A new method of inverse finite element deformation reconstruction based on virtual deformation field physical constraint

Abstract

The present application relates to the technical field of structural deformation shape reconstruction, and particularly relates to a new method of inverse finite element deformation reconstruction based on virtual deformation field physical constraint. The method uses the virtual displacement field obtained by inverse finite element reconstruction of sparse strain as the strain extrapolation physical constraint; adopts the iterative idea to use the extrapolated strain and the measured strain for inverse finite element deformation reconstruction again to obtain the new virtual displacement field, so as to constrain the strain extrapolation again. Thus, the virtual deformation and the extrapolated strain are reconstructed iteratively, and the real structural deformation is finally reconstructed; the accuracy of the deformation characteristic value is determined based on the actual measured actual deformation characteristic value and the deformation characteristic value determined based on the extrapolated strain data, and the deformation reconstruction state is determined based on the accuracy. In the deformation reconstruction process, the present application iteratively extrapolates the strain measuring points and uses the virtual displacement field as the physical constraint, so as to improve the accuracy of the deformation reconstruction.

Description

Technical Field

[0001] This invention relates to the technical field of structural deformation shape reconstruction, and in particular to a novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints. Background Technology

[0002] In recent years, with the continuous development of aerospace technology, the performance of high-end equipment has been constantly improving. To reduce maintenance time, increase equipment service life, lower maintenance costs, and improve structural safety and reliability, the development of structural health monitoring technology is crucial. Shape sensing technology, as a structural health monitoring method, can monitor structural deformation, stress state, and damage state in real time. Furthermore, it can provide important feedback for the development and application of drive and control systems for some intelligent structures. Among these, the inverse finite element method (iFEM) deformation reconstruction method based on strain data is currently the most promising research direction in shape sensing technology, providing effective means and methods for detecting the overall deformation characteristics of equipment and optimizing structural performance.

[0003] The key to accurately reconstructing structural deformation using iFEM lies in having sufficient strain data. However, reality presents numerous limitations: strain measurement points are scarce and unevenly distributed. Therefore, various methods must be used to augment the measured strain in order to reconstruct a relatively accurate structural deformation using iFEM. Some researchers use function fitting and SEA methods, which only perform direct mathematical processing on strain without clarifying the physical mechanism. The accuracy of strain augmentation is greatly affected by the polynomial form and SEA hyperparameters, requiring extensive experimentation and proving impractical in real-world engineering. Others have attempted to introduce physical constraints to augment strain; however, these constraints require explicit load and material information, making them too restrictive and difficult to implement.

[0004] Chinese Patent Publication No. CN118687495A discloses a method for reconstructing the dynamic large deformation field of a plate and shell structure. The method includes: Step 1: Dividing the plate and shell structure into multiple units and attaching fiber optic grating sensors to the strain measurement points of each unit; setting the load step s = 0; Step 2: Testing the plate and shell structure to obtain the initial center wavelength; Step 3: Applying a displacement load to the plate and shell structure to obtain the measured strain of the current load step, and using the measured strain of the current load step to obtain the strain of the current load step relative to the previous load step; Step 4: Using the strain of the current load step relative to the previous load step to obtain the coordinates of all unit nodes of the current load step; Step 5: s = s + 1, determining whether s is equal to a set threshold. If yes, proceed to Step 6; if no, increase the displacement load and then return to Step 3; Step 6: Outputting the coordinates of all unit nodes of each load step.

[0005] It is evident that the existing technology has the following problems: the scarcity of strain measurement points and the strong physical constraints during deformation reconstruction lead to low accuracy of deformation reconstruction. Summary of the Invention

[0006] To address this, the present invention provides a novel inverse finite element deformation reconstruction method based on physical constraints of a virtual deformation field, which overcomes the problem of low accuracy in deformation reconstruction caused by the scarcity of strain measurement points and strong physical constraints in the existing technology.

[0007] To achieve the above objectives, this invention provides a novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints, comprising:

[0008] The plate shell is divided into grids of equal area, and strain sensors are placed in each grid area to acquire several strain measurement data to form a strain measurement dataset.

[0009] Several deformation characterization values ​​of the plate and shell are determined using inverse finite element methods based on several measured strain data and extrapolated initial strain data, wherein the inverse finite element method is a unit solved based on the inverse finite element equation;

[0010] If there exists an inverse finite element that does not contain the measured strain data, the deformation characterization values ​​are fitted to determine the virtual strain field.

[0011] The mapping coefficient field function is determined based at least on the mapping coefficients calculated from the virtual strain field and the measured strain data;

[0012] The extrapolated strain data is determined based on the location information of the measured strain data and the linear characterization value of the mapping coefficient.

[0013] Using inverse finite element methods, several deformation characterization values ​​of the plate and shell are re-determined based on several measured strain data and extrapolated strain data. It is then determined whether these deformation characterization values ​​are acceptable. If they are unacceptable, the extrapolated strain data is repeatedly determined until the determined deformation characterization values ​​are acceptable.

[0014] Among them, the criterion for determining whether a number of deformation characterization values ​​are qualified is whether all the inverse finite elements contain the strain data in the measured strain dataset.

[0015] The accuracy of the deformation characterization values ​​is determined based on several actual deformation characterization values ​​determined by actual measurement and several deformation characterization values ​​determined by extrapolated strain data. Based on the accuracy, the deformation reconstruction state is determined. Based on the deformation reconstruction state, it is determined whether to add plastic strain increment to the virtual deformation field. The virtual deformation field is adjusted multiple times by relaxation factor.

[0016] Furthermore, the process of determining the mapping coefficient field function based at least on the mapping coefficients calculated from the virtual strain field and the measured strain data includes: constructing a strain matrix based on the measured strain data and the extrapolated strain data; determining the mapping coefficients based on the strain matrix and the virtual strain field; and fitting the mapping coefficients using a set of linearly independent basis vectors to obtain the mapping coefficient field function.

[0017] Furthermore, the process of determining the location of the extrapolated strain data includes: determining the extrapolation step size based on the location information of the measured strain data and the linear characterization value of the mapping coefficient; and determining the location of the strain to be extrapolated based on the extrapolation step size.

[0018] Further, the process of determining the extrapolated strain data includes: determining the extrapolation mapping coefficients based on the mapping coefficient field function; determining the extrapolated virtual strain data based on the virtual strain field; determining the local extrapolated strain data based on the extrapolation mapping coefficients and the extrapolated virtual strain data; and determining the extrapolated strain data based on the local extrapolated strain data and the initial extrapolated strain data. During the iteration process, the initial extrapolated strain data is the previously determined extrapolated strain data, and each extrapolated strain data determined during the iteration process is added to the measured strain dataset.

[0019] Furthermore, when the deformation reconstruction state is determined to be the first state based on the accuracy, a monitoring point-strain curve is plotted. If the average value of the curve tangent is greater than the preset average value, the determination is made based on the yield strain of the plate and shell. The accuracy of the first state is that the accuracy is less than or equal to the first preset accuracy and greater than the second preset accuracy. If the strain at any monitoring point is greater than the yield strain, it is determined that the plate and shell have undergone local plastic deformation. The plastic strain increment is used as an additional variable of the virtual deformation field, and the virtual deformation field is adjusted by a relaxation factor. The relaxation factor is adjusted based on the difference between the strain and the yield strain and the ratio of the yield strain.

[0020] Furthermore, the relaxation factor is reduced based on the ratio of the difference between the strain and the yield strain to the yield strain, and the ratio is proportional to the reduction in the relaxation factor.

[0021] Furthermore, after adjusting the relaxation factor, deformation reconstruction is performed again. If the deformation reconstruction state is the first state, the step of reducing the relaxation factor is repeated at least once until the stopping condition is met. The stopping condition is that the deformation reconstruction state is qualified when the number of reductions is less than or equal to the preset number of reductions, or when the number of reductions is greater than the preset number of reductions. If the deformation reconstruction state is still unqualified after stopping the repeated execution of the step of reducing the relaxation factor, the number of mesh divisions is adjusted based on the ratio of strain to preset strain in the region where the strain is greater than the preset strain.

[0022] Furthermore, the number of mesh divisions is increased based on the ratio of the strain to the preset strain, and the ratio is proportional to the increase in the number of mesh divisions.

[0023] Furthermore, when the deformation reconstruction state is determined to be in the second state based on the accuracy, the gradient scale of the plate and shell is obtained; the interval distance of the strain sensors is adjusted based on the gradient scale; wherein, the accuracy of the second state is less than or equal to a second preset accuracy.

[0024] Furthermore, the process of adjusting the interval distance of the strain sensors based on the gradient scale includes: if the gradient scale is less than or equal to a preset gradient scale, increasing the interval distance of the sensors based on the gradient scale, and the increase in the gradient scale is proportional to the increase in the interval distance of the sensors; if the gradient is greater than the preset gradient scale, decreasing the interval distance of the sensors based on the gradient scale, and the decrease in the gradient scale is proportional to the decrease in the interval distance of the sensors.

[0025] Compared with existing technologies, the beneficial effects of this invention are that the method uses only the virtual displacement field obtained by reconstructing sparse strain through inverse finite element method as the physical constraint for strain extrapolation; employing an iterative approach, the extrapolated strain and the measured strain are used again for inverse finite element deformation reconstruction to obtain a new virtual displacement field, thereby constraining strain extrapolation again. This iterative reconstruction of virtual deformation and extrapolated strain continues until the actual structural deformation is reconstructed; and the accuracy of the deformation characterization values ​​is determined based on several actual measured deformation characterization values ​​and several deformation characterization values ​​determined by extrapolated strain data, and the deformation reconstruction state is determined based on the accuracy. This invention improves the accuracy of deformation reconstruction by iteratively extrapolating strain measurement points and utilizing the virtual displacement field as a physical constraint during the deformation reconstruction process.

[0026] Furthermore, this invention uses only the virtual displacement field obtained from sparse strain reconstructed via inverse finite element method as the physical constraint for strain extrapolation. Employing an iterative approach, the extrapolated strain and the measured strain are used again for inverse finite element deformation reconstruction to obtain a new virtual displacement field, which can then constrain strain extrapolation again. This iterative reconstruction of virtual deformation and extrapolated strain continues until the actual structural deformation is reconstructed. Strain augmentation is achieved by using the deformation characteristics of the virtual deformation field as the extrapolation constraint. A virtual strain field is obtained from the virtual deformation field through geometric equations, serving as the strain extrapolation reference. Elementary transformations are then used to construct a mapping relationship between sparse strain and the virtual strain field, enabling strain extrapolation through the mapping function and the virtual strain field. Based on the spatial distribution density of the measured strain sensors, the region for each strain extrapolation is selected, allowing for local or global extrapolation, achieving one or more iterative strain augmentations. Based on the currently augmented strain data and the measured strain, a new virtual displacement field can be reconstructed using a conventional inverse finite element method framework, updating the physical constraints, which can then be used to extrapolate strain again until the actual structural deformation is reconstructed.

[0027] Furthermore, by repeatedly determining whether the plate or shell has undergone local plastic deformation and adjusting the virtual deformation field based on the determination results, the present invention can make the adjustment of the virtual deformation field more effective, thereby improving the accuracy of deformation reconstruction.

[0028] Furthermore, the present invention adjusts the relaxation factor by the ratio of the difference between strain and yield strain to the yield strain. This can prevent mesh distortion by forcing local stress release in the virtual deformation field by reducing the relaxation factor, thereby improving the accuracy of deformation reconstruction.

[0029] Furthermore, the present invention also repeats the step of reducing the relaxation factor until the stopping condition is met. If the reconstruction state is still unqualified after stopping the execution, the number of mesh divisions is adjusted. This allows the number of mesh divisions to be adjusted when the effect is still not achieved after adjusting the relaxation factor, making the measured strain data more effective, thereby improving the accuracy of the extrapolated strain data and thus improving the accuracy of deformation reconstruction.

[0030] Furthermore, the present invention adjusts the number of network divisions by the ratio of strain to preset strain. This allows for adjustment of the number of network divisions when the strain is greater than the preset strain, thereby reducing the impact of plate and shell distortion on the measured strain data and improving the accuracy of deformation reconstruction.

[0031] Furthermore, the present invention also improves the accuracy of deformation reconstruction by adjusting the spacing between strain sensors when the deformation reconstruction state is in the second state, thereby adjusting the layout of the sensors according to the gradient scale of the structure. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the inverse finite element deformation reconstruction system based on virtual deformation field physical constraints according to an embodiment of the present invention;

[0033] Figure 2 This is a flowchart illustrating the steps of the inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to an embodiment of the present invention.

[0034] Figure 3 This is a flowchart of the main process of the novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints in an embodiment of the present invention.

[0035] Figure 4 This is a flowchart illustrating the steps of determining the accuracy rate based on the comparison result between the accuracy rate and the pre-stored preset accuracy rate in an embodiment of the present invention.

[0036] Figure 5 This is a reconstruction target image of a square aluminum alloy sheet and its deformation result image in an embodiment of the present invention;

[0037] Figure 6 This is the strain diagram of the sparse measuring points reconstructed by inverse finite element method in the first embodiment of the present invention, and the deformation result diagram obtained therefrom.

[0038] Figure 7 These are schematic diagrams of the virtual displacement field, virtual y-direction bending strain field, mapping coefficient, and mapping coefficient field function obtained by the first inverse finite element reconstruction in this embodiment of the invention.

[0039] Figure 8 Each of the embodiments of the present invention has undergone Figure 7 A schematic diagram showing the augmented strain after the first iteration, the augmented strain after the second iteration, and the augmented strain after the third iteration;

[0040] Figure 9 These are the deformation curves and deformation error curves under the actual working conditions, initial reconstruction, and first to third iteration reconstruction in the embodiments of the present invention. Detailed Implementation

[0041] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0042] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0043] It should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0044] Please see Figure 1 As shown, it is a schematic diagram of the inverse finite element deformation reconstruction system based on virtual deformation field physical constraints according to an embodiment of the present invention.

[0045] The structure includes an acquisition unit, a deformation characterization value determination unit, a virtual strain field determination unit, a mapping coefficient field function determination unit, an extrapolated strain data determination unit, a first analysis unit, and a second analysis unit.

[0046] The acquisition unit is used to divide the plate shell into grids of equal area, and to arrange strain sensors in each grid area to acquire several measured strain data to form a measured strain dataset.

[0047] A deformation characterization value determination unit, which is connected to the acquisition unit, is used to determine several deformation characterization values ​​of the plate and shell based on several measured strain data and extrapolated strain initial data using an inverse finite element, wherein the inverse finite element is a unit based on solving the inverse finite element equation.

[0048] A virtual strain field determination unit, which is connected to the deformation characterization value determination unit, is used to fit several deformation characterization values ​​to determine the virtual strain field if there is an inverse finite element that does not contain the measured strain data.

[0049] A mapping coefficient field function determination unit, which is connected to the virtual strain field determination unit, is used to determine the mapping coefficient field function based at least on the mapping coefficients calculated from the virtual strain field and the measured strain data.

[0050] An extrapolated strain data determination unit, which is connected to the mapping coefficient field function determination unit, is used to determine extrapolated strain data based on the location information of the measured strain data and the linear characterization value of the mapping coefficient;

[0051] The first analysis unit, which is connected to the extrapolated strain data determination unit, is used to redetermine several deformation characterization values ​​of the plate and shell based on several measured strain data and extrapolated strain data using inverse finite elements, and determine whether several deformation characterization values ​​are qualified. If they are not qualified, the extrapolated strain data is repeatedly determined until the determined several deformation characterization values ​​are qualified. The criterion for determining whether several deformation characterization values ​​are qualified is whether all the inverse finite elements contain the strain data in the measured strain data set.

[0052] The second analysis unit, connected to the first analysis unit, is used to determine the accuracy of the deformation characterization values ​​based on several actual deformation characterization values ​​determined by actual measurement and several deformation characterization values ​​determined by extrapolated strain data, and to determine the deformation reconstruction state based on the accuracy, and to determine whether to add plastic strain increment to the virtual deformation field based on the deformation reconstruction state, and to adjust the virtual deformation field multiple times through relaxation factors.

[0053] Please see Figure 2 As shown, it is a flowchart of the steps of the inverse finite element deformation reconstruction method based on virtual deformation field physical constraints.

[0054] The following is a flowchart of the inverse finite element deformation reconstruction method based on virtual deformation field physical constraints:

[0055] S1, the plate shell is divided into grids of equal area by acquiring the unit, and strain sensors are arranged in each grid area to acquire several measured strain data to form a measured strain dataset;

[0056] S2, the deformation characterization value determination unit connected to the acquisition unit uses an inverse finite element to determine several deformation characterization values ​​of the plate and shell based on several measured strain data and extrapolated strain initial data, wherein the inverse finite element is a unit based on the inverse finite element equation;

[0057] S3, if there is an inverse finite element that does not contain the measured strain data, the virtual strain field determination unit connected to the deformation characterization value determination unit fits several deformation characterization values ​​to determine the virtual strain field.

[0058] S4, the mapping coefficient field function is determined by the mapping coefficient field function determination unit connected to the virtual strain field determination unit, based at least on the mapping coefficients calculated by the virtual strain field and the measured strain data;

[0059] S5, the extrapolated strain data is determined by the extrapolated strain data determination unit connected to the mapping coefficient field function determination unit based on the position information of the measured strain data and the linear characterization value of the mapping coefficient;

[0060] S6, the first analysis unit connected to the extrapolated strain data determination unit uses inverse finite elements to re-determine several deformation characterization values ​​of the plate and shell based on several measured strain data and extrapolated strain data, and determines whether several deformation characterization values ​​are qualified. If they are not qualified, the extrapolated strain data is determined repeatedly until the determined several deformation characterization values ​​are qualified. The criterion for determining whether several deformation characterization values ​​are qualified is whether all the inverse finite elements contain the strain data in the measured strain data set.

[0061] S7, the accuracy rate of the deformation characterization value is determined by the second analysis unit connected to the first analysis unit based on several actual deformation characterization values ​​and several deformation characterization values ​​determined by extrapolated strain data, and the deformation reconstruction state is determined based on the accuracy rate, and whether the virtual deformation field should be added with plastic strain increment is determined based on the deformation reconstruction state, and the virtual deformation field is adjusted multiple times by relaxation factor.

[0062] Specifically, please refer to Figure 3 As shown, this is the main flowchart of a new inverse finite element deformation reconstruction method based on virtual deformation field physical constraints. The specific implementation includes the following steps:

[0063] 1) Initialize extrapolated strain.

[0064] 2) By collecting sparse measured strain and extrapolated strain (for the first time, without extrapolated strain data) from the plate and shell structure, a deformation result is directly reconstructed using a conventional inverse finite element method. Because this reconstructed deformation result uses measured strain for reconstruction, the reconstructed curve around the measured strain contains characteristics of the true deformation.

[0065] Determine if all inverse finite elements have measured strain. If the result is Yes, then step 2) reconstructs the actual structural deformation; if the result is No, then strain augmentation must be performed, proceeding to step 3).

[0066] 3) Based on the deformation data obtained from the initial reconstruction in step 2), a set of spatially linearly independent basis vectors is used to fit the deformation to obtain a continuous virtual displacement field function. The linearly independent basis vector set includes, but is not limited to, polynomials and trigonometric functions. The selection of the basis vector set needs to consider the number of measurement points and the complexity of the deformation curve to be reconstructed. When performing the fitting, three key points need to be met: (1) The fitting curve should satisfy the boundary conditions as much as possible. (2) The fitting curve should be close to the reconstructed deformation curve around the measured strain to retain deformation characteristics similar to the real curve. (3) The requirement of continuity and differentiability should be met. Based on the deformation trend of the measured strain, the order of differentiability of the virtual displacement field function can be preliminarily determined.

[0067] 4) Based on the virtual deformation field function obtained by fitting in step 3), derive the virtual strain field according to the geometric equation.

[0068] 5) Combining the virtual strain field derived in step 4) with the measured strain, a series of discrete mapping coefficients are obtained by dividing element-wise using ". / ". The mapping coefficients are defined as follows: where the superscript indicates that the strain is taken from the position corresponding to the measured strain, and the superscript indicates that the strain is taken from the position corresponding to the extrapolated strain.

[0069] 6) Based on the discrete mapping coefficients calculated in step 5), a continuous mapping coefficient field function is fitted using the linearly independent basis vector set used in step 3) to construct the virtual displacement field function.

[0070] 7) Based on the spatial distribution of the measured strain and the linearity of the discrete mapping coefficients, select the extrapolation step size and determine the location where the strain needs to be extrapolated. Based on the selected extrapolated strain location, first use the mapping coefficient field function fitted in step 6) to directly calculate the extrapolated mapping coefficients. Then, based on the virtual strain field derived in step 3), calculate the virtual strain at the extrapolated location. Finally, use the inverse operation to multiply element-wise to obtain the extrapolated strain data.

[0071] 8) Augment the strain matrix obtained from the extrapolation in step 7) to the initial input strain in step 2) to obtain a new input strain for reconstruction. Then, jump to step 2 to perform the next strain extrapolation iteration. After multiple extrapolation strains, the actual structural deformation is gradually approximated.

[0072] Please see Figure 4 The diagram shows the steps of determining the deformation reconstruction state based on the comparison result between the accuracy rate and the pre-stored preset accuracy rate in an embodiment of the present invention. When the deformation reconstruction state is determined to be the first state based on the accuracy rate, a monitoring point-strain curve is plotted. If the average value of the curve tangent is greater than a preset average value, a determination is made based on the yield strain of the shell. The accuracy rate of the first state is that the accuracy rate is less than or equal to a first preset accuracy rate and greater than a second preset accuracy rate. If the strain at any monitoring point is greater than the yield strain, it is determined that local plastic deformation has occurred in the shell. The increment of plastic strain is used as an additional variable of the virtual deformation field, and the virtual deformation field is adjusted by a relaxation factor. The relaxation factor is adjusted based on the difference between the strain and the yield strain and the ratio of the yield strain.

[0073] Specifically, the accuracy L0 can be divided into a first preset accuracy L1 and a second preset accuracy L2. In the accuracy standard, the first preset accuracy L1 = 0.95, and the second preset accuracy L2 = 0.85. It should be noted that in other cases, the values ​​of L1 and L2 can also be determined according to the deformation reconstruction requirements. The comparison process between accuracy L and L1 and L2 is as follows:

[0074] If the accuracy L is greater than the first preset accuracy L1, the deformation reconstruction is determined to meet the standard.

[0075] If the accuracy L is less than or equal to the first preset accuracy L1 and greater than the second preset accuracy L2, the accuracy is low, and the deformation reconstruction state is recorded as the first state.

[0076] If the accuracy L is less than or equal to the second preset accuracy L2, the deformation reconstruction state is recorded as the second state.

[0077] Specifically, during the yielding stage of plastic deformation, when the strain of the same mesh exceeds the elastic limit, the strain will continue to increase due to the sudden large slippage of displacement. Therefore, the tangent of the plotted monitoring point-strain curve will fluctuate greatly. When this happens, the ASTM E8 / E21 standard test is used to determine whether the strain is greater than the yield strain. If the strain is greater than the yield strain, it is determined that the plate and shell have undergone local plastic deformation.

[0078] Specifically, the plastic strain increment Δε ρAs an additional variable to the virtual deformation field, the virtual displacement field is iteratively corrected to make the deformation reconstruction more accurate. The formula for the virtual displacement field after adding the plastic strain variable is:

[0079] ε k+1 (x,y)=ε k (x,y)+βΔε ρ

[0080] Where, ε k (x,y) represents the virtual displacement field at time k, and β is the convergence factor.

[0081] Specifically, the iterative correction of the virtual displacement field is mainly achieved by adjusting the relaxation factor β, the difference between strain and yield strain, and the preset ratio M0 = 0.15 of the yield strain. The comparison process between the ratio M and the preset ratio M0 is as follows:

[0082] If the ratio M is less than or equal to the preset ratio M0, the relaxation factor will be adjusted to 0.83 times the original relaxation factor.

[0083] If the ratio M is greater than the preset ratio M0, the relaxation factor will be adjusted to 0.76 times the original relaxation factor.

[0084] Specifically, after adjusting the relaxation factor, deformation reconstruction is performed again. If the deformation reconstruction state is still in the first state, the relaxation factor is adjusted multiple times until the deformation reconstruction state is adjusted to be acceptable within the prediction count or the number of adjustments reaches the preset number. When the preset number of adjustments is reached and the deformation reconstruction state is still unacceptable, for grid regions where the strain is greater than the preset strain, the number of grid divisions is adjusted based on the ratio of strain to preset strain. This can refine the grid in regions with significant features, making sensor monitoring more accurate and thus deformation reconstruction more accurate.

[0085] Specifically, if the preset ratio N0 of the strain to the preset strain is 1.2, then the comparison process based on the ratio N and the preset ratio N0 is as follows:

[0086] If the ratio N is less than or equal to the preset ratio N0, the number of grid divisions will be adjusted to 1.3 times the original number of divisions;

[0087] If the ratio N is greater than the preset ratio N0, the number of grid divisions will be adjusted to 1.7 times the original number of divisions.

[0088] Specifically, in this embodiment of the invention, when the deformation reconstruction state is determined to be the second state based on the accuracy, the gradient scale of the plate and shell is obtained; the interval distance of the strain sensors is adjusted based on the gradient scale; wherein, the accuracy of the second state is less than or equal to a second preset accuracy.

[0089] Specifically, when the deformation reconstruction state is in the second state, it indicates a problem with the sensor layout. Low detection accuracy occurs at locations with large gradient scales, such as hole edges and welds, leading to inaccurate strain measurement. Therefore, the spacing between strain sensors is adjusted based on the gradient scale. Specifically, when the gradient scale is less than or equal to the preset gradient scale, the sensor spacing needs to be increased, and fewer sensors are needed for monitoring. When the gradient scale is greater than the preset gradient scale, the sensor spacing needs to be decreased, and the sensors in areas with smaller gradient scales need to be arranged more closely to more accurately reconstruct the deformation.

[0090] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments.

[0091] Example 1

[0092] Specifically, with Figure 5 (a) shows a 2mm thick square aluminum alloy sheet, fixed at one end and subjected to a 10mm bending deformation at the other end as the reconstruction target. The method of this invention will be described to... Figure 6 The sparse measurement point scheme shown in (a) is gradually reconstructed through three iterations of extrapolation. Figure 5 (b) shows the actual deformation.

[0093] use Figure 6 The strain at the sparse measurement points shown in (a) is directly obtained through inverse finite element reconstruction, as shown in the following figure. Figure 6 As shown in (b), the maximum bending deformation is -0.8324 mm, occurring at the free end. The following section will introduce a novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints, in conjunction with the present invention. Figure 3 The flowchart shown illustrates the iterative extrapolation of strain process, with the specific steps as follows:

[0094] (1) The deformation results obtained from the first inverse finite element reconstruction, such as Figure 6 As shown in (b). It was determined that not all inverse finite element elements had measurement points at this point, therefore the first iteration of strain augmentation was initiated. Using a polynomial, and based on the fitting requirements described in step 3 of the invention, the following was fitted: Figure 7 (a) shows the virtual displacement field.

[0095] (2) Based on the small deformation assumption, the bending strain in the y-direction can be obtained by deriving the displacement field with respect to the x-coordinate and taking its negative value. Therefore, we can obtain the following: Figure 7 (b) shows the virtual y-direction bending strain field.

[0096] (3) Based on the definition of strain mapping coefficient in step 5 of the invention, the discrete mapping coefficients are calculated, such as... Figure 7 As shown in (c).

[0097] (4) Based on Figure 7 The discrete mapping coefficients in (c) are also fitted to the full-field function using a polynomial to obtain... Figure 7 (c) shows the full-field function of the mapping coefficients.

[0098] (5) To ensure the accuracy of extrapolation and reduce errors, the area selected for the first extrapolation is the area inside the measurement point and its surrounding area, such as... Figure 7 As shown in (d), extending the extrapolated strain to the measured strain completes the strain augmentation.

[0099] (6) Adopt Figure 7 (d) The augmented strain is then subjected to deformation reconstruction to obtain the following result: Figure 8 The reconstructed deformation is shown in (a). Since the measured strain data is still missing at this point, a second iteration to augment the strain is required. Jump to step 2 to perform strain augmentation again.

[0100] (7) The subsequent iteration process is similar to the first one, and the reconstruction deformation after the second iteration is as follows: Figure 8 As shown in (b), the reconstruction deformation after the third iteration is as follows: Figure 8 As shown in (c). After three iterations, all elements have strain input, thus exiting the loop. The reconstructed deformation result at this point is the final output reconstructed deformation result.

[0101] In this embodiment, the iterative reconstruction method described in this invention completes all strain in just three iterations. Figure 6 (b) shows the deformation curves of section AA under various working conditions, summarizing the deformation curves under the actual working conditions, initial reconstruction, and first to third iteration reconstructions. Figure 9 (a). And based on the defined error calculation formula, the following were calculated respectively. Figure 6 The error of the curve in (a). From Figure 9 (b) The deformation error curves reconstructed after three iterations of strain augmentation show that as the iterations proceed, the reconstruction results gradually approach the actual bending deformation. Within the 0-100mm range, it almost coincides with the exact finite element solution, after which the error gradually increases. With further iterations, the error in the bending deformation reconstruction results gradually decreases, from an initial 91.7203% to -11.3463%.

[0102] This invention uses only the virtual deformation field reconstructed from sparse strain data as the physical constraint for strain extrapolation, greatly reducing the difficulty of introducing constraints and improving the accuracy of strain extrapolation. The iterative method allows for successive extrapolation of strain across different regions, reducing extrapolation errors. This new method is highly versatile, applicable not only to cases with uniform spatial distribution of measurement points but also to cases with sparse and unevenly distributed sensor arrays.

[0103] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0104] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints, characterized in that, include: The plate shell is divided into grids of equal area, and strain sensors are placed in each grid area to acquire several strain measurement data to form a strain measurement dataset. Several deformation characterization values ​​of the plate and shell are determined using inverse finite element methods based on several measured strain data and extrapolated initial strain data, wherein the inverse finite element method is a unit solved based on the inverse finite element equation. If there exists an inverse finite element that does not contain the measured strain data, the deformation characterization values ​​are fitted to determine the virtual strain field. The mapping coefficient field function is determined based at least on the mapping coefficients calculated from the virtual strain field and the measured strain data; The extrapolated strain data is determined based on the location information of the measured strain data and the linear characterization value of the mapping coefficient. Using inverse finite element methods, several deformation characterization values ​​of the plate and shell are re-determined based on several measured strain data and extrapolated strain data. It is then determined whether these deformation characterization values ​​are acceptable. If they are unacceptable, the extrapolated strain data is repeatedly determined until the determined deformation characterization values ​​are acceptable. Among them, the criterion for determining whether a number of deformation characterization values ​​are qualified is whether all the inverse finite elements contain the strain data in the measured strain dataset. The accuracy of the deformation characterization values ​​is determined based on several actual deformation characterization values ​​determined by actual measurement and several deformation characterization values ​​determined by extrapolated strain data. Based on the accuracy, the deformation reconstruction state is determined. Based on the deformation reconstruction state, it is determined whether to add plastic strain increment to the virtual deformation field. The virtual deformation field is adjusted multiple times by relaxation factor.

2. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 1, characterized in that, The process of determining the mapping coefficient field function based at least on the mapping coefficients calculated from the virtual strain field and the measured strain data includes: A strain matrix is ​​constructed based on measured strain data and extrapolated strain data; The mapping coefficients are determined based on the strain matrix and the virtual strain field; The mapping coefficients are fitted using a set of linearly independent basis vectors to obtain the mapping coefficient field function.

3. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 1, characterized in that, The process of determining the location of the extrapolated strain data includes: The extrapolation step size is determined based on the location information of the measured strain data and the linear characterization value of the mapping coefficient; The location where the extrapolation strain needs to be determined is based on the extrapolation step size.

4. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 1, characterized in that, The process of determining the extrapolated strain data includes: The extrapolated mapping coefficients are determined based on the mapping coefficient field function; Based on the virtual strain field, extrapolated virtual strain data are determined; Local extrapolated strain data are determined based on the extrapolation mapping coefficients and the extrapolated virtual strain data; Extrapolated strain data is determined based on the local extrapolated strain data and the initial extrapolated strain data. In the iterative process, the initial extrapolated strain data is the previously determined extrapolated strain data. Each extrapolated strain data determined in the iterative process is added to the measured strain dataset.

5. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 1, characterized in that, When the deformation reconstruction state is determined to be the first state based on the accuracy, the monitoring point-strain curve is plotted. If the average value of the curve tangent is greater than the preset average value, the judgment is made based on the yield strain of the plate and shell. The accuracy of the first state is that the accuracy is less than or equal to the first preset accuracy and greater than the second preset accuracy. If the strain at any monitoring point is greater than the yield strain, it is determined that the plate and shell have undergone local plastic deformation. The plastic strain increment is used as an additional variable in the virtual deformation field, and the virtual deformation field is adjusted by a relaxation factor, wherein the relaxation factor is adjusted based on the difference between the strain and the yield strain and the ratio of the yield strain.

6. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 5, characterized in that, The relaxation factor is reduced based on the difference between the strain and the yield strain and the ratio of the yield strain, and the ratio is proportional to the reduction in the relaxation factor.

7. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 6, characterized in that, After adjusting the relaxation factor, the deformation and reconstruction are performed again. If the deformation and reconstruction state is the first state, the step of reducing the relaxation factor is repeated at least once until the stopping condition is met. The stopping condition is that the deformation and reconstruction state is qualified when the number of reductions is less than or equal to the preset number of reductions, or when the number of reductions is greater than the preset number of reductions. If the deformation reconstruction state is still unqualified after stopping the repeated execution of the step of reducing the relaxation factor, the number of mesh divisions is adjusted based on the ratio of strain to preset strain in the region where the strain is greater than the preset strain.

8. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 7, characterized in that, The number of mesh divisions is increased based on the ratio of the strain to the preset strain, and the ratio is proportional to the increase in the number of mesh divisions.

9. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 1, characterized in that, When the deformation reconstruction state is determined to be the second state based on the accuracy, the gradient scale of the plate and shell is obtained. The interval distance of the strain sensors is adjusted based on the gradient scale; wherein the accuracy rate of the second state is less than or equal to the second preset accuracy rate.

10. The novel inverse finite element deformation reconstruction method based on virtual deformation field physical constraints according to claim 9, characterized in that, The process of adjusting the interval distance of the strain sensors based on gradient scale includes: If the gradient scale is less than or equal to the preset gradient scale, the sensor spacing is increased based on the gradient scale, and the increase in the gradient scale is proportional to the increase in the sensor spacing. If the gradient is greater than the preset gradient scale, the sensor spacing is reduced based on the gradient scale, and the gradient scale is proportional to the reduction in the sensor spacing.

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