Turbulence model intelligent recommendation method based on clustering weight optimization and random forest

Abstract

The application discloses a turbulent flow model intelligent recommendation method based on clustering weight optimization and random forest, relates to the field of combination of fluid mechanics and artificial intelligence, and comprises the following steps: determining input working conditions and a candidate turbulent flow model set, and constructing an evaluation index system; constructing a fuzzy comprehensive evaluation model and initializing the index weight of the fuzzy comprehensive evaluation model; constructing a feature space, adopting K-means clustering to establish a physical consistency constraint, and establishing a loss function containing an entropy regularization term through a same-cluster similarity consistency principle to iteratively optimize the index weight and obtain adaptive weight; calculating the comprehensive score of each candidate turbulent flow model according to the adaptive weight, and taking the turbulent flow model with the highest score as an optimal model label; and training a random forest multi-classifier by using a training data set to obtain a turbulent flow model intelligent recommendation model. The application solves the problems that the existing method is highly dependent on experience, the evaluation weight is subjective and difficult to adapt to cross-working conditions, and there is a lack of an interpretable recommendation mechanism.

Description

Technical Field

[0001] This invention relates to the field of fluid mechanics and artificial intelligence, specifically to an intelligent recommendation method for turbulence models based on clustering weight optimization and random forest. Background Technology

[0002] Computational Fluid Dynamics (CFD) is widely used in aerodynamic analysis and design in aerospace engineering. In engineering practice, the RANS method has become the mainstream industrial CFD due to its balance between computational cost and predictive capability; however, its prediction accuracy is highly dependent on the selection of the turbulence closure model and its correction terms. In existing CFD solution processes, the selection of turbulence models largely relies on engineering experience, lacking unified, quantifiable, and interpretable evaluation criteria. Under complex conditions such as transonic shock waves and boundary layer disturbances, and separated flows, different models show significant differences in performance regarding key aerodynamic parameters such as shock wave location, separation range, and pressure recovery. Incorrect selection will lead to result deviations or increased computational costs. Furthermore, single indicators (such as considering only error or only time consumption) are insufficient to meet the comprehensive trade-off between accuracy, efficiency, and stability in engineering; multi-indicator evaluations based on expert weighting suffer from strong subjectivity and difficulty in adapting to changing operating conditions.

[0003] In summary, to address the technical challenges of turbulence model selection relying on experience, difficulty in objectively determining weights, and insufficient consistency across operating conditions, it is necessary to propose an intelligent recommendation method for turbulence models that integrates multi-index quantitative evaluation, adaptive weight optimization, and machine learning prediction. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides an intelligent recommendation method for turbulence models based on clustering weight optimization and random forests. This method solves the problems of existing methods, such as turbulence model selection being highly dependent on experience, subjective evaluation weights that are difficult to adapt across operating conditions, and a lack of interpretable recommendation mechanisms.

[0005] To achieve the aforementioned objectives, the present invention employs the following technical solution: an intelligent recommendation method for turbulence models based on clustering weight optimization and random forests, comprising the following steps:

[0006] S1: Determine the input conditions and candidate turbulence model set, and construct an evaluation index system for computational fluid dynamics solutions;

[0007] S2: Based on the evaluation index system, construct a fuzzy comprehensive evaluation model and initialize its index weights;

[0008] S3: The flow condition parameters and the identities of the candidate turbulence models are used to form a feature space. K-means clustering is used to establish physical consistency constraints. A loss function containing entropy regularization is established through the principle of similarity within the same cluster. The index weights are iteratively optimized to obtain adaptive weights.

[0009] S4: Calculate the comprehensive score of each candidate turbulence model based on adaptive weights, and take the turbulence model with the highest score as the optimal model label under the corresponding working condition;

[0010] S5: Using the working condition description parameters as input features and the optimal model label as output label, construct a training dataset and use the training dataset to train a random forest multi-classifier to obtain an intelligent recommendation model for turbulence models.

[0011] S6: Input the operating condition to be predicted into the turbulence model intelligently recommends a model and outputs the recommended turbulence model scheme.

[0012] Furthermore, the evaluation index system includes:

[0013] Primary indicators include computational accuracy and computational efficiency;

[0014] Secondary metrics include root mean square error, average relative error, convergence time, and number of iterations.

[0015] Furthermore, the fuzzy comprehensive evaluation model is as follows:

[0016]

[0017] in, The overall score for the candidate turbulence models. Mach number, For the angle of attack, For the first One candidate model, As the weight of the primary indicator, As the weight of the second-level accuracy indicator, As the weight of the secondary efficiency indicator, This is a measure of the root mean square error after normalization or homing. This refers to the normalized or homogenized measure of the average relative error. To shorten the convergence time, This represents the number of iteration steps.

[0018] Furthermore, the loss function containing the entropy regularization term is:

[0019]

[0020]

[0021] in, For loss function, For the indicator weight vector, The comprehensive score output by the fuzzy comprehensive evaluation model. The total number of samples, For the first The feature space of each sample For the weight vector, For the first The cluster center of the cluster to which each sample belongs. The regularization coefficient is... For the weight entropy function, Weight vector The One portion, It is the natural logarithm function. This represents the number of weight parameters.

[0022] Furthermore, an iterative strategy of inner and outer loops is adopted to iteratively optimize the indicator weights. The outer loop is used to update the clustering results, while the inner loop is used to optimize the indicator weights with the clustering results fixed.

[0023] Furthermore, the step of training a random forest multi-classifier using the training dataset to obtain a turbulence model intelligent recommendation model specifically involves:

[0024] The random forest multi-classifier uses Bootstrap sampling with replacement to generate multiple training subsets. Each training subset is used to train a decision tree. The node splitting criterion is either information entropy or the Gini coefficient. Finally, the prediction results are output through a majority voting mechanism.

[0025]

[0026] in, This is the final recommendation output of the random forest classifier. It is the mode function. This is the vector describing the working conditions to be recommended. For the first The prediction of the number of trees, The number of trees.

[0027] Furthermore, the formula for calculating the information entropy is:

[0028]

[0029] in, For information entropy, For the sample dataset, For the first Class sample proportion Number of categories;

[0030] Information gain is:

[0031]

[0032] in, For information gain function, Features used for partitioning, For feature taking No. The sample subset corresponding to each value. Features The number of possible values.

[0033] The beneficial effects of this invention are as follows: This invention transforms the selection of turbulence models from a traditional experience-driven approach to a data-driven quantitative evaluation and learning prediction mechanism, thereby significantly reducing subjectivity and uncertainty; by introducing a weight optimization strategy of "clustering consistency + entropy regularization", it achieves adaptive adjustment of index weights for different flow conditions and physical consistency constraints, avoiding weight extremes and improving recommendation stability; by adopting a random forest multi-classification recommendation model, the system still has good generalization ability when facing nonlinear and multi-peak flow conditions, and supports outputting Top-3 alternative solutions to enhance engineering applicability; in the verification of typical airfoil transonic conditions, it can achieve high recommendation accuracy and good geometric generalization performance, providing a feasible decision support module for intelligent CFD software. Attached Figure Description

[0034] Figure 1 This is a flowchart of an intelligent recommendation method based on clustering weight optimization and random forest in a turbulence model.

[0035] Figure 2 This is a schematic diagram showing the cluster distribution of samples under different operating conditions in the feature space.

[0036] Figure 3 This diagram illustrates the training and evaluation of a random forest recommendation model.

[0037] Figure 4 This is a schematic diagram illustrating the multiple solution recommendations for the engineering extension module.

[0038] Figure 5 This is a schematic diagram comparing the pressure coefficient distribution under typical working conditions.

[0039] Figure 6 This is a comparison of flow field prediction results under high angle of attack transonic conditions.

[0040] Figure 7 This is a statistical diagram illustrating the coverage of the Top-3 recommendation results in a variable geometry test case. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0042] like Figure 1 As shown, an intelligent recommendation method based on clustering weight optimization and random forest in a turbulence model includes the following steps:

[0043] S1: Determine the input conditions and candidate turbulence model set, and construct an evaluation index system for computational fluid dynamics solutions;

[0044] Let the vector describing the working conditions to be recommended be:

[0045]

[0046] Where Ma is the Mach number and AoA is the angle of attack; the candidate turbulence model set is:

[0047]

[0048] Thirteen candidate schemes are included, consisting of SA series modification items and SST series modification items (e.g., SA: BCM, COMPRESSIBILITY, EDWARDS, NEGATIVE, NONE, QCR2000, ROTATION, WITHFT2; SST: KATO_LAUNDER, SUSTAINING, V1994m, V2003m, VORTICITY).

[0049] S2: Based on the evaluation index system, construct a fuzzy comprehensive evaluation model and initialize its index weights;

[0050] The evaluation index system includes:

[0051] Primary indicators include computational accuracy and computational efficiency;

[0052] Secondary metrics include root mean square error (RMSE), mean relative error (MRE), convergence time, and number of iterations.

[0053] RMSE and MRE are the surface pressure coefficients calculated by the turbulence model to be evaluated. Pressure coefficient at sampling points corresponding to the reference high-precision solution This was obtained through point-by-point comparison calculations. Let the airfoil surface have a total of... If there are discrete sampling points, then:

[0054] The root mean square error (RMSE) is expressed as:

[0055]

[0056] The mean relative error (MRE) is expressed as:

[0057]

[0058] in, Indicates the candidate turbulence model in the th The pressure coefficient predicted at each sampling point This represents the pressure coefficient at the sampling point corresponding to the reference solution (e.g., high-precision fine-grid calculation results or experimental data).

[0059] Based on the above definitions, RMSE is used to reflect the overall error magnitude and is more sensitive to large local deviations; MRE is used to measure the relative error proportion and can reflect the degree of overall distribution deviation. Combining the two can comprehensively characterize the computational accuracy of turbulence models in pressure distribution prediction.

[0060] Based on the AHP (Automatic High Power) hierarchical structure, and within the fuzzy comprehensive evaluation framework, mapping each secondary index to a unified evaluation space, we obtain the evaluation results for each candidate turbulence model scheme under the operating conditions. The overall score is as follows.

[0061] The fuzzy comprehensive evaluation model is as follows:

[0062]

[0063] in, The overall score for the candidate turbulence models. Mach number, For the angle of attack, For the first One candidate model, Weights for primary indicators (accuracy and efficiency). The weights for the two precision indicators (RMSE and MRE) are used. The weights for the secondary efficiency indicators (convergence time and number of iterations) are determined by these factors. The measure is the root mean square error after normalization or homogenization (e.g., the interval is scaled to [0,1], and the score is guaranteed to be "the smaller the value, the better" or uniformly mapped to "the larger the value, the better"). This refers to the normalized or homogenized measure of the average relative error. To shorten the convergence time, This represents the number of iteration steps.

[0064] The weight vector is denoted as:

[0065]

[0066] For weight initialization, expert experience weights can be used as prior initial values, or they can be randomly initialized and then constrained and normalized.

[0067] S3: The flow condition parameters and the identities of the candidate turbulence models are used to form a feature space. K-means clustering is used to establish physical consistency constraints. A loss function containing entropy regularization is established through the principle of similarity within the same cluster. The index weights are iteratively optimized to obtain adaptive weights.

[0068] Constructing a three-dimensional feature space:

[0069]

[0070] in, Indicates working condition The "initial optimal model number" or "current optimal model number" is obtained based on the current scoring model.

[0071] K-means clustering was performed on the above samples. The number of clusters k can be traversed between 2 and 5. The silhouette coefficient was used to select the optimal number of clusters, thus forming the physical consistency constraint basis of "similar working conditions / similar model identities should show similar scores".

[0072] The loss function that includes the entropy regularization term is:

[0073]

[0074] Introducing an entropy regularization term suppresses weight "extremes" and improves stability:

[0075]

[0076] in, For loss function, For the indicator weight vector, The comprehensive score output by the fuzzy comprehensive evaluation model. The total number of samples, For the first The feature space of each sample For the weight vector, For the first The cluster center of the cluster to which each sample belongs. The regularization coefficient is... For the weight entropy function, Weight vector The One portion, It is the natural logarithm function. This represents the number of weight parameters.

[0077] The Nelder–Mead simplex method was used to... Derivativeless optimization is performed to accommodate the non-smooth / implicit mapping characteristics that may exist in the evaluation model.

[0078] An iterative strategy with inner and outer loops is used to iteratively optimize the index weights. The outer loop is used to update the clustering results (e.g., 10 times), while the inner loop is used to optimize the index weights with fixed clustering results (e.g., 5 weight optimizations within each cluster).

[0079] When the change in total loss is less than a threshold (e.g., 10) -8 When the maximum number of iterations is reached, stop iterating and output the final optimized weights.

[0080] S4: Calculate the comprehensive score of each candidate turbulence model based on adaptive weights, and take the turbulence model with the highest score as the optimal model label under the corresponding working condition;

[0081] After step S3 outputs the weights, for each working condition... The 13 candidate models were used to calculate a comprehensive score. The highest score is selected as the "optimal model label" for that working condition. .

[0082] S5: Using the working condition description parameters as input features and the optimal model label as output label, construct a training dataset and use the training dataset to train a random forest multi-classifier to obtain an intelligent recommendation model for turbulence models.

[0083] by Using the input features, the optimal model labels obtained in step S4 are used. To produce the output, construct a supervised learning training set:

[0084]

[0085] The random forest multi-classifier uses Bootstrap sampling with replacement to generate multiple training subsets. Each training subset is used to train a decision tree. The node splitting criterion is either information entropy or the Gini coefficient. Finally, the prediction results are output through a majority voting mechanism.

[0086]

[0087] in, This is the final recommendation output of the random forest classifier. It is the mode function. This is the vector describing the working conditions to be recommended. For the first The prediction of the number of trees, The number of trees.

[0088] The formula for calculating information entropy is:

[0089]

[0090] in, For information entropy, For the sample dataset, For the first Class sample proportion Number of categories;

[0091] Information gain is:

[0092]

[0093] in, For information gain function, Features used for partitioning, For feature taking No. The sample subset corresponding to each value. Features The number of possible values.

[0094] S6: Input the operating condition to be predicted into the turbulence model intelligently recommends a model and outputs the recommended turbulence model scheme.

[0095] In one embodiment of this invention, the typical transonic airfoil RAE2822 is selected as the research object. This airfoil exhibits significant shock-boundary layer interaction under transonic conditions and is therefore widely used for turbulence model verification. Two computational systems are established in the numerical simulation: one is a high-precision reference computational system used to obtain high-fidelity pressure distribution data; the other is an engineering computational system used to obtain the computational results of different turbulence models under an engineering grid. The engineering computational system can be implemented using a RANS solver, such as the SU2 solver. In some embodiments, the engineering grid size is approximately 2 × 10⁻⁶. 4 The mesh size is on the order of magnitude of 10, while the reference solution mesh size is approximately 10. 5 Order of magnitude. By comparing the engineering calculation results with the reference solution under the same flow conditions, the error and efficiency indices of each candidate turbulence model under different operating conditions can be obtained.

[0096] In terms of flow condition construction, this embodiment uses the free-flow Mach number Ma and angle of attack AoA as flow condition variables, and its input feature vector is expressed as:

[0097]

[0098] To ensure uniform sample distribution within the parameter space, 150 sets of flow condition samples were generated using Latin hypercube sampling within the range of Ma ∈ [0.30, 0.75] and AoA ∈ [-2°, 5°]. In some implementations, the Reynolds number is kept at a fixed value, for example, Re = 6.5 × 10⁻⁶. 6 Therefore, it is not used as an input feature for machine learning.

[0099] Regarding the candidate model set, this embodiment establishes a model library containing 13 turbulence model modification schemes, including various engineering modifications of the SA and SST models, such as SA-BCM, SA-EDWARDS, SA-QCR2000, SA-ROTATION, and SST-KATO-LAUNDER, SST-V1994m, and SST-VORTICITY. For each flow condition, all candidate models are run and the calculation results are recorded, including the airfoil surface pressure coefficient distribution. Calculate the convergence time With iteration steps .

[0100] Figure 2 The clustering distribution of samples under different operating conditions in the feature space is presented. It can be seen that samples in similar flow regions are divided into the same cluster, thus ensuring the physical consistency of the model recommendations. Figure 3 The classification results of the random forest model on the training data are presented.

[0101] In the engineering extension module, a multi-scheme extension module was developed, which can output the top three candidate solutions while predicting the optimal solution, providing a wider selection space for practical engineering decisions. This mechanism not only improves the robustness of the model, but also provides reliable alternatives when the optimal solution is limited, such as... Figure 4 The results of the multi-scheme predictions are shown.

[0102] To verify the consistency between the recommended results and the flow physics, this embodiment selects typical operating conditions for analysis. For example, in Under these conditions, the optimal model provided by the recommender system is SA-BCM. For example... Figure 5 As shown, (a) presents the comparison results of all schemes with the reference solution, and (b) presents the comparison results of the top three schemes with the reference solution. By comparing the pressure coefficient distribution obtained by this model with the reference solution, it can be found that it has high prediction accuracy in the leading-edge pressure gradient region and the mid-chord pressure plateau region, while some other models show significant deviations in the trailing-edge region. On the other hand, under high angle-of-attack transonic conditions, for example... A significant shock-induced separation phenomenon occurs in the flow field. In this case, the optimal model provided by the recommendation system is SST-VORTICITY, such as... Figure 6 As shown, (a) is the SST-VORTICITY prediction result and (b) is the reference solution. This model can accurately predict the shock wave location and pressure recovery process.

[0103] Furthermore, to verify the generalization ability of the method, this embodiment selects the NACA0012 airfoil as a test case that did not participate in the training. Maintaining the same flow parameter range as in the training phase, predictions were made for multiple test conditions, and the Top-3 coverage of the recommended results was statistically analyzed. The success rate is defined as:

[0104]

[0105] in, This indicates the number of models in the predicted Top-3 set that overlap with the actual Top-3 set. This indicates the number of test conditions. Statistical results are as follows: Figure 7 As shown, the left circle represents the predicted result, and the right circle represents the actual result. In the test sample, the average overlap rate between the predicted Top-3 solutions and the actual Top-3 solutions can reach more than 80%.

[0106] In summary, the verification results of the RAE2822 and NACA0012 airfoil examples demonstrate that the intelligent turbulence model recommendation method based on clustering weight optimization and random forest proposed in this invention can automatically select appropriate turbulence models under different flow conditions while maintaining high prediction accuracy and stability. It can provide an effective turbulence model selection decision module for intelligent CFD software.

[0107] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A turbulence model-based intelligent recommendation method based on clustering weight optimization and random forest, characterized in that, Includes the following steps: S1: Determine the input conditions and candidate turbulence model set, and construct an evaluation index system for computational fluid dynamics solutions; S2: Based on the evaluation index system, construct a fuzzy comprehensive evaluation model and initialize its index weights; S3: The flow condition parameters and the identities of the candidate turbulence models are used to form a feature space. K-means clustering is used to establish physical consistency constraints. A loss function containing entropy regularization is established through the principle of similarity within the same cluster. The index weights are iteratively optimized to obtain adaptive weights. S4: Calculate the comprehensive score of each candidate turbulence model based on adaptive weights, and take the turbulence model with the highest score as the optimal model label under the corresponding working condition; S5: Using the working condition description parameters as input features and the optimal model label as output label, construct a training dataset and use the training dataset to train a random forest multi-classifier to obtain an intelligent recommendation model for turbulence models. S6: Input the operating condition to be predicted into the turbulence model intelligently recommends a model and outputs the recommended turbulence model scheme.

2. The intelligent recommendation method for turbulence models based on clustering weight optimization and random forest as described in claim 1, characterized in that, The evaluation index system includes: Primary indicators include computational accuracy and computational efficiency; Secondary metrics include root mean square error, average relative error, convergence time, and number of iterations.

3. The intelligent recommendation method for turbulence models based on clustering weight optimization and random forest as described in claim 2, characterized in that, The fuzzy comprehensive evaluation model is as follows: ； in, The overall score for the candidate turbulence models. Mach number, For the angle of attack, For the first One candidate model, As the weight of the primary indicator, As the weight of the second-level accuracy indicator, As the weight of the secondary efficiency indicator, This is a measure of the root mean square error after normalization or homing. This refers to the normalized or homogenized measure of the average relative error. To shorten the convergence time, This represents the number of iteration steps.

4. The intelligent recommendation method for turbulence models based on clustering weight optimization and random forest as described in claim 3, characterized in that, The loss function that includes the entropy regularization term is: ； ； in, For loss function, For the indicator weight vector, The comprehensive score output by the fuzzy comprehensive evaluation model. The total number of samples, For the first The feature space of each sample For the weight vector, For the first The cluster center of the cluster to which each sample belongs. The regularization coefficient is... For the weight entropy function, Weight vector The One portion, It is the natural logarithm function. This represents the number of weight parameters.

5. The intelligent recommendation method for turbulence models based on clustering weight optimization and random forest as described in claim 4, characterized in that, An iterative strategy with inner and outer loops is adopted to iteratively optimize the index weights. The outer loop is used to update the clustering results, while the inner loop is used to optimize the index weights with the clustering results fixed.

6. The intelligent recommendation method for turbulence models based on clustering weight optimization and random forest as described in claim 5, characterized in that, The process of training a random forest multi-classifier using the training dataset to obtain an intelligent recommendation model for turbulence is as follows: The random forest multi-classifier uses Bootstrap sampling with replacement to generate multiple training subsets. Each training subset is used to train a decision tree. The node splitting criterion is either information entropy or the Gini coefficient. Finally, the prediction results are output through a majority voting mechanism. ； in, This is the final recommendation output of the random forest classifier. It is the mode function. This is the vector describing the working conditions to be recommended. For the first The prediction of the number of trees, The number of trees.

7. The intelligent recommendation method for turbulence models based on clustering weight optimization and random forest as described in claim 6, characterized in that, The formula for calculating information entropy is: ； in, For information entropy, For the sample dataset, For the first Class sample proportion Number of categories; Information gain is: ； in, For information gain function, Features used for partitioning, For feature taking No. The sample subset corresponding to each value. Features The number of possible values.

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