A flexible structure shape reconstruction method and system based on limited strain measurement

Abstract

The present application belongs to the technical field of structure shape perception, and discloses a flexible structure shape reconstruction method and system based on limited strain measurement, which comprises the following steps: establishing a strain input feature according to the strain value monitoring results of multiple strain measuring points on the flexible structure; taking the strain input feature as input, and using multiple pre-trained prediction sub-models to predict the displacement of the displacement measuring points on the flexible structure for shape reconstruction; wherein each prediction sub-model corresponds to part of the displacement measuring points on the flexible structure, and the multiple prediction sub-models cover all the displacement measuring points on the flexible structure. The present application proposes to divide the flexible structure into zones for modeling, which can fully utilize the correlation between the local space node displacements of the high-order complex deformation of the flexible structure, is conducive to learning the high-resolution accurate expression of the displacement field by the model, improves the prediction accuracy and speed, and can meet the high-order shape perception requirements of "real-time, high-resolution, high-precision and embeddability".

Description

Technical Field

[0001] This invention belongs to the field of structural shape perception technology, and more specifically, relates to a method and system for reconstructing the shape of flexible structures based on finite strain measurement. Background Technology

[0002] With the development and increasing application demands in fields such as robotics, aerospace, and electronic equipment, research on flexible structures has received widespread attention. Unlike rigid structures, flexible structures utilize low-elastic-modulus materials (such as rubber, silicone, and other non-metallic materials) and low-stiffness structural designs, exhibiting characteristics such as high compliance, lightweight, simple structure, and large geometrical nonlinear deformation. Figure 1 Flexible structures typically exhibit complex, high-order deformation patterns: 3D structures can deform into various configurations, possessing high degrees of freedom in deformation, enabling bending, torsion, and even composite, layered, and multi-directional deformation within a single configuration. This high-order deformation mode allows them to move and deform in complex environments (such as biomimetic flexible robots). Such morphological changes cannot be represented by simplified curve fitting or local point data; precise capture of the complete deformation state requires obtaining the nodal position information of the entire flexible surface.

[0003] The following are two typical application scenarios for flexible structures: First, flexible soft robots (such as bionic bird and bionic fish robots) can perform complex tasks that are difficult for rigid robots due to their high compliance and high degree of freedom. To achieve precise closed-loop control of these robots and ensure the accuracy of their movements and the stability of their operations, it is necessary to accurately perceive the real-time shape of their flexible surfaces, and the perception module must meet the actual installation requirements of the embedded flexible terminal. Second, with the continuous breakthroughs in aerospace technology, space flexible array thin-film antennas are widely used in aerospace engineering due to their light weight, high gain, and flexible beam adjustment. However, they operate in complex environments such as near-space and are subjected to various external loads such as alternating wide temperature range, wind load, acceleration, and gravity, as well as the heat generated by the electrical components themselves. At the same time, the antenna itself is a low-stiffness, non-homogeneous multilayer thin-film structure, which causes its deformation to exhibit complex and irregular high-order morphology. This deformation directly affects the electrical performance of the antenna. Therefore, it is necessary to acquire complete and accurate deformation field data in real time and use phase shifters to compensate for electrical performance to ensure the normal operation of the antenna.

[0004] To address the problem of structural shape perception, existing technologies have developed various perception methods. These methods achieve shape reconstruction based on different perception principles, but they all have certain limitations in meeting the high-order shape perception requirements of flexible structural objects, such as "real-time performance, high resolution, high precision, and embeddability," as follows: The first category is the point-to-point attitude reconstruction method, which uses a dense sensor array to acquire position and attitude information of the acquisition points for shape reconstruction. While this method can obtain relatively detailed attitude data, it suffers from complex wiring and electrical connections. Its scalability and practical applicability are easily limited by the high degree of freedom deformation of flexible structures. The second category is the discrete curve fitting surface method, which reconstructs the shape of discrete curves by measuring curvature data and then obtains the complete surface shape through spatial curve interpolation. This method can achieve shape fitting reconstruction of simple surfaces, but its accuracy is insufficient for reconstructing complex deformation forms of flexible structures with high degrees of freedom at displacement points. The third category is the visual perception method, which achieves high-precision 3D shape reconstruction of structures through a stereo vision system. This method can achieve good perception results in a controlled laboratory environment, but the system is large, has stringent environmental requirements, cannot be embedded in miniaturized flexible terminals, and is difficult to adapt to the perception scenarios of this invention. The fourth category is... Physical methods, such as the inverse finite element method, Ko displacement theory, and modal superposition method, can reconstruct full-field displacement from discrete strain and have been widely used in structures such as wing boxes, plates, variable cross-section beams, and trusses. Although these methods achieve accurate shape perception, their complex modeling and solution processes are not suitable for flexible structures with geometric nonlinearity. The fifth category is the finite element method, which generates high-precision virtual data based on structural geometry and material properties and achieves shape evaluation through simulation analysis. However, its high computational cost cannot meet real-time requirements. The sixth category is data-driven methods, which construct the mapping relationship between sensing measurements and shape using a large amount of training data. Examples include regularized least squares method based on piezoelectric sensing, weighted linear interpolation method, and randomized configuration network method based on discrete strain points. These methods usually use a single model to map sensing and deformation, which is difficult to accurately predict for high-order, high-resolution complex nonlinear deformation flexible structures.

[0005] Existing structural shape sensing methods cannot meet the high-order shape sensing requirements of flexible structures, which include "real-time performance, high resolution, high precision, and embeddability". Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a flexible structure shape reconstruction method and system based on finite strain measurement. This method solves the problem that existing structural shape sensing methods cannot meet the high-order shape sensing requirements of flexible structures, namely "real-time performance, high resolution, high precision, and embeddability," and achieves high-resolution, high-precision real-time reconstruction from discrete strain data to the full displacement field.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for reconstructing the shape of a flexible structure based on finite strain measurement is provided, comprising: Based on the strain value monitoring results of multiple strain measurement points on the flexible structure, strain input characteristics are established; Using strain input features as input, multiple pre-trained prediction sub-models are used to predict the displacement of displacement measurement points on a flexible structure for shape reconstruction; each prediction sub-model corresponds to a portion of the displacement measurement points on the flexible structure, and multiple prediction sub-models cover all displacement measurement points on the flexible structure.

[0008] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, the establishment of strain input features specifically includes: The strain monitoring results are arranged according to the numbering order of the strain measurement points to form a strain vector with multiple strain channels; The strain values ​​of each strain channel are increased in dimensionality through linear mapping to obtain high-dimensional strain features; Each strain channel is assigned a position encoding vector using a triangular encoding method based on its strain channel number, where the dimension of the position encoding vector corresponds to the dimension of the high-dimensional strain feature. The high-dimensional strain features corresponding to each strain channel are fused with the position encoding vector to obtain the strain input features.

[0009] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, a position vector is assigned to each strain channel using a triangular coding method based on the strain channel number, as follows:

[0010]

[0011]

[0012] in, For the first Position encoding vector of strain channel number; and For the first The strain channel position encoding vector of the first strain channel position encoding vector and the Each dimension component ; This represents the dimension of the position encoding vector.

[0013] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, the division of the prediction sub-model is as follows: Based on all displacement measurement points on the flexible structure, a window containing a preset number of displacement measurement points is used to slide from the predicted position of all displacement measurement points along the direction of displacement measurement point arrangement with a preset step size until the sliding window covers all displacement measurement points. Each sliding window corresponds to a prediction sub-model, and the displacement prediction value of the displacement measurement point corresponding to the sliding window is output.

[0014] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, the flexible structure has Displacement measurement points, using a combination of... If a window for each displacement node slides from its corner position along the row and column directions, then the number of sliding windows is determined. for:

[0015] Wherein, the sliding step size of the sliding window along the row direction is The sliding step size along the column direction is , This is the floor operator. , .

[0016] The flexible structure shape reconstruction method based on finite strain measurement provided by the present invention utilizes multiple prediction sub-models to predict the displacement of displacement measurement points on the flexible structure for shape reconstruction, specifically including: Each prediction sub-model takes strain input features as input and outputs the predicted displacement value of the corresponding displacement measurement point; When there are displacement measurement points with common coverage among multiple prediction sub-models, the displacement prediction values ​​output by multiple prediction sub-models are averaged or weighted averaged to obtain the final displacement value of the displacement measurement points with common coverage.

[0017] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, a loss function is constructed based on the error between the displacement prediction value and the sample displacement value and the L2 regularization loss during the training of the prediction sub-model, and the model parameters are updated based on the loss function.

[0018] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, the loss function during the training of the prediction sub-model is as follows:

[0019] in, For the first The loss function of each prediction sub-model; the learnable parameters of the model are... ; This represents the number of machine learning batches. This represents the number of displacements in three directions at the corresponding displacement measurement points of the model. For the first The number of rows and columns corresponding to the displacement measurement points in each prediction sub-model; This represents the three-directional displacement vector of the corresponding displacement measurement point output by the model in a batch; For strain input features; This corresponds to the actual displacement vector; The L2 regularization coefficient; The number of strain channels, To predict the number of hidden layers in the sub-model, For the first The layer outputs the corresponding weight parameters.

[0020] According to the flexible structure shape reconstruction method based on finite strain measurement provided by the present invention, the dataset for training the prediction sub-model includes strain value samples and displacement value samples. Preprocessing of the sample data is also included before training the prediction sub-model, specifically including: The strain values ​​are normalized based on the maximum and minimum values ​​of the strain values ​​corresponding to the same strain channel in the dataset, and strain input features corresponding to the samples are established based on the normalized strain data; and the displacement values ​​are normalized based on the maximum and minimum values ​​of the displacement values ​​in the same direction in the dataset. Correspondingly, the process of establishing strain input features during online reconstruction, before obtaining high-dimensional strain features, also includes: normalizing the strain values ​​based on the maximum and minimum values ​​of the corresponding strain values ​​of the same strain channel in the dataset.

[0021] According to another aspect of the present invention, a flexible structure shape reconstruction system based on finite strain measurement is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps of the flexible structure shape reconstruction method based on finite strain measurement described above.

[0022] In summary, compared with the prior art, the flexible structure shape reconstruction method and system based on finite strain measurement provided by the present invention offer the following advantages: 1. This paper proposes setting up multiple prediction sub-models. Each prediction sub-model predicts the displacement of some displacement measurement points based on the strain characteristics of the full-field finite strain measurement points. By using multiple prediction sub-models, the displacement prediction of all displacement measurement points in the entire field can be realized. Ultimately, it realizes the prediction from discrete strain data to the full displacement field, which has strong embeddability. Moreover, this method of partitioning flexible structures can make full use of the correlation between the displacements of local spatial nodes in the high-order complex deformation of flexible structures. This is conducive to the model learning a high-resolution and accurate expression of the displacement field, improving prediction accuracy and achieving high-resolution accurate prediction. At the same time, the parallel operation of multiple prediction sub-models reduces the computational cost of a single sub-model, which also helps to improve prediction speed and real-time performance. It can meet the high-order shape perception requirements of "real-time performance, high resolution, high accuracy, and embeddability", and provide a basis for applications requiring shape perception. 2. The proposed high-order deformation sensing model for flexible structures includes a strain position encoding module. The strain position encoding adopts feature embedding and triangular encoding. The relative positional relationship between the input strain number sequence is introduced through linear transformation, which corresponds to the actual spatial relative positional relationship. That is, when using measurement data, the relative position of the strain channel number is introduced into the model, i.e., the spatial relative positional relationship, so that the model can learn the difference in contribution of strain values ​​at different positions to the displacement of the measuring point. 3. A sliding window integrated learning prediction module is proposed. The sliding window outputs the displacement of the measurement point in the region through the partition modeling method. The loss function enables the model to fully learn the complex high-order deformation relationship of the local region. During prediction, different sub-models are combined and weighted to improve the prediction robustness. Finally, high-resolution, high-precision real-time shape reconstruction of finite strain measurement is achieved. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the high-order deformation modes and reconstruction targets of a flexible structure.

[0024] Figure 2 This is a diagram of the architecture of a high-order deformation sensing model for flexible structures provided by the present invention, which includes a strain position encoding module and a sliding window integrated learning and prediction module.

[0025] Figure 3 These are the sine / cosine position coding curves corresponding to different strain numbers provided by this invention.

[0026] Figure 4 This is a heat map of the strain position coding matrix provided by the present invention, where the color intensity represents the magnitude of the coding value. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0028] Please see Figure 1 and Figure 2 This embodiment provides a method for reconstructing the shape of a flexible structure based on finite strain measurement. The shape reconstruction method includes: Based on the strain value monitoring results of multiple strain measurement points on the flexible structure, strain input characteristics are established. Using strain input features as input, multiple pre-trained prediction sub-models are used to predict the displacement of displacement measurement points on a flexible structure for shape reconstruction; each prediction sub-model corresponds to a portion of the displacement measurement points on the flexible structure, and multiple prediction sub-models cover all displacement measurement points on the flexible structure.

[0029] This embodiment provides a real-time shape reconstruction method that simultaneously utilizes limited measurement information and displacement information. Compared to traditional methods that typically use a single prediction model to predict the entire field displacement, this embodiment proposes setting up multiple prediction sub-models. Specifically, each prediction sub-model predicts the displacement of a portion of the displacement measurement points based on the strain characteristics of the limited strain measurement points across the entire field. By utilizing multiple prediction sub-models, the displacement prediction of all displacement measurement points in the entire field is achieved, ultimately realizing shape prediction reconstruction from discrete strain data to full displacement field prediction. This method of partitioning and modeling flexible structures can fully utilize the correlation between the displacements of local spatial nodes in the high-order complex deformation of flexible structures, which is beneficial for the model to learn a high-resolution and accurate expression of the displacement field, improving prediction accuracy and achieving high-resolution and accurate prediction. At the same time, the parallel operation of multiple prediction sub-models results in a relatively small computational load for a single sub-model, which also helps to improve prediction speed and real-time performance.

[0030] This embodiment utilizes discrete strain measurements to reconstruct the displacement field of flexible structures with high degrees of freedom and large deformation irregular curved surfaces. It can meet the high-order shape perception requirements of "real-time performance, high resolution, high precision, and embeddability", providing a basis for applications requiring shape perception.

[0031] In some embodiments, establishing strain input features specifically includes: The strain monitoring results are arranged according to the numbering order of the strain measurement points to form a strain vector with multiple strain channels; The strain values ​​of each strain channel are increased in dimensionality through linear mapping to obtain high-dimensional strain features; Each strain channel is assigned a position encoding vector using a triangular encoding method based on its strain channel number, where the dimension of the position encoding vector corresponds to the dimension of the high-dimensional strain feature. The high-dimensional strain features corresponding to each strain channel are fused with the position encoding vector to obtain the strain input features.

[0032] In some embodiments, the dataset used for training the prediction sub-model includes strain value samples and displacement value samples. Preprocessing of the sample data is also included before training the prediction sub-model, specifically including: The strain values ​​are normalized based on the maximum and minimum values ​​of the strain values ​​corresponding to the same strain channel in the dataset, and strain input features corresponding to the samples are established based on the normalized strain data; and the displacement values ​​are normalized based on the maximum and minimum values ​​of the displacement values ​​in the same direction in the dataset. Correspondingly, the process of establishing strain input features during online reconstruction, before obtaining high-dimensional strain features, also includes: normalizing the strain values ​​based on the maximum and minimum values ​​of the corresponding strain values ​​of the same strain channel in the dataset.

[0033] In some embodiments, this embodiment addresses the problem that it is difficult to achieve high-precision, high-resolution, and real-time sensing of the deformation of flexible structures with high degrees of freedom, large deformation, and irregular curved surfaces using traditional methods. It proposes a method for full-field shape reconstruction of flexible structures using discrete strain measurements and an ensemble learning model algorithm combining strain position encoding and a sliding window. This algorithm is written and run on a computer using Python and the PyTorch environment. The ensemble learning model consists of two parts: strain position encoding and sliding window partitioning prediction, including model training and prediction. The main technical solutions are as follows: Step 1: Dataset Partitioning: The true discrete strain value is defined as... The actual displacement field of the flexible structure to be perceived is The strain and displacement are divided into a training set (corresponding to the subscript "train"), a validation set (corresponding to the subscript "val"), and a test set (corresponding to the subscript "test") according to a certain ratio:

[0034]

[0035] in These are the surface strain monitoring values ​​of the flexible structure. The number of strain gauge locations is the number of strain gauge points. Subscript Indicates the sequential numbering of the measuring point locations. , This indicates the measurement direction of the strain gauge at a given measurement point. The strains correspond to the 0°, 45°, and 90° directions on the coordinate axes, respectively. That is, the shear strain can be calculated using strain along these three axes. In practice, strain rosettes monitor the 0°, 45°, and 90° axial strains, with each location monitoring the three-dimensional strain. For simplicity, let... ,in This represents the total number of strain gauge channels; , These represent the number of rows and columns of displacement measurement points on the flexible structure, respectively. Representing along the coordinate axes Displacement components in three directions.

[0036] Step 2: Strain With displacement Normalization was performed separately, with strain adjusted according to column (different strain characteristics) and displacement in three directions:

[0037]

[0038]

[0039]

[0040] in , For the training set Maximum and minimum values ​​of strain channel number 1 ; Indicates the first Strain monitoring values ​​of strain channel number 1; Indicates the first Normalized strain values ​​for strain channel number 1; , , This represents the displacement components in the three directions after normalization; , , , , , These represent the maximum and minimum displacements in the three directions within the training set.

[0041] Step 3: Perform position encoding on the input strain to obtain input data with spatial relative position information. Position encoding consists of two parts: strain feature embedding and position encoding. Each strain channel is upgraded in dimensionality through linear mapping as shown in Equation (7) to obtain discrete high-dimensional features. Then, a position vector is assigned to each strain using a triangular coding method. Integrating high-dimensional discrete strain with position encoding: This constitutes strain input features with position encoding. Furthermore, in practical applications, the measurement positions of the same strain gauge may differ slightly in different directions, so position coding is performed for each measurement channel. The first strain input feature Features corresponding to strain channel number 1 For the discrete high-dimensional features, the first Features corresponding to strain channel number 1 For the first The position encoding vector corresponding to each strain channel is assigned according to its number using a triangular encoding method, as shown in equations (8), (9), and (10) below:

[0042]

[0043]

[0044]

[0045] in , respectively representing the first The number of strain channels corresponds to the weight matrix and bias vector of the linear dimensionality increase process; and express The calculation method for each dimension of the strain encoding vector. ; The dimension of the position encoding vector; that is and The first The strain channel position encoding vector of the first strain channel position encoding vector and the Dimensional components. Figure 3 For different strain numbers, the corresponding sine or cosine coded values ​​are... Figure 4 A heatmap encoding matrix for strain location.

[0046] The numbering of strain measurement points on flexible structures can be continuous or regularly arranged, meaning adjacent numbers should have an adjacent positional relationship, such as following a serpentine, circular, or other pattern. Figure 2 The strain channels are numbered according to a pattern shown; thus, when strain monitoring is performed according to the strain measurement point numbers to form a strain vector, the sequence of strain channel numbers is consistent with the sequence of strain measurement point numbers. This ensures that the positional encoding vector assigned to each strain channel reflects the relative positional relationship between the strain measurement point numbers. The specific principle is as follows: Position The strain code can be expressed as position Encoding about distance A linear combination of these, and the projection matrix does not depend on any position index (reflecting the relative positional relationship of strain numbers, corresponding to spatial positions):

[0047] in , This is the projection matrix.

[0048] Step 4: Divide the flexible structure into regions and establish sub-models. The specific division of the prediction sub-models is as follows: Based on all displacement measurement points on the flexible structure, a window containing a preset number of displacement measurement points is used to slide from the predicted position of all displacement measurement points along the direction of displacement measurement point arrangement with a preset step size until the sliding window covers all displacement measurement points. Each sliding window corresponds to a prediction sub-model, and the displacement prediction value of the displacement measurement point corresponding to the sliding window is output.

[0049] For example, flexible structures have Displacement measurement points, using a combination of... The window for each displacement measurement point slides from the corner position along the row and column directions. Let the sliding step size of the sliding window along the row direction (R-axis) be... The sliding step size along the column direction (L axis) is Then the number of sliding windows is determined. for: There are several regions, among which This is a floor function; if the number of nodes is not divisible, it ensures the window does not exceed the node boundaries of the flexible structure. , The surface of the flexible structure can be rectangular or other shapes, with the aim of ensuring that the sliding window can cover all displacement measurement points. The specific shape and sliding method are not limited.

[0050] Each window region corresponds to a multilayer perceptron (MLP) predictive sub-model. The input to each model in this partitioned sliding window modeling method is a position-encoded strain measurement. The output is the predicted displacement in three directions for all displacement measurement points within the window. By fully utilizing the correlation between local spatial node displacements in high-order complex deformation of flexible structures, the model can learn a high-resolution and accurate expression of the displacement field through the loss function. When using measurement data, the relative position of the strain number sequence is introduced into the model, i.e., the spatial relative position relationship, so that the model can learn the difference in contribution of different strains to the node displacement within the window.

[0051] No. Each predictive sub-model MLP is defined as: ,in for The flattened vector, i.e. the flattened strain input feature, is represented by the following mapping relationship:

[0052]

[0053] in , Here are the weight matrix and bias vector for each layer of the MLP. For the output of each layer, For the activation function, the ReLU function can be used. , , Let be the number of hidden layers, Equation (12) represents the mapping from the last hidden layer to the output layer, and Equation (13) represents the mapping from the input layer to the th hidden layer. Layer mapping process.

[0054] During the training of the prediction sub-model, a loss function is constructed based on the error between the predicted displacement value and the sample displacement value, as well as the L2 regularization loss. The model parameters are then updated based on this loss function. The loss function of each predictive sub-model is The MSE error between the predicted and actual displacements is used as the loss for parameter updates. L2 regularization is employed to reduce overfitting and improve generalization, as follows:

[0055] Wherein, the loss is about the model's learnable parameters. , , The function, , , , For the weights and biases of the embedding layer, i.e., the linear mapping dimensionality increase process, , For MLP weights and biases, For machine learning batch size, This represents the number of displacements in three directions at the corresponding displacement measurement points of the model. For the first The number of rows and columns corresponding to the displacement measurement points in each prediction sub-model; This represents the three-directional displacement vectors of the corresponding displacement measurement points output by the model in a batch. To correspond to the actual displacement vector, The L2 regularization coefficient is... The number of strain channels, To predict the number of hidden layers in the sub-model, For all weight parameters (including the embedding layer and the MLP layer), specifically the first... The layer outputs the corresponding weight parameters.

[0056] Parameter updates use the ADAM optimizer to update the input embedding layer parameters. , and MLP parameters , Simultaneously updated:

[0057]

[0058]

[0059] in , , , , , Represents the training set loss function Regarding the gradients of all learnable parameters at the t-th iteration update, and For the first and second moments of the gradient, , The hyperparameters for estimating the exponential decay rate are typically taken as 0.9 and 0.999 for the first and second moments, respectively. , For correction of first-order and second-order moment deviations, The initial learning rate is typically set to 0.001. To prevent division by zero for small constants, the initial learning rate... It can be adjusted based on the losses during the training process.

[0060] Step 5: Sub-model training. For example, for the first... Each sub-model uses the ADAM optimizer during training based on the batch loss function of the training set. Gradient updates are performed on the parameters; an early stopping strategy is used to control the model termination: to further avoid overfitting, when the validation set loss... Continuous preset wheel (e.g., take) If the value of the validation set does not decrease in any round, training is terminated, expressed by the following formula: Set the initial optimal validation set loss. The corresponding optimal iteration round ;

[0061]

[0062]

[0063] in, To verify the total number of samples in the validation set, This represents the total number of node displacements in three directions for each deformation sample. These are the predicted displacement and the actual displacement, respectively. To monitor losses in the early termination validation set, The optimal loss during training is recorded on the optimal validation set during the training process. And the corresponding optimal number of iterations, when The training is stopped when the early stopping condition is triggered; after training terminates, the model will proceed to the optimal number of iterations. The corresponding parameters are used as the final parameters, that is... .

[0064] Step Six: Sub-model Integration and Prediction. During online reconstruction, multiple prediction sub-models are used to predict the displacement of displacement measurement points on the flexible structure for shape reconstruction. Specifically, this includes: Each prediction sub-model takes strain input features as input and outputs the predicted displacement value of the corresponding displacement measurement point. When there are displacement measurement points with common coverage among multiple prediction sub-models, the predicted displacement values ​​output by multiple prediction sub-models are averaged or weighted averaged to obtain the final displacement of the displacement measurement point with common coverage.

[0065] In other words, the displacements of nodes in the common coverage area among the sub-models are averaged or weighted to improve prediction robustness, while the displacements of nodes in the non-common area are directly output, ultimately enabling the input of test strain. After feature embedding And add position encoding The predicted displacement is obtained by inputting it into each sliding window MLP sub-model. = After inverse standardization following integration of sub-models, the following is obtained: Ultimately, this achieves high-resolution, high-precision, real-time shape reconstruction.

[0066]

[0067]

[0068]

[0069] In other embodiments, a flexible structure shape reconstruction system based on finite strain measurement is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the steps of the flexible structure shape reconstruction method based on finite strain measurement described in any of the above embodiments.

[0070] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 method for reconstructing the shape of a flexible structure based on finite strain measurement, characterized in that, include: Based on the strain value monitoring results of multiple strain measurement points on the flexible structure, strain input characteristics are established; Using strain input features as input, multiple pre-trained prediction sub-models are used to predict the displacement of displacement measurement points on a flexible structure for shape reconstruction; each prediction sub-model corresponds to a portion of the displacement measurement points on the flexible structure, and multiple prediction sub-models cover all displacement measurement points on the flexible structure.

2. The method for reconstructing the shape of flexible structures based on finite strain measurement as described in claim 1, characterized in that, Establishing strain input characteristics specifically includes: The strain monitoring results are arranged according to the numbering order of the strain measurement points to form a strain vector with multiple strain channels; The strain values ​​of each strain channel are increased in dimensionality through linear mapping to obtain high-dimensional strain features; Each strain channel is assigned a position encoding vector using a triangular encoding method based on its strain channel number, where the dimension of the position encoding vector corresponds to the dimension of the high-dimensional strain feature. The high-dimensional strain features corresponding to each strain channel are fused with the position encoding vector to obtain the strain input features.

3. The method for reconstructing the shape of flexible structures based on finite strain measurement as described in claim 2, characterized in that, Each strain channel is assigned a position vector using a triangular coding method based on its strain channel number, as follows: in, For the first Position encoding vector of strain channel number; and For the first The strain channel position encoding vector of the first strain channel position encoding vector and the Each dimension component ; is the dimension of the position encoding vector.

4. The method for reconstructing the shape of flexible structures based on finite strain measurement as described in claim 1, characterized in that, The specific division of the prediction sub-models is as follows: Based on all displacement measurement points on the flexible structure, a window containing a preset number of displacement measurement points is used to slide from the predicted position of all displacement measurement points along the direction of displacement measurement point arrangement with a preset step size until the sliding window covers all displacement measurement points. Each sliding window corresponds to a prediction sub-model, and the displacement prediction value of the displacement measurement point corresponding to the sliding window is output.

5. The flexible structure shape reconstruction method based on finite strain measurement as described in claim 4, characterized in that, Flexible structures have Displacement measurement points, using a combination of... If a window for each displacement node slides from its corner position along the row and column directions, then the number of sliding windows is determined. for: Wherein, the sliding step size of the sliding window along the row direction is The sliding step size along the column direction is , This is the floor operator. , .

6. The method for reconstructing the shape of flexible structures based on finite strain measurement as described in claim 1, characterized in that, Displacement prediction at displacement measurement points on a flexible structure is performed using multiple prediction sub-models for shape reconstruction. Specifically, this includes: Each prediction sub-model takes strain input features as input and outputs the predicted displacement value of the corresponding displacement measurement point; When there are displacement measurement points with common coverage among multiple prediction sub-models, the displacement prediction values ​​output by multiple prediction sub-models are averaged or weighted averaged to obtain the final displacement value of the displacement measurement points with common coverage.

7. The method for reconstructing the shape of flexible structures based on finite strain measurement as described in claim 2, characterized in that, During the training of the prediction sub-model, a loss function is constructed based on the error between the predicted displacement value and the sample displacement value, as well as the L2 regularization loss, and the model parameters are updated based on the loss function.

8. The method for reconstructing the shape of a flexible structure based on finite strain measurement as described in claim 7, characterized in that, The loss function for training the prediction sub-model is as follows: in, For the first The loss function of each prediction sub-model; the learnable parameters of the model are... ; This represents the number of machine learning batches. This represents the number of displacements in three directions at the corresponding displacement measurement points of the model. For the first The number of rows and columns corresponding to the displacement measurement points in each prediction sub-model; This represents the three-directional displacement vector of the corresponding displacement measurement point output by the model in a batch; For strain input features; This corresponds to the actual displacement vector; The L2 regularization coefficient; The number of strain channels, To predict the number of hidden layers in the sub-model, For the first The layer outputs the corresponding weight parameters.

9. The method for reconstructing the shape of a flexible structure based on finite strain measurement as described in claim 2, characterized in that, The dataset used for training the prediction sub-model includes strain value samples and displacement value samples. Preprocessing of the sample data is also included before training the prediction sub-model, specifically: The strain values ​​are normalized based on the maximum and minimum values ​​of the strain values ​​corresponding to the same strain channel in the dataset, and strain input features corresponding to the samples are established based on the normalized strain data; and the displacement values ​​are normalized based on the maximum and minimum values ​​of the displacement values ​​in the same direction in the dataset. Correspondingly, the process of establishing strain input features during online reconstruction, before obtaining high-dimensional strain features, also includes: normalizing the strain values ​​based on the maximum and minimum values ​​of the corresponding strain values ​​of the same strain channel in the dataset.

10. A flexible structure shape reconstruction system based on finite strain measurement, characterized in that, The invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the program, it implements the steps of the flexible structure shape reconstruction method based on finite strain measurement as described in any one of claims 1 to 9.

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