An AUV multidisciplinary sequential optimization method based on high-fidelity sample migration and front credibility enhancement
By employing high-fidelity sample transfer and Pareto front reliability enhancement methods, the problems of high cost of high-fidelity sample acquisition and insufficient reliability of Pareto front in AUV multidisciplinary design optimization are solved, achieving efficient multi-objective optimization and accurate Pareto solution set acquisition.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGSU UNIV OF SCI & TECH
- Filing Date
- 2026-04-21
- Publication Date
- 2026-07-31
AI Technical Summary
Existing AUV multidisciplinary design optimization methods suffer from high costs in obtaining high-fidelity samples, low efficiency in expanding the joint design space, and insufficient reliability in critical regions of the Pareto front.
We employ high-fidelity sample transfer and frontier credibility enhancement methods. By generating high-fidelity geometric samples in the geometric parameter space, we construct a high-fidelity hydrodynamic sample library. We then use the nearest neighbor transfer strategy based on normalized Euclidean distance to expand the system-level training samples in the joint design space. Combined with the Kriging surrogate model, we perform multi-objective optimization and frontier credibility enhancement, and select key points for high-fidelity CFD verification.
It significantly reduces sample construction costs, improves optimization efficiency and solution set reliability, and achieves efficient multi-objective search and local accuracy improvement of Pareto front in high-dimensional joint design space.
Smart Images
Figure CN122491103A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to engineering design and optimization methods, specifically to an AUV multidisciplinary sequence optimization method based on high-fidelity sample migration and frontier credibility enhancement. Background Technology
[0002] In missions such as ocean exploration, resource surveys, environmental monitoring, and underwater operations, AUVs (Autonomous Underwater Vehicles) typically need to navigate stably along a pre-set three-dimensional path. Path-tracking performance is not only related to controller and guidance parameters but is also influenced by factors such as hull shape, hydrodynamic coefficients, and rudder effectiveness, exhibiting significant multidisciplinary coupling characteristics. Therefore, in the AUV design process, it is difficult to simultaneously optimize a single discipline—such as geometry, hydrodynamics, control, or path guidance—at the system level, taking into account comprehensive performance indicators such as path-tracking accuracy and energy consumption.
[0003] There are two main types of existing multidisciplinary design optimization methods for AUVs: one type uses empirical formulas or low-fidelity models to predict system performance. Although the computational efficiency is high, it is difficult to accurately reflect the impact of shape changes on hydrodynamic characteristics and closed-loop path tracking performance. The other type directly embeds high-fidelity CFD numerical simulation into the optimization iteration process. Although the physical reliability is high, it requires a large number of sample calculations in the high-dimensional design space, resulting in huge computational costs, low optimization efficiency, and poor engineering applicability.
[0004] In the joint design problem considering AUV shape parameters, control parameters, and path guidance parameters simultaneously, direct high-fidelity sampling across the entire design space will result in significant dimensionality curse. Conversely, relying solely on traditional surrogate models for one-time modeling can easily lead to large prediction errors and insufficient front reliability due to insufficient samples in local regions near the Pareto front. Therefore, there is an urgent need to propose a sequence optimization method that can inherit the physical reliability of high-fidelity hydrodynamic samples, efficiently expand samples in a multidisciplinary high-dimensional space, and perform adaptive accuracy correction for key Pareto regions. Summary of the Invention
[0005] Purpose of the invention: The purpose of this invention is to provide an AUV multidisciplinary sequence optimization method based on high-fidelity sample migration and enhanced frontier reliability, in order to solve the problems of high cost of high-fidelity sample acquisition, low efficiency of joint design space expansion, and insufficient reliability of key regions of the Pareto front in existing AUV multidisciplinary optimization methods.
[0006] Technical solution: The present invention provides an AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier confidence enhancement, comprising:
[0007] S1: Several sets of high-fidelity geometric samples are generated by sampling in the geometric parameter space. High-fidelity CFD numerical calculations are performed on each set of high-fidelity geometric samples to determine the corresponding high-fidelity hydrodynamic response vector and construct a high-fidelity hydrodynamic sample library. The high-fidelity hydrodynamic response vector includes position hydrodynamic coefficient, rotation hydrodynamic coefficient and rudder coefficient.
[0008] S2: Generate several sets of system-level initial samples within the joint design space. The joint design variables include geometric parameters, control parameters, and path guidance parameters.
[0009] S3: Based on the nearest neighbor migration strategy of normalized Euclidean distance, the geometric parameters in the initial system-level samples are mapped to the nearest neighbor high-fidelity geometric samples, and the corresponding high-fidelity hydrodynamic response vectors are inherited to obtain the mapped system samples; all mapped system samples are input into the multidisciplinary coupled simulation model to obtain the path tracking error index and the relative energy consumption index of the servo motor, and to construct the system-level training sample set.
[0010] S4: Based on the system-level training sample set, establish a system-level Kriging proxy model and train the model for the path tracking error target and the servo relative energy consumption target respectively;
[0011] S5: The NSGA-II algorithm is used to perform multi-objective optimization search in the joint design space to obtain the predicted Pareto optimal solution set; during the optimization process, the Kriging surrogate model is used to quickly predict the target value;
[0012] S6: A frontier credibility enhancement strategy based on the coupling index of hypervolume contribution and prediction uncertainty, which selects key points from the Pareto optimal solution set;
[0013] S7: Perform high-fidelity CFD verification on each key point, perform dynamic point supplementation and Kriging proxy model update based on the key point verification error, and repeat steps S5 to S7 until the termination condition is met, and output the final Pareto optimal solution set.
[0014] Furthermore, in step S1, the first Group of high-fidelity geometric samples ,in For the rudder root chord length; To steer the course and extend the horizon; The relative thickness ratio of the rudder; The longitudinal position of the rudder; It is half an angle of the stern cone of the boat; The number of high-fidelity geometric sample groups;
[0015] High-fidelity hydrodynamic sample library ,in For the first High-fidelity hydrodynamic response vectors corresponding to a set of high-fidelity geometric samples.
[0016] Furthermore, in step S2, the first Group system-level initial samples ,in For geometric parameter subvectors; For control parameter subvectors; This is a sub-vector of path guidance parameters; This represents the initial number of sample groups at the system level.
[0017] Furthermore, in step S3, for the first... Group system-level initial samples and calculate their geometric parameter subvectors. With high-fidelity hydrodynamic sample library The Middle Group of high-fidelity geometric samples Normalized Euclidean distance:
[0018]
[0019] in, and These are the upper and lower bound vectors of the geometric parameter space, respectively;
[0020] Based on the nearest neighbor principle, determine the sub-vectors with geometric parameters. Nearest Neighbor High-Fidelity Geometric Sample Number:
[0021]
[0022] The first Geometric parameter subvectors in the initial samples of the group system Using nearest-neighbor high-fidelity geometric samples Replace and inherit. The corresponding high-fidelity hydrodynamic response vector Thus, the mapped system sample is obtained:
[0023]
[0024] All mapped system samples Input a multidisciplinary coupled simulation model to obtain a system-level training sample set:
[0025]
[0026] Among them, system-level target response , Indicates the path tracking error index. This indicates the relative energy consumption of the servo motor.
[0027] Furthermore, in step S3, the multidisciplinary coupled simulation model includes a parametric modeling module, a hydrodynamic calculation module, a motion module, a control module, and a path guidance module. The parametric modeling module generates the AUV's shape based on geometric parameters; the hydrodynamic calculation module calls a high-fidelity hydrodynamic response vector; and the path guidance module employs a three-dimensional adaptive line-of-sight guidance method to calculate the desired heading angle based on the current position and a preset path. and desired pitch angle The control module uses a PID control law to output rudder and elevator control commands based on guidance commands and actual attitude deviations. The motion module calculates the state response based on the dynamic equations and kinematic equations, and uses the fourth-order Runge-Kutta method for time-domain integral propulsion.
[0028] Furthermore, in step S4, the Kriging surrogate model represents the unknown response as the sum of the global trend term and the random bias term:
[0029]
[0030] in, This is a global trend item. Zero-mean random term;
[0031] For any sample point to be predicted Its Kriging prediction value is expressed as:
[0032]
[0033] in, This is a global trend item. For the regression basis function vector, These are estimates of the regression coefficients. This is the correlation vector between the sample point to be predicted and the training sample; For the training sample correlation matrix; To train the response vector; This is the regression matrix;
[0034] Based on this, path tracking error proxy models were established respectively. Relative energy consumption proxy model of servo motor .
[0035] Furthermore, in step S5, the multi-objective optimization model is as follows:
[0036]
[0037]
[0038]
[0039] in, For joint design variables; The vector of state variables of the system; The derivative of the state variable with respect to time; It is a time variable; and These are the lower and upper bounds of the variable, respectively. This represents a multidisciplinary coupled residual relationship;
[0040] Path tracking error is defined as:
[0041]
[0042] in, Let the objective function be the path tracking error. To simulate the total number of discrete steps, For the first The spatial error between the actual position of the AUV and the reference path at each moment;
[0043] The relative energy consumption of a servo motor is defined as:
[0044]
[0045] in, The objective function for servo motor energy consumption; Total energy consumption; The start time; End time; The rudder angle, For elevator angle, and These are the angular velocities of the corresponding control surfaces; It is a time variable.
[0046] Furthermore, in step S6, let the predicted Pareto optimal solution set be... ,in Indicates the number of Pareto solutions;
[0047] First, the Kriging surrogate model provides the predicted standard deviation of each Pareto solution on both objectives. and Based on this, a comprehensive uncertainty index is constructed:
[0048]
[0049] Secondly, select a reference point. ,in:
[0050]
[0051] in, For reference point In the The weight of each goal =1,2; The scaling factor is the reference point. The predicted Pareto optimal solution set; Pareto solution In the Predicted values on each objective function;
[0052] Then, calculate the first... The contribution of each Pareto solution to the hypervolume of the global front:
[0053]
[0054] in, Indicates the excess volume value. Indicates the first The solution set obtained by removing Pareto solutions from the predicted Pareto optimal solution set;
[0055] Based on this, the normalized hypervolume contribution and the normalized comprehensive uncertainty index are weighted and coupled to obtain the key point scoring function:
[0056]
[0057] in, This represents the normalized hypervolume contribution. This represents the normalized overall uncertainty index; weighting coefficients. The value ranges from 0 to 1;
[0058] Based on the key point scoring function Sort all Pareto solutions and select the K Pareto solutions with the highest scores as key points to include in the key point set.
[0059] Furthermore, in step S6, the minimum solution for relative energy consumption of the servo motor and the minimum solution for path tracking error are also included in the key point set.
[0060] Furthermore, in step S7, for each key point, high-fidelity CFD numerical calculations are re-executed, and multidisciplinary coupled simulations are carried out in conjunction with control parameters and path guidance parameters to obtain the true target value. ;
[0061] Next, the predicted values from the Kriging surrogate model are calculated. Compared with the actual target value The relative error between them:
[0062]
[0063] When the error of a keypoint on any target exceeds the preset error limit, the corresponding keypoint is added to the system-level training sample set for retraining the Kriging surrogate model. When the relative error of the keypoint on all targets remains below the preset error limit in a certain round or several consecutive rounds, or when the preset high-fidelity CFD computation budget limit is reached, the sequence optimization process is terminated.
[0064] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:
[0065] (1) This invention focuses high-fidelity CFD calls on the geometric parameter space and a small number of key points for verification. It constructs a system-level training sample set through a high-fidelity sample transfer method, avoiding large-scale direct high-fidelity sampling in a high-dimensional joint design space and significantly reducing the sample construction cost.
[0066] (2) By using the system-level Kriging surrogate model to establish a fast mapping between joint design variables and path tracking error and relative energy consumption of servo motor, the NSGA-II algorithm can efficiently complete multi-objective search in high-dimensional joint design space, thus improving the optimization solution efficiency;
[0067] (3) A credibility enhancement strategy for key regions of the Pareto front is proposed, which can simultaneously consider the contribution of the solution to the coverage of the front and the prediction risk of the surrogate model in that region, so that the limited high-fidelity computing resources are prioritized to the regions that need the most correction, thereby improving the local accuracy and overall stability of the front.
[0068] (4) This invention is applicable to AUV system-level optimization problems with high-fidelity evaluation costs and complex interdisciplinary coupling relationships. While taking into account physical fidelity, it achieves a synergistic improvement in optimization efficiency and solution set reliability, and has good engineering application value. Attached Figure Description
[0069] Figure 1 This is a flowchart of an AUV multidisciplinary sequence optimization method based on high-fidelity sample migration and frontier credibility enhancement provided by an embodiment of the present invention;
[0070] Figure 2 This is a schematic diagram of the AUV structure in an embodiment of the present invention;
[0071] Figure 3 This is a schematic diagram of a multidisciplinary coupled simulation model in an embodiment of the present invention;
[0072] Figure 4 This is a flowchart of the frontier credibility enhancement strategy based on the coupling index of hypervolume contribution and prediction uncertainty in an embodiment of the present invention.
[0073] Figure 5 This is a diagram showing the optimized results in an embodiment of the present invention. Detailed Implementation
[0074] The invention will now be further described with reference to the accompanying drawings.
[0075] like Figure 1 As shown, this embodiment of the invention provides an AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier confidence enhancement, including:
[0076] S1: Several sets of high-fidelity geometric samples are generated by sampling in the geometric parameter space. High-fidelity CFD numerical calculations are performed on each set of high-fidelity geometric samples to determine the corresponding high-fidelity hydrodynamic response vector and construct a high-fidelity hydrodynamic sample library. The high-fidelity hydrodynamic response vector includes position hydrodynamic coefficient, rotation hydrodynamic coefficient and rudder coefficient.
[0077] Geometric parameters include rudder root chord length rudder extension rudder relative thickness ratio longitudinal position of the rudder and the half angle of the tail cone The value range is set to: rudder root chord length. The rudder span is 0.25–0.50 m. The relative thickness of the rudder is 0.28–0.42 m. The longitudinal position of the rudder is 0.10 to 0.30. The stern cone angle is 0.22–0.48 m. The angle is 7° to 20°. The AUV structure is as follows: Figure 2 As shown.
[0078] Generate using the optimal Latin hypercube sampling method in the geometric parameter space A set of high-fidelity geometric samples, in which the number of dimensions Therefore, the number of high-fidelity geometric samples is 50. The high-fidelity geometric sample group is represented as follows:
[0079]
[0080] For 50 sets of high-fidelity geometric samples, high-fidelity CFD numerical calculations were carried out under oblique navigation, rotary arm operation, and different rudder angle deflection conditions to identify the positional hydrodynamic coefficients. , , , Rotational hydrodynamic coefficient , , , and rudder coefficient , , , Therefore, the high-fidelity hydrodynamic response vector corresponding to each set of high-fidelity geometric samples can be obtained:
[0081]
[0082] Furthermore, a high-fidelity hydrodynamic sample library will be constructed:
[0083]
[0084] All hydrodynamic data in this high-fidelity hydrodynamic sample library are derived from high-fidelity CFD numerical calculations, and therefore can serve as a highly reliable sample basis for subsequent joint design space expansion.
[0085] S2: Generate several sets of system-level initial samples within the joint design space. The joint design variables include geometric parameters, control parameters, and path guidance parameters.
[0086] There are a total of 13 joint design variables, including the 5 geometric parameters mentioned above, 6 control parameters, and 2 path guidance parameters. The control parameters are: heading proportional gain... Heading integral gain Heading differential gain Pitch ratio gain Pitch integral gain and pitch differential gain The path guidance parameters are the horizontal forward look-ahead distance and the horizontal forward look-ahead distance, respectively. and vertical forward viewing distance The value range is set to: heading proportional gain. and pitch ratio gain All are 0.4–0.8, heading integral gain Pitch integral gain All are 0 to 0.2, heading differential gain and pitch differential gain All are 5-9; Horizontal forward sight distance and vertical forward viewing distance All range from 40 to 120 meters.
[0087] To subsequently construct a system-level Kriging proxy model, it is necessary to obtain training samples with relatively uniform coverage within the joint design space. This embodiment employs the optimal Latin hypercube sampling method to generate training samples within the joint design space. Group system-level initial samples, where the number of dimensions Therefore, the initial number of system-level samples is 130.
[0088] No. The initial samples at the group system level are denoted as:
[0089]
[0090] in, For geometric parameter subvectors; For control parameter subvectors; This is a sub-vector of path guidance parameters.
[0091]
[0092]
[0093]
[0094] Since the geometric parameters in the above system-level initial samples have not all been calculated using high-fidelity CFD numerical methods, the corresponding high-fidelity hydrodynamic response vectors cannot be obtained directly. Further expansion using a high-fidelity sample migration strategy is required.
[0095] S3: Based on the nearest neighbor migration strategy of normalized Euclidean distance, the geometric parameters in the initial system-level samples are mapped to the nearest neighbor high-fidelity geometric samples, and the corresponding high-fidelity hydrodynamic response vectors are inherited to obtain the mapped system samples; all mapped system samples are input into the multidisciplinary coupled simulation model to obtain the path tracking error index and the relative energy consumption index of the servo motor, and to construct the system-level training sample set.
[0096] For the Group system-level initial samples and calculate their geometric parameter subvectors. With high-fidelity hydrodynamic sample library The Middle Group of high-fidelity geometric samples Normalized Euclidean distance:
[0097]
[0098] in, and These are the upper and lower bound vectors of the geometric parameter space, respectively. This normalization process can reduce the impact of differences in the dimensions of different variables on the distance calculation results.
[0099] Based on the nearest neighbor principle, determine the sub-vectors with geometric parameters. Nearest Neighbor High-Fidelity Geometric Sample Number:
[0100]
[0101] Then, the first Geometric parameter subvectors in the initial samples of the group system Using nearest-neighbor high-fidelity geometric samples Replace and inherit. The corresponding high-fidelity hydrodynamic response vector Thus, the mapped system sample is obtained:
[0102]
[0103] When all Once the initial system-level samples are mapped, the high-fidelity hydrodynamic information in the geometric parameter space can be effectively extended to the 13-dimensional joint design space without adding new high-fidelity CFD samples, thus balancing the uniformity of the joint space sample distribution and the sample construction cost.
[0104] like Figure 3 As shown, the multidisciplinary coupled simulation model includes a parametric modeling module, a hydrodynamic calculation module, a motion module, a control module, and a path guidance module. These modules are coupled and communicate with each other through parameters and state variables. Specifically, the parametric modeling module generates the AUV's shape based on geometric parameters; the hydrodynamic calculation module calls high-fidelity hydrodynamic response vectors; and the path guidance module employs a three-dimensional adaptive line-of-sight guidance method, calculating the desired heading angle based on the current position and a preset path. and desired pitch angle The control module uses a PID control law to output rudder and elevator control commands based on guidance commands and actual attitude deviations. The motion module calculates the state response based on the dynamic equations and kinematic equations, and uses the fourth-order Runge-Kutta method for time-domain integral propulsion.
[0105] For each mapped system sample The above multidisciplinary coupled simulation model is used to perform a complete path tracking numerical calculation to obtain the corresponding system-level target response:
[0106]
[0107] in, Indicates the path tracking error index. This indicates the relative energy consumption of the servo motor.
[0108] The system-level training sample set is:
[0109]
[0110] S4: Based on the system-level training sample set, establish a system-level Kriging proxy model and train the model for the path tracking error target and the servo relative energy consumption target, respectively.
[0111] The Kriging surrogate model represents the unknown response as the sum of the global trend term and the random bias term, i.e.:
[0112]
[0113] in, This is a global trend item. Zero-mean random term;
[0114] For any sample point to be predicted Its Kriging prediction value is expressed as:
[0115]
[0116] in, This is a global trend item. For the regression basis function vector, These are estimates of the regression coefficients. This is the correlation vector between the sample point to be predicted and the training sample; For the training sample correlation matrix; To train the response vector; This is the regression matrix;
[0117] Based on this, path tracking error proxy models were established respectively. Relative energy consumption proxy model of servo motor This enables a rapid predictive mapping from 13-dimensional joint design variables to bi-objective responses, allowing for quick invocation in subsequent multi-objective non-dominated searches.
[0118] S5: The NSGA-II algorithm is used to perform multi-objective optimization search in the joint design space to obtain the predicted Pareto optimal solution set; during the optimization process, the Kriging surrogate model is used to quickly predict the target value.
[0119] The multi-objective optimization model is as follows:
[0120]
[0121]
[0122]
[0123] in, For joint design variables; The vector of state variables of the system; The derivative of the state variable with respect to time; It is a time variable; and These are the lower and upper bounds of the variable, respectively. This represents a multidisciplinary coupled residual relationship;
[0124] In this embodiment, the population size of the NSGA-II algorithm is set to 100, and the maximum number of iterations is set to 100. During the optimization process, the objective function value of each candidate individual is no longer calculated by directly calling a high-fidelity CFD or a complete multidisciplinary time-domain simulation model, but is quickly predicted by the Kriging surrogate model, thereby significantly reducing the computational cost of a single optimization iteration.
[0125] After fast non-dominated sorting, crowding distance calculation, and iterative evolution, the predicted Pareto optimal solution set is obtained. This solution set reflects the trade-off between path tracking accuracy and relative servo power consumption of the AUV.
[0126] Path tracking error is defined as:
[0127]
[0128] in, Let the objective function be the path tracking error. To simulate the total number of discrete steps, For the first The spatial error between the actual position of the AUV and the reference path at each moment;
[0129] The relative energy consumption of a servo motor is defined as:
[0130]
[0131] in, The objective function for servo motor energy consumption; Total energy consumption; The start time; End time; The rudder angle, For elevator angle, and These are the angular velocities of the corresponding control surfaces; It is a time variable.
[0132] S6: A frontier credibility enhancement strategy based on the coupling index of hypervolume contribution and prediction uncertainty to select key points from the Pareto optimal solution set.
[0133] Since the Kriging surrogate model may still have prediction biases in local regions of the Pareto front, this embodiment further enhances the credibility assessment of the predicted Pareto front by identifying key points in the Pareto optimal solution set, and then performs high-fidelity CFD verification on the key points.
[0134] Let the predicted Pareto optimal solution set be:
[0135]
[0136] in, Indicates the number of Pareto solutions;
[0137] First, the Kriging surrogate model provides the predicted standard deviation of each Pareto solution on both objectives. and Based on this, a comprehensive uncertainty index is constructed:
[0138]
[0139] Secondly, select a reference point. ,in:
[0140]
[0141] in, For reference point In the The components of each target (here) =1,2); The scaling factor is the reference point. The predicted Pareto optimal solution set; Pareto solution In the Predicted values on each objective function;
[0142] Then, calculate the first... The contribution of each Pareto solution to the hypervolume of the global front:
[0143]
[0144] in, Indicates the excess volume value. Indicates the first The solution set obtained by removing Pareto solutions from the predicted Pareto optimal solution set;
[0145] Based on this, the normalized hypervolume contribution and the normalized comprehensive uncertainty index are weighted and coupled to obtain the key point scoring function:
[0146]
[0147] in, This represents the normalized hypervolume contribution. This represents the normalized overall uncertainty index; weighting coefficients. The value ranges from 0 to 1;
[0148] Based on the key point scoring function All Pareto solutions are sorted, and the five Pareto solutions with the highest scores are selected as key points and included in the key point set. Meanwhile, to ensure the reliability of the extreme solutions at both ends of the Pareto front, the solutions with the minimum relative servo power consumption and the solutions with the minimum path tracking error are also included in the key point set.
[0149] S7: Perform high-fidelity CFD verification on each key point, perform dynamic point supplementation and Kriging proxy model update based on the key point verification error, and repeat steps S5 to S7 until the termination condition is met, and output the final Pareto optimal solution set.
[0150] For each key point, its geometric parameters are re-extracted, and new high-fidelity CFD numerical calculations are performed to obtain the true position hydrodynamic coefficients, rotational hydrodynamic coefficients, and rudder coefficients corresponding to that key point. Then, its control parameters, path guidance parameters, and the true hydrodynamic coefficients along with the rudder coefficients are input into a multidisciplinary coupled simulation model to obtain the true target values. .
[0151] Next, the predicted values from the Kriging surrogate model are calculated. Compared with the actual target value The relative error between them:
[0152]
[0153] When the relative error of a keypoint on any target exceeds a preset error limit, the corresponding keypoint is identified as an inaccurate point and added to the system-level training sample set for retraining the Kriging surrogate model. Then, the Pareto front prediction is re-solved and new keypoints are selected. Figure 4 This paper presents a cutting-edge credibility enhancement strategy based on a coupled index of hypervolume contribution and prediction uncertainty.
[0154] When the relative error of the key points on all targets remains below the preset error limit in a certain round or several consecutive rounds, or when the preset high-fidelity CFD calculation budget limit is reached, the sequence optimization process is terminated, and the final Pareto optimal solution set is output.
[0155] In this embodiment, the entire sequence optimization underwent six rounds of keypoint verification. In each round, five keypoints were selected for high-fidelity CFD verification, resulting in a total of 30 high-fidelity verification points. Sixteen keypoints were added to the system-level training sample set and used to update the Kriging surrogate model because their relative errors exceeded a preset error limit. After the sixth round of keypoint verification, the relative errors of all keypoints met the accuracy requirements, indicating that the system-level Kriging surrogate model had high predictive reliability in the Pareto front key region, and the optimization process reached convergence. Finally, 35 Pareto optimal solutions were obtained, reflecting the typical conflict between the root mean square error of path tracking and the relative energy consumption of the servo motor in AUVs; that is, as the path error gradually decreases, the relative energy consumption of the servo motor shows a significant increasing trend. The optimization results are as follows: Figure 5 As shown. Figure 5 This indicates that the final Pareto optimal solution forms a relatively continuous descent front in the target space, suggesting that the servo motor's relative energy consumption... There is a significant conflict between this and the root mean square error (RMSE) of path tracking. With... As the value increases, the overall RMSE tends to decrease, meaning that improving path tracking accuracy usually requires higher servo motor movement costs.
[0156] The correlation results show a Pearson correlation coefficient of -0.875 and a Spearman correlation coefficient of -0.989, indicating a strong correlation between the two objectives, and this relationship exhibits significant monotonicity. The scatter points in the graph are mainly concentrated in the low-to-medium energy consumption region, suggesting that this region offers many compromise solutions and represents the primary effective range for optimization. Meanwhile, the red trend curve indicates that in the low-energy consumption phase, appropriately increasing the servo motor's energy consumption can significantly reduce path error; however, as energy consumption continues to increase, the rate of decrease in RMSE gradually diminishes, indicating that the improvement in system performance begins to plateau, and the energy cost required to further reduce error increases significantly.
[0157] therefore, Figure 5 This study clearly reveals the trade-off between accuracy and energy consumption in the AUV path tracking problem, and also demonstrates that the proposed optimization method can effectively identify Pareto solutions with different performance preferences, providing a basis for subsequent engineering decisions.
Claims
1. An AUV multidisciplinary sequential optimization method based on high fidelity sample migration and frontiers credibility enhancement, characterized in that, include: S1: Several sets of high-fidelity geometric samples are generated by sampling in the geometric parameter space. High-fidelity CFD numerical calculations are performed on each set of high-fidelity geometric samples to determine the corresponding high-fidelity hydrodynamic response vector and construct a high-fidelity hydrodynamic sample library. The high-fidelity hydrodynamic response vector includes position hydrodynamic coefficient, rotation hydrodynamic coefficient and rudder coefficient. S2: Generate several sets of system-level initial samples within the joint design space. The joint design variables include geometric parameters, control parameters, and path guidance parameters. S3: Based on the nearest neighbor migration strategy of normalized Euclidean distance, the geometric parameters in the initial system-level samples are mapped to the nearest neighbor high-fidelity geometric samples, and the corresponding high-fidelity hydrodynamic response vectors are inherited to obtain the mapped system samples; all mapped system samples are input into the multidisciplinary coupled simulation model to obtain the path tracking error index and the relative energy consumption index of the servo motor, and to construct the system-level training sample set. S4: Based on the system-level training sample set, establish a system-level Kriging proxy model and train the model for the path tracking error target and the servo relative energy consumption target respectively; S5: The NSGA-II algorithm is used to perform multi-objective optimization search in the joint design space to obtain the predicted Pareto optimal solution set; during the optimization process, the Kriging surrogate model is used to quickly predict the target value; S6: A frontier credibility enhancement strategy based on the coupling index of hypervolume contribution and prediction uncertainty, which selects key points from the Pareto optimal solution set; S7: Perform high-fidelity CFD verification on each key point, perform dynamic point supplementation and Kriging proxy model update based on the key point verification error, and repeat steps S5 to S7 until the termination condition is met, and output the final Pareto optimal solution set.
2. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier credibility enhancement as described in claim 1, characterized in that, In step S1, the first set of high-fidelity geometry samples wherein is the rudder chord length; is the rudder span length; is the rudder relative thickness ratio; is the rudder longitudinal position; is the stern post half angle; is the number of high-fidelity geometry samples High fidelity hydrodynamic sample library wherein is the high fidelity hydrodynamic response vector corresponding to the high fidelity geometric sample of the group.
3. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and enhanced frontier credibility as described in claim 2, characterized in that, In step S2, the first Group system-level initial samples ,in For geometric parameter subvectors; For control parameter subvectors; This is a sub-vector of path guidance parameters; This represents the initial number of sample groups at the system level.
4. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and enhanced frontier credibility as described in claim 3, characterized in that, In step S3, for the first Group system-level initial samples and calculate their geometric parameter subvectors. With high-fidelity hydrodynamic sample library The Middle Group of high-fidelity geometric samples Normalized Euclidean distance: in, and These are the upper and lower bound vectors of the geometric parameter space, respectively; Based on the nearest neighbor principle, determine the sub-vectors with geometric parameters. Nearest Neighbor High-Fidelity Geometric Sample Number: The first geometric parameter sub-vectors in the group system-level initial samples with nearest neighbor high-fidelity geometric samples are replaced and inherited corresponding high-fidelity hydrodynamic response vectors , so as to obtain the mapped system samples: All mapped system samples are collected Input the multi-disciplinary coupled simulation model to obtain the system-level training sample set: wherein the system-level target response , denotes a path tracking error indicator, denotes a relative energy consumption indicator of the steering mechanism.
5. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier credibility enhancement as described in claim 1, characterized in that, In step S3, the multidisciplinary coupled simulation model includes a parametric modeling module, a hydrodynamic calculation module, a motion module, a control module, and a path guidance module, wherein the parametric modeling module generates the shape of the AUV based on geometric parameters; The hydrodynamic calculation module calls high-fidelity hydrodynamic response vectors; the path guidance module adopts a three-dimensional adaptive line-of-sight guidance method, calculating the desired heading angle based on the current position and the preset path. and desired pitch angle The control module uses a PID control law to output rudder and elevator control commands based on guidance commands and actual attitude deviations. The motion module calculates the state response based on the dynamic equations and kinematic equations, and uses the fourth-order Runge-Kutta method for time-domain integral propulsion.
6. The AUV multidisciplinary sequential optimization method based on high fidelity sample migration and frontiers credibility enhancement according to claim 1, characterized in that, In step S4, the Kriging surrogate model represents the unknown response as the sum of the global trend term and the random bias term: in, This is a global trend item. A zero-mean random term; For any sample point to be predicted whose Kriging predictor is expressed as: in, This is a global trend item. For the regression basis function vector, These are estimates of the regression coefficients. This is the correlation vector between the sample point to be predicted and the training sample; For the training sample correlation matrix; To train the response vector; This is the regression matrix; Accordingly, a path tracking error agent model and a relative energy consumption agent model of the steering engine are established respectively.
7. The AUV multidisciplinary sequential optimization method based on high fidelity sample migration and frontiers credibility enhancement according to claim 6, characterized in that, In step S5, the multi-objective optimization model is as follows: in, For joint design variables; The vector of state variables of the system; The derivative of the state variable with respect to time; It is a time variable; and These are the lower and upper bounds of the variable, respectively. This represents a multidisciplinary coupled residual relationship; Path tracking error is defined as: in, Let the objective function be the path tracking error. To simulate the total number of discrete steps, For the first The spatial error between the actual position of the AUV and the reference path at each moment; The relative energy consumption of a servo motor is defined as: in, The objective function for servo motor energy consumption; Total energy consumption; The start time; End time; The rudder angle, For elevator angle, and These are the angular velocities of the corresponding control surfaces; It is a time variable.
8. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier credibility enhancement according to claim 7, characterized in that, In step S6, let the predicted Pareto optimal solution set be... ,in Indicates the number of Pareto solutions; First, the Kriging surrogate model provides the predicted standard deviation of each Pareto solution on both objectives. and Based on this, a comprehensive uncertainty index is constructed: Secondly, select a reference point. ,in: in, For reference point In the The weight of each goal =1,2; The scaling factor is the reference point. The predicted Pareto optimal solution set; Pareto solution In the Predicted values on each objective function; Then, calculate the first... The contribution of each Pareto solution to the hypervolume of the global front: in, Indicates the excess volume value. Indicates the first The solution set obtained by removing Pareto solutions from the predicted Pareto optimal solution set; Based on this, the normalized hypervolume contribution and the normalized comprehensive uncertainty index are weighted and coupled to obtain the key point scoring function: in, This represents the normalized hypervolume contribution. This represents the normalized overall uncertainty index; weighting coefficients. The value ranges from 0 to 1; Based on the key point scoring function Sort all Pareto solutions and select the K Pareto solutions with the highest scores as key points to include in the key point set.
9. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier credibility enhancement as described in claim 8, characterized in that, In step S6, the minimum solution for relative energy consumption of the servo motor and the minimum solution for path tracking error are also included in the key point set.
10. The AUV multidisciplinary sequence optimization method based on high-fidelity sample transfer and frontier credibility enhancement according to claim 1, characterized in that, In step S7, for each key point, high-fidelity CFD numerical calculations are re-executed, and multidisciplinary coupled simulations are carried out in conjunction with control parameters and path guidance parameters to obtain the true target value. ; Next, the predicted values from the Kriging surrogate model are calculated. Compared with the actual target value The relative error between them: When the error of a keypoint on any target exceeds the preset error limit, the corresponding keypoint is added to the system-level training sample set for retraining the Kriging surrogate model. When the relative error of the keypoint on all targets remains below the preset error limit in a certain round or several consecutive rounds, or when the preset high-fidelity CFD computation budget limit is reached, the sequence optimization process is terminated.