Blended wing body underwater glider shape transfer design method based on manifold learning

Abstract

This invention belongs to the field of underwater glider shape design, specifically involving a transfer design method based on manifold learning. The method first uses commercial computational fluid dynamics software to perform two-dimensional simulations of two types of underwater gliders with different shapes, generating flow field information such as pressure and velocity contour maps. One type is a traditional rotary glider with extensive mature design experience, and the other is a blended wing-body underwater glider (BWBUG), also belonging to the underwater glider field. Next, the velocity and pressure contour maps of both gliders are processed to generate data matrices characterizing their hydrodynamic performance. Then, manifold learning is used to map the high-dimensional data matrices containing the flow field information of both gliders to a latent space of the same dimension, and then excellent samples from the rotary glider samples are transferred to the BWBUG samples. Afterwards, an evolutionary algorithm is used to search for the optimal solution in the target domain BWBUG design space, and a real function is used to evaluate the potential optimal point to determine the optimal individual in this iteration. Finally, the design variables of both gliders are changed to obtain a new shape, and the above steps are repeated until the number of evaluation iterations is exhausted or the termination condition is met, ending the loop and outputting the optimal shape solution of the new BWBUG glider. This invention significantly improves the efficiency of underwater glider shape design optimization.

Description

Technical Field

[0001] This invention belongs to the field of underwater glider shape design, specifically involving a transfer design method based on manifold learning. Background Technology

[0002] The blended-wing-body underwater glider (BWBUG) is a novel type of underwater vehicle. Designers often employ a blended-wing-body configuration that achieves a high lift-drag ratio (LDR) while meeting internal space requirements, and have successfully applied it to marine natural resource exploration. Compared to traditional rotary-body gliders, the blended-wing-body configuration has attracted increasing attention from scholars and research institutions due to its longer range, lower energy consumption, higher autonomy, greater stealth, and stronger adaptability. To further improve its underwater gliding efficiency, the BWBUG's shape design has become a research hotspot in marine engineering in recent years. However, existing shape optimization design processes rarely utilize prior knowledge and are typically designed from scratch. It is worth noting that since optimization design problems rarely exist in isolation, solving the shape problems of traditional rotary-body gliders may provide useful information for the design of similar products; however, differences in design spatial dimensions hinder information transfer and knowledge interaction between similar problems.

[0003] In this context, we recognize that knowledge transfer from one task to another is crucial for design optimization. Based on existing design cases, similar errors can be avoided, allowing designers to extend their existing knowledge to the domain of new problems. Compared to traditional optimization methods, transfer learning uses data from similar problems to enhance the optimization efficiency and results for new problems. Traditional gliders and BWBUG share similar task requirements, functional characteristics, objectives, and constraints, but differ in structural form and layout, resulting in significant differences in their design spaces. Solving the shape problem of traditional gliders might provide useful information for BWBUG design, but the different design spaces make this a heterogeneous transfer problem, making it difficult to transfer the acquired knowledge to another design.

[0004] Because different products often have different design spaces, optimization information is difficult to transfer directly between different design spaces. However, the design metrics of products in a series are usually similar, which makes information transfer possible to some extent. Therefore, finding common characteristics across different design spaces is an effective strategy for solving this type of problem.

[0005] In recent decades, transfer learning methods have primarily included isomorphic transfer design (design space features are the same) and heterogeneous transfer design (design space features are different). These methods have been widely applied in image classification and text processing, demonstrating the powerful information-sharing capabilities of transfer algorithms. In recent years, the engineering field has gradually adopted this design approach, improving the design efficiency of new products and shortening the design cycle. However, problems remain, such as limited applicability and difficulty in knowledge transfer between different design problems. In particular, when the transferred knowledge is incorrect, it can lead to negative transfer, increasing the time cost of another design or reducing its efficiency.

[0006] As a general knowledge transfer method, manifold learning is an effective approach to mapping different design spaces and utilizing information resources. Its main idea is to find common low-dimensional features of design problems with different dimensions and map design data from different dimensions into a low-dimensional latent space through a Gaussian joint distribution. If the design goals are similar, meaning the latent spaces of the two problems are considered correlated, the information transfer within the latent spaces can be used to assist in the internal analysis and design optimization of the new problem. Manifold learning has advantages such as deterministic convergence, the existence of a global loss function, automatic parameter adjustment, and a rigorous mathematical expression. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a method for shape transfer optimization of blended wing-body underwater gliders. It primarily utilizes fluid simulation, image processing, manifold learning, and a surrogate model-assisted optimization (ESAO) algorithm. This method transforms design space data from different dimensions into a latent space of the same dimension using generative topographic mapping (GTM) technology, thereby leveraging existing design experience to improve optimization efficiency for similar problems in the same domain. The invention describes a manifold learning-based glider shape knowledge transfer method and the specific steps applied to the shape optimization design of blended wing-body gliders.

[0008] Figure 1 illustrates the general flow of this shape design method. First, two-dimensional simulations of two different underwater glider shapes are performed using commercial Computational Fluid Dynamics (CFD) software, generating flow field information such as pressure and velocity contour maps. One of the two types of underwater gliders is a traditional rotating glider with extensive mature design experience, and the other is the BWBUG, which also belongs to the underwater glider field. Next, the velocity and pressure contour maps of both are processed to generate data matrices characterizing their hydrodynamic performance. Then, manifold learning is used to map the high-dimensional data matrices containing the flow field information of both gliders to a latent space of the same dimension. Afterward, an evolutionary algorithm is used to search for the optimal solution in the target domain BWBUG design space, and a true function is used to evaluate the potential optimal point to determine the optimal individual in this iteration. Finally, the design variables of both gliders are changed to obtain a new shape, and the above steps are repeated until the number of evaluation iterations is exhausted or the termination condition is met, thus obtaining the optimal shape solution for the new BWBUG glider. This invention addresses the shortcomings of existing underwater glider shape design methods by improving the utilization rate of design optimization data from different dimensions or for different problems, thus significantly increasing the efficiency of underwater glider shape design optimization. Furthermore, this method is also applicable to multidisciplinary optimization design of underwater vehicles, making its application quite broad.

[0009] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0010] Step 1: Parametrically model the source domain objects and the target domain objects to obtain the design space of the traditional rotating body glider, i.e., the source domain space variables, and the design space of the blended wing-body underwater glider, i.e., the target domain space variables.

[0011] Traditional gliders and blended wing-body gliders differ significantly in appearance, with complex and varied external profiles determined by numerous variables. However, it's noteworthy that they share a very similar cross-sectional shape and evaluation objective. To ensure effective transfer learning, the two-dimensional cross-sectional shape of the glider was chosen as the learning object in the transfer evaluation process.

[0012] Step 1-1: Parametric modeling of the target domain object, namely the blended wing-body underwater glider:

[0013] The initial shape design of a blended wing-body underwater glider essentially involves determining the shape of the main fuselage and selecting the appropriate cross-sectional shape. In practical engineering, the cross-sectional shape of a glider is modified more frequently than its profile shape; therefore, this paper primarily studies the influence of the profile shape on the glider's overall profile.

[0014] Define the target domain space variable set as T = {x} T1 ,x T2 ,x T3 ,…,xTn}, x Ti ∈[lower_T i upper_T i Let ] be the i-th target domain variable, where i = 1, 2, ..., n, lower_T i Upper_T represents the lower bound of the i-th target domain variable. i The upper bound of the i-th target domain variable is represented; n represents the number of target domain spatial variables; the airfoil section is parameterized using the CST (Class-shape-transformation) method, and the OXY coordinate system formula is as follows:

[0015]

[0016] In the formula, y0 represents the coordinates of the original airfoil, x represents the normalized coordinates, and K... i,4 The Bernstein coefficients can be calculated sequentially, A i These are the polynomial coefficients that influence the cross-sectional shape. Therefore, for the shape optimization of a blended wing-body glider, the number of variables in the objective domain space is n=5, making it a five-dimensional problem.

[0017] T = {x T1 ,x T2 ,x T3 ,…,x Tn} = [A1, A2, A3, A4, A5], x Ti ∈[lower_T i upper_T i ]

[0018] Steps 1-2: Parametric modeling of the source domain object, i.e., a traditional rotating glider:

[0019] Define the source domain space variable set as S = {x} s1 ,x s2 ,x s3 ,…,x sm}, x si ∈[lower_S i upper_S i Let ] be the i-th source domain variable, where i = 1, 2, ..., m, and lower_S i Upper_S represents the lower bound of the i-th source domain variable. i This represents the upper bound of the i-th target domain variable; m is the number of variables;

[0020] Traditional rotating gliders are modeled using Granville curves, where the entire glider is represented by a two-dimensional linear shape formed by the nose and tail curves rotating around a central axis. The nose and tail curves are modeled using Granville's two-parameter square root polynomials with mathematical expressions:

[0021]

[0022]

[0023] Where qh1, qh2, qt1, and qt2 are four adjustable parameters, qh1 represents the dimensionless radius of curvature at the junction of the straight front face and the tail, qh2 represents the dimensionless rate of change of curvature at the junction of the straight front face and the tail, qt1 represents the dimensionless slope at the junction of the linear shape and the tail surface, and qt2 represents the dimensionless rate of change of curvature at the junction of the linear shape and the head. x in the formula is a standardized parameter that can be changed according to the actual length. Therefore, for the parameterization of the shape of a rotating glider, there are four most important parameters, namely the source domain spatial variable S={x s1 ,x s2 ,x s3 ,…,x sm}=[qh1,qh2,qt1,qt2],x si ∈[lower_S i ipper_S i With the number of variables m=4, this shape problem has a four-dimensional design space.

[0024] Step 2: Establish initial sample points for the source and target domains:

[0025] The Latin hypercube sampling method is used to randomly select M from the source domain space and the target domain space respectively. T S target domain sampling points T i ∈T={x T1 ,x T2 ,x T3 ,…,x Tn}, i = 1, 2, 3, ..., and M S S source domain sampling points S i ∈S={x s1 ,x s2 ,x s3 ,…,x sm}, i = 1, 2, 3, ..., M S , representing the sample number;

[0026] Step 3: Evaluate the initial sample points in the source and target domains to establish latent space mapping relationships and complete knowledge transfer.

[0027] LDR (Lift Drag) is a key performance indicator for gliders, and its lift is caused by the pressure difference resulting from the velocity difference between the upper and lower surfaces. Under the same conditions, the larger the high-pressure area at the tail, the greater the induced drag of the glider. In addition, when the water separates from the glider, a wake is generated. The wider the wake, the more severe the velocity loss. Therefore, in the shape optimization problem, the smaller the wake width, the better.

[0028] Step 3-1: In this method, we use the glider cross-section to optimize the high-pressure area at the tail end through two-dimensional simulation. and wake width As the evaluation target, it is obtained by simulation calculation from the source domain and target domain samples, where the superscript i represents the evaluation function corresponding to the i-th sample.

[0029] Step 3-2: Define the numerical relationship of the objective function using the source and target domain spatial variables defined in Step 2; define the source domain evaluation value as...

[0030]

[0031] Where x si Let be the i-th source domain variable, and let be the source domain evaluation value determined by m source domain space variables; define the target space evaluation value as .

[0032]

[0033] Where x Ti Let be the i-th target domain variable, and the target domain evaluation value is jointly determined by n target domain spatial variables;

[0034] The source domain sample dataset can be obtained by summarizing the above three steps. and target domain sample dataset

[0035] Step 4: Generate a low-dimensional space using Generative Topological Mapping (GTM), map the best samples from the source domain to a latent space with the same dimension as the target domain, and then transfer the latent samples to the target domain through inverse mapping to assist in optimization.

[0036] Define the latent space variable set as L = {x} L1 ,x L2 ,x L3 ,…,x Ll}, x Pi ∈[lower_L i upper_L i Let ] be the i-th latent space variable, where i = 1, 2, ..., l, lower_L i Upper_L represents the lower bound of the i-th latent space variable. iThis represents the upper bound of the i-th target domain variable;

[0037] The GTM method assumes a probability density model of N data points in a D-dimensional data space, T = {t1,…,tn}, where this data set is coupled to an L-dimensional latent space. There are relationships between certain variables. This process is based on a radial basis function neural network y(x, W) with a network of K latent variables. Establishing connections. The probability distribution in the data space is assumed to be based on a variance of β. -1 The model is a Gaussian mixture distribution with its center as a high-dimensional point of the function y(x, W), where W is the weight. The variables W and β are parameters determined by maximizing the log-likelihood of the model using EM. It is assumed that the Gaussian center y(x, W) is a grid of the regression equation for the weights W and the basis functions Φ(x), and that there is a one-to-one correspondence between each point in the high-dimensional space and each point in the low-dimensional space through mapping.

[0038] The parameters of the model are determined by a training process designed to maximize the likelihood of generating a hypothetical probability dataset from a set of potential points, thereby finding potential advantages by updating the posterior probability through maximum likelihood.

[0039] Step 4-1: Generate dataset: Sample set S s,T The dataset contains normalized variables and an objective function, with dimensions m and n. A Morris-Mitchell Latin hypercube is filled with space using the maxi-min criterion. The validation dataset is randomly selected from sample points, with the remaining data points used as the training set.

[0040] Step 4-2: GTM Data Training to Find a Suitable Mapping Relationship: The parameters of the model are determined by a training process designed to maximize the likelihood of the latent point set generating the hypothesis probability dataset, thus maximizing the likelihood as an update before the posterior probability. The width σ of the basis function is considered a constant. This is now a hyperparameter that must be estimated before GTM training. For each value, the trained GTM and the value that produces the maximum log-likelihood during training are considered the optimal values ​​of σ, thus yielding a suitable mapping relationship.

[0041] Step 4-3: Update the latent space with sample points: Search for a suitable latent space to update in the target space samples. The search function is the regression equation y(x, W) = Φ(x)W, where W is the weight matrix trained by GTM, and Φ is the basis function matrix. This equation maps any latent point x to a data point y. Therefore, similar to t, y has D columns of data variables and D+1... th The column function values ​​are given by the GTM training. The real function values ​​are then evaluated using the variable y and the values ​​used by the genetic algorithm.

[0042] Step 4-4: Map the optimal sample from the source domain to the latent space and return it to the target domain space: You can view the sample dataset from the source domain space in the latent space. The data points in the latent space L = {x}. L1 ,x L2 ,x L3 ,…,x Ll The positions of} can be replaced by Φ in the regression equation to obtain their positions in the target domain space T={x T1 ,x T2 ,x T3 ,…,x Tn The corresponding point in}.

[0043] Steps 4-5: Update the training set. Target domain samples. As the number increases, it will be added to the training dataset, and the above steps will continue to be performed in a series of iterations.

[0044] Step 5: Iterate through the improved evolutionary sampling-assisted optimization algorithm until the optimal conditions are reached. The optimization steps are as follows:

[0045] The objective domain evaluation value is determined by n spatial variables of the objective domain; the objective truth function is designed and represented by y, i.e., the maximum and minimum values ​​are obtained.

[0046] maxy = y(x T1 ,x T2 ,x T3 ,…,x Tn )

[0047] The dynamic performance of a glider in water is mainly determined by its lift and drag coefficient. To improve its gliding efficiency, we use the lift-to-drag ratio (LDR) as the target for shape optimization.

[0048] Max = Lift-to-drag ratio(x),

[0049] x∈T={x T1 ,x T2 ,x T3 ,…,x Tn},

[0050] x Ti ∈[lower_T i upper_T i ]

[0051] Step 5-1: Obtain the initial sample That is, the target domain sample S calculated in steps 1 to 3 T i ∈T={x T1 ,xT2 ,x T3 ,…,x Tn The potential advantage samples obtained from the source domain migration in step 5 are used to establish the initial data sample;

[0052] Step 5-2: Use the Differential Evolution (DE) method to generate offspring from the initial samples, and use the information already in the database to build a Radical Basis Function (RBF) model;

[0053] Step 5-3: Use real functions to determine and evaluate the optimal individual under the model, and compare the optimal individual with its parent individual. If the function value of the optimal individual is better than the function value of its parent individual, it will replace its parent individual in the population.

[0054] Step 5-4: Establish a local proxy model in the current optimal region; search for a local optimum in the local proxy model; if a better point is found locally, it will be added to the candidate pool;

[0055] Step 5-5: Throughout the process, the optimal point in the global scope is also alternately searched; global search and local search are performed alternately until the iteration termination condition is reached, completing one migration optimization.

[0056] Step 6: Update the target domain samples after each iteration. A new low-dimensional latent space for the new problem is established, and the optimal solution in the source domain space is added to the target domain optimization population through a new mapping to complete knowledge transfer and then the evolutionary algorithm is re-introduced for optimization iteration.

[0057] Step 7: When the number of evaluations (NFE) reaches the set maximum number of evaluations (NFEmax), end the optimization loop and output the final optimization result.

[0058] The method for optimizing the shape of an underwater glider based on manifold learning, as described in this invention, has the following beneficial effects:

[0059] Unlike traditional glider design methods that only use simulation results of the design object itself, the transfer learning optimization method makes better use of and references existing experience, namely the optimization data of traditional rotary gliders in this method, or the data accumulated in similar fields. This makes the shape design optimization process more cost-effective, faster, and more efficient in utilizing data. Attached Figure Description

[0060] Figure 1 A flowchart of the shape transfer design method for blended wing-body underwater gliders based on manifold learning;

[0061] Figure 2 This is a flowchart of the parameterization and fluid simulation process of this invention;

[0062] Figure 3 This is a flowchart of the image processing in the embodiment;

[0063] Figure 4 This is a schematic diagram of manifold learning in the embodiment;

[0064] Figure 5 The flowchart of the ESAO optimization algorithm in the embodiment is shown below;

[0065] Figure 6 The diagram shows the optimized results in the example.

[0066] Figure 7 This is a comparison chart of the performance of the proposed method and the traditional optimization method in the embodiments. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0068] First, parametric models of traditional gliders and blended wing-body gliders are performed to establish source and target domain samples for transfer learning. The CST method is used to parametrically model the blended wing-body shape:

[0069]

[0070] It includes five-dimensional variables [A1, A2, A3, A4, A5] specifying the variable interval x. Ti ∈[lower_T i upper_T i ];

[0071] Specifically, the shape of the source domain object, i.e., the traditional gyroplane, is achieved through a two-dimensional linear rotation composed of curves at the head and tail. Granville curves are used to model the shape of the traditional gyroplane:

[0072]

[0073]

[0074] It contains four-dimensional variables [qh1,qh2,qt1,qt2], with a specified variable interval x. Ti ∈[lower_S i upper_S i ]

[0075] Based on the variables from the previous step, the corresponding shape data is first obtained using Matlab, and then an unstructured mesh is created using the commercial simulation software COMSOL. An appropriate computational domain size is set, with the left boundary of the domain designated as the velocity inlet and the right boundary as the pressure outlet. An unstructured mesh is generated to obtain the viscous boundary layer. Solver parameters, boundary conditions, and iterative convergence criteria are set; all of these operations are automatically generated by the script.

[0076] After the fluid simulation based on the above settings reaches the convergence condition, it outputs velocity and pressure contour maps and transmits them to Matlab for image processing.

[0077] Matlab was used to read the velocity and pressure contour maps. Grayscale and binary images were then used to convert the contour maps containing flow field simulation information into a data matrix, where each element represents the pixel size in the image. The wake width W, determined by the current variable, was calculated from the data matrix. v Size A of the high-voltage zone at the tail p ; Source domain evaluation function y s With the target domain evaluation function y T These are the weighted sums of their respective wake widths and the area of ​​the high-pressure region at the tail:

[0078] y s =y s (qh1,qh2,qt1,qt2)=w1A pS +w2W vS

[0079] y T =y T (A1,A2,A3,A4,A5)=w1A pT +w2W vT

[0080] Repeat steps n1 and n2 above to obtain the source domain sample X. S Compared with the initial sample X in the target domain T Where X S ={x S 1 ,x S 2 ,x S 3 ,...,x S n1} respectively with Y S ={y S 1 ,y S 2 ,y S 3 ,...,y S n1One-to-one correspondence; X T ={x T 1 ,x T 2 ,x T 3 ,...,x T n2} respectively with Y T ={y T 1 ,y T 2 ,y T 3 ,...,y T n2 A one-to-one correspondence; superscripts indicate sample numbers; in summary, the source domain sample dataset can be obtained. and target domain sample dataset

[0081] Next, a low-dimensional space is generated using GTM to transfer the best samples of traditional gliders in the source domain to the design optimization space of the target domain BWBUG. Potential samples of the design target are obtained through reflection to aid optimization. The GTM model represents a D-dimensional high-dimensional dataset T = {t1, ..., t2} through the mapping Y = (x, W). n} and K latent variable points x = {x1, ..., x2} n The mapping represents N points in the L-dimensional space of the latent variable space, and maps each point in the latent variable space to the center of the Gaussian mixture distribution of the data. Based on the above definition, the latent points have a prior probability distribution with a discrete δ function p(x), and it is assumed that the dataset T has a Gaussian mixture probability distribution.

[0082] The corresponding mapping relationship η is obtained by training GTM using samples from the source and target domains respectively. S and η T Mapping excellent latent samples from the source domain to an l-dimensional latent space:

[0083]

[0084] Map the target domain samples to a latent space of the same l-dimensional dimension:

[0085]

[0086] The mapping relationship η is then obtained by training with samples from the target domain. T inverse mapping Reflecting the potentially excellent samples in the latent space into the target domain space:

[0087]

[0088] From this point on, in addition to the original initial sample set, the target domain has a large number of potential samples obtained by mapping from the source domain space. That is, the potential samples are added to the target domain optimization database, waiting for the next step of the evolutionary algorithm to find the best use.

[0089] The ESAO optimization algorithm is adopted, and the differential evolution principle is used to generate evolutionary offspring from the initial sample set. A global RBF model is established using all candidate samples, and the actual LDR size under the parameter is obtained using a real function, i.e., three-dimensional fluid simulation (automatically performed by the script), to determine and evaluate the optimal individual under the model.

[0090] If the function value of the best individual generated at this time is less than the function value of its parent individual, it will replace its parent individual in the population.

[0091] A local proxy model is established in the current optimal region; a local optimum is searched in the local proxy model; if a better point is found locally, it will be added to the pool of alternative solutions; throughout the process, the global optimum is searched alternately with the local optimum.

[0092] After each iteration, update the target domain design variable iteration database. The low-dimensional latent space of the new problem and its relative mapping relationship are re-established, and the optimal solution in the source domain space is supplemented into the target domain optimization population through the new mapping, thus completing knowledge transfer and evolutionary optimization.

[0093] Once the set number of real function evaluations (NFEmax) is reached, the iteration ends, and the final optimization result is output. Specific implementation examples:

[0095] This invention proposes a manifold learning-based method for optimizing the shape of a blended wing-body underwater glider. The flowchart of the optimization method is shown in the figure, which consists of four parts: ① fluid simulation, ② image processing, ③ manifold learning, and ④ evolutionary algorithm for finding the optimal point.

[0096] The following example, along with accompanying drawings, illustrates the optimization of the shape of a blended wing-body glider.

[0097] Key optimization processes include:

[0098] 1. Identifying the Optimization Target: Blended wing-body gliders exhibit excellent underwater performance due to their high durability, long range, and low energy consumption. A higher lift-to-drag ratio is beneficial for improving gliding efficiency. This method uses the glider's high lift-to-drag ratio (LDR) as the optimization objective, i.e., measuring the ratio of lift coefficient to drag coefficient for different glider shapes under the same boundary conditions, and selecting the glider shape with the highest LDR as the optimization result. Since problems rarely exist in isolation, the optimization problems of traditional wing-body gliders can provide useful information for the optimization of blended wing-body glider shapes. In this example, transfer learning is used to refer to the optimization results of traditional gliders to assist the optimization process of the blended wing-body glider.

[0099] 2. Parametric modeling of blended wing-body gliders and conventional gliders was performed using CST and Granville curves, respectively. The blended wing-body glider included five-dimensional variables [A1, A2, A3, A4, A5], while the conventional glider included four-dimensional variables [qh1, qh2, qt1, qt2]. The lift of a glider is caused by the pressure difference resulting from the velocity difference between the upper and lower surfaces. The vortex generated when water separates from the glider's tail typically forms a high-pressure region at the tail. Under the same conditions, the larger the high-pressure region at the tail, the greater the induced drag of the glider; therefore, designers aim to reduce the high-pressure region at the tail. Furthermore, the separation of water from the glider produces a wake; the wider the wake, the greater the velocity loss, therefore, a smaller wake width is preferable. In this method, we use the high-pressure area and wake width as transfer targets.

[0100] like Figure 2 Parametric modeling and fluid simulation show that the corresponding shape data was obtained using Matlab software, and then an unstructured mesh was created using the commercial software COMSOL. The size of the computational domain was set to 2.6 × 1.4 meters. The left boundary of the domain was set as the velocity inlet, and the right boundary as the pressure outlet. An unstructured mesh was generated to obtain the viscous boundary layer. The fluid medium was set as incompressible water with a density of 998.2 kg / m³ and a dynamic viscosity of 1.003 × 10⁻³ Pa / s. The stress transfer (SST) turbulence model was used to solve the governing equations; the inlet velocity and angle of attack were set to 1.028 m / s and 6 degrees, respectively. The convergence criteria were a root mean square residual less than 10⁻⁵ or a total number of iterations reaching 300. The obtained velocity and pressure contour maps were then extracted and processed in Matlab.

[0101] 3. For example Figure 3Image processing is shown below. The purpose of this step is to obtain the tail high-pressure area and wake width from the contour map. Based on simulation data and analysis of the pressure and velocity on the fuselage surface, we set the high-pressure boundary to 100 Pa and the velocity boundary to 0.7 m / s. Then, we use Matlab to read the preprocessed contour map and convert it into a data matrix using grayscale and binary images, where the elements represent the pixel values ​​in the image. By reading the number of elements in the matrix, we can obtain the area of ​​the tail high-pressure region and the wake width. The obtained data will be weighted and combined for subsequent manifold learning. By changing the design variables of BWBUG and traditional rotating gliders, and repeating the above steps, we can obtain the initial samples of the target and source domains respectively. To ensure the transfer results, this example repeats the process 500 times for initial sample sampling.

[0102] 4. We define the influence of the high-pressure region at the tail and the wake width as equal, therefore we normalize and sum the data, and set the weight parameters w1 and w2 of the evaluation function to 0.5. The source domain and the target domain each form a new target with a value between 0 and 1.

[0103]

[0104]

[0105] like Figure 4 Manifold learning sets the dimension l of the low-dimensional latent space projected by GTM to 2, i.e., L = {x} L1 ,x L2}, to achieve visualization purposes; using GTM training to generate a low-dimensional latent space, the source domain S={x s1 ,x s2 ,x s3 ,…,x sm The optimal evaluation samples for the rotating glider in}=[qh1,qh2,qt1,qt2] are transferred to the same latent space L as the target domain, and then, through reverse mapping, the two-dimensional sample points in the latent space are transferred to the target domain T={x T1 ,x T2 ,x T3 ,…,x Tn The five-dimensional variable design space of [A1, A2, A3, A4, A5] is used to obtain potential samples of the optimization problem to assist in optimization.

[0106] 5. This methodological framework applies the ESAO optimization algorithm to the shape optimization design of BWBUG. The initial sample size of the experiment is 3*n+2=17, where n=5 represents the dimension of the target domain space, generated by a Latin hypercube.

[0107] like Figure 5The ESAO optimization algorithm employs a global-local evolutionary algorithm to iteratively optimize data points in the database. Differential evolution (DE) is used to generate offspring, establishing a global RBF model, and the optimal individual under this model is determined and evaluated using a real function. If the function value of the optimal individual is less than that of its parent, it will replace its parent in the population. Then, a local surrogate model is established in the current optimal region. If a better point is found locally, it will be added to the candidate pool. Throughout the process, global and local searches alternate. During this time, potential advantageous samples mapped from the source domain to the low-dimensional latent space are migrated to the target domain sample library by a real-time updated inverse mapping relationship to aid optimization, and the mapping relationship is iteratively trained in real-time by the target domain samples as the database is updated. It is important to note that the goal of manifold learning is the weighted sum of the tail high-pressure region and the wake width, while the optimization goal is to maximize the LDR (Low-Depth Reduction). The optimization formula can be expressed as:

[0108] Max = Lift-to-drag ratio(x)

[0109] x s ∈[lb s ,ub s ], i = 1, 2, ..., 4

[0110] x t ∈[lb t ,ub t ], i = 1, 2, ..., 5

[0111] lb t = [-0.072, -0.0618, -0.06925, -0.0411, -0.0718]

[0112] ub t =[0.072,0.0618,0.06925,0.0411,0.0718]

[0113] lb s =[3,2,2,12]ub s =[4,5,5,30]

[0114] The maximum number of optimization iterations, NFEmax, is set to 500 steps. The optimization result is output when the algorithm terminates (NFE > NFEmax). Figure 6The optimization results are compared from left to right: the initial model, the traditional optimization output model, and the optimized model of our method. It can be seen that the transfer optimization result based on manifold learning has a higher lift-to-drag ratio (LDR). To compare the efficiency of the transfer algorithm and the traditional optimization algorithm, the traditional optimization mode was set as the control group. That is, the ESAO algorithm was only used to search in the five-dimensional space of the BWBUG and did not transfer the optimization data points of the traditional rotating glider.

[0115] like Figure 7 The optimization performance comparison shows the iterative graph of the LDR results based on the number of iterations (NFE), intuitively comparing the optimization performance of the manifold learning-based underwater glider optimization algorithm with that of the traditional single optimization algorithm: Overall, the transfer design can find a shape with a larger LDR. Although the traditional design quickly escapes the initial local traps, it quickly falls into the next, more difficult trap. In contrast, although the manifold learning-based blended wing-body underwater glider shape optimization method uses more iterations to overcome the initial local traps, as the transfer model improves and the efficiency of knowledge transfer increases, its ability to escape local optima is significantly enhanced, and it tends to converge after 320 steps.

[0116] The detailed steps and results of the above embodiments demonstrate that the proposed manifold learning-based method for optimizing the shape of a blended wing-body underwater glider utilizes the generative topological mapping (GTM) concept, which can handle mappings between different dimensions. It transfers optimization knowledge from the traditional rotating glider problem, which is similar to the optimization problem of a blended wing-body underwater glider, to the former's shape optimization problem. Furthermore, leveraging the high efficiency of the ESAO optimization algorithm's combination of global and local search, a blended wing-body glider shape with a high lift-to-drag ratio (LDR) is obtained. Compared to traditional optimization methods that calculate from scratch, this method effectively accelerates the entire shape optimization process and improves data computation efficiency.

[0117] This invention addresses the limitations of existing methods for optimizing the shape of blended wing-body underwater gliders, improving the logic and efficiency of shape optimization.

[0118] The underwater wing-body blended underwater glider shape transfer design method based on manifold learning is also applicable to the optimization design of other disciplines of underwater vehicles, and has a wide range of applications.

Claims

1. A method for shape transfer design of blended wing-body underwater gliders based on manifold learning, characterized in that, Includes the following steps: Step 1: Parametrically model the source domain objects and target domain objects to obtain the design space of a traditional rotating glider (i.e., the source domain space variables) and the design space of a blended wing-body underwater glider (i.e., the target domain space variables); including the following sub-steps: Step 1-1: Parametric modeling of the target domain object, namely the blended wing-body underwater glider: Define the target domain space variable set as T = {x} T1 ,x T2 ,x T3 ,…,x Tn }, x Ti ∈[lower_T i upper_T i Let ] be the i-th target domain variable, where i = 1, 2, ..., n, lower_T i Upper_T represents the lower bound of the i-th target domain variable. i This represents the upper bound of the i-th target domain variable; n represents the number of variables in the target domain space. The airfoil section is parameterized using the CST (Class-shape-transformation) method, and the formula for the OXY coordinate system is as follows: In the formula, y0 represents the coordinates of the original airfoil, x represents the normalized coordinates, and K... i,4 The Bernstein coefficients can be calculated sequentially, A i These are the polynomial coefficients affecting the cross-sectional shape; therefore, for the shape optimization of a blended wing-body glider, the number of variables in the objective domain space is n=5, making it a five-dimensional problem, i.e. T={x T1 ,x T2 ,x T3 ,…,x Tn }=[A1,A2,A3,A4,A5],x Ti ∈[lower_T i ,upper_T i ] Steps 1-2: Parametric modeling of the source domain object, i.e., a traditional rotating glider: Define the source domain space variable set as S = {x} s1 ,x s2 ,x s3 ,…,x sm }, x si ∈[lower_S i upper_S i Let ] be the i-th source domain variable, where i = 1, 2, ..., m, and lower_S i Upper_S represents the lower bound of the i-th source domain variable. i This represents the upper bound of the i-th target domain variable; m is the number of variables; Traditional rotating gliders are modeled using Granville curves, where the entire glider is represented by a two-dimensional linear shape formed by the nose and tail curves rotating around a central axis. The nose and tail curves are modeled using Granville two-parameter square root polynomials with mathematical expressions. Where qh1, qh2, qt1, and qt2 are four adjustable parameters, qh1 represents the dimensionless radius of curvature at the junction of the straight front face and the tail, qh2 represents the dimensionless rate of change of curvature at the junction of the straight line and the tail, qt1 represents the dimensionless slope at the junction of the linear shape and the tail surface, and qt2 represents the dimensionless rate of change of curvature at the junction of the linear shape and the head. x in the formula is a standardized parameter that can be changed according to the actual length. Therefore, for the parameterization of the shape of a rotating glider, there are four most important parameters, namely the source domain space S = {x}. s1 ,x s2 ,x s3 ,…,x sm }=[qh1,qh2,qt1,qt2],x si ∈[lower_S i upper_S i With the number of variables m=4, this shape problem has a four-dimensional design space; Step 2: Establish initial sample points for the source and target domains: The Latin hypercube sampling method is used to randomly select M from the source domain space and the target domain space respectively. T S target domain sampling points T i ∈T={x T1 ,x T2 ,x T3 ,…,x Tn }, i = 1, 2, 3, ..., and M S S source domain sampling points S i ∈S={x s1 ,x s2 ,x s3 ,…,x sm }, i = 1, 2, 3, ..., M s , representing the sample number; Step 3: Evaluate the initial sample points in the source and target domains to establish latent space mapping relationships and complete knowledge transfer. This includes the following sub-steps: Step 3-1: Optimize the high-pressure area at the tail using the glider cross-section in two-dimensional simulation. and wake width W v i As the evaluation target, it is obtained by simulation calculation from the source domain and target domain samples, where the superscript i represents the evaluation function corresponding to the i-th sample; Step 3-2: Define the numerical relationship of the objective function using the source and target domain spatial variables defined in Step 2; Define the source domain evaluation value as Where x si Let be the i-th source domain variable, and let be the source domain evaluation value determined by m source domain space variables; define the target space evaluation value as . Where x Ti Let be the i-th target domain variable, and the target domain evaluation value is jointly determined by n target domain spatial variables; In summary, the source domain sample dataset is obtained. and target domain sample dataset Step 4: Generate a low-dimensional space using Generative Topological Mapping (GTM), mapping the best samples from the source domain to a latent space with the same dimension as the target domain. Then, transfer the latent samples to the target domain through inverse mapping to aid optimization. Define the latent space variable set as L = {x} L1 ,x L2 ,x L3 ,…,x Ll }, x Pi ∈[lower_L i upper_L i Let ] be the i-th latent space variable, where i = 1, 2, ..., l, lower_L i Upper_L represents the lower bound of the i-th latent space variable. i This represents the upper bound of the i-th target domain variable; Step 4-1: Generate dataset: Sample set S S,T The dataset contains normalized variables and an objective function, with dimensions m and n; it is filled with a Morris-Mitchell Latin hypercube using a space filled with the maxi-min criterion; the validation dataset is randomly selected from sample points, and the remaining data points are used as the training set. Step 4-2: GTM Data Training to Find a Suitable Mapping Relationship: The parameters of the model are determined by a training process designed to maximize the likelihood of the latent point set generating the hypothesis probability dataset, thus maximizing the likelihood as an update before the posterior probability; the width σ of the basis function is considered a constant; this is now a hyperparameter that must be estimated before GTM training; for each value, the trained GTM and the value that produces the maximum log-likelihood during training are considered the optimal values ​​of σ, thus obtaining a suitable mapping relationship; Step 4-3: Update the latent space with sample points: Search for a suitable latent space to update in the target space samples. The search function is the regression equation y(x, W) = Φ(x)W, where W is the weight matrix trained by GTM, and Φ is the basis function matrix. This equation maps any latent point x to a data point y. Therefore, similar to t, y has D columns of data variables and D+1... th The column function values ​​are given by the GTM training; then the actual function values ​​are evaluated using the variable y and the value used by the genetic algorithm. Step 4-4: Map the optimal sample from the source domain to the latent space and return it to the target domain space: You can view the sample dataset from the source domain space in the latent space. The data points in the latent space L = {x}; these data points are in the latent space L = {x} L1 ,x L2 ,x L3 ,…,x Ll The positions of} can be replaced by Φ in the regression equation to obtain their positions in the target domain space T={x T1 ,x T2 ,x T3 ,…,x Tn The corresponding point in}; Steps 4-5: Update the training set; target domain samples As the number increases, it will be added to the training dataset, and the above steps will continue to be performed in a series of iterations; Step 5: Iterate through the improved evolutionary sampling-assisted optimization algorithm until the optimal conditions are reached. The optimization steps are as follows: The target domain evaluation value is determined by n target domain spatial variables; the target truth function is designed and represented by y, that is, the maximum and minimum values ​​are obtained; The lift-to-drag ratio (LDR) is used as the target for shape optimization: Max = Lift-to-drag ratio(x), x∈T={x T1 ,x T2 ,x T3 ,…,x Tn }, x Ti ∈[lower_T i ,upper_t i ] Step 5-1: Obtain the initial sample That is, the target domain sample S calculated in steps 1 to 3 T i ∈T={x T1 ,x T2 ,x T3 ,…,x Tn The potential advantage samples obtained from the source domain migration in step 5 are used to build an optimized data sample, including the following sub-steps: Step 5-2: Use the Differential Evolution (DE) method to generate offspring from the initial samples, and use the information already in the database to build a Radical Basis Function (RBF) model; Step 5-3: Use real functions to determine and evaluate the optimal individual under the model, and compare the optimal individual with its parent individual. If the function value of the optimal individual is better than the function value of its parent individual, it will replace its parent individual in the population. Step 5-4: Establish a local proxy model in the current optimal region; search for a local optimum in the local proxy model; if a better point is found locally, it will be added to the candidate pool; Step 5-5: Throughout the process, the search for the optimal point in the global scope is also carried out alternately; the global search and the local search are carried out alternately until the iteration termination condition is reached, and one migration optimization is completed. Step 6: Update the target domain samples after each iteration. A new low-dimensional latent space for the new problem is re-established, and the optimal solution in the source domain space is supplemented into the target domain optimization data sample through a new mapping to complete the knowledge transfer. Step 7: When the number of evaluations (NFE) reaches the set maximum number of evaluations (NFEmax), end the optimization loop and output the final optimization result.

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