Double-paddle stirring power prediction method and system based on residual neural network correction
By using a residual neural network correction method, combined with dimensional analysis and response surface methodology, the problems of low power prediction accuracy and insufficient physical interpretability in complex double-layer stirring systems are solved. This method achieves high-precision and low-cost stirring power prediction, which is suitable for stirring equipment in chemical mixing processes.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-31
- Publication Date
- 2026-04-07
AI Technical Summary
In existing technologies, the power prediction accuracy of complex double-layer stirring systems is low, pure neural network models lack physical interpretability, and high-precision torque sensors are costly and easily damaged, making them difficult to widely apply in industrial settings.
A method based on residual neural network correction is adopted, which combines dimensional analysis and response surface methodology to construct a hybrid feature set. The residual neural network is optimized by a tree-structured Parsons estimator, and power prediction is performed using readily available rotational speed, viscosity, and geometric parameters, thus establishing a physically interpretable high-precision prediction model.
It achieves high-precision power prediction for complex double-layer stirring systems without relying on high-cost torque sensors, reducing equipment costs and improving the interpretability and robustness of predictions. It also provides a basis for selecting stirring motors and reduces the energy consumption of chemical stirring equipment.
Smart Images
Figure CN121809264A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of chemical mixing process modeling and optimization control technology, specifically to a method and system for predicting the power of a dual-blade mixer based on residual neural network correction. Background Technology
[0002] Agitation is a core unit in chemical processes. To enhance the flow field and suppress dead zones, dual-layer impeller systems are often used in industry, such as the combination of a novel biomimetic fishtail impeller and a PBT impeller, which has attracted much attention due to its high efficiency and energy saving. However, the complex nonlinear fluid coupling effect between the two impellers makes their power characteristics difficult to predict.
[0003] Currently, industrial sites primarily rely on online torque sensors to monitor stirring power in real time. However, high-precision torque sensors are expensive and easily damaged in high-temperature and corrosive environments, resulting in significant maintenance costs and hindering their widespread adoption on all equipment. Therefore, "soft measurement" technology that uses readily available parameters such as rotational speed and viscosity to estimate power has become an urgent need.
[0004] Among existing soft measurement methods: traditional empirical formulas are difficult to adapt to complex two-layer coupled systems and have low accuracy; CFD numerical simulations take too long to meet real-time requirements; while pure data-driven neural network models have acceptable accuracy, they lack physical interpretability and have poor generalization ability for small sample data.
[0005] Therefore, there is an urgent need for a hybrid modeling method that integrates physical mechanisms and data-driven approaches to achieve high-precision, low-cost prediction of the power of complex two-layer stirring systems without relying on expensive torque sensors, thereby guiding motor selection. Summary of the Invention
[0006] This invention aims to solve the problems of low power prediction accuracy and lack of physical interpretability of pure neural network models in the prior art for complex double-layer impeller systems, and provides a double-impeller stirring power prediction method and system based on residual neural network correction.
[0007] The technical solution adopted in this invention is as follows: a dual-blade stirring power prediction method based on residual neural network correction, comprising the following steps: Step 1: Obtain the geometric parameter data and real-time operating condition data of the double-layer mixing system; Step 2: Perform physical feature engineering on the data collected in Step 1 to construct a hybrid feature set including dimensional variables, dimensionless numbers, and physical interaction terms; Step 3: Based on the data collected in Step 1, calculate the baseline power value using a pre-defined power metric correlation or quadratic polynomial regression model, according to the principles of dimensional analysis or response surface methodology. ; Step 4: Construct a residual neural network RNet, and use the tree-structured Parsons estimator TPE algorithm to globally optimize the hyperparameters of the residual neural network with the goal of minimizing the power prediction residual, to obtain the optimized residual neural network model. Step 5: Input the mixed feature set into the optimized residual neural network to predict the power and residual value. ; Step 6: Set the reference power value With power prediction residual Add them together to output the final predicted stirring power value. .
[0008] Furthermore, the mixed feature set includes: The dimensional variables include at least the blade inclination angle from the geometric parameter data. The interlayer spacing C, and the stirring speed N and fluid viscosity in the operating condition data. ; The dimensionless number includes at least the interlayer pitch-to-blade diameter ratio. propeller diameter ratio Liquid height ratio Reynolds number Re and Froude number Fr; The physical interaction term includes at least a rotational square term. Coupled term of the square of rotational speed and tilt angle Logarithmic term of rotational speed and the ratio of dip angle to inter-story spacing .
[0009] Furthermore, in step 3, the preset power coefficient correlation is constructed based on the blade type; When the two propellers are straight-bladed, the power coefficient Np is calculated using the following dimensional analysis model: ; Where K,a,b,c,d are the model constants to be fitted, ρ is the fluid density, N is the stirring speed, D1 is the upper impeller diameter, D2 is the lower impeller diameter, T is the stirring tank diameter, H is the liquid level height, Re is the Reynolds number, and Fr is the Froude number. When the twin propellers are oblique blade propellers, an introduction angle is used ( The modified dimensional analysis model: ; Where θ is the blade tilt angle; Then the reference power value Calculated using the following formula: .
[0010] Furthermore, in step 3, the baseline power value is calculated using the quadratic polynomial regression model constructed using the response surface methodology (RSM). The response surface model is based on the Box-Behnken design, and its functional relationship is as follows: ; Where y is the predicted power. and The normalized design variables include rotational speed, interlayer spacing, blade tilt angle, and glycerol concentration. For constant terms, These are the regression coefficients for the linear, quadratic, and interaction terms, respectively.
[0011] Furthermore, in step 4, the optimization objective of the tree-structured Parsons estimator TPE algorithm is to minimize the root mean square error (RMSE) on the validation set. The hyperparameter search space of the residual neural network RNet includes at least the number of hidden layers, the number of neurons in each layer, the learning rate, and the batch size.
[0012] Furthermore, in step 4, the residual neural network RNet adopts a fully connected feedforward structure, with batch normalization layers and ReLU activation functions set between network layers to capture nonlinear power bias.
[0013] A dual-blade stirring power prediction system based on residual neural network correction is provided. The system includes a data acquisition module, a feature engineering conversion module, a physical benchmark calculation module, an intelligent residual calculation module, a result fusion output module, and an output display module. The data acquisition module is used to collect the stirring speed signal of the stirring system in real time, and to acquire the preset geometric parameters of the stirring system and the viscosity data of the fluid material. The feature engineering conversion module is connected to the data acquisition module. Based on the acquired data, it constructs a hybrid feature set containing dimensional variables, dimensionless numbers, and physical interaction terms. The physical reference calculation module is connected to the data acquisition module. It is used to store the preset physical reference mathematical model and calculate the reference power based on the rotational speed, geometric parameters and viscosity data provided by the data acquisition module. The intelligent residual calculation module uses a Bayesian optimization algorithm to automatically find the optimal hyperparameters for the residual neural network, and calculates the mixed feature data received from the feature engineering conversion module based on the optimized model, outputting the predicted power residual value. The result fusion output module is connected to the physical reference calculation module and the intelligent residual calculation module respectively, and is used to fuse the reference power value and the power residual value to output the final power prediction value. The output display module is used to output the predicted value through a display terminal.
[0014] Furthermore, the intelligent residual calculation module includes a feature input unit, a Bayesian optimization unit, and a deep learning inference unit; the feature input unit is connected to the feature engineering conversion module and is used to receive the mixed feature set; the Bayesian optimization unit uses the tree-structured Parsons estimator algorithm to globally optimize the hyperparameters of the residual neural network to obtain the optimized network model; the deep learning inference unit is connected to both the feature input unit and the Bayesian optimization unit and is used to input the mixed feature set into the optimized network model to predict the power residual value.
[0015] By employing the above-described technology, the beneficial effects of the present invention compared to the prior art are as follows: 1) This invention establishes a dimensional analysis model based on fluid dynamics, which associates complex power characteristics with explicit dimensionless numbers, thus significantly improving the interpretability of prediction results; 2) This invention introduces a residual neural network optimized by a tree-structured Parsons estimator (TPE), which can compensate for nonlinear biases missed in the physical model and eliminate systematic errors while maintaining physical interpretability. 3) This invention employs two approaches to constructing physical benchmarks: dimensional analysis and response surface methodology. The appropriate modeling approach can be selected based on the needs of different industrial scenarios. 4) This invention only requires the collection of parameters that are easy to measure online, such as rotational speed, viscosity and geometric parameters, to achieve real-time soft measurement of power, which can simplify the system hardware structure and reduce equipment costs; 5) The high-precision power prediction value provided by this invention provides a reliable basis for the selection of stirring motors, thereby reducing the operating energy consumption of chemical stirring equipment from the source. Attached Figure Description
[0016] Figure 1 This is a hardware schematic diagram of the laboratory environment in an embodiment of the present invention; The torque sensor is used to collect real power data to train and calibrate the physical benchmark model and residual neural network. In practical industrial applications, the trained system can remove the torque sensor and work solely based on the prediction model of this invention. Figure 1 In the middle: 1. Frequency converter; 2. Motor; 3. Torque sensor; 4. Data acquisition card; 5. Computer; 6. Baffle; 7. Mixing vessel; 8. Upper stirring blade; 9. Lower stirring blade; 10. Stirring shaft; 11. Rheometer; Figure 2 This refers to the size of the fishtail propeller in this embodiment of the invention; Figure 3 This refers to the PBT paddle size in an embodiment of the present invention; Figure 4 This is the overall algorithm flowchart of the method of the present invention; Figure 5 This is a schematic diagram of the architecture of the TPE-RNet residual correction network in this invention; Figure 6 This is a comparison chart of the prediction performance of the hybrid model (DA+RNet and RSM+RNet) in this invention; Figure 7 This is a comparison diagram of the dimensional analysis model, response surface model, and hybrid model of the present invention. Detailed Implementation
[0017] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0019] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.
[0020] Example: A method for predicting the stirring power of a dual-propeller system based on residual neural network correction. This example uses a fishtail-PBT combined propeller system as an example. Step 1: Data Acquisition
[0021] like Figure 1 As shown, this embodiment uses a transparent acrylic cylindrical stirring tank with a diameter and liquid level height of 160mm, and four standard baffles are built in. The stirring assembly adopts a double-layer configuration of an upper four-bladed PBT impeller with a diameter of 81mm and a lower biomimetic fishtail impeller. In this embodiment, pure water and glycerol aqueous solutions with a mass fraction of 25% and 50% were selected to simulate the viscosity changes of industrial materials. Power data was collected in real time using a torque sensor, and a total of 252 valid samples were accumulated.
[0022] The raw data obtained includes: Geometric parameters: upper impeller diameter D1=81mm, lower impeller diameter D2=81mm, mixing tank diameter T=160mm, liquid level height H=160mm, interlayer spacing C varies within the range of 10-50mm, and impeller inclination angle θ varies within the range of 45°-75° (oblique blade impeller) or 90° (straight blade impeller).
[0023] Real-time operating data: The stirring speed N varies in the range of 100-400 rpm, and the fluid viscosity μ is controlled by the glycerol concentration (0-50% mass fraction).
[0024] Step 2: Based on the raw data obtained in Step 1, perform physical feature engineering to construct a hybrid feature set. This feature set contains three types of features: Dimensional variables: Directly extracted raw parameters, including blade tilt angle θ, interlayer spacing C, stirring speed N, and fluid viscosity μ.
[0025] Dimensionless number: A standard criterion number constructed based on the principle of dimensional analysis, which includes the interlayer pitch diameter ratio. , propeller diameter and kettle height ratio Liquid height ratio The Reynolds number Re and the Froude number Fr.
[0026] Physical interaction terms: To capture nonlinear coupling effects, the following interaction terms are constructed: rotational speed squared term. Coupled term of the square of rotational speed and tilt angle Logarithmic term of rotational speed and the ratio of dip angle to inter-story spacing .
[0027] Finally, the three types of features are combined into a 13-dimensional hybrid feature set for subsequent model training.
[0028] Step 3: Calculation of reference power value
[0029] This embodiment provides two methods for calculating the reference power, which can be selected according to actual needs: Method 1: Construct a dimensional analysis model based on the principles of fluid dynamics as the core calculation benchmark.
[0030] For the fishtail-PBT combined propeller, this embodiment constructs a power metric (PBT) Correlation: or ; The optimal physical parameters for this specific system were determined by nonlinear regression fitting of 252 sets of experimental data. Straight-blade combined propeller: K=5.3608, a=0.0096, b=0.0498, c=0.6617, d=0.2334; Inclined-blade combined propeller: K=3.9935, a=-0.00971, b=0.05179, c=-0.02647, d=1.3222; The reference power value is calculated using the following formula: .
[0031] Method 2: Alternative benchmark model based on response surface methodology
[0032] To verify the diversity of the model and analyze the interaction effects, this embodiment can also use the Response Surface Method (RSM) as another benchmark power calculation method.
[0033] A Box-Behnken design (BBD) was used, with rotational speed X1, interlayer spacing X2, blade tilt angle X3, and glycerol concentration X4 as independent variables, to construct a quadratic polynomial regression model: ; The rotational speed range is 100-400 rpm, the interlayer spacing range is 10mm-50mm, the blade inclination angle is 45°-75° or 90°, and the glycerol concentration is 0-50%. In this example, a quadratic polynomial regression model was also fitted to both the straight-blade and oblique-blade propellers. Straight-blade propeller: ; Slanted blade propeller: ; This model quantifies the interaction effects between key variables such as rotational speed, viscosity, angle, and interlayer spacing using statistical methods, and has independent application value in engineering scenarios.
[0034] Step 4: Residual Correction Based on Bayesian Optimization
[0035] To address the minor nonlinear deviations remaining in the aforementioned physical benchmark model within the highly turbulent region, this embodiment constructs a Bayesian-optimized residual neural network (RNet) for compensation and correction. The specific implementation steps are as follows: Figure 3 As shown: Residual definition: The difference between the predicted value and the actual value of the physical baseline model.
[0036] Network construction: A fully connected feedforward structure is adopted. The input layer receives the 13-dimensional hybrid feature set constructed in step 2. Batch normalization layers and ReLU activation functions are set between the hidden layers. The output layer predicts the power residual value ΔP.
[0037] Intelligent optimization: The Tree-structured Parsons Estimator (TPE) algorithm is employed to globally optimize hyperparameters (including the number of hidden layers, the number of neurons per layer, the learning rate, and the batch size) with the objective of minimizing the root mean square error (RMSE) on the validation set. After 30 iterations, the TPE algorithm converges rapidly, determining the optimal combination of hyperparameters and obtaining the optimized residual neural network model.
[0038] Result Prediction: Final Predicted Power .
[0039] Step 5: Power Residual Prediction
[0040] The hybrid feature set constructed in step 2 is input into the residual neural network optimized in step 4 to predict the power residual value ΔP.
[0041] Step 6: Final power prediction output
[0042] The reference power value calculated in step 3 Add the predicted power residual value ΔP from step 5 to output the final predicted stirring power value: .
[0043] Verification of the overall performance of the method in this embodiment: like Figure 6 As shown, the two hybrid models proposed in this embodiment are compared. The results show that this invention employs a strategy of combining high-precision physical formulas with intelligent residual correction, eliminating systematic errors while preserving the interpretability of the physical model, and achieving accurate prediction of complex two-layer propeller systems. The ensemble average results of ten independent training rounds demonstrate that dimensional analysis combined with residual neural networks (DA+RNet) and response surface methodology combined with residual neural networks (RSM+RNet) are more effective. The data have all improved significantly, as can be seen from the model comparison. Figure 7 As can be seen from the figure, the hybrid model effectively overcomes the problem of limited accuracy of traditional models in two-layer propeller systems. At the same time, the problem of lack of interpretability of pure neural networks can also be solved by the dimensional analysis model in this invention, realizing high-precision and robust power soft measurement.
[0044] The above method is based on a prediction system, which includes: The data acquisition module is used to collect the stirring speed signal of the stirring system in real time, and to obtain the preset geometric parameters of the stirring system and the viscosity data of the fluid material.
[0045] The feature engineering conversion module is connected to the data acquisition module. Based on the acquired data, it constructs a hybrid feature set containing dimensional variables, dimensionless numbers, and physical interaction terms.
[0046] The physical reference calculation module is connected to the data acquisition module. It is used to store the preset physical reference mathematical model and calculate the reference power based on the rotational speed, geometric parameters and viscosity data provided by the data acquisition module.
[0047] The intelligent residual calculation module includes a feature input unit, a Bayesian optimization unit, and a deep learning inference unit. The feature input unit is connected to the feature engineering transformation module and is used to receive the mixed feature set. The Bayesian optimization unit uses the tree-structured Parsons estimator algorithm to globally optimize the hyperparameters of the residual neural network to obtain the optimized network model. The deep learning inference unit is connected to both the feature input unit and the Bayesian optimization unit and is used to input the mixed feature set into the optimized network model to predict the power residual value.
[0048] The result fusion output module is connected to the physical reference calculation module and the intelligent residual calculation module, respectively, and is used to fuse the reference power value and the power residual value to output the final power prediction value.
[0049] The output display module is used to output the predicted value through a display terminal.
Claims
1. A method for predicting the power of a dual-blade stirring apparatus based on residual neural network correction, characterized in that, Includes the following steps: Step 1: Obtain the geometric parameter data and real-time operating condition data of the double-layer mixing system; Step 2: Perform physical feature engineering on the data collected in Step 1 to construct a hybrid feature set including dimensional variables, dimensionless numbers, and physical interaction terms; Step 3: Based on the data collected in Step 1, calculate the baseline power value using a pre-defined power metric correlation or quadratic polynomial regression model, according to the principles of dimensional analysis or response surface methodology. ; Step 4: Construct a residual neural network RNet, and use the tree-structured Parsons estimator TPE algorithm to globally optimize the hyperparameters of the residual neural network with the goal of minimizing the power prediction residual, to obtain the optimized residual neural network model. Step 5: Input the mixed feature set into the optimized residual neural network to predict the power and residual value. ; Step 6: Set the reference power value With power prediction residual Add them together to output the final predicted stirring power value. .
2. The dual-blade stirring power prediction method based on residual neural network correction according to claim 1, characterized in that, The set of mixed features: The dimensional variables include at least the blade inclination angle from the geometric parameter data. The interlayer spacing C, and the stirring speed N and fluid viscosity in the operating condition data. ; The dimensionless number includes at least the interlayer pitch-to-blade diameter ratio. propeller diameter ratio Liquid height ratio Reynolds number Re and Froude number Fr; The physical interaction term includes at least a rotational square term. Coupled term of the square of rotational speed and tilt angle Logarithmic term of rotational speed and the ratio of dip angle to inter-story spacing .
3. The dual-blade stirring power prediction method based on residual neural network correction according to claim 1, characterized in that, In step 3, the preset power coefficient correlation is constructed based on the blade type; When the two propellers are straight-bladed, the power coefficient Np is calculated using the following dimensional analysis model: ； Where K, a, b, c, d are the model constants to be fitted, ρ is the fluid density, N is the stirring speed, D1 is the diameter of the upper impeller, D2 is the diameter of the lower impeller, T is the diameter of the stirring tank, H is the liquid level height, Re is the Reynolds number, and Fr is the Froude number. When the twin propellers are oblique blade propellers, an introduction angle is used ( The modified dimensional analysis model: ； Where θ is the blade tilt angle; Then the reference power value Calculated using the following formula: 。 4. The dual-blade stirring power prediction method based on residual neural network correction according to claim 1, characterized in that, In step 3, the baseline power value is calculated using the quadratic polynomial regression model constructed using the response surface methodology (RSM). The response surface model is based on the Box-Behnken design, and its functional relationship is as follows: ； Where y is the predicted power. and The normalized design variables include rotational speed, interlayer spacing, blade tilt angle, and glycerol concentration. For constant terms, These are the regression coefficients for the linear, quadratic, and interaction terms, respectively.
5. The method for predicting the power of a dual-blade stirring apparatus based on residual neural network correction according to claim 1, characterized in that, In step 4, the optimization objective of the tree-structured Parsons estimator TPE algorithm is to minimize the root mean square error (RMSE) on the validation set. The hyperparameter search space of the residual neural network RNet includes at least the number of hidden layers, the number of neurons in each layer, the learning rate, and the batch size.
6. The method for predicting the power of a dual-blade stirring apparatus based on residual neural network correction according to claim 1, characterized in that, In step 4, the residual neural network RNet adopts a fully connected feedforward structure, with batch normalization layers and ReLU activation functions set between network layers to capture nonlinear power bias.
7. A double-layer impeller stirring power prediction system based on residual neural network correction, used to implement the method according to any one of claims 1-6, characterized in that, The system includes a data acquisition module, a feature engineering conversion module, a physical benchmark calculation module, an intelligent residual calculation module, a result fusion output module, and an output display module; The data acquisition module is used to collect the stirring speed signal of the stirring system in real time, and to acquire the preset geometric parameters of the stirring system and the viscosity data of the fluid material. The feature engineering conversion module is connected to the data acquisition module. Based on the acquired data, it constructs a hybrid feature set containing dimensional variables, dimensionless numbers, and physical interaction terms. The physical reference calculation module is connected to the data acquisition module. It is used to store the preset physical reference mathematical model and calculate the reference power based on the rotational speed, geometric parameters and viscosity data provided by the data acquisition module. The intelligent residual calculation module uses a Bayesian optimization algorithm to automatically find the optimal hyperparameters for the residual neural network, and calculates the mixed feature data received from the feature engineering conversion module based on the optimized model, outputting the predicted power residual value. The result fusion output module is connected to the physical reference calculation module and the intelligent residual calculation module respectively, and is used to fuse the reference power value and the power residual value to output the final power prediction value. The output display module is used to output the predicted value through a display terminal.
8. The dual-blade stirring power prediction system based on residual neural network correction according to claim 7, characterized in that, The intelligent residual calculation module includes a feature input unit, a Bayesian optimization unit, and a deep learning inference unit. The feature input unit is connected to the feature engineering conversion module and is used to receive the mixed feature set. The Bayesian optimization unit uses the tree-structured Parsons estimator algorithm to globally optimize the hyperparameters of the residual neural network to obtain the optimized network model. The deep learning inference unit is connected to both the feature input unit and the Bayesian optimization unit and is used to input the mixed feature set into the optimized network model to predict the power residual value.