An underwater vehicle-oriented hydrodynamic performance prediction method

Abstract

The application provides an underwater vehicle-oriented water dynamic performance prediction method, which comprises the following steps: firstly, obtaining an underwater vehicle model example and determining a target physical quantity; then, sampling model parameters of an SST model, performing a CFD simulation operation on the example based on the model parameter samples, and obtaining sample set data according to the model parameter samples and the simulation results; then, constructing a proxy model based on the sample set data and calculating Sobol sensitivity indexes of each model parameter; then, calibrating the SST model parameters by using a Bayesian inference method to obtain parameter calibration values; finally, substituting the parameter calibration values into the SST model and using the calibrated SST model to predict the target physical quantity. The method can significantly improve the prediction accuracy of the water dynamic performance of the turbulence model in the field of underwater vehicle CFD, has good generalization, and can be used for water dynamic performance prediction of underwater vehicles with different configurations and working conditions.

Description

Technical Field

[0001] This invention relates to the field of computational fluid dynamics, and more particularly to a method for predicting the hydrodynamic performance of underwater vehicles. Background Technology

[0002] In recent years, with the continuous growth in demand for deep-sea resource development and marine scientific research, the research and development of manned deep-sea submersible equipment and intelligent unmanned underwater vehicles has become an important development direction in the field of shipbuilding and marine engineering, and their hydrodynamic design has also received significant attention from the engineering community. To enable underwater vehicles to achieve hydrodynamic performance such as low drag, good maneuverability, and stability, and to meet more stringent maneuverability requirements, the design requirements for the hydrodynamic performance of underwater vehicles are constantly changing, while also placing higher demands on the performance of their research tools.

[0003] With the development of Computational Fluid Dynamics (CFD) and the advancement of computer technology, CFD has become an indispensable tool for studying the hydrodynamic characteristics of underwater vehicles. In the long-term development, research, and application of CFD, the importance of turbulence models has increasingly attracted researchers' attention. The Shear Stress Transport (SST) model, as a widely used two-equation turbulence model, combines the advantages of the k-ε and k-ω models, possesses broad applicability, and exhibits high accuracy and computational efficiency in predicting boundary layers and separated flows. It is currently one of the most widely used turbulence models in the engineering field.

[0004] However, with the increasing complexity of fluid mechanics problems, the traditional SST method has encountered new challenges in predicting eddy viscosity in turbulence models, mainly including:

[0005] First, the SST model is highly complex and cannot accurately quantify the impact of different factors on the results in complex fluid mechanics problems.

[0006] Secondly, the SST model introduces a large number of structured parameters through a series of assumptions and simplifications during its construction. These assumptions and simplifications are usually proposed for specific flow conditions. Therefore, when the SST model is applied to other types of flow, the model's prediction accuracy will be significantly affected. Summary of the Invention

[0007] To address the aforementioned problems and improve the simulation accuracy of the hydrodynamic characteristics of underwater vehicles, this invention provides a method for predicting the hydrodynamic performance of underwater vehicles, comprising the following steps:

[0008] S1. Determine the underwater vehicle model case used for the calibration of the shear stress transport SST model, obtain the hydrodynamic performance experimental results of the case, and determine the target physical quantity to be predicted.

[0009] S2. Sample the model parameters of the SST model within a pre-selected uncertainty interval to obtain a model parameter sample set;

[0010] S3. Based on the model parameter samples in the model parameter sample set, perform CFD simulation on the example using the SST model to obtain the simulation results of the target physical quantity; summarize the model parameter samples and the corresponding simulation results to obtain sample set data;

[0011] S4. Construct a proxy model based on the sample set data;

[0012] S5. Calculate the Sobol sensitivity index for each model parameter based on the surrogate model;

[0013] S6. Construct a likelihood function based on the hydrodynamic performance experimental results, surrogate model, and sensitivity index; determine the prior distribution based on the uncertainty interval; construct a Bayesian model; sample from the posterior distribution of the Bayesian model to obtain posterior samples; after sampling, obtain the posterior distribution based on the posterior samples; and obtain the parameter calibration values ​​of the model parameters based on the posterior distribution.

[0014] S7. Substitute the parameter calibration value into the SST model to obtain the calibrated SST model; use the calibrated SST model to predict the target physical quantity.

[0015] In some embodiments, after determining the underwater vehicle model case, the method further includes: determining the computational domain and boundary conditions of the case, and performing mesh generation and mesh independence analysis on the underwater vehicle model to obtain a mesh model that meets the mesh independence requirements for CFD simulation calculation.

[0016] In some embodiments, the sampling of model parameters of the shear stress transport SST model within a pre-selected uncertainty interval is accomplished by any one of the Latin hypercube method, Monte Carlo sampling method, Sobol sequence sampling method, or orthogonal experimental method.

[0017] In some embodiments, the construction of the proxy model based on the sample set data is accomplished using any one of the following methods: non-intrusive chaotic multinomial method, response surface methodology, kriging method, or artificial neural network method.

[0018] In some embodiments, after constructing a proxy model based on the sample set data, the method further includes: calculating the relative error of the proxy model, and determining whether the proxy model meets the requirements based on the relative error of the proxy model; the relative error of the proxy model is the relative error between the target physical quantity calculated by the proxy model and the target physical quantity in the sample set data.

[0019] In some embodiments, after calculating the Sobol sensitivity index for each model parameter, the method further includes: selecting key model parameters based on the sensitivity index;

[0020] The construction of the likelihood function based on hydrodynamic performance experimental results, surrogate model, and sensitivity index specifically includes assigning high weights to the key model parameters in the likelihood function.

[0021] In some embodiments, the sampling from the posterior distribution of the Bayesian model is performed using any one of the Markov chain Monte Carlo method, Hamiltonian Monte Carlo method, or importance sampling method.

[0022] In some embodiments, obtaining the parameter calibration value of the model parameters based on the posterior distribution specifically includes: setting the parameter value with the highest probability in the posterior probability distribution as the parameter calibration value.

[0023] In some embodiments, the target physical quantity is the wall friction coefficient.

[0024] This invention provides a method for predicting the hydrodynamic performance of underwater vehicles. Based on an underwater vehicle model example, the method performs uncertainty analysis on the SST model parameters and quantifies the impact of different structured parameters on the model prediction results using a parameter sensitivity index, thereby identifying the key parameters with the greatest influence on the prediction results. Subsequently, a Bayesian algorithm is used to calibrate the key parameters of the SST model, and the calibrated SST model is used to predict the hydrodynamic performance of the underwater vehicle. This significantly improves the prediction accuracy of turbulence models in the field of underwater vehicle CFD and has good generalization ability, enabling it to be used for hydrodynamic performance prediction of underwater vehicles with different configurations and operating conditions. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This invention provides a flowchart of a hydrodynamic performance prediction method.

[0027] Figure 2 The simulation results (solid line) and experimental data (triangle points) of the standard SST model for the wall friction coefficient are shown.

[0028] Figure 3 The simulation results (solid line) and experimental data (triangle points) of the standard SST model for pressure coefficient are shown.

[0029] Figure 4 The relative errors of the surrogate model at each observation point in this embodiment of the invention are shown.

[0030] Figure 5 The posterior distribution of the key model parameter a1 in an embodiment of the present invention is shown;

[0031] Figure 6 The following figures illustrate the predicted results of the wall friction coefficient by the embodiments of the present invention, the standard SST model, and the experimental values ​​of the wall friction coefficient. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be described below with reference to the accompanying drawings.

[0033] To improve the accuracy of hydrodynamic performance prediction, this invention provides a method for predicting the hydrodynamic performance of underwater vehicles. The flowchart of the method is as follows: Figure 1 As shown, it includes the following steps:

[0034] S1. Determine the underwater vehicle model case for the calibration of the shear stress transport SST model, obtain the hydrodynamic performance experimental results of the case, and determine the target physical quantity to be predicted.

[0035] The determination of underwater vehicle model examples specifically includes: obtaining the configuration and operating conditions of the underwater vehicle to be predicted, and determining underwater vehicle model examples based on the configuration and operating conditions of the underwater vehicle to be predicted. Specifically, from the underwater vehicle model example library, the example whose configuration and operating conditions are most similar to the underwater vehicle to be predicted is selected as the example for SST model calibration.

[0036] The underwater vehicle model case study includes the geometry of the underwater vehicle model, the operating conditions of the underwater vehicle, and the corresponding hydrodynamic performance test results. The above information can be obtained from the underwater vehicle model case study database.

[0037] After selecting an underwater vehicle model case, the method further includes: determining the computational domain and boundary conditions of the case, performing mesh generation and mesh independence analysis on the underwater vehicle model in the case, selecting a mesh with appropriate density, and obtaining a mesh model that meets the mesh independence requirements.

[0038] Mesh independence analysis aims to determine whether the impact of mesh resolution (number of meshes / density) on simulation results is negligible, thus ensuring that the simulation results reflect real physical phenomena rather than human error caused by the mesh. In mesh independence analysis, a key physical quantity is first identified as the monitoring target. This key physical quantity can be the target physical quantity to be predicted or other outputs from the CFD simulation (such as drag, wall pressure coefficient, etc.). Then, under the same boundary conditions and algorithm, the underwater vehicle model is simulated using meshes of different densities to obtain the key physical quantity output values ​​for each set of meshes. Finally, the mesh model is selected based on the key physical quantity output values ​​of each set of meshes. If, as the mesh density increases, the change in the key physical quantity output values ​​slows down and the difference between adjacent density meshes is less than an acceptable error (e.g., 2%), then mesh independence is considered achieved. In this case, a mesh that meets the accuracy requirements and has a reasonable computational cost can be selected as the final mesh model.

[0039] The target physical quantities (Quantities of Interests, QoIs) to be predicted are selected according to the actual hydrodynamic performance prediction requirements, and can be wall friction coefficient, pressure coefficient, etc.

[0040] The above describes the specific details of this step. Below is a specific implementation example.

[0041] A suboff bare boat model under the condition of 5.144 m / s was selected as a case study for underwater vehicle model calibration.

[0042] The Suboff bare hull model was a model specifically designed by the U.S. Defense Advanced Research Projects Agency (DARPA) to establish a CFD analysis software verification database. The U.S. Taylor Shipbuilding Pool used this hull type as a standard model to conduct systematic hydrodynamic tests and flow field measurements, and provided a large amount of hydrodynamic performance and flow field data, including speed, pressure, frictional resistance, Reynolds stress, and drag.

[0043] Retrieve the experimental results of the model geometry and hydrodynamic performance of the suboff bare boat model from the database.

[0044] Based on the geometry of the suboff bare boat model, meshes of different densities were constructed, and mesh independence analysis was performed based on the drag calculation results. The mesh independence analysis results are shown in Table 1.

[0045] Table 1 Results of Mesh Independence Analysis

[0046]

[0047] As shown in Table 1, considering both computational cost and accuracy, a medium-density grid model is selected for subsequent CFD simulations.

[0048] Next, the target physical quantities in this embodiment are determined by comparing the CFD simulation results and experimental data of the standard SST model. Considering the core requirements of underwater vehicle hydrodynamic design, the wall friction coefficient and pressure coefficient, which significantly affect drag, are analyzed as candidate physical quantities. The CFD simulation results and experimental values ​​of the wall friction coefficient and pressure coefficient are shown below. Figure 2 , Figure 3 As shown. Comparison Figure 2 , Figure 3 It is evident that the CFD simulation results of the wall friction coefficient still have a large error compared with the experimental values. Therefore, it is used as the target physical quantity for subsequent analysis.

[0049] This embodiment uses the wall friction coefficient as the target physical quantity. In the hydrodynamic design of underwater vehicles, frictional drag is a major component of the total drag. The wall friction coefficient is a dimensionless parameter defining local wall shear stress and is closely related to the frictional drag value. The distribution and magnitude of the wall friction coefficient are one of the core physical quantities for evaluating and optimizing the drag performance of underwater vehicles, and are crucial to the drag characteristics and maneuverability of underwater vehicles.

[0050] The above describes how to determine the underwater vehicle model calculation examples and target physical quantities, and provides a specific implementation example. The following section, based on the above implementation example, will further explain how to optimize and calibrate the SST model parameters based on the calculation examples.

[0051] S2. Sample the model parameters of the SST model within a pre-selected uncertainty interval to obtain a model parameter sample set.

[0052] When selecting an uncertainty interval, it is necessary to ensure that the uncertainty interval meets the following requirements as much as possible: when using parameters within the uncertainty interval to perform CFD simulation calculations on the underwater vehicle model example, it can ensure that the CFD calculation converges, and the simulation results of the target physical quantities can cover most of the hydrodynamic performance experimental results in the example. Repeated selection can be used to ensure that the finally selected uncertainty interval meets the above requirements.

[0053] In this embodiment, the uncertainty interval boundary is taken as ±40% of the parameter reference value. The reference values ​​and uncertainty intervals of each parameter are shown in Table 2.

[0054] Table 2. Baseline values ​​and uncertainty ranges of SST model parameters

[0055]

[0056] After determining the parameter uncertainty interval, the model parameters of the SST model are sampled from the uncertainty interval to obtain the model parameter sample set. The sampling method can be any one of the Latin hypercube method, Monte Carlo sampling method, Sobol sequence sampling method, or orthogonal experimental method.

[0057] The embodiments in this specification use the Latin hypercube method in Isight to sample model parameters.

[0058] Before sampling, it is necessary to determine the number of samples required in the model parameter sample set. The required number of samples can be determined by the number of parameters in the SST model, the oversampling rate, and the expansion order (used to balance accuracy and cost).

[0059] In the embodiments described in this specification, the model parameter sample set includes a training set and a validation set, wherein the required number of samples for the training set is [number missing]. , where n p The oversampling rate is typically set to 2; P is the parameter expansion order, calculated by combining the number of parameters n and the expansion order p. The expansion order p is typically 1-3. In this embodiment, the expansion order p is 2. The SST model has n=9 structural parameters, therefore the number of training set samples N t The training set consists of 110 groups, and the number of samples in the validation set is 30% of the number of samples in the training set, with 33 groups in total.

[0060] Within the aforementioned uncertainty range, the model parameters are sampled to obtain a model parameter sample set.

[0061] S3. Based on the model parameter samples in the model parameter sample set, use the SST model to perform CFD simulation on the example to obtain the simulation results of the target physical quantity; summarize the model parameter samples and the corresponding simulation results to obtain the sample set data.

[0062] Using model parameter sample points from the model parameter sample set as model parameters for the SST model, CFD calculations are performed on the simulation example to obtain simulation results for the target physical quantity. Before each simulation calculation, a script program records the previous simulation results and reads the new model parameter sample point data. The script program can automatically modify the model parameters and extract the simulation results of the target physical quantity at the flow field measurement points, and process and summarize them. After all simulation calculations are completed, the model parameter samples and corresponding simulation results are summarized to obtain sample set data. The sample set data is obtained from the model parameter sample set through CDF simulation calculations and also includes a training set and a validation set.

[0063] The above describes how to obtain the sample set data. The following section describes how to build a proxy model based on the sample set data.

[0064] S4. Construct a proxy model based on the sample set data.

[0065] A surrogate model is a data-driven, simplified mathematical model used to replace computationally expensive real simulation models (such as CFD simulation models) for calculations. Surrogate models can significantly accelerate the uncertainty quantification process while maintaining acceptable accuracy. Essentially, they construct a mapping relationship between input parameters and output responses using a finite number of real simulation samples (such as the sample set data in this embodiment), achieving a "space-for-time" tradeoff.

[0066] Proxy models can be constructed using methods such as Non-Intrusive PolynomialChaos (NIPC), response surface methodology, Kriging, and artificial neural networks. Among these, NIPC focuses solely on the relationship between the output and input, avoiding modifications to the solver's internal structure, and has been widely used in Proxy model construction. The embodiments in this specification use the NIPC method to construct a Proxy model.

[0067] Suppose a dataset obtained by a CFD solver. ,in Let λ represent the model parameters and Y be the target physical quantity. Here, both λ and Y are considered random variables, and their polynomial expansion is as follows:

[0068] (1)

[0069] (2)

[0070] Where: i, j are fluid coordinates; N is the number of samples; D is the total number of model parameters, and d refers to the d-th model parameter; c k , λ dk Let K be the coefficients of the polynomial to be solved; K, K d This represents the number of expanded items; ζ is a basis function; ζ is a random variable used to describe the inherent uncertainty of the model parameters.

[0071] Substitute the sample set data as dataset B into the above polynomial, first use the training sample set in the sample set data to solve the polynomial coefficients, and then use the validation sample set to validate the surrogate model to obtain the trained surrogate model.

[0072] After constructing the surrogate model, the method further includes: calculating the relative error of the surrogate model at each observation point of the turbulence model, and judging whether the surrogate model meets the requirements based on the relative error. The relative error of the surrogate model is: the relative error between the target physical quantity calculated by the surrogate model and the target physical quantity in the sample set data, and its calculation formula is shown in Equation (3).

[0073] (3)

[0074] Where Y sur Y is the target physical quantity calculated by the surrogate model. val The simulation results are for the target physical quantity in the sample set data.

[0075] The relative error calculation results of the surrogate model for each observation point in the embodiments of this specification are as follows: Figure 4 As shown, by Figure 4 It can be seen that the relative error of the surrogate model in this embodiment is generally less than 5%. Therefore, the established surrogate model can meet the needs of uncertainty analysis for this problem.

[0076] S5. Calculate the Sobol sensitivity index of each model parameter based on the surrogate model, and select key model parameters according to the sensitivity index.

[0077] The Sobol sensitivity index quantifies the proportion of the uncertainty of a random input parameter to the uncertainty of the output response. The larger the Sobol sensitivity index, the more significant the influence of that parameter on the output result. The Sobol sensitivity index of the d-th parameter can be obtained from Equation 4.

[0078] (4)

[0079] Among them, S d Y is the first-order Sobol exponent of the d-th parameter; Y is the output response of the surrogate model (i.e., the target physical quantity output by the surrogate model); X d Let X be the d-th input parameter (random variable); d To divide X d All other input parameters besides E; x~d (Y|X d ) for a fixed X d Under the condition that Y is related to all other parameters X~ d The conditional expectation of S. d The molecules are fixed X d The variance of the conditional expectation of Y reflects the variance of X. d Independent contribution to output Y; S d The denominator is the total variance of Y.

[0080] After obtaining the sensitivity indices of each parameter, key model parameters are selected based on these indices. When selecting key model parameters, parameters with sensitivity indices higher than a certain threshold can be chosen; alternatively, all model parameters can be sorted from highest to lowest sensitivity index, and the parameters with the highest sensitivity indices can be selected sequentially as key model parameters.

[0081] The sensitivity coefficients of different parameters were calculated according to equation (4), and the average Sobol exponents of each parameter at various positions in the main region of the example were obtained. The results are shown in Table 3. Among them, the Sobol exponent of parameter a1 is significantly the largest, followed by κ, which means that they are the most important for predicting the surface friction coefficient. According to Table 3, the three parameters with the highest sensitivity exponents were selected as key model parameters, and they were calibrated to optimize the SST model and improve the prediction accuracy of the SST model for the target physical quantity (surface friction coefficient).

[0082] Table 3. Average Sensitivity Index of Parameters

[0083]

[0084] S6. Use Bayesian inference to calibrate the parameters of the SST model.

[0085] S61. Construct a likelihood function based on hydrodynamic performance experimental results, surrogate model and sensitivity index, determine the prior distribution based on uncertainty interval, and construct a Bayesian model.

[0086] Bayes' theorem transforms the parameter estimation problem into a probabilistic inference problem by calculating the posterior probability distribution of the parameters, providing a comprehensive description of the uncertainty of the model parameters. According to Bayes' theorem, the posterior distribution of the model parameters... It can be written as:

[0087] (5)

[0088] in, Let be a multidimensional original model parameter matrix, and D be a set of observation data. For the prior distribution of the model parameters, Let be the likelihood function. It is a posterior distribution.

[0089] The prior distribution reflects our knowledge of the parameters before observing the dataset, the likelihood function describes the probability of observing the dataset given the current parameter combination, and the posterior distribution describes the conditional probability distribution of the parameters after observing the dataset. According to Bayes' theorem, the posterior distribution of the parameters can be calculated from the prior distribution and the likelihood function, and the posterior distribution is proportional to the product of the prior distribution and the likelihood function.

[0090] Based on the fundamental principles of Bayesian inference, the prior distribution and likelihood function of the model parameters are determined, a Bayesian model is constructed, and the posterior distribution of the model parameters is obtained. The key model parameters are then calibrated based on the posterior distribution.

[0091] The prior distribution reflects the knowledge of the parameters before the observation dataset is obtained, and can be determined based on the baseline values ​​of the parameters in the SST model or the uncertainty range of the parameters. When sufficient calibration data is available, a uniform distribution can be chosen as the prior distribution for closed-loop parameters.

[0092] The likelihood function describes the probability of observing a target physical quantity (such as the experimentally measured wall friction coefficient) in a sample set under a given combination of parameters (prior distribution). It can be constructed based on the experimental results of the hydrodynamic performance of the example (i.e., observation data), surrogate models, and parameter sensitivity indices.

[0093] Specifically, the likelihood function measures the likelihood of a given set of model parameters. In this case, the degree of agreement between the model's predicted values ​​and the experimentally observed data. Assume set D = {(x (i) , y (i) )} L i=1 Given a set of observation data, x (i) For the observation location, the scalar y (i) Let L represent the total number of data points, and w(•) represent the unknown true function. We can obtain:

[0094] (6)

[0095] in, This represents the surrogate model, where Λ is the original model parameter matrix. For model error, This is for measurement error.

[0096] Given any set of parameters Λ, y (i) They are also mutually independent Gaussian random variables, that is:

[0097] (7)

[0098] Where N represents a normal distribution, Let represent the mean and variance of parameter Λ, respectively. For model uncertainty variance, To observe the uncertainty variance, combining equation (5), the likelihood function is expressed as:

[0099] (8)

[0100] in The experimental observation value of the target physical quantity comes from observation data; The model prediction value of the target physical quantity can be obtained through a surrogate model.

[0101] Sensitivity indices can provide a priority basis for constructing likelihood functions. In step S5, key model parameters (such as a1 and κ) that have the greatest impact on the target physical quantity have been identified based on the sensitivity indices. When constructing the likelihood function, these key model parameters need to be assigned higher weights, making the likelihood function more focused on the core variables affecting the output, thereby improving the efficiency and accuracy of subsequent calibration. Furthermore, the weights of other non-key parameters can be determined based on the sensitivity index values ​​of the parameters.

[0102] The above describes how to determine the prior distribution and likelihood function to construct a Bayesian model. The following describes how to obtain parameter calibration values ​​based on the Bayesian model.

[0103] S62. After constructing a Bayesian model based on the prior distribution and the likelihood function, sample from the posterior distribution of the Bayesian model to obtain posterior samples.

[0104] In some embodiments, the sampling from the posterior distribution of the Bayesian model can be accomplished using any one of the following sampling methods: Markov Chain Monte Carlo (MCMC), Hamiltonian Monte Carlo, or importance sampling.

[0105] This embodiment employs the Markov Chain Monte Carlo (MCMC) method to sample the posterior distribution. The MCMC method is a numerical computation method that approximates complex probability distributions (such as the Bayesian posterior distribution) through random sampling. Its core mechanism is to construct a Markov chain that walks in the parameter space. Through an intelligent random walk mechanism (such as the Metropolis-Hastings algorithm), it efficiently explores and converges to the target distribution (i.e., the posterior distribution) in the parameter space. By collecting all the parameter points visited after chain convergence, an approximate sample (i.e., the posterior sample) of the target distribution can be obtained. Based on this sample, the sample characteristics of the target distribution (such as mean, variance, etc.) can be obtained.

[0106] This embodiment uses the MCMC method to sample the posterior distribution. The MCMC sampling employs the Metropolis-Hastings algorithm, and the sampling process includes: Let the current sample point be x. t Obtain new sample points from the proposed distribution. Calculate the acceptance probability The sample is calibrated based on the acceptance probability: if the acceptance probability is greater than a preset value, the sample is accepted and transferred. Otherwise, the transfer will be refused. Among them, the probability of acceptance With the current sample point x t and new sample points It is related to the ratio of the posterior probability density, if the current sample point x tIf the posterior probability of the current sample point x is higher than the posterior probability of the new sample point, then the acceptance probability is 1 (it will definitely be accepted). According to Bayes' theorem, the current sample point x... t and new sample points The posterior probability density is proportional to the product of the prior probability and the likelihood probability of the sample point, and can be obtained from the prior distribution and the likelihood function. The MCMC method tends to walk through high-probability intervals during the sampling process, so that most sampling points are located in this interval, while retaining some suboptimal solutions.

[0107] When sampling the posterior distribution, a large number of iterative calculations are required to achieve statistical convergence of the Markov chain. Each iteration requires solving the likelihood function, and the model predictions are an indispensable key part of the likelihood function. Therefore, each iteration requires the simulation of the entire model, which is often uneconomical in terms of computational resources. To address this, the embodiments in this specification construct a surrogate model. The surrogate model is used to replace the SST model when solving the likelihood function, which can effectively extract samples from the posterior distribution and reduce computational costs.

[0108] To ensure that the posterior samples come from the convergence region, each calibration generates posterior samples while excluding the initial 20% of the samples in the Markov chain. To reduce the correlation between samples, only one sample out of every five is selected for retention, resulting in the final effective posterior samples.

[0109] S63. After sampling is completed, the posterior distribution is obtained based on the posterior samples, and the parameter calibration values ​​of the model parameters are obtained based on the posterior distribution.

[0110] In some embodiments, obtaining the parameter calibration value of the model parameters based on the posterior distribution specifically includes: setting the parameter value with the highest probability in the posterior probability distribution as the parameter calibration value.

[0111] The above describes how to use Bayesian inference to calibrate the parameters of the SST model and obtain the parameter calibration values. First, a likelihood function is constructed based on the hydrodynamic performance experimental results, the surrogate model, and the sensitivity index. The prior distribution is determined based on the uncertainty interval, and a Bayesian model is constructed. Next, samples are taken from the posterior distribution of the Bayesian model to obtain posterior samples. Finally, the posterior distribution is obtained based on the posterior samples, and the parameter calibration values ​​of the model parameters are obtained based on the posterior distribution.

[0112] In one embodiment, step S6 specifically includes: calibrating the SST model parameters using Bayesian inference methods based on experimental data of the surface friction coefficient from the suboff model. For this purpose, a surrogate model of the MCMC sampling parameters was reconstructed. After collecting 50,000 samples, the posterior distribution of the parameters was obtained using the PYMC3 probabilistic programming library. The posterior distribution of the key model parameter a1 is shown below. Figure 5As shown, the value with the highest probability in the posterior probability distribution is set as the parameter calibration value, and the parameter calibration value of the key parameter a1 is 0.34. Similarly, the parameter calibration values ​​of other parameters can be obtained as shown in Table 4.

[0113] Table 4 Parameter Calibration Values

[0114]

[0115] S7. Substitute the parameter calibration value into the SST model to obtain the calibrated SST model; use the calibrated SST model to predict the target physical quantity.

[0116] Substitute the parameter calibration values ​​into the model and recalculate the wall friction coefficient. The result is as follows: Figure 6 As shown, the red dashed line represents the prediction curve after substituting the calibrated parameters, the black solid line represents the prediction curve of the standard SST model, and the triangles represent the experimental values ​​of the wall friction coefficient. It is evident that the calibrated SST model significantly improves its ability to predict the surface friction coefficient of the example. This improvement outperforms the standard SST model, and the prediction results are very close to the experimental data. This indicates that using the Bayesian method for model parameter uncertainty quantification analysis can effectively improve the model's prediction accuracy.

[0117] The calibrated SST model was applied to resistance calculations for other working conditions and similar models. The resistance calculation results are shown in Table 5. It can be seen that the calibrated SST model also performs well for other similar working conditions and models, demonstrating good generalization and effectiveness.

[0118] Table 5 Comparison of Resistance Values

[0119]

[0120] As can be seen from the above, compared with the prior art, the present invention has the following beneficial effects:

[0121] 1. A dedicated SST model parameter calibration system was derived using Bayesian inference to address the low-speed, low-turbulence flow field characteristics of underwater vehicles. Substituting the calibration values ​​into the model significantly improved the prediction accuracy of the wall friction coefficient, a core indicator for underwater vehicles, and the deviation between the calibrated model's drag calculation results and experimental data was greatly reduced.

[0122] 2. By accurately identifying the key model parameters that have the most significant impact on the target physical quantity through the Sobol sensitivity index, and assigning higher weights to these key model parameters during the Bayesian inference process, Bayesian directional calibration is carried out around the key model parameters, eliminating the invalid calibration of parameters with weak influence on the underwater flow field, and realizing the accurate prediction of the core indicators related to the drag of underwater vehicles by the SST model.

[0123] 3. The hydrodynamic performance prediction method provided by this invention has good generalization in all working scenarios of underwater vehicles and can be used to predict the hydrodynamic performance of underwater vehicles with different speeds and different configurations, such as bare boats and fully-fledged boats.

[0124] 4. The hydrodynamic performance prediction method provided by this invention can accurately quantify the influence of different factors on the hydrodynamic performance prediction results, and can accurately identify the key model parameters that have the most significant impact on the target physical quantity, thus providing support for the theoretical analysis of hydrodynamic performance.

[0125] In the description of the embodiments of this application, the words "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the words "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a specific manner.

[0126] In the description of the embodiments of this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, B existing alone, and A and B existing simultaneously. Furthermore, unless otherwise stated, the term "multiple" means two or more.

[0127] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and their variations all mean "including but not limited to," unless otherwise specifically emphasized.

[0128] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the hydrodynamic performance of underwater vehicles, characterized in that, Includes the following steps: A calculation case of an underwater vehicle model is determined for calibration of the shear stress transport SST model. The hydrodynamic performance experimental results of the calculation case are obtained, and the target physical quantity to be predicted is determined. The model parameters of the SST model are sampled within a pre-selected uncertainty interval to obtain a model parameter sample set; Based on the model parameter samples in the model parameter sample set, the SST model is used to perform CFD simulation on the example to obtain the simulation results of the target physical quantity; The model parameter samples and corresponding simulation results are summarized to obtain the sample set data; Construct an agent model based on the sample set data; The Sobol sensitivity index of each model parameter is calculated based on the surrogate model, and key model parameters are selected based on the sensitivity index. Based on the hydrodynamic performance experimental results, surrogate model and sensitivity index, a likelihood function is constructed, and the prior distribution is determined according to the uncertainty interval to obtain the Bayesian model; samples are taken from the posterior distribution of the Bayesian model to obtain posterior samples; after sampling, the posterior distribution is obtained based on the posterior samples, and the parameter calibration values ​​of the model parameters are obtained based on the posterior distribution. The construction of the likelihood function based on hydrodynamic performance experimental results, surrogate model, and sensitivity index specifically includes assigning high weights to the key model parameters in the likelihood function; Substitute the parameter calibration values ​​into the SST model to obtain the calibrated SST model; use the calibrated SST model to predict the target physical quantity.

2. The method according to claim 1, characterized in that, After determining the underwater vehicle model case, the method further includes: determining the computational domain and boundary conditions of the case, and performing mesh generation and mesh independence analysis on the underwater vehicle model to obtain a mesh model that meets the mesh independence requirements for CFD simulation calculation.

3. The method according to claim 1, characterized in that, The model parameters of the shear stress transport SST model are sampled within a pre-selected uncertainty interval, which can be accomplished by any of the following methods: Latin hypercube method, Monte Carlo sampling method, Sobol sequence sampling method, or orthogonal experimental method.

4. The method according to claim 1, characterized in that, The proxy model is constructed based on the sample set data, using any one of the following methods: non-intrusive chaotic multinomial method, response surface methodology, kriging method, or artificial neural network method.

5. The method according to claim 1, characterized in that, After constructing the surrogate model based on the sample set data, the method further includes: calculating the relative error of the surrogate model, and judging whether the surrogate model meets the requirements based on the relative error of the surrogate model; the relative error of the surrogate model is the relative error between the target physical quantity calculated by the surrogate model and the target physical quantity in the sample set data.

6. The method according to claim 1, characterized in that, Selecting key model parameters based on the sensitivity index specifically includes: selecting parameters with a sensitivity index higher than a certain threshold as key model parameters; or sorting all model parameters from highest to lowest sensitivity index, and selecting the parameters with the highest sensitivity index as key model parameters based on the sorting results.

7. The method according to claim 1, characterized in that, The sampling from the posterior distribution of the Bayesian model is accomplished using any one of the following methods: Markov chain Monte Carlo method, Hamiltonian Monte Carlo method, or importance sampling method.

8. The method according to claim 1, characterized in that, The step of obtaining the parameter calibration value of the model parameters based on the posterior distribution specifically includes: setting the parameter value with the highest probability in the posterior probability distribution as the parameter calibration value.

9. The method according to claim 1, characterized in that, The target physical quantity is the wall friction coefficient.

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