Composite material temperature field reconstruction method based on FBG array and improved interpolation

Abstract

The invention discloses a composite material temperature field reconstruction method based on an FBG array and improved interpolation, and relates to the technical field of composite material structure health monitoring, and the method comprises the steps: S1, carrying out the calibration through a constant temperature calibration experiment, and obtaining a measured value and a theoretical value of a temperature sensitivity coefficient; s2, constructing an array type thermal environment simulation and acquisition system; s3, self-adaptive region reconstruction based on working condition characteristics: mapping real-time discrete temperature data into a two-dimensional coordinate grid, and selecting an interpolation strategy to carry out full-field temperature reconstruction according to data distribution characteristics and boundary constraint conditions of a region to be reconstructed; the interpolation strategy comprises an improved linear segmentation interpolation strategy and a three-point sliding window average interpolation strategy; s4, temperature field visualization and error evaluation are carried out; according to the composite material temperature field reconstruction method based on the FBG array and the improved interpolation provided by the invention, the problems of boundary region calculation failure, precision loss, complex nonlinear thermal field fitting distortion and the like in the prior art are solved.

Description

Technical Field

[0001] This invention relates to the field of composite material structural health monitoring technology, and in particular to a composite material temperature field reconstruction method based on FBG array and improved interpolation. Background Technology

[0002] With the development of aerospace technology, advanced composite materials such as carbon fiber reinforced polymer (CFRP) have become the preferred materials for the main load-bearing structures of modern commercial aircraft due to their lightweight and high strength properties. However, composite materials are susceptible to defects such as impact and delamination during manufacturing and service, which are often accompanied by localized abnormal heat conduction. Therefore, building a real-time and accurate temperature field monitoring system is crucial for ensuring flight safety.

[0003] Currently, fiber Bragg grating (FBG) sensors are widely used to acquire temperature information of critical parts of composite materials due to their advantages such as anti-interference, small size, and ease of embedding. However, FBG is essentially a "point-based" or "quasi-distributed" monitoring method, providing only discrete data. To assess the overall health status, interpolation algorithms must be used to extrapolate the continuous temperature field over a finite number of discrete points. The current mainstream method is linear piecewise interpolation, which, while computationally simple, has significant limitations when dealing with anisotropic thermal conductivity and complex boundary conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a composite material temperature field reconstruction method based on FBG array and improved interpolation, which solves the problems of boundary region calculation failure and accuracy loss, and fitting distortion of complex nonlinear thermal fields in existing technologies.

[0005] To achieve the above objectives, this invention provides a composite material temperature field reconstruction method based on FBG array and improved interpolation, comprising the following steps: S1. Select a sensor and calibrate it through a constant temperature calibration experiment to obtain the measured and theoretical values ​​of the temperature sensitivity coefficient; S2. Construct an array-type thermal environment simulation and acquisition system to acquire discrete center wavelength signals and obtain discrete temperature data; S3. Adaptive Region Reconstruction Based on Operating Condition Characteristics: Real-time discrete temperature data is mapped onto a two-dimensional coordinate grid. Based on the data distribution characteristics and boundary constraints of the region to be reconstructed, an interpolation strategy is selected to reconstruct the temperature across the entire field. The interpolation strategies include an improved linear piecewise interpolation strategy and a three-point sliding window average interpolation strategy. S4. Temperature field visualization and error assessment.

[0006] Preferably, in S1: S11. Select sensors and models; A temperature response model based on the Bragg reflection effect was constructed by selecting a fiber Bragg grating (FBG) sensor. S12. Construct the theoretical expression for the temperature sensitivity coefficient; By taking the total differential of the expression characterizing the center wavelength of the FBG sensor, the theoretical expression for the temperature sensitivity coefficient is obtained. Characterizing the center wavelength of the FBG sensor The expression is: ; In the formula, Indicates the effective refractive index of the fiber core; Indicates the grid period; Temperature sensitivity coefficient The theoretical expression is: ; In the formula, Indicates the initial center wavelength; This represents the coefficient of thermal expansion of the optical fiber; This represents the thermo-optic coefficient of the optical fiber; S13. Set up the calibration experimental setup and conduct a constant temperature calibration experiment; S14. Calculate the temperature sensitivity coefficient; By using linear regression analysis, the center wavelength drift data at different temperature points obtained in the experiment were calculated to obtain the measured value of the temperature sensitivity coefficient of the FBG sensor; based on the initial center wavelength in the experiment, the theoretical value of the temperature sensitivity coefficient of the FBG sensor was obtained through the theoretical formula of the temperature sensitivity coefficient. S15. Determine whether the calibration results are qualified; If the deviation between the measured value and the theoretical value is not greater than the preset threshold and the temperature error is not greater than 1.5℃, the calibration is deemed qualified; otherwise, the calibration is deemed unsuccessful and recalibration is required.

[0007] Preferably, in S13: S131. Fix the ceramic tube on the heating platform, and pass the FBG sensor through the ceramic tube and place it in the middle section of the ceramic tube. S132. Fix the grating-covered part of the optical fiber to the heating platform, keep one end of the optical fiber free, and connect the other end of the optical fiber to the demodulator to collect spectral signals and obtain the center wavelength. S133. Place the thermocouple temperature measuring point in the middle section of the ceramic tube, connect the thermocouple temperature measuring point to the temperature demodulator, and collect the real-time temperature. S134. By generating temperature changes through the heating stage, the center wavelength drift data and the corresponding real-time temperature at different temperature points are obtained.

[0008] Preferably, in S2: S21. Build the hardware architecture, including heating platform, temperature control instrument, PID control loop and PLC central controller; The heating platform is composed of several independent heating modules arranged in a matrix. This indicates the number of heating modules. Each heating module is separated by a heat insulation gap to prevent thermal crosstalk. Each heating module is equipped with an independent temperature controller and a PID control loop, and multi-channel coordinated control is achieved through a PLC central controller. S22. Prepare the sample, including the composite laminate sample and the FBG sensor array; the composite laminate sample is obtained by hot pressing of multi-layer unidirectional prepreg; the FBG sensor array is embedded into the composite laminate sample by interlayer cutting during the layup process, the embedding direction is consistent with the direction of the reinforcing fiber, and each sensor node is distributed in a grid pattern on the plane. S23. Set the temperature field conditions, including linear gradient conditions and radiation diffusion conditions; S24. Place the composite laminate sample with embedded FBG sensor array onto the heating platform, and control the heating platform to generate the corresponding thermal distribution environment according to the preset temperature field conditions. S25. The discrete center wavelength signal output by the FBG sensor array is acquired by the fiber optic grating demodulator, and combined with the measured value of the temperature sensitivity coefficient obtained in S1, the real-time discrete temperature data of each sensor node position is obtained.

[0009] Preferably, the composite laminate sample is prepared from unidirectional carbon fiber prepreg with a single layer thickness of 0.2 mm; the FBG sensor array is arranged in the middle layer of the composite laminate sample in the thickness direction, and the specific layup sequence is as follows: ,in The location of the sensor is indicated; the flatness error of the heating platform does not exceed 0.1 mm / m, and a coating with a thermal conductivity of not less than 1.5 W / (m) is applied between the composite laminate sample and the heating platform. K) heat-conducting medium.

[0010] Preferably, under linear gradient conditions, the heating platform is controlled to generate a temperature distribution that decreases monotonically along a certain coordinate axis. Under radiation diffusion conditions, the central area of ​​the control heating platform is at a higher temperature than the surrounding area, while the surrounding area is at a lower temperature than the central area, forming a nonlinear temperature field that radiates from the center to the surrounding areas.

[0011] Preferably, in S3: For boundary region data with single-endpoint constraints or no endpoint constraints, an improved linear piecewise interpolation strategy is adopted. By reusing the functional relationship between adjacent effective intervals, the continuous reconstruction of the boundary region is achieved. For internal region data with nonlinear gradient changes, a three-point sliding window average interpolation strategy is adopted. By constructing a local high-order fitting function and performing weighted fusion of overlapping regions, the smooth reconstruction of complex gradient regions is achieved.

[0012] Preferably, S31, an improved linear piecewise interpolation strategy; S311. Let the interpolation interval be... Selecting from the interpolation interval Each of the following points is distinct and serves as an interpolation node; the set of interpolation nodes is: And satisfy Then the set of function values ​​is ,in The left endpoint of the interpolation interval, The right endpoint of the interpolation interval. Indicates the first Interpolation nodes, Indicates the first The function values ​​of each interpolation node; S312. Set constraints and make judgments: Traverse the sub-intervals to be interpolated. ,in Indicates the left endpoint of the sub-interval to be interpolated. This represents the right endpoint of the sub-interval to be interpolated. It identifies whether there is an under-constrained end interval containing one known node or no known node. If an under-constrained end interval exists, it is processed according to S313. If no under-constrained end interval exists, it means that the current sub-interval is a "valid interpolation segment with two endpoint constraints". Standard linear interpolation calculation can be performed on these regular intervals. S313. Construct an adjacent reuse mechanism; If an under-constrained interval is identified at the left end of the interpolation interval, and this interval is adjacent to a valid interpolation segment with two endpoint constraints. Then extract the valid interpolation segment. The corresponding linear function ,Will The domain is extended to the left to cover the under-constrained interval at the left end of the interpolation interval, and the extended domain is... As the interpolation function for the under-constrained interval at the left end of the interpolation interval; If an under-constrained interval is identified at the right end of the interpolation interval, and this interval is adjacent to a valid interpolation segment with two endpoint constraints. Then extract the valid interpolation segment. The corresponding linear function ,Will The domain is extended to the right to cover the under-constrained interval at the right end of the interpolation interval, and the extended domain is... As the interpolation function for the under-constrained interval at the right end of the interpolation interval; S314, Global Synthesis: The end interpolation results generated in S313 are spliced ​​with the results of the effective interpolation segments in the middle of the interpolation interval to obtain a global continuous one-dimensional interpolation curve; S315, Dimension Expansion: Create a two-dimensional coordinate system, including the X-axis and the Y-axis; perform one-dimensional interpolation along the Y-axis on each column of discrete data according to the strategy described in steps S311 to S314 to obtain multiple auxiliary curves; based on the data points on the auxiliary curves, perform one-dimensional interpolation along the X-axis according to the strategy described in steps S311 to S314 to obtain two-dimensional temperature field data.

[0013] The preferred method is S32, a three-point sliding window average interpolation strategy; S321. Suppose the total number of known discrete temperature data points is... Arrange the known discrete temperature data points in ascending order of their coordinates, and denote the resulting set of nodes as follows: Set the total number of sliding windows to And satisfy A sliding window is formed by selecting three adjacent nodes from known discrete temperature data points. Each sliding window corresponds to a local interpolation sub-interval; introducing As the sequence number of the sliding window, Among them, the first The sliding window contains three nodes, namely the starting node and the... Intermediate nodes and end node ; S322, Local higher-order fitting: For the first A set of sliding windows is used to construct a quadratic interpolation equation using the Lagrange interpolation principle. The expression is: ; In the formula, For interpolation variables; For the loop variable in the summation operation, ; Indicates the first The first sliding window Temperature function values ​​of each node; Let be a Lagrange basis function, whose expression satisfies: ; In the formula, For the loop variable in the multiplication operation, ,and ; and They represent the first The first sliding window The and the first The coordinates of each node; S323. Overlap Region Identification: Identify the overlapping region between adjacent sliding window sets. Local interpolation sub-intervals of a set of sliding windows With the Local interpolation sub-intervals of a set of sliding windows The overlapping region is ,in ; S324. Perform weighted fusion calculation to eliminate the discontinuity of derivatives at the segmentation points and generate a smooth interpolation curve; For the first non-overlapping interval The quadratic interpolation equation of the first sliding window cover; For the non-overlapping interval at the tail segment , by the Quadratic interpolation equations for a sliding window cover; For any overlapping interval in the middle This interval is simultaneously occupied by the first The function of the sliding window and the first The function coverage of a sliding window is used, and the arithmetic mean of the two interpolation results is taken as the final result. The expression is: .

[0014] Preferably, in S4: the reconstructed full-field temperature data is mapped with a color cloud map to generate a visualized temperature field distribution map; the reconstruction result is compared with the preset standard temperature field or simulation model result, the relative error of key nodes is calculated, and the reconstruction accuracy is verified.

[0015] Therefore, the composite material temperature field reconstruction method based on FBG array and improved interpolation described above has the following beneficial effects: (1) Solved the problem of boundary region reconstruction failure: By using the adjacent function reuse mechanism, the functional relationship of the adjacent effective intervals is used to repair the edge data; Experiments show that the temperature distribution is successfully completed when there is no sensor coverage at the physical edge of the sample, and the interpolation error of the edge region (high temperature end and low temperature end) is reduced to 1%; (2) Achieving smooth and high-precision reconstruction of complex nonlinear thermal fields: By using three-point sliding window average interpolation, and through local quadratic curve fitting and overlapping domain averaging, the "edges" and "severity" of the cloud map caused by traditional linear methods are eliminated; Under radiation diffusion conditions, the reconstructed cloud map presents a natural and continuous concentric circle shape, and the key point error is controlled within 10%, effectively restoring the thermal diffusion process. (3) A reliable physical verification system was established: a complete test system including an array-type precision temperature control platform and a signal processing unit was constructed, which overcame the idealization defects of pure simulation verification and provided technical support with greater engineering application value for the health monitoring of aerospace structures.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is an overall flowchart of the composite material temperature field reconstruction method based on FBG array and improved interpolation of the present invention; Figure 2 This is a schematic diagram of the temperature field node layout in an embodiment of the present invention, where (a) represents the linear gradient condition and (b) represents the radiation diffusion condition. Figure 3 This is a schematic diagram of the measured value of the temperature sensitivity coefficient obtained by linear fitting of calibration experimental data in an embodiment of the present invention; Figure 4 This is a schematic diagram of the temperature verification results after the temperature calibration experiment in an embodiment of the present invention. Figure 5 This is a schematic diagram of an array-type heating platform for a temperature field experiment according to an embodiment of the present invention; Figure 6 The temperature field comparison diagrams under the linear gradient condition in the embodiments of the present invention are shown, where (a) is the interpolation cloud map and (b) is the simulation cloud map. Figure 7 The following are temperature field comparison diagrams under radiation diffusion conditions in embodiments of the present invention, where (a) is an interpolated cloud map and (b) is a simulation cloud map.

[0018] Figure Labels 1. Temperature control system; 2. Heating plate; 3. Asbestos insulation pad; 4. Flat reference plate. Detailed Implementation

[0019] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0020] Please see Figure 1-7 A complete testing system was constructed, comprising intelligent composite material samples, an array-type precision temperature control platform, and a signal processing unit. The system underwent full-process verification for two typical complex thermal conditions: linear gradient and radiative diffusion. The composite material temperature field reconstruction method based on FBG array and improved interpolation includes the following steps: Step 1: Preparation of smart composite material samples and sensor calibration.

[0021] First, a composite laminate sample (hereinafter referred to as the sample) for the embedded FBG sensor array was prepared. The matrix material was T700 grade unidirectional carbon fiber prepreg, with a single layer thickness of 0.2 mm. The layered structure is designed to simulate the anisotropic characteristics of actual structural components. In the sensor placement phase, to balance sensing sensitivity and structural integrity, the FBG sensor array is embedded along the fiber direction (0° direction) into the interface of the third layer (intermediate layer), specifically at the following location: The FBG sensor uses a custom-made grating from the Fiber Optic Center of Wuhan University of Technology, with a grating length of [missing information]. To ensure precise positioning, the locations of 7×9 and 3×4 grid nodes were pre-marked on the prepreg surface using laser projection, such as... Figure 2 As shown. Using a high-precision displacement stage for assisted positioning, the optical fiber was accurately placed at the preset node, and both ends were fixed with a small amount of instant adhesive. When the fiber optic sensor was embedded, it was protected by a copper tube to prevent signal errors caused by board strain; a thermocouple was embedded near the FBG sensor to simultaneously collect temperature data. Subsequently, the remaining two layers of prepreg were laid and placed in an autoclave for standard curing. The cured sample was then subjected to ultrasonic C-scan testing to confirm the absence of defects such as pores, delamination, and fiber breaks.

[0022] Given that the temperature-sensitive properties of the optical fiber may drift due to residual stress from the matrix curing after embedding, in-situ calibration was performed on the molded composite laminate samples. The calibration principle is based on the differential form of the Bragg equation of the fiber grating. Regarding the quartz optical fiber used in this embodiment, thermo-optic coefficient Theoretically, in the 1550nm band, its sensitivity should be approximately... The sample was placed in a constant temperature stage with a temperature control accuracy of 0.1℃ and subjected to graded heating tests within the range of 50℃ to 300℃. Each temperature step was held for 20 minutes until the internal temperature reached equilibrium, and then the center wavelength of the FBG was recorded using a fiber optic demodulator. Linear regression analysis was performed on the data. The experimentally acquired center wavelength data showed a highly linear relationship with temperature, and the measured sensitivity coefficient obtained from the linear fitting was [value missing]. ,like Figure 3-4As shown in the figure. The results agree well with the theoretical values, and the temperature inversion error is 1.5℃, which meets the data source requirements for high-precision monitoring.

[0023] Step 2: Construct an array-type thermal simulation platform.

[0024] To generate a controllable complex temperature field, an array-type heating platform was independently developed, such as... Figure 5 As shown, the system includes a temperature control system 1, heating plates 2, asbestos insulation pads 3, and a planar reference plate 4. The planar reference plate 4, asbestos insulation pads 3, and heating plates 2 are arranged sequentially from bottom to top on the temperature control system 1. Hardware-wise, 16 cast aluminum heating plates, each 100mm × 1000mm × 20mm in size, are used as the heat source, with a power of 300W per plate. The heating plates are fixed to the 430mm × 430mm aluminum alloy reference plate in a 4×4 matrix arrangement, with a 10mm gap between adjacent plates to block lateral heat conduction and ensure independent temperature control for each zone. For control, each heating plate is connected to an independent solid-state relay and a Yudian AI-516 temperature controller. All instruments communicate with the host PLC via an RS485 bus. By writing a PLC control program, different temperature setpoints can be issued to each of the 16 heating units, thereby synthesizing arbitrary temperature fields such as linear gradients, concentric circle radiation, and checkerboard distributions on a macroscopic scale. Thermal grease is applied between the sample and the heating platform to reduce contact thermal resistance, and non-metallic pressure blocks are used to fix the four corners to prevent the sample from shifting during heating.

[0025] Step 3: Verification of linear gradient field reconstruction and boundary compensation strategy.

[0026] Based on the heating platform established in step 2, the hybrid interpolation strategy of this invention was further compared and verified to address two key technical challenges: missing edge data and complex internal gradients. To address the issue of missing boundary data caused by the sensor not covering the physical edge of the sample, a "linear gradient" condition was set for verification. The heating platform was controlled to generate a unidirectional steady-state temperature field decreasing from 100°C to room temperature from left to right. Specifically, the first column of heating plates was set to 100°C, while the other columns were not activated. After the system started, and after approximately 30 minutes of thermal equilibrium, a stable temperature field monotonically decreasing from left to right was formed on the sample surface. At this point, temperature data from the 3×4 array (12 in total) FBG sensor nodes embedded inside the sample were collected as the input source for the reconstruction algorithm.

[0027] Because the FBG sensor array does not cover the outermost edge of the sample, a "blank area" exists between the physical boundary of the sample and the outermost sensor node. According to traditional algorithms, this interval falls under the category of "extrapolation," making it impossible to directly construct a linear function. Typically, it can only be assumed that the temperature remains constant, which clearly contradicts the physical fact of linear decrease, leading to significant errors in the boundary region. This invention employs an adjacent function reuse mechanism for processing. Step 1: Y-direction interpolation; First, interpolate the three columns of data along the Y-axis. Since the operating condition is designed as isothermal in the Y-direction, the data is distributed in a horizontal straight line. The algorithm identifies the lack of constraints at both ends of the Y-axis and automatically determines it as an under-constrained interval. The program reads the linear function of the effective interval in the middle of this column (where the slope is close to 0) and directly extends its domain upwards and downwards. The calculation results show that the reconstructed Y-direction temperature curve is a straight line, consistent with physical expectations. Step 2: X-direction interpolation; Based on the mesh data generated in Step 1, interpolation is performed along the X-axis; For the left boundary region, the algorithm detects the effective interpolation segment immediately adjacent to the right side of this region, consisting of the first and second columns of sensors, and extends the calculation range to the left edge of the sample; For the right boundary region, the linear equation of the rightmost effective segment is reused similarly. The reconstructed results are compared with the finite element simulation cloud map, as shown... Figure 6 As shown in the figure. The results show that the temperature distribution in the edge region was successfully completed through the adjacent function reuse mechanism. At the high-temperature end (left edge) and low-temperature end (right edge) of the sample, the interpolation error was reduced to 1%. This result demonstrates the extremely high fidelity of the improved algorithm to linear fields under sparse boundary conditions.

[0028] Step 4: Reconstruction of the radial temperature field and verification of the smoothing strategy.

[0029] To address the issue of derivative discontinuities (fragmented contour maps) caused by traditional interpolation in nonlinear thermal fields, a "radiative diffusion" scenario was implemented for verification. The heating platform was controlled to heat only the central region to 80°C, while the surrounding areas remained at room temperature, forming a nonlinear concentric elliptical temperature distribution. After data acquisition, the three-point sliding window average interpolation strategy of this invention was used for reconstruction. Specifically, the radiation diffusion scenario adjusted the heating platform control logic, activating only the four heating plates in the central region of the matrix, setting the target temperature to 80°C, while the remaining peripheral heating plates were turned off (maintaining an ambient temperature of approximately 24°C). After heating for a period of time, heat diffused from the center outwards, forming a typical nonlinear radial temperature field with a "high temperature in the center and low temperature around the edges." Temperature data from 7×9 array (63 nodes in total) FBG nodes were collected.

[0030] Radiation-like temperature fields typically exhibit a Gaussian or cosine-like distribution in space, with continuously varying curvature. Traditional linear interpolation approximates this curve using multiple straight line segments, inevitably resulting in sharp angles at connection points. This invention employs a three-point sliding window averaging interpolation method, the core idea of ​​which is "fitting a local area with a quadratic curve" plus "averaging of overlapping regions." The first step involves constructing a sliding window algorithm, sequentially capturing three points in each row of data (e.g., points 1, 2, 3; points 2, 3, 4, etc.). For each set of three points, a parabola is fitted using the Lagrange formula, passing through these three points. The parabola has a second derivative and naturally possesses smooth curvature, better describing the heat diffusion process than a straight line. The second step involves weighted fusion of the overlapping region between points 2 and 3, which belongs to both the first window (1-2-3) and the second window (2-3-4). The parabola in the first window predicts the shape of the interval based on the trends of points 1, 2, and 3; the parabola in the second window predicts the shape of the interval based on the trends of points 2, 3, and 4; these two predictions often differ slightly. By averaging the two, the interpolation curve is forced to transition smoothly at the connection points, eliminating the slight angles that may occur when splicing single parabolas. The reconstructed temperature cloud map exhibits a continuous and natural concentric circle shape, eliminating the diamond-shaped artifacts and sharp angles common in traditional methods. The reconstruction error of key points is controlled within 10%, such as... Figure 7 As shown.

[0031] Therefore, this invention adopts the above-mentioned composite material temperature field reconstruction method based on FBG array and improved interpolation, which solves the problem of boundary region reconstruction failure, realizes smooth and high-precision reconstruction of complex nonlinear thermal fields, establishes a reliable physical verification system, overcomes the idealization defects of pure simulation verification, and provides more engineering application value for the health monitoring of aerospace structures.

[0032] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A composite material temperature field reconstruction method based on FBG array and improved interpolation, characterized in that, Includes the following steps: S1. Select a sensor and calibrate it through a constant temperature calibration experiment to obtain the measured and theoretical values ​​of the temperature sensitivity coefficient; S2. Construct an array-type thermal environment simulation and acquisition system to acquire discrete center wavelength signals and obtain discrete temperature data; S3. Adaptive Region Reconstruction Based on Operating Condition Characteristics: Real-time discrete temperature data is mapped onto a two-dimensional coordinate grid. Based on the data distribution characteristics and boundary constraints of the region to be reconstructed, an interpolation strategy is selected to reconstruct the temperature across the entire field. The interpolation strategies include an improved linear piecewise interpolation strategy and a three-point sliding window average interpolation strategy. S4. Temperature field visualization and error assessment.

2. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 1, characterized in that, In S1: S11. Select sensors and models; A temperature response model based on the Bragg reflection effect was constructed by selecting a fiber Bragg grating (FBG) sensor. S12. Construct the theoretical expression for the temperature sensitivity coefficient; By taking the total differential of the expression characterizing the center wavelength of the FBG sensor, the theoretical expression for the temperature sensitivity coefficient is obtained. Characterizing the center wavelength of the FBG sensor The expression is: ； In the formula, Indicates the effective refractive index of the fiber core; Indicates the grid period; Temperature sensitivity coefficient The theoretical expression is: ； In the formula, Indicates the initial center wavelength; This represents the coefficient of thermal expansion of the optical fiber; This represents the thermo-optic coefficient of the optical fiber; S13. Set up the calibration experimental setup and conduct a constant temperature calibration experiment; S14. Calculate the temperature sensitivity coefficient; By using linear regression analysis, the center wavelength drift data at different temperature points obtained in the experiment were calculated to obtain the measured value of the temperature sensitivity coefficient of the FBG sensor; based on the initial center wavelength in the experiment, the theoretical value of the temperature sensitivity coefficient of the FBG sensor was obtained through the theoretical formula of the temperature sensitivity coefficient. S15. Determine whether the calibration results are qualified; If the deviation between the measured value and the theoretical value is not greater than the preset threshold and the temperature error is not greater than 1.5℃, the calibration is deemed qualified; otherwise, the calibration is deemed unsuccessful and recalibration is required.

3. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 2, characterized in that, In S13: S131. Fix the ceramic tube on the heating platform, and pass the FBG sensor through the ceramic tube and place it in the middle section of the ceramic tube. S132. Fix the grating-covered part of the optical fiber to the heating platform. Connect one end of the optical fiber to the demodulator to collect the spectral signal and obtain the center wavelength. Keep the other end of the optical fiber free. S133. Place the thermocouple temperature measuring point in the middle section of the ceramic tube, connect the thermocouple temperature measuring point to the temperature demodulator, and collect the real-time temperature. S134. By generating temperature changes through the heating stage, the center wavelength drift data and the corresponding real-time temperature at different temperature points are obtained.

4. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 3, characterized in that, In S2: S21. Build the hardware architecture, including heating platform, temperature control instrument, PID control loop and PLC central controller; The heating platform is composed of several independent heating modules arranged in a matrix. This indicates the number of heating modules. Each heating module is separated by a heat insulation gap to prevent thermal crosstalk. Each heating module is equipped with an independent temperature controller and a PID control loop, and multi-channel coordinated control is achieved through a PLC central controller. S22. Prepare the sample, including the composite laminate sample and the FBG sensor array; the composite laminate sample is obtained by hot pressing of multi-layer unidirectional prepreg; the FBG sensor array is embedded into the composite laminate sample by interlayer cutting during the layup process, the embedding direction is consistent with the direction of the reinforcing fiber, and each sensor node is distributed in a grid pattern on the plane. S23. Set the temperature field conditions, including linear gradient conditions and radiation diffusion conditions; S24. Place the composite laminate sample with embedded FBG sensor array onto the heating platform, and control the heating platform to generate the corresponding thermal distribution environment according to the preset temperature field conditions. S25. The discrete center wavelength signal output by the FBG sensor array is acquired by the fiber optic grating demodulator, and combined with the measured value of the temperature sensitivity coefficient obtained in S1, the real-time discrete temperature data of each sensor node position is obtained.

5. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 4, characterized in that: The composite laminate specimens were prepared using unidirectional carbon fiber prepreg with a single layer thickness of 0.2 mm. The FBG sensor array was positioned in the middle layer along the thickness direction of the composite laminate specimens, with the specific layup sequence as follows: ,in The location of the sensor is indicated; the flatness error of the heating platform does not exceed 0.1 mm / m, and a coating with a thermal conductivity of not less than 1.5 W / (m) is applied between the composite laminate sample and the heating platform. K) heat-conducting medium.

6. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 5, characterized in that: Under linear gradient conditions, the heating platform is controlled to generate a temperature distribution that decreases monotonically along a certain coordinate axis. Under radiation diffusion conditions, the central area of ​​the control heating platform is at a higher temperature than the surrounding area, while the surrounding area is at a lower temperature than the central area, forming a nonlinear temperature field that radiates from the center to the surrounding areas.

7. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 6, characterized in that, In S3: For boundary region data with single-endpoint constraints or no endpoint constraints, an improved linear piecewise interpolation strategy is adopted; for internal region data with nonlinear gradient changes, a three-point sliding window average interpolation strategy is adopted.

8. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 7, characterized in that: S31, Improved linear piecewise interpolation strategy; S311. Let the interpolation interval be... Selecting from the interpolation interval Each of the following points is distinct and serves as an interpolation node; the set of interpolation nodes is: And satisfy Then the set of function values ​​is ,in The left endpoint of the interpolation interval, The right endpoint of the interpolation interval. Indicates the first Interpolation nodes, Indicates the first The function values ​​of each interpolation node; S312. Set constraints and make judgments: Traverse the sub-intervals to be interpolated. ,in Indicates the left endpoint of the sub-interval to be interpolated. This indicates the right endpoint of the sub-interval to be interpolated. It identifies whether there is an under-constrained end interval with one known node or no known node. If there is an under-constrained end interval, it is processed according to S313. If there is no under-constrained end interval, standard linear interpolation calculation is performed. S313. Construct an adjacent reuse mechanism; If an under-constrained interval is identified at the left end of the interpolation interval, and this interval is adjacent to a valid interpolation segment with two endpoint constraints. Then extract the valid interpolation segment. The corresponding linear function ,Will The domain is extended to the left to cover the under-constrained interval at the left end of the interpolation interval, and the extended domain is... As the interpolation function for the under-constrained interval at the left end of the interpolation interval; If an under-constrained interval is identified at the right end of the interpolation interval, and this interval is adjacent to a valid interpolation segment with two endpoint constraints. Then extract the valid interpolation segment. The corresponding linear function ,Will The domain is extended to the right to cover the under-constrained interval at the right end of the interpolation interval, and the extended domain is... As the interpolation function for the under-constrained interval at the right end of the interpolation interval; S314, Global Synthesis: The end interpolation results generated in S313 are spliced ​​with the results of the effective interpolation segments in the middle of the interpolation interval to obtain a global continuous one-dimensional interpolation curve; S315, Dimension Expansion: Create a two-dimensional coordinate system, including the X-axis and the Y-axis; execute the strategies described in S311 to S314 on each column of discrete data along the Y-axis to obtain multiple auxiliary curves; based on the data points on the auxiliary curves, execute the strategies described in S311 to S314 along the X-axis to obtain two-dimensional temperature field data.

9. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 8, characterized in that: S32, Three-point sliding window average interpolation strategy; S321. Suppose the total number of known discrete temperature data points is... Arrange the known discrete temperature data points in ascending order of their coordinates, and denote the resulting set of nodes as follows: ; Set the total number of sliding windows to And satisfy A sliding window is formed by selecting three adjacent nodes from known discrete temperature data points. Each sliding window corresponds to a local interpolation sub-interval; introducing As the sequence number of the sliding window, Among them, the first The sliding window contains three nodes, namely the starting node and the... Intermediate nodes and end node ; S322, Local higher-order fitting: For the first A set of sliding windows is used to construct a quadratic interpolation equation using the Lagrange interpolation principle. The expression is: ； In the formula, For interpolation variables; For the loop variable in the summation operation, ; Indicates the first The first sliding window Temperature function values ​​of each node; Let be a Lagrange basis function, whose expression satisfies: ； In the formula, For the loop variable in the multiplication operation, ,and ; and They represent the first The first sliding window The and the first The coordinates of each node; S323. Overlap Region Identification: Identify the overlapping region between adjacent sliding window sets. Local interpolation sub-intervals of a set of sliding windows With the Local interpolation sub-intervals of a set of sliding windows The overlapping region is ,in ; S324. Perform weighted fusion calculation to eliminate the discontinuity of derivatives at the segmentation points and generate a smooth interpolation curve; For the first non-overlapping interval The quadratic interpolation equation of the first sliding window cover; For the non-overlapping interval at the tail segment , by the Quadratic interpolation equations for a sliding window cover; For any overlapping interval in the middle This interval is simultaneously occupied by the first The function of the sliding window and the first The function coverage of a sliding window is used, and the arithmetic mean of the two interpolation results is taken as the final result. The expression is: 。 10. The composite material temperature field reconstruction method based on FBG array and improved interpolation according to claim 9, characterized in that, In S4: The reconstructed full-field temperature data is mapped with a color cloud map to generate a visualized temperature field distribution map; the reconstruction results are compared with the preset standard temperature field or simulation model results, the relative error of key nodes is calculated, and the reconstruction accuracy is verified.

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