Method for obtaining double-face strain of single-face thermal excitation structure based on agent model

Abstract

The application discloses a kind of based on agent model's single surface thermal excitation structure double-face strain acquisition method, comprising: using strain sensor to monitor the three-dimensional strain data of structure cold surface multiple test points under thermal excitation load, and monitor the out-of-plane displacement data of cold surface multiple test points;Supplement the strain data not collected to test point;Using curved surface fitting function to fit cold surface test point data, obtain structure three-dimensional strain and out-of-plane displacement field;Calculate the three-dimensional strain difference distribution field of cold and hot surface;Calculate the three-dimensional strain of key point of expected output;Combining the measured cold and hot surface temperature constructs training sample;Establish single surface strain temperature-cold and hot double-face key point strain output agent model, and the acquisition of double-face strain is realized by using agent model.The agent model of the present application is constructed by measured data and cold and hot double-face strain data, to solve the problem that existing single surface thermal excitation structure cannot arrange strain sensor on hot surface, so that hot surface strain data cannot be acquired.

Description

Technical Field

[0001] This invention belongs to the field of engineering structure deformation monitoring, specifically relating to a method for obtaining the double-sided strain of a single-sided thermally excited structure based on a surrogate model. Background Technology

[0002] Aerospace composite material engineering structures, such as large deployable spaceborne antennas, may be subjected to unilateral thermal excitation loads due to heat generated by the environment or functional components. Under unilateral thermal excitation loads, composite material structures undergo thermo-mechanical coupling, resulting in complex thermal deformations that severely impact structural safety and functionality. Real-time online monitoring of structural deformation is crucial for ensuring reliable and safe operation.

[0003] Among existing structural deformation monitoring technologies, deformation monitoring algorithms based on structural strain information, such as the inverse finite element method, acquire strain in real time through sensors and combine it with the displacement-strain mechanical relationship to achieve online perception of the deformation state of aerospace structures, which has received widespread attention in the engineering field. However, for aerospace composite material engineering structures under single-sided thermal excitation loads, their structural deformation mainly originates from the thermal expansion difference caused by the temperature inconsistency between the cold and hot surfaces of the structure. Therefore, their thermal deformation includes in-plane thermal expansion deformation and out-of-plane bending deformation. The strain generated on the structural surface is the superposition of the strain generated by in-plane deformation and the strain generated by out-of-plane deformation. Relying solely on the strain data of a single surface through the strain-displacement relationship is insufficient to accurately reconstruct the deformation state of a single-sided thermally excited structure.

[0004] Furthermore, due to structural functional limitations, such as the fact that heat-generating functional devices are all installed on the hot side, strain sensors cannot be installed on the hot side. Instead, strain sensors can only be placed on the cold side of the structure to obtain cold side strain data. There is a lack of hot side strain information to achieve structural deformation reconstruction based on mechanical models.

[0005] Therefore, there is an urgent need for a method to obtain the strain of a single-sided thermally excited structure on both sides, so as to effectively obtain the strain of key points on the cold and hot sides of the structure through measured data of the cold side, which can provide key support for subsequent online deformation reconstruction algorithms of the structure. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, the present invention aims to provide a method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model. The present invention solves the problem that existing single-sided thermally excited structures cannot place strain sensors on the hot side, resulting in the inability to obtain hot-side strain data by constructing a surrogate model of measured data and cold-hot double-sided strain data.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] The present invention provides a method for obtaining the double-sided strain of a single-sided thermally excited structure based on a surrogate model, comprising the following steps:

[0009] (1) For a single-sided thermally excited structure, strain sensors are used to monitor the triaxial strain data of multiple test points on the cold side of the structure under thermally excited load, and displacement sensors are used to monitor the out-of-plane displacement data of multiple test points on the cold side.

[0010] (2) Based on the triaxial strain coupling model, the strain data that was not collected at the test points were supplemented; then the surface fitting function was used to fit the test point data on the cold surface to obtain the triaxial strain and out-of-plane displacement field of the structure.

[0011] (3) Based on the displacement-curvature-strain difference model, the three-dimensional strain difference distribution field of the hot and cold surfaces is calculated by using the out-of-plane displacement field obtained by fitting.

[0012] (4) Calculate the triaxial strain at the key points of the desired output based on the triaxial strain difference distribution field and the triaxial strain of the structure; construct training samples by combining the measured hot and cold surface temperatures;

[0013] (5) Train a parallel multilayer perceptron surrogate model, establish a single-sided strain temperature-cold and hot double-sided key point strain output surrogate model, and apply the surrogate model to obtain double-sided strain.

[0014] Furthermore, in step (1), the triaxial strain data of multiple test points on the cold surface under thermal excitation load is monitored, including: 0° strain of N1 test points, 45° strain of N2 test points, and 90° strain of N3 test points; the out-of-plane displacement data of multiple test points on the cold surface is monitored as the out-of-plane displacement data of N4 test points, and the position of each test point is specifically designed according to the structural deformation; the monitoring data is collected at certain time intervals, and a total of T sets are collected.

[0015] Furthermore, the triaxial strain coupling model in step (2) is specifically as follows:

[0016] ε 45° =p1ε 0° +p2ε 90° +p3

[0017] Where, ε 0° ε 45° ε 90° These represent strain in the 0°, 45°, and 90° directions, respectively; p1, p2, and p3 are strain coupling coefficients, obtained through finite element simulation or experiment; this model represents the relationship between strain in the 0° and 90° directions and strain in the 45° direction, supplementing the 45° direction strain test data with strain in the 0° and 90° directions at specific test points.

[0018] Furthermore, in step (2), a surface fitting function is used to fit the cold surface test point data to obtain the triaxial strain and out-of-plane displacement field of the structure, specifically as follows:

[0019] Based on the strain and displacement data collected in the experiment, combined with the sensor position coordinates, and using the Matlab internal fitting function, the strain and displacement data collected in the experiment are matched one-to-one with the position coordinates of the structure to obtain the triaxial strain and out-of-plane displacement field of the structure.

[0020] Furthermore, the step in step (3) of calculating the strain difference distribution field based on the displacement-curvature-strain difference model is as follows:

[0021] (31) The curvature is obtained by differentiating the out-of-plane displacement field of the cold surface, as follows:

[0022]

[0023] In the formula, w(x,y) is the out-of-plane displacement field of the cold surface, κ x (x,y) represents the curvature field in the x-direction, κ y (x,y) represents the curvature field in the y-direction, κ xy (x,y) represents the torsional field in the xy direction;

[0024] (32) The strain difference distribution field of the cold and hot surfaces is calculated based on the curvature, as follows:

[0025]

[0026] In the formula, {ε x (x,y) heat ε y (x,y) heat γ xy (x,y) heat} represent the strain field in the x-direction, strain field in the y-direction, and shear strain field of the hot surface, respectively, {ε x (x,y) cool ε y (x,y) cool γ xy (x,y) cool} represent the strain field in the x-direction, strain field in the y-direction, and shear strain field in the xy-direction of the cold surface, respectively, and H is the thickness of the structure.

[0027] Furthermore, in step (4), C key points are defined structurally. The strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction corresponding to each key point are calculated using the following formula:

[0028]

[0029] Where, {ε x,heat ε y,heat γ xy,heat} represents the key points on the hot surface, specifically the strain in the x-direction, strain in the y-direction, and the shear strain in the xy-direction, {ε x,cool ε y,cool γ xy,cool} represents the key points of strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction on the cold surface, {κ x ,κ y ,κ xy} represents the curvature in the x-direction, curvature in the y-direction, and torsion in the xy-direction at the key points; finally, the x, y, and xy three-dimensional strain data of C key points on both the hot and cold sides are obtained, with a size of 6×C.

[0030] Further, in step (4), the input to the training sample is a vector of length 1×(N1+N2+N3+K), where K is the number of temperature test points; the output of the training sample is a strain vector of length 1×C.

[0031] The training samples are divided into 6 categories, which output the strain in the hot surface x direction, the strain in the hot surface y direction, the shear strain in the hot surface xy direction, the strain in the cold surface x direction, the strain in the cold surface y direction, and the shear strain in the cold surface xy direction, respectively, and are denoted as U1, U2, U3, U4, U5, and U6; from the T sets of data, T training samples are obtained from U1, U2, U3, U4, U5, and U6 respectively.

[0032] Further, the parallel multilayer perceptron surrogate model in step (5) consists of 6 sub-models, denoted as sub-models M1, M2, M3, M4, M5, and M6; the 6 sub-models have the same structure, with the number of neurons in the input layer being 1×(N1+N2+N3+K) and the number of neurons in the output layer being C; sub-model M1 is trained using data U1, sub-model M2 using data U2, sub-model M3 using data U3, sub-model M4 using data U4, sub-model M5 using data U5, and sub-model M6 using data U6, thereby establishing a single-sided strain temperature-cold and hot double-sided key point strain output surrogate model.

[0033] The beneficial effects of this invention are:

[0034] The method of this invention applies a single-sided thermal excitation load, monitors and fits the displacement and strain of key points on the cold side of the structure; calculates the strain difference between the cold and hot surfaces of the structure through a displacement-curvature-strain difference model, and obtains the triaxial strain of key points on the hot side of the structure; measures the temperature data of the cold and hot surfaces under different thermal excitation loads, trains a parallel multilayer perceptron surrogate model, and establishes a single-sided strain-temperature-strain output surrogate model for key points on both the cold and hot sides. This method can effectively obtain the strain of key points on the cold and hot surfaces of the structure through measured data of the cold side, and can provide key support for subsequent online deformation reconstruction algorithms of the structure. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention.

[0036] Figure 2 This is a physical diagram of the antenna sub-board structure in the embodiment.

[0037] Figure 3 This is a schematic diagram of the measured strain discrete points in the embodiment.

[0038] Figure 4 This is a schematic diagram of the measured temperature discrete points in the example.

[0039] Figure 5 This is a schematic diagram of the measured displacement discrete points in the embodiment.

[0040] Figure 6 This is a schematic diagram of the fitting of a typical out-of-plane displacement field on a cold surface in the embodiment.

[0041] Figure 7 This is a diagram showing the distribution of key points in the antenna sub-board structure in the embodiment.

[0042] Figure 8 This is a schematic diagram illustrating the thermal surface strain calculation of key points in the antenna sub-board structure in the embodiment.

[0043] Figure 9 This is a schematic diagram of the proxy model in the embodiment.

[0044] Figure 10 This is a schematic diagram of the sub-model structure of the proxy model in the embodiment.

[0045] Figure 11 This is a schematic diagram of the thermal surface output results in a typical two-sided strain. Detailed Implementation

[0046] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0047] Reference Figure 1 As shown, the present invention provides a method for obtaining the strain of a single-sided thermally excited structure based on a surrogate model, comprising the following steps:

[0048] (1) For a single-sided thermally excited structure, strain sensors are used to monitor the triaxial strain data of multiple test points on the cold side of the structure under thermally excited load, and displacement sensors are used to monitor the out-of-plane displacement data of multiple test points on the cold side.

[0049] In step (1), the triaxial strain data of multiple test points on the cold surface under thermal excitation load is monitored, including: 0° strain of N1 test points, 45° strain of N2 test points, and 90° strain of N3 test points; the out-of-plane displacement data of multiple test points on the cold surface is monitored as the out-of-plane displacement data of N4 test points, and the position of each test point is specifically designed according to the structural deformation; the monitoring data is collected at certain time intervals, and a total of T sets are collected.

[0050] (2) Based on the triaxial strain coupling model, the strain data that was not collected at the test points were supplemented; then the surface fitting function was used to fit the test point data on the cold surface to obtain the triaxial strain and out-of-plane displacement field of the structure.

[0051] The triaxial strain coupling model is as follows:

[0052] ε 45° =p1ε 0° +p2ε 90° +p3

[0053] Where, ε 0° ε 45° ε 90° These represent strain in the 0°, 45°, and 90° directions, respectively; p1, p2, and p3 are strain coupling coefficients, obtained through finite element simulation or experiment; this model represents the relationship between strain in the 0° and 90° directions and strain in the 45° direction, supplementing the 45° direction strain test data with strain in the 0° and 90° directions at specific test points.

[0054] In step (2), a surface fitting function is used to fit the cold surface test point data to obtain the triaxial strain and out-of-plane displacement field of the structure, specifically as follows:

[0055] Based on the strain and displacement data collected in the experiment, combined with the sensor position coordinates, and using the Matlab internal fitting function, the strain and displacement data collected in the experiment are matched one-to-one with the position coordinates of the structure to obtain the triaxial strain and out-of-plane displacement field of the structure.

[0056] (3) Based on the displacement-curvature-strain difference model, the three-dimensional strain difference distribution field of the hot and cold surfaces is calculated by using the out-of-plane displacement field obtained by fitting.

[0057] The steps for calculating the strain difference distribution field based on the displacement-curvature-strain difference model are as follows:

[0058] (31) The curvature is obtained by differentiating the out-of-plane displacement field of the cold surface, as follows:

[0059]

[0060] In the formula, w(x,y) is the out-of-plane displacement field of the cold surface, κx (x,y) represents the curvature field in the x-direction, κ y (x,y) represents the curvature field in the y-direction, κ xy (x,y) represents the torsional field in the xy direction;

[0061] (32) The strain difference distribution field of the cold and hot surfaces is calculated based on the curvature, as follows:

[0062]

[0063] In the formula, {ε x (x,y) heat ε y (x,y) heat γ xy (x,y) heat} represent the strain field in the x-direction, strain field in the y-direction, and shear strain field of the hot surface, respectively, {ε x (x,y) cool ε y (x,y) cool γ xy (x,y) cool} represent the strain field in the x-direction, strain field in the y-direction, and shear strain field in the xy-direction of the cold surface, respectively, and H is the thickness of the structure.

[0064] (4) Calculate the triaxial strain at the key points of the desired output based on the triaxial strain difference distribution field and the triaxial strain of the structure; construct training samples by combining the measured hot and cold surface temperatures;

[0065] Structurally, C key points are defined. The strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction corresponding to each key point are calculated using the following formula:

[0066]

[0067] Where, {ε x,heat ε y,heat γ xy,heat} represents the key points on the hot surface, specifically the strain in the x-direction, strain in the y-direction, and the shear strain in the xy-direction, {ε x,cool ε y,cool γ xy,cool} represents the key points of strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction on the cold surface, {κ x ,κ y ,κ xy} represents the curvature in the x-direction, curvature in the y-direction, and torsion in the xy-direction at the key points; finally, the x, y, and xy three-dimensional strain data of C key points on both the hot and cold sides are obtained, with a size of 6×C.

[0068] The input to the training samples is a vector of length 1×(N1+N2+N3+K), where K is the number of temperature test points; the output of the training samples is a strain vector of length 1×C.

[0069] The training samples are divided into 6 categories, which output the strain in the hot surface x direction, the strain in the hot surface y direction, the shear strain in the hot surface xy direction, the strain in the cold surface x direction, the strain in the cold surface y direction, and the shear strain in the cold surface xy direction, respectively, and are denoted as U1, U2, U3, U4, U5, and U6; from the T sets of data, T training samples are obtained from U1, U2, U3, U4, U5, and U6 respectively.

[0070] (5) Train a parallel multilayer perceptron proxy model, establish a single-sided strain temperature-cold and hot double-sided key point strain output proxy model, and apply the proxy model to realize the acquisition of double-sided strain.

[0071] Specifically, the parallel multilayer perceptron surrogate model in step (5) consists of 6 sub-models, denoted as sub-models M1, M2, M3, M4, M5, and M6. The 6 sub-models have the same structure, with 1×(N1+N2+N3+K) input layer neurons and C output layer neurons. Sub-model M1 is trained using data U1, sub-model M2 using data U2, sub-model M3 using data U3, sub-model M4 using data U4, sub-model M5 using data U5, and sub-model M6 using data U6, thereby establishing a single-sided strain temperature-cold and hot double-sided key point strain output surrogate model.

[0072] This embodiment uses a large on-orbit deployable antenna sub-board structure as the object;

[0073] like Figure 2 As shown, the antenna sub-plate structure is a crucial structural unit for large, deployable on-orbit satellites, primarily serving as the carrier for antenna functional components. Its dimensions are 1500mm × 3125mm × 20mm, and its composition is 0.4mm epoxy glass cloth (upper skin) / 19.2mm (aramid paper honeycomb) / 0.4mm epoxy glass cloth (lower skin). Furthermore, T-shaped aluminum supports are embedded at the four corners of the antenna sub-plate structure for positioning, assembly, and fixation. Heating elements simulating the heating of functional components are arranged on one side of the structure; current is applied via a DC power supply to generate heat, simulating single-sided thermal excitation conditions. Forty-three fiber optic strain sensors are arranged on the cold side of the structure. Figure 3 As shown, 21 sensors measure strain at 0°, 20 at 90°, and 2 at 45°. Structurally, temperature reference fiber optic grating sensors are arranged on the cold side to collect temperature data, with 43 sensors on the cold side and 3 sensors on the hot side. Figure 4 As shown. The out-of-plane displacement data of the cold surface of the structure was measured using a laser displacement sensor. The displacement measurement data was 1×49, and the displacement measurement points are shown below. Figure 5 As shown.

[0074] Thermal load tests were conducted on the antenna sub-board structure. The structure was heated using heating elements, and temperature data and measured displacement data at key locations were acquired during the heating process. Data was acquired at 1-second intervals for a total of 10 minutes, resulting in 600 sets of data.

[0075] Based on the measured displacement data of the cold surface test points, the out-of-plane displacement field is fitted using a surface fitting function. A typical out-of-plane displacement field of a structural cold surface is shown below. Figure 6 As shown. Furthermore, based on the measured triaxial strain data at 0°, 45°, and 90° at the cold surface test points, and after supplementing the strain data not collected at the test points according to the triaxial strain coupling model, a surface fitting function was used to fit the strain fields in the 0°, 45°, and 90° directions, respectively. Based on the strain relationship in mechanics, the strain fields in the 0°, 45°, and 90° directions were converted into x-direction strain, y-direction strain, and xy-direction shear strain. Based on the displacement-curvature-strain difference model, the fitted out-of-plane displacement fields were used to calculate the x-direction strain difference distribution field, y-direction strain difference distribution field, and xy-direction shear strain difference distribution field of the hot and cold surfaces, respectively.

[0076] Determine the key points of the antenna sub-board structure, such as Figure 7 As shown, there are a total of 144, therefore the strain data at the key points can be calculated as 6×144, namely, 1×144 strain in the x-direction of the hot surface, 1×144 strain in the y-direction of the hot surface, 1×144 xy shear strain of the hot surface, 1×144 strain in the x-direction of the cold surface, 1×144 strain in the y-direction of the cold surface, and 1×144 xy shear strain of the cold surface. Figure 8 As shown.

[0077] Constructing agent model sub-models such as Figure 9 , Figure 10 As shown, the hidden layers consist of three layers with 256, 512, and 512 neurons per layer, respectively, and the activation function is ReLU. The number of neurons in the output layer is the same as the number of strain data extraction points, and the activation function is a non-linear activation function. The network weights are initialized using the He initialization method; the mean squared error loss function is selected as the loss function, and the network parameters are optimized using the Adam algorithm. Six models are trained with a learning rate of 1×10⁻⁴ and a training termination condition of 500 iterations. Cold surface strain data and temperature data are input into the multilayer perceptron strain output surrogate model to obtain strain data at key locations on the hot and cold surfaces of the structure. Typical strain results are shown below. Figure 11 As shown.

[0078] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model, characterized in that, The steps are as follows: (1) For a single-sided thermally excited structure, strain sensors are used to monitor the triaxial strain data of multiple test points on the cold side of the structure under thermally excited load, and displacement sensors are used to monitor the out-of-plane displacement data of multiple test points on the cold side. (2) Based on the triaxial strain coupling model, the strain data that was not collected at the test points were supplemented; then the surface fitting function was used to fit the test point data on the cold surface to obtain the triaxial strain and out-of-plane displacement field of the structure. (3) Based on the displacement-curvature-strain difference model, the three-dimensional strain difference distribution field of the hot and cold surfaces is calculated by using the out-of-plane displacement field obtained by fitting. (4) Calculate the triaxial strain at the key points of the desired output based on the triaxial strain difference distribution field and the triaxial strain of the structure; construct training samples by combining the measured hot and cold surface temperatures. (5) Train a parallel multilayer perceptron proxy model, establish a single-sided strain temperature-cold and hot double-sided key point strain output proxy model, and apply the proxy model to realize the acquisition of double-sided strain; The triaxial strain coupling model in step (2) is specifically as follows: ； in, , , These represent strain in the 0°, 45°, and 90° directions, respectively. , and The strain coupling coefficient is used; the model represents the relationship between strain in the 0° and 90° directions and strain in the 45° direction, and the 45° direction strain test data is supplemented by the 0° and 90° direction strains at specific test points. The steps in step (3) for calculating the strain difference distribution field based on the displacement-curvature-strain difference model are as follows: (31) The curvature is obtained by differentiating the out-of-plane displacement field of the cold surface, as follows: ； In the formula, For the out-of-plane displacement field of the cold surface, Represents the curvature field in the x-direction. This represents the curvature field in the y-direction. Represents the torsional field in the xy direction; (32) The strain difference distribution field of the cold and hot surfaces is calculated based on the curvature, as follows: ； In the formula, Let x represent the strain field in the x-direction, the strain field in the y-direction, and the shear strain field of the hot surface, respectively. These represent the strain field in the x-direction, strain field in the y-direction, and shear strain field in the xy-direction of the cold surface, respectively, with H being the structural thickness.

2. The method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model according to claim 1, characterized in that, The step (1) involves monitoring the triaxial strain data at multiple test points on the cold surface under thermal excitation load, including: Strain at 0° direction at each test point Strain at 45° direction at each test point Strain at 90° direction at each test point; out-of-plane displacement data at multiple test points on the cold surface were monitored. The out-of-plane displacement data of each test point is designed according to the specific structural deformation; the monitoring data is collected at certain time intervals, and a total of T sets are collected.

3. The method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model according to claim 1, characterized in that, In step (2), a surface fitting function is used to fit the cold surface test point data to obtain the structural triaxial strain and out-of-plane displacement field, specifically as follows: Based on the strain and displacement data collected in the experiment, combined with the sensor position coordinates, and using the Matlab internal fitting function, the strain and displacement data collected in the experiment are matched one-to-one with the position coordinates of the structure to obtain the triaxial strain and out-of-plane displacement field of the structure.

4. The method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model according to claim 1, characterized in that, In step (4), C key points are defined structurally. The strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction corresponding to each key point are calculated using the following formula: ； in, The key points are the strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction on the hot surface. The key points are the strain in the x-direction, strain in the y-direction, and shear strain in the xy-direction on the cold surface. The curvature in the x-direction, curvature in the y-direction, and torsion in the xy-direction at the key points are given; the x, y, and xy three-dimensional strain data of C key points on both the hot and cold sides are obtained, with a size of 6×C.

5. The method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model according to claim 1, characterized in that, The input for constructing the training samples in step (4) is A vector of length, where K is the number of temperature test points; The training samples output a 1×C strain vector; The training samples are divided into 6 categories, which output the strain in the hot surface x direction, the strain in the hot surface y direction, the shear strain in the hot surface xy direction, the strain in the cold surface x direction, the strain in the cold surface y direction, and the shear strain in the cold surface xy direction, respectively, and are denoted as U1, U2, U3, U4, U5, and U6; from the T sets of data, T training samples are obtained from U1, U2, U3, U4, U5, and U6 respectively.

6. The method for obtaining double-sided strain of a single-sided thermally excited structure based on a surrogate model according to claim 1, characterized in that, The parallel multilayer perceptron surrogate model in step (5) consists of six sub-models, denoted as sub-models M1, M2, M3, M4, M5, and M6; these six sub-models have the same structure, and the number of neurons in the input layer is... The number of neurons in the output layer is C; sub-model M1 is trained using data U1, sub-model M2 using data U2, sub-model M3 using data U3, sub-model M4 using data U4, sub-model M5 using data U5, and sub-model M6 using data U6, thus establishing a single-sided strain temperature-cold and hot double-sided key point strain output proxy model.

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