Method for predicting convection heat transfer coefficient of cooling flow channel of machine tool column based on small sample surrogate model

Abstract

The application discloses a kind of based on small sample agent model's machine tool stand cooling flow passage convection heat transfer coefficient prediction method, belong to precision CNC machine tool temperature control field.For the existing convection heat transfer coefficient calculation relies on flow-thermal coupling simulation long time-consuming, difficult to meet the problem of fast iteration demand, the application will channel attention mechanism and residual connection neural network (SE-FFN-Res) be combined to predict cooling flow passage convection heat transfer coefficient.This method first constructs parameterized flow-thermal coupling finite element model, obtains appropriate high-fidelity simulation data by Latin hypercube sampling;Subsequently, an agent model containing SE module and nonlinear activation layer is constructed, the long-distance residual projection structure is used to enhance the feature transmission and gradient stability under limited samples, and the hyperparameters are optimized by genetic algorithm.This method has excellent convection heat transfer coefficient prediction accuracy and generalization ability in small sample data scenarios, and can quickly evaluate the effect of stand cooling flow passage design scheme.

Description

Technical Field

[0001] This invention belongs to the field of temperature control technology for precision CNC machine tools, and particularly relates to a method for predicting the convective heat transfer coefficient of machine tool column cooling channels based on a small sample surrogate model. Background Technology

[0002] During operation, high-speed CNC machine tools continuously generate heat from components such as the spindle system, servo drive, and guideway motion pairs. This heat can easily lead to uneven temperature distribution within the machine tool column, causing thermal bending deformation and reducing machining accuracy. To achieve precise temperature control of the column and improve the uniformity of the temperature field distribution, cooling channels are typically arranged inside the column in engineering practice to remove heat through forced convection. The convective heat transfer coefficient is the core physical quantity determining the heat dissipation efficiency of the cooling channels. This coefficient depends not only on the fluid velocity but is also significantly influenced by the channel geometry (such as cross-sectional shape and aspect ratio). The quality of the channel structure design directly determines the convective heat transfer coefficient, which in turn affects the overall heat dissipation capacity of the channel and the uniformity of the temperature field inside the column, ultimately determining the thermal accuracy and stability of the entire machine. However, the convective heat transfer coefficient is subject to strong nonlinear coupling from multiple factors, making it difficult to accurately solve analytically. In existing engineering designs, empirical correlations or numerical simulation methods are typically used to determine the heat transfer coefficient. Empirical formulas are mostly based on idealized assumptions or simple flow channel structures, which have limited applicability under complex flow channel shapes and actual working conditions, and the calculation accuracy is difficult to guarantee. On the other hand, numerical simulation methods based on CFD or flow-heat coupling have higher accuracy, but the modeling process is complex, the calculation cycle is long, and the computational resources are large, making it difficult to meet the needs of rapid iterative design of cooling flow channel structures.

[0003] With the development of surrogate modeling technology, constructing approximate prediction models using a limited number of simulation samples to provide a rapid prediction method for complex physical problems has become a feasible approach. However, in the cooling channel design stage, due to simulation costs, only a small amount of sample data is often available. How to accurately predict the convective heat transfer coefficient under small sample conditions still lacks an effective and reliable technical solution. Therefore, it is necessary to propose a surrogate modeling method based on small sample simulation data to achieve rapid prediction of the convective heat transfer coefficient of machine tool column cooling channels, providing efficient technical support for cooling channel structure design and parameter optimization. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the convective heat transfer coefficient of machine tool column cooling channels based on a small sample surrogate model. This method obtains a number of samples through finite element simulation and constructs a surrogate model to achieve rapid prediction of the convective heat transfer coefficient under the conditions of changes in cooling channel geometric parameters and fluid flow velocity.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for predicting the convective heat transfer coefficient of a machine tool column cooling channel based on a small-sample surrogate model includes the following steps:

[0007] Step 1: Determine the range of values ​​for the geometric design parameters and fluid operation parameters of the cooling channel;

[0008] Step 2: Simulate the original simulation dataset based on the flow-thermal coupled finite element model;

[0009] A three-dimensional model of the cooling channel of the machine tool column is established. The heat generation rate, fluid operation parameters and medium physical property parameters are applied as boundary conditions. The flow field distribution in the cooling channel of the column is solved and the average convective heat transfer coefficient is calculated.

[0010] Several parameter combinations are generated using Latin hypercube sampling, automatic batch simulation is performed, and the corresponding average convective heat transfer coefficient is output to construct the original simulation dataset.

[0011] Step 3: Construct a few-shot neural network surrogate model that combines residual structure with channel attention mechanism;

[0012] Step 3-1: Construct a multilayer feedforward neural network; the multilayer feedforward neural network (MLP) takes the geometric design parameters of the cooling channel and the fluid operation parameters as inputs, and the average convective heat transfer coefficient as the output target.

[0013] Step 3-2: Construct a channel attention mechanism layer; perform global average pooling on the input feature matrix to compress each feature channel into a scalar; pass the scalar through the first fully connected layer, a non-linear activation function, the second fully connected layer, and the Sigmoid activation function in sequence to generate the weight vector of each channel; perform Hadamard product operation on the weight vector and the original input feature matrix to obtain a weighted new feature matrix;

[0014] Step 3-3: Construct a nonlinear layer; the nonlinear layer consists of multiple fully connected neurons, and the layers are connected by nonlinear activation functions;

[0015] Steps 3-4: Construct the output layer and introduce residual projection; the output features of the first hidden layer in the multi-layer feedforward neural network are transformed by a linear projection layer and then directly superimposed onto the output of the output layer; output predicted value. , This is the deep feature vector after processing through the channel attention mechanism layer and the nonlinear layer. These are the shallow features output by the first hidden layer. and These are the weight matrix and bias vector of the main output layer and the residual projection layer, respectively;

[0016] Step 4: Construct the loss function and optimize model parameters;

[0017] Huber Loss is used as the target loss function. The key hyperparameters of the neural network surrogate model are optimized based on the genetic algorithm. The global optimal solution is found through selection, crossover and mutation operations, thereby establishing the final neural network surrogate model.

[0018] Step 5: Using the final neural network surrogate model, quickly predict the geometric design parameters and fluid operation parameters of the newly input cooling channel to obtain the corresponding predicted value of the convective heat transfer coefficient.

[0019] Furthermore, in step 1, the geometric design parameters are parameters characterizing the trapezoidal cross-section cooling channel, including the upper base dimension a, the lower base dimension b, and the angle s between the lower base and the side.

[0020] Furthermore, in step 1, the fluid operating parameters include flow rate.

[0021] Furthermore, in step 2, the input vector is preprocessed using Min-Max normalization.

[0022] Furthermore, in step 2, the heat generation rate includes the frictional heat generation rate between the slider and the guide rail, and the bearing heat generation rate;

[0023] Frictional heat generation rate between slider and guide rail ,in The coefficient of friction; The speed of the slider movement; The normal load on the guide rail is calculated based on the overturning moment and cutting force components of the spindle system; the four sliders jointly bear the radial cutting force. and the additional positive pressure caused by the overturning moment of the spindle system , Radial cutting force With main cutting force There is a proportional relationship. Cutting force Determined by empirical formulas in metal cutting theory: ,in The coefficient representing the influence of the workpiece on the cutting force; This refers to the depth of cut. For feed rate; This refers to the cutting speed; For cutting parameters; This is the correction factor.

[0024] bearing heat generation rate , It is the heat generated by friction in a single bearing. It refers to the bearing speed; It is the total frictional torque of a single bearing.

[0025] Furthermore, in steps 3-4, the nonlinear activation function used is the Swish activation function.

[0026] The beneficial effects of this invention are as follows: A small-sample surrogate model combining residual structure and channel attention mechanism is used to solve the problem of rapid prediction of convective heat transfer coefficients under limited simulation data constraints. Addressing the issues of overfitting and insufficient feature extraction in classical surrogate models when sample size is insufficient, this invention constructs a lightweight residual network incorporating SE-Block and utilizes the channel attention mechanism to automatically learn the nonlinear feature weights between channel geometry parameters and flow parameters. This achieves adaptive weighting and recalibration of key physical features, thus ensuring the model's generalization ability and robustness under small sample conditions. The model can still achieve high-precision predictions using only hundreds of samples, with MAE and RMSE reduced by more than 35% compared to classical response surface methodology. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the structure of the SE-FFN-Res model proposed in this invention.

[0028] Figure 2 This is a comparison chart showing the fitting performance of the SE-FFN-Res model of this invention and the classic response surface model on the training set.

[0029] Figure 3 This is a comparison chart of the prediction performance of the SE-FFN-Res model of this invention and the classical response surface model on the test set.

[0030] Figure 4 This is a comparison chart of the prediction residuals of the two models on the test set.

[0031] Figure 5 This is a comparison chart of the error metrics (MAE, RMSE) of the two models on the test set. Detailed Implementation

[0032] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0033] This embodiment discloses a method for predicting the convective heat transfer coefficient of a machine tool column cooling channel based on a small-sample surrogate model, comprising the following steps:

[0034] Step 1: Determine the range of values ​​for the geometric design parameters and fluid operation parameters of the cooling channel;

[0035] Based on the overall design requirements of the machine tool column cooling system, the composition of the model input variables is first clarified, including the geometric design parameters of the cooling channel and the fluid operation parameters. The selection of design variables follows the following principles: meeting the structural strength and manufacturing constraints of the column, and ensuring the convective heat transfer capacity of the cooling system. A trapezoidal cross-section cooling channel structure is adopted. To quantify the influence of the channel geometry on the convective heat transfer performance, the trapezoidal cross-section is defined as: upper base dimension a (mm), lower base dimension b (mm), and the angle s (°) between the lower base and the side. Based on the column wall thickness, cooling arrangement space, and manufacturing process capabilities, the variable range is set as: a∈(2~10)mm, b∈(6~16)mm, s∈(30°~90°). In this embodiment, the fluid operation parameters refer to the fluid velocity. Fluid velocity is a key operating parameter affecting the forced convection heat transfer coefficient h. An aqueous solution is selected as the cooling medium, and the velocity range is set to v∈(0.1~0.6)m / s to cover typical laminar to turbulent conditions and meet engineering application requirements.

[0036] Step 2: Simulate the original simulation dataset based on the flow-thermal coupled finite element model;

[0037] The heat source of the column structure originates from the frictional heat generated during the relative motion of the guide rail and slider, as well as the heat generated by the bearings during operation due to friction and energy loss. The heat generation rate of these heat sources is quantitatively calculated. The frictional heat generation rate between the slider and the guide rail is also considered. ,in The coefficient of friction; The speed of the slider movement; The normal load on the guide rail is calculated based on the overturning moment and cutting force components of the spindle system. The four sliders share the radial cutting force. and the additional positive pressure caused by the overturning moment of the spindle system , Radial cutting force With main cutting force There is a proportional relationship. According to metal cutting theory, cutting force , Cutting force (N); The coefficient representing the influence of the workpiece on the cutting force; The cutting depth is in mm. The feed rate is (mm / min). Cutting speed (m / min); For cutting parameters; This is the correction factor.

[0038] The bearing heat generation rate was estimated using the Palmgren empirical formula. , It is the frictional heat generation power (W) of a single bearing. It refers to the bearing speed (rpm); It is the total frictional torque of a single bearing (N) mm).

[0039] A three-dimensional model of the column cooling channel was established, and boundary conditions such as heat generation rate, flow velocity, and medium properties were applied to solve the flow field distribution within the column cooling channel and calculate the average convective heat transfer coefficient h. The flow field results were then mapped to a steady-state thermal model for analyzing the temperature distribution within the column.

[0040] Latin hypercube sampling (LHS) is used to generate several parameter combinations for automated batch simulation, and the corresponding average convective heat transfer coefficient h is output to construct the original simulation dataset. Min-Max normalization is performed on the input design variables to eliminate the order-of-magnitude differences between parameters of different dimensions, accelerating the gradient descent convergence process and improving the model training stability.

[0041] Min-Max normalization: , where x represents the original channel geometry or velocity parameters; and These represent the minimum and maximum values ​​of the parameter across all simulation sample data, respectively; x' is the normalized dimensionless value.

[0042] Step 3: Construct a few-shot neural network surrogate model SE-FFN-Res (Squeeze-and-Excitation Feedforward Network with Residual connection, SE-FFN-Res) that combines residual structure with channel attention mechanism;

[0043] Step 3-1: Construct a multi-layer feedforward neural network (MLP);

[0044] The multilayer feedforward neural network (MLP) takes the cooling channel geometry parameters (a, b, s) and fluid velocity (v) as inputs, and the average convective heat transfer coefficient h as the output target. The MLP network contains four hidden layers with the number of neurons m1, m2, m3, and m4, respectively.

[0045] Input vector ,

[0046] Output depth features ,

[0047] in, ~ These are the weighting coefficients. ~ For the bias number, This is the activation function.

[0048] Step 3-2: Construct the channel attention mechanism layer SE-Block;

[0049] To capture the nonlinear contribution weights of different flow channel geometries and flow velocities to the heat transfer coefficient, a compression-excitation module (SE) is introduced. This module can automatically identify and enhance feature channels that significantly affect heat transfer performance while suppressing irrelevant features, thereby improving the feature extraction efficiency of the model on small sample data. First, the feature matrix from the previous hidden layer... (B is the batch size, C is the number of feature channels) Perform global average pooling to compress the global spatial information of each channel into a scalar. .

[0050] Subsequently, the feature vectors enter the activation phase, where the nonlinear interdependencies between channels are learned through a bottleneck structure consisting of two fully connected layers. The first fully connected layer reduces the feature dimension by a factor of r (r is the dimensionality reduction ratio) and uses LeakyReLU activation. The second fully connected (FC) layer restores the dimensions and uses the sigmoid function to normalize the weights to the (0,1) interval. ; These are trainable parameters. It is the Sigmoid function.

[0051] Finally, the learned channel weights Based on Hadama volume Multiply back the original feature matrix This allows for the reweighting of the original features, resulting in a new feature matrix. .

[0052] Step 3-3: Construct a nonlinear layer;

[0053] After completing the input feature normalization and attention-weighted feature recalibration, this embodiment further constructs multiple nonlinear mapping layers in the backbone network to characterize the highly nonlinear mapping relationship between cooling channel geometry parameters, fluid velocity, and convective heat transfer coefficient. The nonlinear mapping layer consists of multiple fully connected neurons, with nonlinear activation functions connecting each layer to enhance the network's ability to express complex input-output relationships. The input feature vector of the layer is Output feature vector , and The first The weight matrix and bias vector of the layer, It is a non-linear activation function.

[0054] Using Swish as a nonlinear activation function, which has the characteristics of being unbounded and smooth and non-monotonic, can effectively alleviate the gradient saturation problem in deep networks and enhance the nonlinear fitting ability of the model under finite sample conditions.

[0055] Nonlinear activation function , For learnable parameters or constants (usually taken as...) ).

[0056] Steps 3-4: Construct the output layer and introduce residual projection;

[0057] After nonlinear mapping through multiple fully connected layers and channel attention feature weighting by the SE-Block module, the network extracts high-dimensional key features characterizing the channel structure and flow state. This embodiment constructs a single-node output layer to achieve processing of a single physical quantity—the average convective heat transfer coefficient. The prediction.

[0058] To enhance the model's ability to preserve shallow semantic information and prevent gradient vanishing, a long-range residual projection structure is introduced. Unlike traditional layer-by-layer residuals, this embodiment projects the output features of the first hidden layer... After the dimensions are transformed by the linear projection layer, the result is directly superimposed onto the output of the final output layer.

[0059] Output ;

[0060] in, This is the deep feature vector after processing by the SE attention module and the Swish activation function. These are shallow features of the first hidden layer after LeakyReLU activation. and These are the weight matrix and bias vector of the main output layer and the residual projection layer, respectively.

[0061] Step 4: Construct the loss function and optimize model parameters;

[0062] To balance prediction accuracy with robustness to anomalous noise in the training data, Huber Loss was used as the target loss function during model training. Compared to Mean Squared Error (MSE), Huber Loss maintains the smoothness of a quadratic function when the error is small, while transforming into a linear function when the error is large, thereby reducing the excessive influence of outliers on the gradient.

[0063] Target loss function ,in, For the simulated sample's true value, These are the model's predicted values. This is the threshold parameter for Huber loss.

[0064] Given that the number of hidden layer nodes (m1, m2, m3, m4) in the network structure has a significant impact on model performance, this embodiment uses a genetic algorithm (GA) to optimize key hyperparameters. Through selection, crossover, and mutation operations, it seeks the global optimum, thereby establishing the final SE-FFN-Res model architecture. Figure 1 As shown.

[0065] Step 5: Using the optimized neural network surrogate model, quickly predict the newly input flow channel geometry design parameters and fluid velocity to obtain the corresponding predicted values ​​of the convective heat transfer coefficient.

[0066] To verify the effectiveness of the SE-FFN-Res model, this embodiment randomly divides the 250 datasets obtained from finite element simulations into training and test sets, with each set containing 110 samples. The remaining 30 samples are used for model fine-tuning. Based on the same 110 training datasets, two models are constructed: the classical response surface model (RSM) based on full second-order polynomials and the SE-FFN-Res neural network model proposed in this embodiment.

[0067] First, the fitting accuracy of the two models on the training set was evaluated, and the results are as follows: Figure 2 As shown, by Figure 2 It is known that the classic RSM model is limited by the second-order polynomial structure and has a poor fitting effect when dealing with strongly nonlinear data; while the SE-FFN-Res model in this embodiment, with its deep mapping and attention mechanism, can accurately capture complex fluctuation features and achieve a high-precision approximation of the training data.

[0068] Subsequently, using 110 test set data points not involved in the modeling as input for the new operating condition, the generalization performance of the two methods on the convective heat transfer coefficient (h) was compared and evaluated. The predicted values ​​of the test set under the new operating condition parameters are as follows: Figure 3 As shown. By Figure 3 It can be seen that the predicted curve of the SE-FFN-Res model proposed in this embodiment has a high degree of overlap with the simulated value curve, and can capture the nonlinear fluctuation trend of the heat transfer coefficient with changes in geometric parameters and flow velocity; the prediction residual is within ±400W / (m²). 2 Within K), the result is as follows Figure 4 As shown; the model prediction error is as follows: Figure 5 As shown, the mean absolute error (MAE) of the SE-FFN-Res model on the test set decreased to 205 W / (m²). 2 The accuracy is improved by 35.88% compared to the classic RSM model, and the root mean square error (RMSE) is reduced to 245 W / (m²). 2The accuracy is around 39.12% higher than that of the classic RSM model, with a value of approximately ·K. The SE-FFN-Res neural network model proposed in this embodiment, under the constraint of limited simulation data, not only effectively overcomes the problem of insufficient accuracy of the classic response surface model, but also controls the prediction error within an acceptable range for engineering applications, providing a reliable technical means for the rapid prediction of the heat transfer coefficient of the machine tool column flow channel.

[0069] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the convective heat transfer coefficient of a machine tool column cooling channel based on a small-sample surrogate model, characterized in that, Includes the following steps: Step 1: Determine the range of values ​​for the geometric design parameters and fluid operation parameters of the cooling channel; Step 2: Simulate the original simulation dataset based on the flow-thermal coupled finite element model; A three-dimensional model of the cooling channel of the machine tool column is established. The heat generation rate, fluid operation parameters and medium physical property parameters are applied as boundary conditions. The flow field distribution in the cooling channel of the column is solved and the average convective heat transfer coefficient is calculated. Several parameter combinations are generated using Latin hypercube sampling, automatic batch simulation is performed, and the corresponding average convective heat transfer coefficient is output to construct the original simulation dataset. Step 3: Construct a few-shot neural network surrogate model that combines residual structure with channel attention mechanism; Step 3-1: Construct a multilayer feedforward neural network; the multilayer feedforward neural network (MLP) takes the geometric design parameters of the cooling channel and the fluid operation parameters as inputs, and the average convective heat transfer coefficient as the output target. Step 3-2: Construct the channel attention mechanism layer; Global average pooling is performed on the input feature matrix to compress each feature channel into a scalar; the scalar is then passed sequentially through a first fully connected layer, a non-linear activation function, a second fully connected layer, and a sigmoid activation function to generate a weight vector for each channel; the weight vector is then subjected to a Hadamard product operation with the original input feature matrix to obtain a weighted new feature matrix. Step 3-3: Construct a nonlinear layer; The nonlinear layer consists of multiple fully connected neurons, and the layers are connected by nonlinear activation functions; Steps 3-4: Construct the output layer and introduce residual projection; the output features of the first hidden layer in the multi-layer feedforward neural network are transformed by a linear projection layer and then directly superimposed onto the output of the output layer; output predicted value. , This is the deep feature vector after processing through the channel attention mechanism layer and the nonlinear layer. These are the shallow features output by the first hidden layer. and These are the weight matrix and bias vector of the main output layer and the residual projection layer, respectively; Step 4: Construct the loss function and optimize model parameters; Huber Loss is used as the target loss function. The key hyperparameters of the neural network surrogate model are optimized based on the genetic algorithm. The global optimal solution is found through selection, crossover and mutation operations, thereby establishing the final neural network surrogate model. Step 5: Using the constructed neural network surrogate model, quickly predict the geometric design parameters and fluid operation parameters of the newly input cooling channel to obtain the corresponding predicted values ​​of the convective heat transfer coefficient.

2. The method for predicting the convective heat transfer coefficient of machine tool column cooling channel based on a small-sample surrogate model according to claim 1, characterized in that, In step 1, the geometric design parameters are parameters that characterize the trapezoidal cross-section cooling channel, including the upper base dimension a, the lower base dimension b, and the angle s between the lower base and the side.

3. The method for predicting the convective heat transfer coefficient of machine tool column cooling channel based on a small-sample surrogate model according to claim 1, characterized in that, In step 1, the fluid operating parameters include flow rate.

4. The method for predicting the convective heat transfer coefficient of machine tool column cooling channel based on a small-sample surrogate model according to claim 1, characterized in that, In step 2, the input vector is preprocessed using Min-Max normalization.

5. The method for predicting the convective heat transfer coefficient of machine tool column cooling channel based on a small-sample surrogate model according to claim 1, characterized in that, In step 2, the heat generation rate includes the frictional heat generation rate between the slider and the guide rail, and the bearing heat generation rate; Frictional heat generation rate between slider and guide rail ,in The coefficient of friction; The speed of the slider movement; The normal load on the guide rail is calculated based on the overturning moment and cutting force components of the spindle system; the four sliders jointly bear the radial cutting force. and the additional positive pressure caused by the overturning moment of the spindle system , Radial cutting force With main cutting force There is a proportional relationship. Cutting force Determined by empirical formulas in metal cutting theory: ,in The coefficient representing the influence of the workpiece on the cutting force; This refers to the depth of cut. For feed rate; This refers to the cutting speed; For cutting parameters; As a correction factor; bearing heat generation rate , It is the heat generated by friction in a single bearing. It refers to the bearing speed; It is the total frictional torque of a single bearing.

6. The method for predicting the convective heat transfer coefficient of machine tool column cooling channel based on a small-sample surrogate model according to claim 1, characterized in that, In steps 3-4, the nonlinear activation function used is the Swish activation function.

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