AUV physical field prediction method based on manifold learning and deep learning

Abstract

The invention belongs to the technical field of autonomous underwater vehicle numerical simulation, and discloses an AUV physical field prediction method based on manifold learning and deep learning, comprising the following steps: performing nonlinear dimension reduction on high-dimensional simulation physical field data based on an Isomap manifold learning algorithm, and extracting low-dimensional manifold features; constructing a deep neural network (DNN) model, and establishing a mapping relation between the working condition parameters and the low-dimensional manifold features; inputting new working condition parameters to the trained deep neural network model, and predicting corresponding low-dimensional manifold features; isomap inverse mapping is realized based on a local linear embedding algorithm, and predicted low-dimensional manifold features are reconstructed into high-dimensional physical field data. Through collaborative prediction of manifold learning and deep learning, the problem that a traditional method is low in calculation efficiency in high-dimensional physical field prediction is solved, prediction precision and real-time performance are remarkably improved, and an efficient tool is provided for AUV design optimization and dynamic control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of numerical simulation of autonomous underwater vehicles, and particularly relates to an AUV physical field prediction method based on manifold learning and deep learning. BACKGROUND

[0002] In scientific research and engineering practice of ocean resource development and utilization and ocean environment dynamic monitoring, autonomous underwater vehicles (AUVs) as key technical equipment undertake important tasks such as data acquisition, environment perception and target detection. The hydrodynamic characteristics and structural safety performance of AUVs are highly dependent on the accurate characterization of physical fields such as the flow field and pressure field around them. In a complex and dynamically changing ocean environment, real-time and accurate acquisition of spatial distribution information of the physical field around the AUV is of great theoretical significance and engineering value for realizing high-precision navigation control of the AUV, optimizing structural design and improving task execution efficiency.

[0003] Currently, traditional physical field prediction methods based on computational fluid dynamics (CFD) and finite element analysis (FEA) have been relatively mature in theoretical system, and can provide high-fidelity numerical simulation results for the design and analysis of AUVs. However, these methods have significant limitations in practical application. Specifically, CFD and FEA methods usually need to construct fine geometric models and complex control equation discretization systems, involving large-scale grid division and iterative solution processes, resulting in extremely high computational complexity, huge demand for computing resources, long calculation period, and difficulty in meeting the timeliness requirements of AUVs in real-time monitoring of physical fields, thus unable to provide effective feedback information for the navigation control system in time, and further limiting the adaptive ability and operation efficiency of AUVs in complex ocean environments.

[0004] With the continuous development of nonlinear data dimensionality reduction theory, manifold learning provides a new theoretical framework for processing high-dimensional physical field data. Among them, the isometric mapping (Isomap) algorithm as a typical nonlinear manifold learning method can effectively capture the nonlinear manifold structure in the data by constructing a neighborhood graph and calculating the geodesic distance, and realize the nonlinear mapping from high-dimensional observation space to low-dimensional essential space. Compared with traditional linear dimensionality reduction methods such as principal component analysis (PCA), the Isomap algorithm has a significant advantage in maintaining the consistency of the data topology, and can more accurately reveal the intrinsic geometric characteristics and distribution of the physical field data, providing an effective technical means for feature extraction and compression of high-dimensional physical field data.

[0005] At the same time, the rise of deep learning technology provides a powerful tool for modeling and predicting complex nonlinear relationships. Deep neural network (DNN) as the core model of deep learning, through multi-layer nonlinear transformation and feature extraction, can automatically learn the complex mapping relationship between input working condition parameters and output physical field characteristics. With its strong feature representation ability and generalization performance, DNN can effectively fuse the nonlinear relationship between low-dimensional features extracted by Isomap manifold learning and working condition parameters, overcome the limitations of traditional interpolation methods in modeling cross-scale feature association, and provide a new technical path for real-time prediction and dynamic characterization of AUV surrounding physical field. SUMMARY

[0006] In view of the problem that the existing AUV high-dimensional physical field real-time and high-precision prediction has insufficient generalization ability, the present application provides an AUV physical field prediction method based on manifold learning and deep learning. The method extracts physical field essential features through Isomap algorithm, constructs DNN to realize intelligent mapping of working condition parameters to low-dimensional manifold, and finally realizes high-dimensional field reconstruction combined with local linear embedding. The present application not only retains the intrinsic topological characteristics of the physical field, but also enhances the cross-condition generalization ability through deep network, providing a new solution for AUV real-time physical field prediction.

[0007] In order to achieve the above technical purpose, the present application specifically adopts the following technical scheme: In one aspect of the present application, an AUV physical field prediction method based on manifold learning and deep learning is provided, comprising the following steps: S1, performing nonlinear dimensionality reduction on high-dimensional simulation physical field data based on Isomap manifold learning algorithm, and extracting low-dimensional manifold features; S2. Construct a deep neural network (DNN) model and establish a mapping relationship between the operating parameters and the low-dimensional manifold features; S3. Input the new operating condition parameters into the trained deep neural network model and predict its corresponding low-dimensional manifold features; S4. Based on the local linear embedding algorithm, implement the Isomap inverse mapping to reconstruct the predicted low-dimensional manifold features into high-dimensional physical field data.

[0008] In one implementation, step S1 includes the following steps: S11. Construct a neighborhood graph of the physical field data; S12. Calculate the shortest path between each pair of points in the neighborhood graph to obtain the geodesic distance matrix; S13. Calculate the center distance matrix based on the geodesic distance matrix; S14. Perform eigenvalue decomposition on the center distance matrix, select the first d eigenvalues ​​and their corresponding eigenvectors, and calculate the low-dimensional manifold features.

[0009] In one implementation, the formula for calculating the low-dimensional manifold features is:

[0010] in, This represents the eigenvector matrix corresponding to the eigenvalues. Represents eigenvalues. This represents the characteristics of a low-dimensional manifold.

[0011] In one implementation, the deep neural network model is a multi-layer fully connected neural network, and its forward propagation formula is:

[0012] in, , For the first i Layer weights and biases This is the activation function.

[0013] In one implementation, the deep neural network model is trained by minimizing the mean squared error between the predicted and true values, with the loss function being:

[0014] in, Indicates the predicted value. Represents the actual value.

[0015] In one implementation, implementing the Isomap inverse mapping based on the Locally Linear Embedding (LLE) algorithm includes the following steps: For each predicted low-dimensional feature sample, find its nearest neighbor; constructing a Gram matrix and introducing a regularization term; calculating reconstruction weights; performing weighted summation on high-dimensional physical field data based on the reconstruction weights to reconstruct a complete high-dimensional physical field.

[0016] In one embodiment, the formula for calculating the reconstruction weights is:

[0017] wherein, represents the reconstruction weights, represents the Gram matrix.

[0018] In one embodiment, the physical field is one of a structural field, a flow field, or a pressure field.

[0019] In another aspect of the present application, a computer readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the AUV physical field prediction method based on manifold learning and deep learning as described above.

[0020] The present application has the following advantages: The present application adopts a prediction framework that cooperates manifold learning and deep learning, combines the advantages of topology structure reservation and deep network nonlinear mapping, and solves the limitations of low computational efficiency and insufficient generalization ability of data-driven algorithms of traditional physical field prediction methods. The Isomap algorithm is used to extract low-dimensional manifold features of high-dimensional physical fields, effectively preserving the inherent topological relationship of the data. The constructed DNN model realizes efficient mapping of working condition parameters to low-dimensional features, and then combines the LLE inverse mapping algorithm for reconstruction, to complete the accurate restoration of the high-dimensional physical field. This complete process significantly improves the speed of physical field prediction, greatly enhances the real-time prediction performance and generalization ability of high-dimensional physical fields compared with traditional methods, and provides reliable support for AUV dynamic control and structural optimization. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a flowchart of an AUV physical field prediction algorithm based on manifold learning and deep learning; Figure 2 is a result graph of a real autonomous underwater vehicle pressure shell structural field in an embodiment of the present application; Figure 3 is a result graph of a predicted autonomous underwater vehicle pressure shell structural field in an embodiment of the present application. DETAILED DESCRIPTION

[0022] The technical solutions of the present application will be described clearly and completely below in conjunction with specific embodiments, but those skilled in the art will understand that the following described embodiments are part of the embodiments of the present application, not all the embodiments, and are only used to illustrate the present application, and should not be regarded as limiting the scope of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor are within the scope of protection of the present application.

[0023] In one specific embodiment of the present application, a physical field prediction method for AUV based on manifold learning and deep learning is provided, specifically as follows: Referring to Figure 1 , first, a neighborhood graph is constructed for the physical field data, the shortest path between each pair of points in the neighborhood graph is calculated based on a graph algorithm to obtain a geodesic distance matrix, a center distance matrix is then calculated, and eigenvalue decomposition is performed. The eigenvalues obtained by decomposition are arranged in descending order, and a required number of eigenvalues and their corresponding eigenvector matrices are selected, so as to calculate the reduced dimension features. Then, a DNN model is constructed to realize the mapping relationship from the working condition parameters to the low-dimensional manifold. After that, the low-dimensional manifold features are predicted through a new simulation condition matrix, the reconstruction weights are calculated and weighted summation is performed, and then the low-dimensional manifold features are reconstructed to complete the prediction of the complete physical field under the new conditions.

[0024] (1) Low-dimensional manifold feature extraction The target physical field data is preprocessed to construct a physical field data matrix , and the physical field data is normalized.

[0025] The shortest path between each pair of points in the neighborhood graph is calculated based on a graph algorithm to obtain a geodesic distance matrix D . The center distance matrix D is calculated from the geodesic distance matrix B according to formula (1).

[0026] Eigenvalue decomposition is performed on the matrix B to obtain eigenvalues and eigenvectors . The eigenvalues are sorted in descending order, and the first d eigenvalues and their corresponding eigenvector matrices are selected. Finally, the reduced dimension features are calculated according to formula (3).

[0027] (1) (2) (3) wherein, yes D element-wise squared matrix It is composed of eigenvectors The matrix formed It is a diagonal matrix, and , H It is a centralized matrix.

[0028] (2) Low-dimensional manifold feature prediction Establishing a simulation condition matrix based on a deep neural network With low-dimensional manifold characteristic matrix The mapping relationship. Constructing a multi-layer fully connected network, its forward propagation formula is: (4) in, , For the first i Layer weights and biases For activation function, x This represents the input vector of operating parameters. Training is performed by minimizing the mean square error between the predicted and actual values. (5) When a new simulation condition matrix is ​​given When, its dimensionality-reduced characteristic matrix It can be calculated using equation (4).

[0029] (3) Low-dimensional manifold feature reconstruction To achieve an accurate inverse mapping from low-dimensional features to a high-dimensional physical field, an inverse reconstruction method based on local linear embedding is employed. For the low-dimensional features of each sample, find... The index of the nearest neighbors And calculate their distance. Construct the Gram matrix according to equation (6). And introduce regularization of equation (7) to avoid ill-conditioned matrices.

[0030] The reconstruction weights are calculated by solving equation (8). By reconstructing the weights The high-dimensional physical fields of the low-dimensional neighbors are weighted and summed, as shown in Equation (9).

[0031] Finally, iterate through all samples to obtain the corresponding predicted high-dimensional physical field matrix. .

[0032] (6) (7) (8) (9) in, Indicates the first i Index of the neighbors. It is known physical field data. It is a reconstruction of physical field data based on predicted low-dimensional features.

[0033] Example The pressure hull structural field dataset used in this embodiment was obtained through structural field simulations at different depths. Of the 22 structural fields, the training dataset includes 18 structural fields, and the prediction dataset consists of the remaining 4. After training the model using the algorithm, the same operating conditions as the prediction dataset are input to predict the simulated structural fields, which are then compared and verified with the prediction dataset.

[0034] (1) Low-dimensional manifold feature extraction The simulated structural field data is preprocessed to extract the equivalent elastic strain values ​​on all grid nodes for each simulation condition. These values ​​are then used to form an N×M structural field data matrix and an M×1 condition parameter matrix, corresponding to 22 structural field datasets and their input conditions. Here, N represents the number of grid nodes, and M=22, corresponding to the 22 different conditions.

[0035] The first 18 columns of the structure field dataset are used as the training dataset, and the last 4 columns are used as the prediction dataset. The structure field matrix is ​​constructed by transposing the training dataset. A neighborhood graph is constructed for it, and a graph algorithm is used to calculate the shortest path between each pair of points in the neighborhood graph, thus obtaining the geodesic distance matrix. D According to equation (1), through the geodesic distance matrix D Calculate the center distance matrix B Where N=18, and M is the number of grid nodes.

[0036] For matrix B Perform eigenvalue decomposition to obtain eigenvalues. and eigenvectors For eigenvalues Sort in descending order and select the top... d Each eigenvalue and its corresponding eigenvector matrix That is, key features are preserved. Finally, the dimensionality reduction features are calculated according to equation (3). .in, d =10.

[0037] (2) Low-dimensional manifold feature prediction Constructing the simulation condition matrix based on the operating condition parameter matrix of the training set And based on the DNN model, a simulation condition matrix is ​​established. and the mapping relationship between the low-dimensional manifold feature matrix and the simulation condition matrix. The DNN model adopts a five-layer fully connected network architecture, the input layer receives the standardized single-dimensional operating condition parameters, the hidden layer extracts nonlinear features through a stepwise structure of 256-128-64 neurons, and the output layer is directly mapped to a 10-dimensional Isomap manifold space. The network uses a ReLU activation function and an Adam optimizer.

[0038] When a new simulation condition matrix is given, i.e., the 4 operating condition parameters of the prediction data set, the completed DNN model can directly output the low-dimensional manifold feature matrix , realizing the rapid prediction of low-dimensional features.

[0039] (3) Low-dimensional manifold feature reconstruction The predicted low-dimensional manifold feature According to formula (6), the Gram matrix is constructed , and the regularization is performed through formula (7). According to formula (8) and formula (9), the reconstruction weight is calculated, and the high-dimensional structure field of the low-dimensional neighbor is weighted and summed, and all samples are iterated to obtain the complete structure field of the 4 input operating conditions of the prediction data set The predicted result.

[0040] (4) Comparative verification The relative error of the predicted complete structure field of the 4 operating conditions of the prediction data set and the corresponding true complete structure field is about 3.624%, and the relative error is within 5%; the single-condition prediction time is less than 0.01s, which is greatly improved in efficiency compared with traditional finite element simulation; the equivalent elastic strain result diagram of the prediction result and the simulation result of one of the operating conditions is shown in Figure 2 , Figure 3 It can be seen that the equivalent elastic strain distribution trends of the two are completely consistent.

[0041] Although the embodiments of the application are described above in combination with the drawings, the application is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and guiding, but not limiting. Those skilled in the art can make many forms under the guidance of this specification and without departing from the scope protected by the claims of the application, which are all included in the protection of the application.

Claims

1. A method for predicting the physical field of AUVs based on manifold learning and deep learning, characterized in that, include: S1. Nonlinear dimensionality reduction of high-dimensional simulated physical field data is performed based on the Isomap manifold learning algorithm to extract low-dimensional manifold features; S2. Construct a deep neural network model and establish a mapping relationship between the operating parameters and the low-dimensional manifold features; S3. Input the new operating condition parameters into the trained deep neural network model and predict its corresponding low-dimensional manifold features; S4. Based on the local linear embedding algorithm, implement the Isomap inverse mapping to reconstruct the predicted low-dimensional manifold features into high-dimensional physical field data.

2. The AUV physical field prediction method according to claim 1, characterized in that, Step S1 includes the following steps: S11. Construct a neighborhood graph of the physical field data; S12. Calculate the shortest path between each pair of points in the neighborhood graph to obtain the geodesic distance matrix; S13. Calculate the center distance matrix based on the geodesic distance matrix; S14. Perform eigenvalue decomposition on the center distance matrix, select the first d eigenvalues ​​and their corresponding eigenvectors, and calculate the low-dimensional manifold features.

3. The AUV physical field prediction method according to claim 2, characterized in that, The formula for calculating the low-dimensional manifold features is as follows: in, This represents the eigenvector matrix corresponding to the eigenvalues. Represents eigenvalues. This represents the characteristics of a low-dimensional manifold.

4. The AUV physical field prediction method according to claim 1, characterized in that, The deep neural network model is a multi-layer fully connected neural network, and its forward propagation formula is: in, , For the first i Layer weights and biases This is the activation function.

5. The AUV physical field prediction method according to claim 1, characterized in that, The deep neural network model is trained by minimizing the mean squared error between the predicted and true values, and the loss function is: in, Indicates the predicted value. Represents the actual value.

6. The AUV physical field prediction method according to claim 1, characterized in that, Implementing the inverse Isomap mapping based on the local linear embedding algorithm includes the following steps: For each predicted low-dimensional feature sample, find its The nearest neighbor; Construct the Gram matrix and introduce a regularization term; Calculate the reconstruction weights; The high-dimensional physical field data is reconstructed by weighted summation based on the reconstruction weights.

7. The AUV physical field prediction method according to claim 6, characterized in that, The formula for calculating the reconstruction weights is as follows: in, Indicates the reconstructed weights. This represents the Gram matrix.

8. The AUV physical field prediction method according to claim 1, characterized in that, The physical field is one of the following: structural field, flow field, or pressure field.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the AUV physical field prediction method according to any one of claims 1 to 8.

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