A double-agent model optimization method for pipeline structure parameters of a wind force snow removing robot

Abstract

A kind of double-agent model optimization method of wind snow-removal robot pipeline structure parameter, specific steps are as follows: (1) according to the initial design of wind snow-removal robot pipeline, determine the design variable and value range of pipeline structure parameter;(2) establish high-dimensional data set;(3) establish low-dimensional data set;(4) select a proxy model to obtain high-dimensional proxy model A and low-dimensional proxy model B;(5) generate active learning candidate sample pool;(6) calculate the under-learning degree score of each candidate learning point;(7) establish active learning point set;(8) carry out CFD simulation to obtain updated data set, continue to train model A, when the prediction accuracy of model A, the prediction accuracy of model B and the inconsistency degree of model A model B prediction result all reach specified threshold, stop active learning.The present application provides an efficient, reliable and engineering applicable method for the optimization of complex pipeline parameters with multiple structural variables and multiple outlet flow responses.

Description

Technical Field

[0001] This invention relates to a method for optimizing the pipe structure parameters of a wind-powered snow removal robot, and more particularly to a dual-surrogate model optimization method for the pipe structure parameters of a wind-powered snow removal robot, belonging to the field of machine learning and engineering optimization technology. Background Technology

[0002] Wind-powered snow removal robots break up, project, and transport snow using high-speed airflow. The pipe structure directly affects the airflow velocity distribution, flow uniformity, and system energy consumption. During the pipe structure design process, computational fluid dynamics (CFD) numerical simulations are typically used to analyze the flow characteristics under different combinations of structural parameters. However, such simulations are computationally intensive and time-consuming, making it difficult to perform efficient optimization directly in a multi-parameter, high-dimensional design space.

[0003] To reduce computational costs, existing research typically introduces surrogate models to approximate CFD simulation results. However, when the dimensionality of pipe structure parameters is high and the simulation output includes high-dimensional responses such as multi-outlet velocity and pressure fields, surrogate models often require a large number of samples to ensure prediction accuracy, which is difficult to meet the requirements of limited computational resources in engineering applications. Some methods reduce the dimensionality of multi-outlet responses into a small number of features for modeling, but this can easily lead to the loss of local flow characteristics, affecting the accuracy of analyzing the spatial distribution characteristics of snow removal performance. Therefore, an optimization method is needed that can simultaneously preserve high-dimensional flow information and accurately model key performance indicators within a limited CFD computational budget, in order to improve the efficiency and reliability of optimizing pipe structure parameters for wind-powered snow removal robots. Summary of the Invention

[0004] To address the aforementioned problems in existing technologies, a dual-proxy model optimization method for the pipe structure parameters of a wind-powered snow removal robot is proposed. This method constructs a collaborative system of a high-dimensional proxy model and a low-dimensional proxy model, and introduces an active learning strategy driven by dual-model consistency for optimizing the pipe structure parameters of the wind-powered snow removal robot.

[0005] A dual-surrogate model optimization method for the pipe structure parameters of a wind-powered snow removal robot is proposed. The specific steps are as follows: (1) Based on the initial design of the wind-powered snow removal robot pipeline, determine the design variables and value range of the pipeline structural parameters. ,in, x i Indicates the first i One pipeline structure variable, m The number of pipeline structure variables. Design space for pipeline structure variables; (2) Generate containingN A set of 0 pipe structure parameters , , Running CFD simulations yields high-dimensional output. Y (i) , Y (i) = Y ( X (i) ), establish a high-dimensional dataset , ,in, Y (⋅) represents the simulation results obtained by CFD simulation of the pipeline structure parameters; (3) To Y (i) Dimensionality reduction process yields low-dimensional output y (i) , y (i) = R ( Y ( X (i) )) , establish a low-dimensional dataset , ,in, R (⋅) indicates the output compression mapping; (4) Select a surrogate model and utilize a high-dimensional dataset. A high-dimensional surrogate model A is obtained through training. , f H (⋅) represents the mapping function of the high-dimensional proxy model. To produce high-dimensional prediction outputs, utilize low-dimensional datasets. The low-dimensional surrogate model B is obtained through training. , f L (⋅) represents the mapping function of the low-dimensional proxy model. This is a low-dimensional prediction output; (5) In Internally generated active learning candidate sample pool , , ,in N p The number of candidate learning points, X (j) For the first candidate sample pool j Candidate learning points j =1- N p ; (6) For each candidate learning point X (j) Calculate underlearning scoreS (j) , S (j) The larger the size, the more worthwhile this point is to learn. ,in, U A ( X ) represents the uncertainty of the prediction result of surrogate model A. For the inconsistency of the A / B model, ε To prevent extremely small positive numbers with a denominator of zero; (7) In Selected rating S (j) The highest n candidate learning points are used to build an active learning point set. , Where argmax represents the design variable when the function reaches its maximum value. X The value of ; (8) Perform CFD simulation to obtain updated datasets , Utilize updated dataset Continue training model A. Stop active learning when the prediction accuracy of model A, the prediction accuracy of model B, and the inconsistency between the prediction results of model A and model B all reach a specified threshold.

[0006] Beneficial technical effects of the present invention: (1) While ensuring the integrity of the multi-outlet flow information of the wind-powered snow removal robot pipeline, the prediction accuracy of key performance indicators can be improved under limited simulations. (2) Use the uncertainty information of the high-dimensional model and the consistency information between the two proxy models to guide the addition of points of the active learning samples, reduce unnecessary CFD simulations, and improve optimization efficiency and computing resource utilization. (3) Provides an efficient, reliable and engineering-applicable method for optimizing complex pipeline parameters with multiple structural variables and multiple outlet flow responses. Attached Figure Description

[0007] Figure 1 This is a flowchart of a dual-proxy model optimization method for the pipeline structure parameters of a wind-powered snow removal robot according to the present invention; Figure 2 This is a schematic diagram of the pipe structure of the wind-powered snow removal robot of the present invention; Figure 3 This is a schematic diagram of the main view structure parameters of the pipeline of the wind-powered snow removal robot of the present invention; Figure 4 This is a schematic diagram of the structural parameters of the pipeline of the wind-powered snow removal robot of the present invention (left view). Detailed Implementation

[0008] Combined with appendix Figure 1-4 This invention describes the steps and specific operations of the present invention. Addressing the problem that the original dataset has a high output dimensionality, requiring a large dataset to ensure the accuracy of the surrogate model during training, while dimensionality-reduced surrogate models lose local flow feature information, this invention achieves efficient optimization of pipeline structure parameters by sampling pipeline structure variables, numerical simulation, performance index aggregation, and collaborative modeling with dual surrogate models, guided by a consistency-driven active learning strategy to update the sample set.

[0009] A dual-surrogate model optimization method for the pipe structure parameters of a wind-powered snow removal robot is proposed. The specific steps are as follows: (1) Based on the initial design of the wind-powered snow removal robot pipeline, determine the design variables and value range of the pipeline structural parameters. ,in, x i Indicates the first i One pipeline structure variable, m The number of pipeline structure variables. Design space for pipeline structure variables; (2) Generate containing N A set of 0 pipe structure parameters , , Running CFD simulations yields high-dimensional output. Y (i) , Y (i) = Y ( X (i) ), establish a high-dimensional dataset , ,in, Y (⋅) represents the simulation results obtained by CFD simulation of the pipeline structure parameters; (3) To Y (i) Dimensionality reduction process yields low-dimensional output y (i) , y (i) = R ( Y ( X (i) )) , establish a low-dimensional dataset , ,in, R (⋅) indicates the output compression mapping; (4) Select a surrogate model and utilize a high-dimensional dataset. A high-dimensional surrogate model A is obtained through training. ,f H (⋅) represents the mapping function of the high-dimensional proxy model. To produce high-dimensional prediction outputs, utilize low-dimensional datasets. The low-dimensional surrogate model B is obtained through training. , f L (⋅) represents the mapping function of the low-dimensional proxy model. This is a low-dimensional prediction output; (5) In Internally generated active learning candidate sample pool , , ,in N p The number of candidate learning points, X (j) For the first candidate sample pool j Candidate learning points j =1- N p ; (6) For each candidate learning point X (j) Calculate underlearning score S (j) , S (j) The larger the size, the more worthwhile this point is to learn. ,in, U A ( X ) represents the uncertainty of the prediction result of surrogate model A. For the inconsistency of the A / B model, ε To prevent extremely small positive numbers with a denominator of zero; (7) In Selected rating S (j) The highest n candidate learning points are used to build an active learning point set. , Where argmax represents the design variable when the function reaches its maximum value. X The value of ; (8) Perform CFD simulation to obtain updated datasets , Utilize updated dataset Continue training model A. Stop active learning when the prediction accuracy of model A, the prediction accuracy of model B, and the inconsistency between the prediction results of model A and model B all reach a specified threshold.

[0010] Specifically, the main steps of the dual-surrogate model optimization method for the pipeline structure parameters of a wind-powered snow removal robot according to the present invention are as follows: 1. Determine design variables and design space The wind-powered snow removal robot piping of this application includes an inlet pipe 1, a connecting pipe 2, and branch pipes 3. The inlet pipe 1 connects to the outlet of the wind-powered snow removal robot's blower. The connecting pipe 2 is closed at both ends and has rounded corners. The inlet pipe 1 is vertically installed in the middle of the connecting pipe 2. Five identical branch pipes 3 are evenly distributed on the connecting pipe 2. The inlet pipe 1 and the five branch pipes 3 are arranged on both sides of the connecting pipe 2. The branch pipes 3 are irregularly shaped pipes, including a first straight pipe 3-1, a first bend 3-2, a second straight pipe 3-3, a second bend 3-4, and a third straight pipe 3-5. The first straight pipe 3-1, the first bend 3-2, the second straight pipe 3-3, the second bend 3-4, and the third straight pipe 3-5 are connected sequentially. The first straight pipe 3-1 is vertically installed on the connecting pipe 2, and the axis of the first straight pipe 3-1 is parallel to that of the inlet pipe 1. The inlet pipe 1, connecting pipe 2 and branch pipe 3 are internally connected to form a wind-powered snow removal robot pipeline with the inlet pipe 1 as the inlet and the third straight pipe 3-5 of the five branch pipes 3 as the outlet.

[0011] A detailed parameter diagram of the wind-powered snow removal robot's pipeline is shown below. Figure 2 , 3 As shown, the pipe structure constants include the diameter of the inlet pipe 1 (150 mm, length 200 mm), the length of the connecting pipe 2 (1500 mm), the spacing of the five identical branch pipes 3 (300 mm), the length of the first straight pipe 3-1 (200 mm), the installation height of the second straight pipe 3-3 (300 mm), and the length of the third straight pipe 3-5 (200 mm).

[0012] The pipe structure variables of the wind-powered snow removal robot include the diameter D1 of the connecting pipe 2, the diameter D2 of the branch pipe 3, the radius R1 of the first bend 3-2 and the second bend 3-4, the fillet radius R2 at both ends of the connecting pipe 2, the bending angle θ1 of the first bend 3-2, and the bending angle θ2 of the second bend 3-4. By adjusting these structural variables, the airflow velocity distribution characteristics and pressure loss inside the pipe can be changed, thereby affecting snow removal performance and system energy consumption.

[0013] The pipe structure variables of the wind-powered snow removal robot are represented as vectors. X =[D1,D2,R1,R2,θ1,θ2] T By setting reasonable value ranges and constraints for each structural parameter, a structural variable design space is formed. The design space is used to ensure that the generated pipeline structure meets the actual engineering design requirements.

[0014] In this embodiment, in addition to limiting the range of values ​​for each variable parameter, the limitations of the pipeline's operating environment must also be met: (1) The installation height H of the piping system is subject to the maximum allowable installation height of the building, which is H. max Strict height restrictions: ; (2) In order to ensure that the high-speed airflow acts on the snow layer and achieves the best purging effect, all outlets must be strictly oriented downwards: θ2 < θ1; (3) The fillet radii at both ends of connecting pipe 2 should not be too large to prevent self-intersection: .

[0015] Based on the range of values ​​for pipeline structural variables and constraints, design the space. It can be represented as:

[0016] 2. Establish a high-dimensional dataset 2.1 Initial Sample Generation Determining structural variables X =[D1,D2,R1,R2,θ1,θ2] T and its design space Then, Latin Hypercube Sampling (LHS) was used to generate a set containing 60 sets of structural variables. , , Latin hypercube sampling is a typical space-filling sampling method. Its basic idea is to divide the value range of each design variable into 60 equal sub-intervals and extract a sample point in each sub-interval, so that the sample uniformly covers the entire design space in all dimensions, thereby improving the representativeness of the sample and reducing the number of simulations required to train the surrogate model under the condition of a limited number of samples.

[0017] This step is implemented using the NumPy, SciPy, and pandas libraries in Python. First, the LatinHypercube method in SciPy is used to create a hypercube in the unit hypercube space [0,1]. 6 The function generates a set of Latin hypercube sampling points, returning a 60×6 sample matrix where each row represents a set of normalized sampled values ​​for a structural variable, and each column corresponds to a structural variable dimension. Subsequently, the sampling point matrix is ​​converted into an array using `np.array` from the NumPy library, and a linear scaling mapping is performed on each design variable to map the sampled values ​​within a unit interval to the actual range of structural variable values. The mapping formula is as follows:

[0018] in: x m For the mapped first mEach structural variable value, m =1~6, u m The value is the sampled value per cubic meter. and These are the lower and upper limits of the structure variable, respectively.

[0019] Next, the 60 sampling points are further filtered based on geometric constraints. A constraint function is constructed, and NumPy's Boolean indexing is used to filter out sample points that do not meet the constraints. Then, Latin hypercube sampling is used again to complete the dataset, resulting in the final initial sample set. , .

[0020] Next, the 60 sets of structured variables were tabulated using DataFrame from the pandas library. The parameter values ​​of each sample were stored in columns, and a sample number field was added to facilitate subsequent batch calls for CFD simulations. The initial sample table was saved as a CSV file using the DataFrame's to_csv interface, which served as the input configuration file for the CFD simulation batch processing.

[0021] 2.2 Obtaining High-Dimensional Datasets After obtaining the initial sample set of structural variables, for each set of structural variables X (i) Run a CFD numerical simulation using the Fluent module in Ansys software. After each simulation, measure the velocity at the outlet section of the five branch pipes. V and pressure drop data Output the corresponding original high-dimensional output data to form a high-dimensional dataset. , .

[0022] 3. Establish a low-dimensional dataset In obtaining high-dimensional datasets Then, for each set of high-dimensional outputs Y (i) Dimensionality reduction is performed, and performance indicators are aggregated based on the physical meaning of the high-dimensional flow output to extract a low-dimensional output vector that can characterize the performance of wind-driven snow removal and the system's energy consumption level. y (i) , y (i) = R ( Y ( X (i) )),in, R (⋅) indicates output compression mapping.

[0023] This step is implemented using libraries such as NumPy and pandas in Python. The pandas library is used to read and process the raw high-dimensional data output from the CFD simulation, for each set of samples... X (i) From its corresponding high-dimensional output Y (i) The velocity information of multiple exit sections is extracted, and the extracted data is statistically calculated using array operation functions in the NumPy library.

[0024] The mean velocity of all outlet sections is calculated using the `np.mean` function in NumPy, thus obtaining the average flow velocity. The calculation formula is:

[0025] The coefficient of variation of the outlet velocity is calculated using the np.std and np.mean functions to obtain the velocity uniformity index. The calculation formula is:

[0026] in, , ε To prevent extremely small positive numbers with a denominator of zero.

[0027] The np.mean function in NumPy is used to calculate the pressure drop across all outlets. The average pressure drop is obtained by taking the mean value. The calculation formula is:

[0028] Through the above index calculation process, the high-dimensional output will be... Y (i) Mapped to a low-dimensional performance metric vector:

[0029] Where 𝑅(⋅) represents the compression mapping function from high-dimensional flow output to low-dimensional performance index.

[0030] Use the pandas library to store the structural variables corresponding to each group of samples. X (i) Its low-dimensional output y (i) Combine the data and store it in tabular form to construct a low-dimensional dataset: .

[0031] 4. Train to obtain high-dimensional and low-dimensional proxy models. The proxy model used in this invention is a neural network model. Neural networks have powerful nonlinear mapping capabilities and high-dimensional data processing capabilities, and can more flexibly capture the complex relationship between input parameters and overall flow characteristics, making them particularly suitable for high-dimensional, nonlinear, and strongly coupled output response modeling.

[0032] Of the two models, Model A aims to maintain the integrity of the flow field data through high-dimensional output, while Model B focuses on low-dimensional prediction of core performance indicators to ensure accuracy. The prediction results of Model B will serve as a calibration benchmark in the subsequent training process of Model A, guiding the active learning process of Model A. Therefore, in this step, we first train Model B until its accuracy reaches the target, and then train Model A.

[0033] 4.1 Training to obtain the low-dimensional surrogate model B Low-dimensional surrogate models are used to establish nonlinear mappings between structural variables and low-dimensional outputs. Their mathematical form can be expressed as:

[0034] in, f L (⋅) represents the neural network mapping function corresponding to the low-dimensional surrogate model, with structural variables as inputs. X (i) The output is the corresponding low-dimensional flow response prediction value. .

[0035] This step is implemented using Python libraries such as pandas, NumPy, scikit-learn, TensorFlow / Keras, and joblib. First, the sample data file is read using `pandas.read_excel`, and the `dropna` function is used to remove samples with missing values ​​in the input structural variable columns and low-dimensional output columns to ensure the integrity of the training data. Then, the structural variable columns and low-dimensional output columns are converted into NumPy floating-point arrays as model input and supervision output, respectively. The `train_test_split` function is used to randomly distribute 60 data sets: 70% for the training set, 15% for the validation set, and 15% for the test set. A fixed random seed ensures the repeatability of the training process. Considering the differences in units and numerical ranges between different structural variables and output indicators, `MinMaxScaler` is used to normalize the input and output before model training. Fitting is performed only on the training set, while the same mapping rule is applied to the validation set to avoid data leakage.

[0036] Subsequently, a custom neural network construction function `build_model_B` is called to build a low-dimensional surrogate model with an input layer dimension of 6. After passing through 3 hidden layers, the prediction results of 3 low-dimensional performance metrics are obtained. The ReLU non-linear activation function is introduced into the network hidden layers, combined with the Dropout mechanism to enhance the model's generalization ability. During the model compilation stage, mean squared error (MSE) is used as the regression loss function, and the Adam optimization algorithm is selected for parameter updates, set to 1×10⁻⁶. -3 Initial learning rate. During training, the model is iteratively updated multiple times using the `model.fit` function, with epochs set to 400 and batch size to 32. An `EarlyStopping` callback mechanism is introduced to monitor the validation set loss (`val_loss`), with a latency of 50. Training is automatically terminated and optimal weights restored when the validation error no longer decreases within 50 consecutive epochs to prevent overfitting. Combined with the `ReduceLROnPlateau` callback, the learning rate is adaptively reduced when the validation error plateaus, resulting in more refined model convergence. The `ModelCheckpoint` callback automatically saves the optimal model parameter file during training. After training, the final model `final_modelB.h5`, the input normalizer `scaler_X_B.pkl`, and the output normalizer `scaler_Y_B.pkl` are saved to specified directories to ensure consistent data mapping between the prediction and training phases.

[0037] The returned test set data is used to calculate the model's prediction accuracy metric and the coefficient of determination between the model's predictions and the actual output. R 2 The root mean square error (RMSE) and the root mean square error (RMSE) are used as indicators of model accuracy, and their calculation formulas are as follows: ,

[0038] in, y (i) For the first i The true output value of each validation sample. The corresponding model prediction value, This is the average value of the actual output of the validation set.

[0039] If the prediction accuracy does not meet the aforementioned threshold requirements, the model's predictive ability is improved by adjusting the hyperparameter configuration of the neural network and re-executing the model training process. Hyperparameter adjustment methods include, but are not limited to, conventional methods such as hidden layer structure, learning rate, regularization strength, and number of training epochs. Once the prediction accuracy meets the preset requirements, the final trained model parameters and corresponding data normalization mapping are saved, and this model is used as a low-dimensional calibration proxy model in subsequent dual-proxy model consistency analysis and active learning iteration processes.

[0040] 4.2 Training to obtain the high-dimensional surrogate model A High-dimensional surrogate models are used to establish nonlinear mapping relationships between structural variables and high-dimensional outputs. Their mathematical form can be expressed as:

[0041] in, f H (⋅) represents the neural network mapping function corresponding to the high-dimensional surrogate model, with structural variables as inputs. X (i) The output is the corresponding high-dimensional flow response prediction value. .

[0042] The high-dimensional surrogate model A is also constructed using Python code, and its model training process, network structure, parameter settings, and training strategy are consistent with those of the low-dimensional surrogate model B. After the high-dimensional surrogate model is trained, the accuracy of the model's prediction results is tested using validation set samples, and the coefficient of determination is used. R 2 The root mean square error (RMSE) is used as an evaluation metric for model prediction performance, reflecting the model's fitting ability.

[0043] If the prediction accuracy is too low, you can try to improve the model accuracy by adjusting the hyperparameters. Unlike the low-dimensional surrogate model B, which is used as a calibration model, the main role of the high-dimensional surrogate model A is to represent the overall mapping relationship between structural variables and high-dimensional flow information. Its prediction accuracy will be gradually improved by continuously introducing new simulation samples in the subsequent consistency-driven active learning iteration process. Therefore, even if the model prediction accuracy does not reach the preset high-precision threshold in the initial training stage, it is not a necessary condition for retraining or parameter adjustment.

[0044] 5. Generate an active learning candidate sample pool After completing the initial training of the high-dimensional surrogate model A and the low-dimensional surrogate model B, in order to identify the most worthwhile sample points for learning the current surrogate model in the structural variable design space, the design space is used to... The same method as in the initial sample generation stage is used to generate a set containing 2000 sets of structural variables, which serves as the active learning candidate sample pool. , , .

[0045] This step is implemented using the NumPy, SciPy, and pandas libraries in Python. The steps are the same as in the "Initial Sample Generation" stage.

[0046] Generated candidate sample pool Instead of directly performing CFD simulations, the model is used as the evaluation object in the subsequent active learning stage. It is input into the trained high-dimensional surrogate model A and low-dimensional surrogate model B for prediction, and the uncertainty of the prediction result of model A and the inconsistency index of the two surrogate models are calculated, which provides a basis for the subsequent underlearning evaluation and active learning sample selection.

[0047] 6. Calculate the underlearning score of candidate learning points. 6.1 Calculation of Uncertainty in Prediction Results of Surrogate Model A The prediction uncertainty is estimated by introducing the MC Dropout mechanism into model A. Dropout activation is maintained during the testing phase for the same candidate point. X (j) conduct T After one random forward propagation, a set of predictions is obtained: Based on this, calculation model A is based on the input. X (j) The predicted mean above: and Model A at input X (j) The predicted variance on: .

[0048] To obtain a single scalar uncertainty for point-based sorting, the uncertainties of the 10 outputs can be aggregated into... .

[0049] The calculation steps for the prediction uncertainty of the surrogate model A are implemented using Python libraries such as TensorFlow / Keras, NumPy, and scikit-learn. First, a normalizer compatible with model A is used to scale the input parameters, ensuring the input distribution during prediction is consistent with that during training. Then, the Dropout layer in the neural network is kept active; that is, training=True is set in the forward propagation call, thus introducing MC-Dropout randomness and applying it to the same candidate point. X (j) implement TThe second random forward propagation uses the `np.array` function from the NumPy library to... T The prediction results obtained from the random forward propagation are converted into an array of shape (T, output_dim), where T `output_dim` represents the number of forward propagations, and `np.mean` represents the model output dimension. The `np.mean` function calculates the predicted mean, the `np.var` function calculates the predicted variance, and the `np.sqrt` function takes the square root of each element of the variance array to obtain the single scalar uncertainty of the output for each candidate point, which is then used for point sorting.

[0050] 6.2 Calculation of the inconsistency between the prediction results of Model A and Model B Since Model A and Model B have different output spaces, they cannot be directly compared. First, the 10-dimensional output of Model A is compressed into a 3-dimensional output aligned with Model B. For any design point... X (j) The prediction results of model A are compressed using the mapping function 𝑅(⋅). Compress to: Meanwhile, model B directly predicts:

[0051] Since the accuracy of model B has reached the threshold during training, the prediction result of model B is used as the calibration value. The relative error between the prediction result of model A and the calibration value is calculated. The relative errors of the three outputs are then fused by taking the norm, and this fusion is used as the basis for model A and model B to learn the candidate points. X (j) Inconsistency in prediction results:

[0052] Implement the discrepancy between the prediction results of model A and model B using Python libraries such as TensorFlow / Keras, NumPy, and scikit-learn. E ( X The calculation steps are as follows: First, the trained high-dimensional surrogate model A and low-dimensional surrogate model B are respectively called to calculate the same candidate point. X (j) Make predictions. Then, use NumPy statistical functions to aggregate the indicators of the prediction vector of model A, and calculate the average value of the five velocity components using np.mean to obtain the result. The coefficient of variation for the velocity components is calculated using np.std / np.mean to obtain... The mean of the five voltage drop components is obtained by applying np.mean. This compresses the predictions of Model A into a 3D index form consistent with Model B.R ( f H ( X (j) Meanwhile, the output of model B is directly obtained. f L ( X (j) The difference vector delta = yA_align - yB is calculated using NumPy vector operations. Then, the relative error is normalized element-wise as delta_norm = delta / (yB + eps). Finally, the L2 norm is calculated using np.linalg.norm(delta_norm, ord=2) to obtain the inconsistency degree of the candidate points.

[0053] 6.3 Calculation of Underlearning Score Due to the inconsistency between the prediction results of model A and model B E ( X ) is the relative error, while the uncertainty of prediction result A is... U A ( X The variance is not on the same order of magnitude as the metric. By converting each indicator into a ranking score, the influence of the units and numerical scale can be eliminated. ,

[0054] in, Indicate candidate points X (j) The corresponding inconsistency ranking score, Indicate candidate points X (j) The corresponding uncertainty ranking score, N p This represents the number of candidate learning points.

[0055] Ranking scores for inconsistency Uncertainty ranking score Average candidate points X (j) underlearning score S (j) :

[0056] This step can be implemented using libraries such as NumPy and Pandas in Python code. This is done for the candidate sample pool. For each candidate point in the dataset, calculate the results separately. and Next, the two types of indicators are stored in a one-dimensional array for unified sorting. The NumPy sorting function `np.argsort` is used to obtain the index sequence of the indicator values ​​of each candidate point from smallest to largest. Then, a ranking array is constructed so that each candidate point corresponds to a ranking value `rank_E[j]` and `rank_U[j]`, where the ranking value is uniformly agreed to be "the larger the value, the higher the ranking". Then, the ranking value is divided by the candidate pool size of 2000 to obtain the result. and In Python, the underlearning score is obtained using np.mean. S (j) .

[0057] 7. Establish a set of active learning points S (j) Used to measure candidate learning points X (j) The learning value for improving the current agent model. S (j) The larger the value, the more worthwhile it is to learn. Selected rating S (j) The top 15 candidate learning points form an active learning point set. , , where argmax represents the value of the independent variable that makes the function reach its maximum value.

[0058] The active learning sample selection step is implemented using NumPy and Pandas libraries in Python. Then, sorting and selection functions such as `np.argsort` or `np.argpartition` in Python are used to sort the underlearning score array in descending order, obtaining a sequence of candidate point indices from high to low scores. The structure variables corresponding to the top 15 candidate points with the highest underlearning scores are selected to form the active learning sample set. .

[0059] 8. Active learning parameter optimization 8.1 Update the dataset After obtaining the active learning point set For each set of structural variables X (j) Run a CFD numerical simulation. After each simulation, record the outlet section velocity V and pressure drop of the five branch pipes 3. data Output, to obtain new high-dimensional output data to form a high-dimensional dataset. , .

[0060] 8.2 Iteration Termination Criteria In the active learning iteration process, to avoid invalid iterations and terminate the sample expansion process while ensuring the prediction accuracy and stability of the surrogate model, this invention sets the following iteration termination criteria: (1) After each round of active learning and addition of points and completion of the update and training of the high-dimensional surrogate model A, the prediction accuracy of the surrogate model on the independent validation sample set is evaluated and the coefficient of determination is used as the evaluation factor. R 2 As a metric for evaluating model accuracy, when the prediction accuracy reaches a preset threshold, the surrogate model is considered to have a high global prediction capability. (2) For all candidate points in the active learning candidate sample pool, calculate the consistency error between the prediction results of model A and model B based on the current surrogate model. When the average inconsistency of the models in the candidate pool is lower than the preset threshold, it indicates that the difference in the prediction of key performance indicators between the two models in the design space has been sufficiently weakened and the conflict between the models has been effectively resolved.

[0061] When the above-mentioned model accuracy condition and model consistency condition are met simultaneously, it is determined that the active learning process has reached a convergence state, and further sample collection and model update iteration are stopped. The final surrogate model and corresponding training dataset are output as the basis for pipeline structure variable optimization and performance prediction.

[0062] Technical effect testing and analysis Based on the above process, the high-dimensional initial dataset is processed. The sample points are increased iteratively. Based on an initial dataset of 60 groups, four iterations are performed, with 15 active learning points added in each iteration. A high-dimensional surrogate model A is trained using the dataset after each iteration. The stopping criterion is set to the average determination coefficient of the prediction results of model A. R 2 >0.95, Inconsistency between models A and B E ( X The coefficient of determination (COP) of the ten predictions for the final model A is less than 0.1. R 2 The inconsistency between models A and B increased from 0.8505 to 0.9893. E ( X The value decreased from the initial 0.199 to 0.079, both reaching the stopping iteration criterion.

[0063] To verify the effectiveness of the method of the present invention, a comparative experiment was conducted using the same high-dimensional initial dataset. Based on the previous model, a random sampling method was used to expand the sample size, with four iterations, each adding 15 sample points. A high-dimensional surrogate model C was trained using the dataset from each iteration. Models A and C were trained using the same method and hyperparameter settings, and the accuracy of both models was evaluated at each iteration, with the model accuracy expressed as the coefficient of determination. R 2 The results of the measurement are shown in Table 1.

[0064]

[0065] As can be seen from the comparison in Table 1, on the one hand, after the same number of iterations starting from the initial dataset of 60, model A trained using the active learning method of this invention consistently achieves higher accuracy than model C trained using the random sampling method. On the other hand, if the model accuracy reaches... R 2 With a target value of 0.94, the method of this invention adds 30 sample points, while the method of randomly adding points adds 60 sample points.

[0066] In summary, the active learning method proposed in this invention can increase accuracy with the same dataset, while also achieving the target accuracy with fewer trials, thus improving experimental efficiency.

Claims

1. A dual-surrogate model optimization method for the pipe structure parameters of a wind-powered snow removal robot, used for optimizing the pipe structure parameters of a wind-powered snow removal robot, the specific steps of which are as follows: (1) Based on the initial design of the wind-powered snow removal robot pipeline, determine the design variables and value range of the pipeline structural parameters. ,in, x i Indicates the first i One pipeline structure variable, m The number of pipeline structure variables. Design space for pipeline structure variables; (2) Generate containing N A set of 0 pipe structure parameters , , Running CFD simulations yields high-dimensional output. Y (i) , Y (i) = Y ( X (i) ), establish a high-dimensional dataset , ,in, Y (⋅) represents the simulation results obtained by CFD simulation of the pipeline structure parameters; (3) To Y (i) Dimensionality reduction process yields low-dimensional output y (i) , y (i) = R ( Y ( X (i) )) , establish a low-dimensional dataset , ,in, R (⋅) indicates the output compression mapping; (4) Select a surrogate model and utilize a high-dimensional dataset. A high-dimensional surrogate model A is obtained through training. , f H (⋅) represents the mapping function of the high-dimensional proxy model. To produce high-dimensional prediction outputs, utilize low-dimensional datasets. The low-dimensional surrogate model B is obtained through training. , f L (⋅) represents the mapping function of the low-dimensional proxy model. This is a low-dimensional prediction output; (5) In Internally generated active learning candidate sample pool , , ,in N p The number of candidate learning points, X (j) For the first candidate sample pool j Candidate learning points j =1- N p ; (6) For each candidate learning point X (j) Calculate underlearning score S (j) , S (j) The larger the size, the more worthwhile this point is to learn. , among which, U A ( X ) represents the uncertainty of the prediction result of surrogate model A. For the inconsistency of the A / B model, ε To prevent extremely small positive numbers with a denominator of zero; (7) In Selected rating S (j) The highest n candidate learning points are used to build an active learning point set. , Where argmax represents the design variable when the function reaches its maximum value. X The value of ; (8) Perform CFD simulation to obtain updated datasets , Utilize updated dataset Continue training model A. Stop active learning when the prediction accuracy of model A, the prediction accuracy of model B, and the inconsistency between the prediction results of model A and model B all reach a specified threshold.

2. A wind-powered snow removal robot pipeline, comprising an inlet pipeline (1), a connecting pipeline (2), and a branch pipeline (3), characterized in that, The inlet pipe (1) connects to the outlet of the blower of the wind-powered snow removal robot. The connecting pipe (2) is closed at both ends and has rounded corners. The inlet pipe (1) is installed vertically in the middle of the connecting pipe (2). Multiple identical branch pipes (3) are evenly distributed on the connecting pipe (2). The inlet pipe (1) and multiple branch pipes (3) are arranged on both sides of the connecting pipe (2). The branch pipes (3) are irregular pipes, including the first straight pipe (3-1), the first bend pipe (3-2), the second straight pipe (3-3), the second bend pipe (3-4), and the third straight pipe (3-5). 3-5), the first straight pipe (3-1), the first bend pipe (3-2), the second straight pipe (3-3), the second bend pipe (3-4) and the third straight pipe (3-5) are connected in sequence. The first straight pipe (3-1) is installed vertically on the connecting pipe (2). The axis of the first straight pipe (3-1) and the inlet pipe (1) are parallel. The inlet pipe (1), the connecting pipe (2) and the branch pipe (3) are internally connected to form a wind-powered snow removal robot pipeline with the inlet pipe (1) as the inlet and the third straight pipe (3-5) of multiple branch pipes (3) as the outlet.

3. The dual-surrogate model optimization method for pipeline structure parameters of a wind-powered snow removal robot according to claim 1, characterized in that, The surrogate model selected in step (4) is a neural network model.

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