are described in any one of Examples 1 to 4. Furthermore, the parameters in the parametric modeling of the curved surface structure of the bonding interface include mid-surface points and strain terms.

[0157] The mid-surface points are shown below:

[0158]

[0159] In the formula, x and y represent the horizontal and vertical coordinates in the spatial coordinate system, respectively. Indicates the middle surface in ξ i Covariant basis vectors / tangential basis vectors in direction. ξ i These represent the curvilinear coordinate parameters of the mid-surface deformable shell. i = 1 corresponds to the x-direction. i = 2 corresponds to the y-direction. This represents the position vector of any point on the mid-surface.

[0160] The strain term is as follows:

[0161]

[0162] In the formula, ε1 and ε2 both represent strain terms. A1 and A2 are the basis modulus lengths of the mid-plane. R1 and R2 are the principal radii of curvature. u1, u2, and u3 represent the displacement components along the x, y, and z directions, respectively. a1 and a2 represent the basis components of the mating interface in the x and y directions, respectively. γ 12 Shear strain reflects the shear deformation between the two curved coordinate directions ξ1 and ξ2 on the mid-surface.

[0163] Example 6:

[0164] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is disclosed in any one of Examples 1 to 5. Further, the control variational form of the nonlinear vibration response model is shown below:

[0165]

[0166] In the formula, t2 and t1 represent the upper and lower limits of the fixed time boundary, respectively. t represents time. δU is the virtual strain energy generated by structural deformation. δW is the virtual work done by the applied load.

[0167] The structural inertial-related virtual kinetic energy δK is shown below:

[0168]

[0169] In the formula, x, y, and z represent the horizontal, vertical, and horizontal coordinates in the spatial coordinate system, respectively. h represents the gap height. Ω0 represents the mid-surface region. These represent the velocity components along the x, y, and z directions, respectively. ρ(x,y,z) represents the material density function. These represent the virtual displacement velocity components along the x, y, and z directions, respectively.

[0170] Solving for the variational form of the control equations, we obtain the system response control equations, as shown below:

[0171]

[0172] In the formula, w1 represents the acceleration, velocity, and displacement of the generalized displacement of the first mode, respectively. γ1 represents the equivalent damping coefficient of the first mode. ω1 is the natural angular frequency of the first mode. ζ1 and ζ2 represent the self-nonlinear stiffness coefficient of the first mode and the coupling nonlinear coefficient of the second mode, respectively. ω2 represents the generalized displacement of the second mode. η1 represents the forced participation coefficient of the first mode. f represents the equivalent external load amplitude. Ω1 represents the external harmonic excitation angular frequency.

[0173] Example 7:

[0174] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is disclosed in any one of Examples 1 to 6. Further, the load function of the pressure sensor is as follows:

[0175] F(x,y) = p(x,y)·A s (11)

[0176] In the formula, x and y represent the abscissa and ordinate in the spatial coordinate system, respectively. F(x,y) represents the equivalent applied load at coordinate (x,y). p(x,y) represents the pressure value measured by the pressure sensor at coordinate (x,y). A s This indicates the effective area of ​​a single pressure sensor.

[0177] Example 8:

[0178] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is provided. The main technical contents are described in any one of Embodiments 1 to 7. Further, the sensor array includes a distributed pressure sensor layer 3.

[0179] The distributed pressure sensor layer 3 includes several pressure sensors 5, signal leads, circuit units, and a flexible substrate layer.

[0180] Several pressure sensors 5 are evenly arranged to form a surface array sensor network, which is used to collect local pressure array signals.

[0181] The signal lead-out line and circuit unit are disposed on one side of the flexible substrate layer.

[0182] The circuit unit is used to receive the local pressure array signal collected by the pressure sensor 5 and to preprocess the received local pressure array signal.

[0183] The preprocessing includes signal amplification, filtering, and level adjustment.

[0184] The signal lead is used to transmit the preprocessed local pressure array signal to an external processing chip.

[0185] The external processing chip stores a mechanical model of the composite material structure.

[0186] The flexible substrate is used to mount an array-type sensor network.

[0187] Structure 1: Distributed sensor array structure, consisting of a flexible substrate layer from top to bottom, used to support the sensor array and attach it between the composite material skin and the base layer; multiple evenly arranged flexible pressure sensor units, forming an area array sensor network; each pressure sensor is set in the corresponding bonding contact area to collect the local pressure at the bonding interface in real time; signal lead-out lines / circuit units are set on one side of the substrate layer to collect and transmit array signals to the processing module.

[0188] Example 9:

[0189] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is described in any one of Examples 1 to 8. Further, when the sensor array is a distributed pressure sensor layer 3, the steps for constructing the mechanical model of the composite material structure are as follows:

[0190] 2.2.1) Construct the load function as follows:

[0191]

[0192] In the formula, Indicates the j-th o The pressure value measured by a pressure sensor. A s This indicates the effective area of ​​a single pressure sensor. Indicates the j-th o The load value at the pressure sensor.

[0193] 2.2.2) Based on the load function, the displacement field is obtained through pressure distribution inversion, as shown below:

[0194]

[0195] In the formula, Indicates the j-th o The displacement field at each pressure sensor. H represents the compliance matrix. Indicates the j-th o The load value at the pressure sensor.

[0196] 2.2.3) Based on the displacement field, a function for solving the gap height is constructed as follows:

[0197]

[0198] In the formula, h represents the gap height. D0 represents the total bending stiffness of the skin structure. This represents the displacement field. 'a' represents the horizontal side length of the interface. 'F' represents the load value measured by the area array sensor network.

[0199] Based on the plate / shell flexibility model of composite material structures, the displacement field is obtained by inversion of pressure distribution. The displacement field A gap height calculation function is introduced to replace the displacement measurement w; the gap height distribution of the target area is reconstructed based on the gap height calculation function.

[0200] Example 10:

[0201] A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor is provided. The main technical contents are described in any one of Examples 1 to 9. Furthermore, the spatial interpolation and fitting algorithm includes cubic spline, RBF, and polynomial regression.

[0202] The continuous bonding gap pattern is shown below:

[0203] h(x j ,y j )=Interp{h j} (15)

[0204] In the formula, a spatial coordinate system is constructed with the lower left corner of the integrated flexible bonding structure layer as the origin, the plane of the integrated flexible bonding structure layer as the xoy plane, and the direction perpendicular to the plane of the integrated flexible bonding structure layer as the z-axis. x and y represent the horizontal and vertical coordinates in the spatial coordinate system, respectively. j represents the index of a point in the integrated flexible bonding structure layer. (x j ,y j h(x) represents the coordinates of the j-th point. j ,y j ) indicates that at coordinate (x j ,y j The patch gap value at point (). Interp represents the spatial interpolation and fitting algorithm.

[0205] Where, in coordinate (x j ,y j The gap height h at point ) j As shown below:

[0206]

[0207] In the formula, D0 represents the total bending stiffness of the skin structure. j This represents the displacement measured at point j. 'a' represents the horizontal side length of the interface. F j This represents the load value measured at the j-th point.

[0208] Example 11:

[0209] See Figures 1 to 6 A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor, the main technical contents of which include:

[0210] 1. Mechanical components and connections include, but are not limited to:

[0211] Structure 1: Distributed sensor array structure, consisting of a flexible substrate layer from top to bottom, used to support the sensor array and attach it between the composite material skin and the base layer; multiple evenly arranged flexible pressure sensor units, forming an area array sensor network; each pressure sensor is set in the corresponding bonding contact area to collect the local pressure at the bonding interface in real time; signal lead-out lines / circuit units are set on one side of the substrate layer to collect and transmit array signals to the processing module.

[0212] Structure 2: The distributed sensor array consists of, from top to bottom, a flexible substrate layer, an integrated flexible bonding structure layer, and a signal lead-out / circuit unit layer. The integrated flexible bonding structure layer integrates the following units: a flexible capacitive displacement sensor array, each capacitor unit including upper and lower electrode structures, positioned perpendicular to the bonding direction, responding to changes in the bonding spacing; a flexible pressure sensor array, interspersed with or integrated in the same layer as the capacitor array, used to measure load distribution during the bonding process; a dielectric layer disposed between the capacitor electrodes to enhance sensitivity and environmental stability; and a multi-channel data lead-out module, connected to a host controller, enabling synchronous acquisition and joint analysis of pressure and displacement signals.

[0213] 2. Working principle and method of gap detection:

[0214] The core measurement principle of this embodiment is the combined application of an array-type capacitive displacement sensor and a composite material structural mechanical model to form a gap measurement method for the bonding process of large-size composite skins. The following uses the single-point gap reconstruction of structure 2 as an example to illustrate the theoretical basis and calculation steps of this embodiment.

[0215] Step 1: Equivalent stiffness modeling of the plate structure. The composite skin is a multi-angle laminated structure, and its out-of-plane stiffness needs to be modeled using equivalent theory. The total bending stiffness D0 of the structure is expressed as follows:

[0216]

[0217] Among them, E M The equivalent Young's modulus (in Pa) is calculated by weighting the ply angle and the single-layer modulus. h is the total skin thickness (in meters). ν M This is the equivalent Poisson's ratio (dimensionless). This parameter will be used as the main control term in the gap inversion model.

[0218] Step 2: Modeling the capacitive displacement sensor. The capacitive displacement sensor is arranged between the mating structures in a flexible array. Its sensing capacitance value and the distance d(x,y) between the mating surfaces satisfy an approximate parallel plate model.

[0219]

[0220] Where C(x,y) is the measured capacitance value (unit: F). ε r ε0 is the equivalent dielectric constant of the bonding interface. ε0 is the vacuum dielectric constant. A is the effective area of ​​the electrode. d(x,y) is the local gap (i.e., the distance between bonding surfaces / distance after deformation).

[0221] By pre-calibrating the curve, the capacitance-displacement conversion relationship can be established:

[0222]

[0223] Here, w(x,y) represents the deformation deflection on the mating surface, serving as a key input for subsequent gap calculations.

[0224] Step 3: Shear Deformation Plate Theory (FSDT). Traditional thin plate theory (Kirchhoff's theory) neglects shear deformation in the thickness direction, which may introduce measurement errors for laminated structures with considerable thickness. Therefore, this invention uses First-order Shear Deformation Theory (FSDT) to describe the displacement field at each point:

[0225]

[0226] Where u0, v0, w0 are the mid-surface displacement functions. φ x ,φ y The x-axis represents the transverse shear angle, and the z-axis represents the thickness direction coordinate. This model significantly improves the accuracy of the deflection w(x,y), especially showing greater stability in the loaded region and edge transition zone.

[0227] Step 4, Adaptation model for curved surface structure, as shown in the attached figure. Figure 5As shown, when there is strong curvature in the mating area, the plate model will produce morphological mismatch errors. To improve adaptability, this invention introduces the mid-surface deformable shell theory to parametrically model the hypercurvature structure. The mid-surface points are represented in the following form:

[0228]

[0229] Based on this, the strain term ε1 is expressed as:

[0230]

[0231] Where A1 is the midplane basic modulus length, and R1 is the principal radius of curvature. i The deformation component is represented by this model. This model supports accurate inversion of gaps in complex shapes such as irregular mold mating areas and spherical / ellipsoidal surfaces.

[0232] Step 5: Modeling the dynamic loading process. For dynamic bonding processes such as automatic pressing and vacuum adsorption, it is necessary to establish the transient relationship between structure, load, and response. This invention establishes a nonlinear vibration response model based on Hamilton's principle, with the control variational form as follows:

[0233]

[0234] Where δU is the virtual strain energy generated by structural deformation. δW is the virtual work done by the applied load. δK is the virtual kinetic energy related to structural inertia.

[0235]

[0236] The system response control equations can be derived as follows:

[0237]

[0238] This equation is used to solve for the transient deflection w(t), providing support for gap reconstruction in the dynamic process of fitting.

[0239] Step 6: Model the pressure sensor array. The pressure sensor array is located below the bonding surface or embedded in the support surface. It is used to measure the local contact load F(x,y) during the pressing process, and the output is the pressure value p(x,y) in N / m. 2 .

[0240] Based on the sensor unit area A s It can be converted into an equivalent load:

[0241] F(x,y)=p(x,y)·A s (10)

[0242] Where p(x,y) is the pressure value, which is directly output by the sensor. A sThe effective area of ​​a single sensor is represented by F(x,y). F(x,y) represents the equivalent applied load in N. Data from multiple array points can be integrated to form a surface load distribution, serving as the boundary load condition for a plate / shell.

[0243] Step 7, Deflection-Load-Clearance Mapping Relationship, based on the above structural response modeling, as shown in the appendix. Figure 4 As shown, the gap height h and the deformation deflection w measured by the capacitor, and the load F and the plate stiffness D0 satisfy the following static mapping:

[0244]

[0245] Where w is the center displacement (m) measured by the capacitor array. F is the load value (N) measured by the pressure sensor array. a is the side length of the bonding surface (m). This formula is the core expression for gap inversion in this method and can be adapted to various bonding conditions such as local loading and uniform adsorption.

[0246] Step 8, Multi-point gap field reconstruction and spectrum generation, for each point (x) in the sensor array i ,y i ), we can obtain:

[0247]

[0248] Generate continuous fit gap maps using spatial interpolation and fitting algorithms (such as cubic splines, RBF, polynomial regression, etc.):

[0249] h(x,y)=Interp{h i}(13)

[0250] The output format can be a two-dimensional heatmap or a three-dimensional mesh diagram, as shown in the attached image. Figure 6 As shown, this enables visualization of fit quality and defect identification.

[0251] Example 12:

[0252] See Figures 1 to 6 A high-precision measurement method for the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor, the main technical contents of which include:

[0253] Gap measurement method based on distributed pressure sensor layer

[0254] When a distributed pressure sensor layer 3 is used as the sensing array, the present invention achieves the measurement of gap height through the following steps:

[0255] 1. Load field construction:

[0256] The pressure value p of each discrete unit in the target area is obtained through the distributed pressure sensor layer 3. j And converted to an equivalent concentrated load by the following formula:

[0257] F j =p j ·A s (1)

[0258] Among them, A s The unit area is denoted as .

[0259] 2. Displacement field inversion:

[0260] Based on a composite material plate / shell mechanical model, a flexibility matrix H is pre-established, which is determined by the material stiffness D0, structural geometric parameters, and boundary conditions. The static inversion relationship is then established.

[0261]

[0262] Obtain the displacement field corresponding to each sensing unit

[0263] 3. Calculation of gap height:

[0264] The displacement field w measured instead of displacement sensor j Introduce the original formula for calculating the gap height:

[0265]

[0266] This leads to the distribution of gap heights in the target area:

[0267] h(x,y)=Interp{h j}(4)4. Calibration Correction:

[0268] To compensate for boundary conditions, temperature effects, or structural uncertainties, a one-time or small-sample calibration can be performed using known standard gap height samples to make proportional or bias corrections to the inversion results.

Claims

1. A high-precision method for measuring the internal gap and minute displacement of a large-format enclosed area based on a flexible pressure sensor, characterized in that, Includes the following steps: 1) Attach the sensor array between the base structure and the skin to collect local array signals at the bonding interface between the base structure and the skin; The sensor array includes a distributed capacitive-pressure coupled sensing sensor layer (4). The distributed capacitive-pressure coupled sensing sensor layer (4) includes an integrated flexible bonding structure layer, signal lead-out lines, circuit units, and a flexible substrate layer; The integrated flexible bonding structure layer includes several pressure sensors (5) and several capacitive displacement sensors (6). Several pressure sensors (5) are evenly arranged to form a surface array sensor network for collecting local pressure array signals; Several capacitive displacement sensors (6) are evenly arranged at a preset interval to form a flexible capacitive displacement sensor array. The flexible capacitive displacement sensor array is used to collect the load distribution during the bonding process of the base structure (2) and the skin (1); The flexible capacitive displacement sensor array and the area array sensor network are interspersed or integrated in the same layer. The signal lead-out line and circuit unit are disposed on one side of the flexible substrate layer; The circuit unit is used to receive the local pressure array signal collected by the pressure sensor (5) and to preprocess the received local pressure array signal. The circuit unit is used to receive the load distribution collected by the capacitive displacement sensor (6) and to preprocess the received load distribution. The preprocessing includes signal amplification, filtering, and level adjustment; The signal lead is used to transmit the preprocessed local pressure array signal and load distribution to an external processing chip. The external processing chip stores a mechanical model of the composite material structure; The flexible substrate layer is used to mount the integrated flexible bonding structure layer; 2) Construct a mechanical model of the composite material structure; When the sensor array is a distributed capacitive-pressure coupled sensing sensor layer (4), the steps for constructing the mechanical model of the composite material structure are as follows: 2.1.1) Construct the stiffness function of the skin structure as follows: （1） In the formula, This represents the total bending stiffness of the skin structure. Indicates the equivalent Young's modulus; Indicates the total thickness of the skin; Indicates the equivalent Poisson's ratio; 2.1.2) Construct a parallel plate model of a capacitive displacement sensor, and then establish the capacitance-displacement conversion relationship to obtain displacement data; The parallel plate model of the capacitive displacement sensor is shown below: （2） In the formula, the lower left corner of the integrated flexible bonding structure layer is taken as the origin, and the plane of the integrated flexible bonding structure layer is... The direction perpendicular to the plane of the integrated flexible bonding structure layer is Axis, constructing a spatial coordinate system These represent the x-coordinate and y-coordinate in a spatial coordinate system, respectively. Indicates coordinates The capacitance value measured by the capacitive displacement sensor at the location; This represents the equivalent dielectric constant of the bonding interface; Represents the vacuum permittivity; This represents the effective area of ​​the capacitive displacement sensor. Indicates coordinates Local gap distance at the location; The capacitance-displacement conversion relationship is as follows: （3） In the formula, Indicates coordinates The interface fits perfectly. Displacement in direction; This represents the conversion formula; 2.1.3) Based on the first-order shear deformation plate theory, the displacement field at any point on the bonding interface is described, and the displacement data is optimized based on the displacement field to obtain the optimized displacement data. 2.1.4) Introducing the mid-surface deformable shell theory, parametric modeling is performed on the curved surface structure of the mating interface to obtain the surface structure adaptation model and determine the mid-surface point location; 2.1.5) Establish the transient relationship between structure-load-response, dynamically model the bonding process between the base structure and the skin, obtain the nonlinear vibration response model, and solve the nonlinear vibration response model based on the optimized displacement data to determine the displacement data of the mid-surface point. 2.1.6) Construct the load function of the pressure sensor; 2.1.7) Based on the stiffness function, displacement data of mid-surface points, and load function, a function for calculating the gap height is constructed as follows: （4） In the formula, Indicates the gap height; , These respectively represent the interface being fitted at... Length in the direction; Indicates coordinates The interface fits perfectly. Displacement in direction; This represents the load value measured by the area array sensor network; 3) Input the collected local array signals into the mechanical model of the composite material structure to obtain the gap height of the bonding interface; 4) Spatial interpolation and fitting algorithms are used to process the gap height of the bonding interface to generate a continuous bonding gap map.

2. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 1, characterized in that, The displacement field at any point on the bonding interface is shown below: （5） In the formula, , These represent the x-coordinate, y-coordinate, and vertical coordinate in a spatial coordinate system, respectively. , , Both are mid-surface displacement functions; All are transverse shear angles; , , Representing the coordinates The interface fits perfectly. , Displacement in direction.

3. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 1, characterized in that, The parameters in the parametric modeling of the curved surface structure of the bonding interface include mid-surface points and strain terms. The mid-surface points are shown below: ， （6） In the formula, These represent the x-coordinate and y-coordinate in a spatial coordinate system, respectively. Indicates the middle surface Covariant basis vectors / tangential basis vectors in direction; The curve coordinate parameters representing the mid-surface deformable shell; correspond direction; correspond direction; Represents the position vector of any point on the mid-surface; The strain term is as follows: （7） In the formula, All represent strain terms; , All are mid-plane basis modulus lengths; , Both are principal radii of curvature; They represent along , Displacement components in the direction; , These respectively represent the interface being fitted at... The basis vector components of the direction; This represents shear strain.

4. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 1, characterized in that, The control variational form of the nonlinear vibration response model is shown below: （8） In the formula, These represent the upper and lower limits of a fixed time boundary, respectively. Indicates time; This refers to the virtual strain energy generated by structural deformation. The virtual work done to apply the load; Among them, the structural inertial related virtual kinetic energy As shown below: （9） In the formula, , These represent the x-coordinate, y-coordinate, and vertical coordinate in a spatial coordinate system, respectively. Indicates the gap height; Indicates the mid-surface region; They represent along , The velocity component in the direction; Represents the material density function; , They represent along , The virtual displacement velocity component in the direction; Solving for the variational form of the control equations, we obtain the system response control equations, as shown below: （10） In the formula, These are represented as the acceleration, velocity, and displacement of the generalized displacement in the first mode, respectively. Expressed as the equivalent damping coefficient for the first mode; The natural angular frequency of the first mode; These are respectively represented as the self-nonlinear stiffness coefficient of the first mode and the coupling nonlinearity coefficient of the second mode; Represented as the generalized displacement of the second mode; Represented as the forced participation coefficient of the first mode; Represented as equivalent external load amplitude; It is represented as the angular frequency of the external harmonic excitation.

5. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 1, characterized in that, The load function of the pressure sensor is shown below: （11） In the formula, These represent the x-coordinate and y-coordinate in a spatial coordinate system, respectively. Indicates coordinates The equivalent applied load at the location; Indicates coordinates The pressure value measured by the pressure sensor at the location; This indicates the effective area of ​​a single pressure sensor.

6. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 1, characterized in that, The sensor array includes a distributed pressure sensor layer (3); The distributed pressure sensor layer (3) includes several pressure sensors (5), signal leads, circuit units, and a flexible substrate layer; Several pressure sensors (5) are evenly arranged to form a surface array sensor network for collecting local pressure array signals; The signal lead-out line and circuit unit are disposed on one side of the flexible substrate layer; The circuit unit is used to receive the local pressure array signal collected by the pressure sensor (5) and to preprocess the received local pressure array signal. The preprocessing includes signal amplification, filtering, and level adjustment; The signal lead is used to transmit the preprocessed local pressure array signal to an external processing chip. The external processing chip stores a mechanical model of the composite material structure; The flexible substrate is used to mount an array-type sensor network.

7. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 6, characterized in that, When the sensor array is a distributed pressure sensor layer (3), the steps for constructing the mechanical model of the composite material structure are as follows: 2.2.1) Construct the load function as follows: （12） In the formula, Indicates the first The pressure value measured by a pressure sensor; This represents the effective area of ​​a single pressure sensor. Indicates the first Load values ​​at each pressure sensor; 2.2.2) Based on the load function, the displacement field is obtained through pressure distribution inversion, as shown below: （13） In the formula, Indicates the first Displacement field at each pressure sensor; Represents the compliance matrix; Indicates the first Load values ​​at each pressure sensor; 2.2.3) Based on the displacement field, a function for solving the gap height is constructed as follows: （14） In the formula, Indicates the gap height; This represents the total bending stiffness of the skin structure. Represents the displacement field; Indicates the horizontal side length of the interface. This represents the load value measured by the area array sensor network.

8. The method for high-precision measurement of internal gaps and minute displacements in a large-format enclosed area based on a flexible pressure sensor according to claim 1, characterized in that, The spatial interpolation and fitting algorithms include cubic splines, RBF, and multinomial regression; The continuous bonding gap pattern is shown below: （15） In the formula, the lower left corner of the integrated flexible bonding structure layer is taken as the origin, and the plane of the integrated flexible bonding structure layer is... The direction perpendicular to the plane of the integrated flexible bonding structure layer is Axis, constructing a spatial coordinate system These represent the x-coordinate and y-coordinate in a spatial coordinate system, respectively. Indicates the index of the midpoint of the integrated flexible bonding structure layer; Indicates the first The coordinates of the points; Indicates coordinates The patch gap value at the point; Indicates spatial interpolation and fitting algorithms; Among them, in coordinates Gap height at point As shown below: （16） In the formula, This represents the total bending stiffness of the skin structure. Indicates the first Displacement measured at each point; Indicates the horizontal side length of the interface being fitted; Indicates the first The load values ​​measured at each point.

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