ELM-IGWO-based dynamic behavior prediction method for liquid drop collision diffusion

Abstract

The invention relates to a droplet collision diffusion dynamic behavior prediction method based on ELM-IGWO, and the method comprises the steps: carrying out the finite element dynamics simulation of a droplet collision and spreading process, obtaining the maximum spreading diameter and center thickness of a droplet, building an orthogonal experiment, generating a training data set of a machine learning prediction method, and carrying out the calculation of the maximum spreading diameter and center thickness of the droplet. An extreme learning machine (ELM-IGWO) prediction model based on an improved grey wolf optimization algorithm is proposed, the initial diameter, speed and height of a liquid drop and a contact angle of a material are used as inputs, the maximum spreading diameter and center thickness of the liquid drop are used as outputs, and the dynamic behavior of liquid drop impact and spreading is predicted. The generalization ability of the ELM-IGWO neural network prediction model is evaluated through cross validation; and the test set is adopted to test the precision of the ELM-IGWO neural network prediction model and perform index evaluation, so that the method can be extended to any similar form prediction of liquid drop impact and spreading, a lot of time can be saved, and the design efficiency of engineers can be improved.

Description

Technical Field

[0001] The present invention relates to a method for predicting the dynamic behavior of droplet collision and diffusion based on ELM-IGWO (Extreme Learning Machine with Improved Grey Wolf Optimization Algorithm), and belongs to the field of biomedical technology. Background Art

[0002] The dynamic contact behavior between a droplet and a solid surface, as an important research content of multiphase interface science, is widespread in nature and engineering technology fields. However, there are differences in the requirements for droplet morphology in different application scenarios. For example, in the preparation of large-area functional coatings and thin-film deposition processes, efficient material utilization and uniform coverage need to be achieved by increasing the droplet spreading diameter while reducing the central liquid film thickness; while in the field of biomedical three-dimensional printing, it is necessary to strictly control the droplet deposition diameter at the micron scale and maintain a relatively high central thickness to ensure the effective encapsulation of bioactive factors and the stable construction of the cell microenvironment. This application-oriented contradiction of morphological parameters reveals the necessity of constructing a droplet collision and diffusion prediction model. However, with the continuous increase in the complexity of computational mechanics problems, traditional finite element methods face significant computational efficiency bottlenecks in the field of engineering simulation.

[0003] During the process of droplet impact and spreading, since there are many factors affecting droplet morphology, the traditional finite element modeling process often involves cumbersome mesh generation, material parameter calibration, and iterative solution processes, resulting in high consumption of computational resources and high time costs. Different from traditional methods, emerging machine learning methods have shown unique advantages. Machine learning has achieved efficient process optimization by introducing new process modeling and optimization methods. Summary of the Invention

[0004] The current finite element simulation work of droplet collision and diffusion has a large amount of calculation and high time cost. In order to overcome the deficiencies of the prior art, the present invention provides a method for predicting the dynamic behavior of droplet collision and diffusion based on ELM-IGWO, aiming to effectively predict the maximum spreading diameter and central thickness of the droplet.

[0005] The method for predicting the dynamic behavior of droplet collision and diffusion based on ELM-IGWO includes the following steps:

[0006] Step 1: Use finite element simulation software to refine the mesh of the droplet dripping path and the droplet spreading part, and perform finite element analysis on the droplet impact and spreading process to obtain the spreading conditions of droplets with different initial states after simulation. After extracting features, calculate the droplet morphology parameters during the spreading process: the maximum spreading diameter and the central thickness, and construct a droplet impact and spreading data set;

[0007] Perform fluid-structure interaction implicit dynamics analysis using the finite element simulation software ANSYS FLUENT, and set the VOF model. When setting the boundary conditions, set the material surface boundary as a fixed boundary, and at the same time set the contact angle of the material surface to simulate the droplet impact and spreading. Create the droplet material properties and set the region, and at the same time set the diameter and height of the droplet. Initialize the model, set the value in the region to 1, representing the inside of the region as the droplet, and set the outside of the region as the air domain, and set the initial velocity of the droplet in the Y-axis direction.

[0008] Construct a finite element model for each group of data, and perform finite element simulations according to different initial states. Obtain the volume fraction cloud map after simulation for each model, extract the features, and calculate its maximum spreading diameter and central thickness through the built-in algorithm of the software to construct a dataset of droplet impact and spreading. Enter the collected data into the software Minitab for range analysis, and quantify the weight of the influence of each factor on the experimental evaluation index through range analysis, so as to obtain the influence law of each factor on the dynamic characteristics of droplet impact and spreading.

[0009] Step 2: Through orthogonal experiments, divide the data in the dataset into a training set and a test set at a ratio of 5:1.

[0010] Step 3: Use the training set to construct a neural network model. The initial diameter of the droplet, the initial velocity, the height, and the contact angle of the material surface are used as input parameters. Calculate the maximum spreading diameter and the central thickness through the ELM-IGWO neural network model, and evaluate the accuracy of the ELM-IGWO neural network prediction model with evaluation indicators. Use the test set to evaluate the generalization ability of the ELM-IGWO neural network prediction model.

[0011] Step 4: Use the test set to test and verify the accuracy of the machine learning prediction model and evaluate it with evaluation indicators. When the accuracy meets the standard, output the ELM-IGWO neural network prediction model. When the accuracy does not meet the standard, repeat Step 3 until the accuracy meets the standard. After the accuracy meets the standard, output the ELM-IGWO neural network prediction model, which is the prediction model of the maximum spreading diameter and the central thickness of the droplet collision and diffusion system.

[0012] Step 5: According to the neural network prediction of the maximum spreading diameter and the central thickness of the droplet, deduce whether it meets the application requirements and determine the initial droplet parameters that meet the droplet collision and diffusion system.

[0013] The specific method for finite element analysis of the droplet impact and spreading process in Step 1 includes:

[0014] S1.1: Preprocessing: The droplet is spherical, and during the droplet impact and spreading process, the shape of the droplet always remains centrally symmetric. The three-dimensional model can be replaced by an axial section to simplify the three-dimensional simulation into a two-dimensional simulation.

[0015] S1.2: Finite element analysis. When setting boundary conditions, set the boundary of the material surface as a fixed boundary and set the contact angle of the material surface at the same time; set the pressure outlet and the initial conditions of the VOF model; define the height and initial diameter of the droplet by creating a region; initialize the droplet, set the created region as 1, indicating that the region is liquid, and the velocity in the Y direction is the initial velocity of the droplet, and conduct finite element simulation analysis on the droplet impact and spreading process;

[0016] S1.3: In the post-processing stage, create an isosurface, record the spreading diameter and thickness during the droplet impact and spreading process, and calculate the maximum spreading diameter and the central thickness of the droplet.

[0017] The dataset in the second step specifically includes: four dimensional parameters of the initial diameter, velocity, height of the droplet and the contact angle of the material surface in the droplet collision and diffusion system, and two output parameters of the maximum spreading diameter and the central thickness. Different finite element models are constructed by changing the magnitudes of these parameters, and the output parameters are the maximum spreading diameter and the central thickness.

[0018] The neural network model in the third step selects the ELM-IGWO neural network; there is a complex non-linear relationship between the input and output. The ELM-IGWO neural network can avoid falling into the local optimal problem and is easier to find the global optimal solution; the number of input parameters is 4, the number of output parameters is 2, the number of neurons in the hidden layer is 7, the maximum number of iteration steps is 1000, and the learning rate is set to 0.1.

[0019] The core of the present invention is to obtain the maximum spreading diameter and the central thickness of the droplet through finite element dynamic simulation of the droplet impact and spreading process. An orthogonal experiment is established to generate a training dataset for the machine learning prediction method, and a prediction model of the extreme learning machine based on the improved grey wolf optimization algorithm (ELM-IGWO) is proposed. Using the initial diameter, velocity, height of the droplet and the contact angle of the material as inputs, and the maximum spreading diameter and the central thickness of the droplet as outputs, predict the dynamic behavior of the droplet impact and spreading, and use cross-validation to evaluate the generalization ability of the ELM-IGWO neural network prediction model; use the test set to test the accuracy of the ELM-IGWO neural network prediction model and conduct index evaluation.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0021] The present invention overcomes the limitations of traditional finite element methods, reduces labor costs, saves time costs, and improves efficiency. The present invention combines finite element simulation with neural networks, avoiding problems such as complex algorithms and large computational amounts caused by overusing neural networks, and also making up for the limitations of finite element simulation analysis. Through the perfect combination of the two technologies, the morphology after droplet collision and diffusion can be predicted quickly and efficiently. This method can be extended to the morphology prediction of any similar droplet impact and spreading, saving a large amount of time and improving the design efficiency of engineers. Brief Description of the Drawings

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0023] Figure 1 It is a schematic diagram of the mesh division for the dynamic behavior prediction method of droplet collision and diffusion based on ELM-IGWO of the present invention.

[0024] Figure 2 It is a three-dimensional model diagram of the dynamic behavior prediction method of droplet collision and diffusion based on ELM-IGWO of the present invention.

[0025] Figure 3 It is a structural diagram of the ELM-IGWO neural network for the dynamic behavior prediction method of droplet collision and diffusion based on ELM-IGWO of the present invention. Detailed Embodiments

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0027] Refer to Figures 1 - 3 , the dynamic behavior prediction method of droplet collision and diffusion based on ELM-IGWO includes the following steps:

[0028] Step 1: Use finite element simulation software to refine the mesh of the droplet dripping path and the droplet spreading part, and conduct finite element analysis on the droplet impact and spreading process to obtain the spreading conditions of droplets after simulation with different initial states. After extracting features, calculate the droplet morphology parameters during the spreading process: the maximum spreading diameter and the central thickness, and construct a dataset of droplet impact and spreading.

[0029] Specifically, ANSYS MESH is used for meshing, and the meshes of the droplet dripping path and the droplet spreading part are refined. As Figure 1 shown, at the center and the wall surface at the bottom, the mesh sizes vary from 0.5 mm to 0.01 mm. A mesh sensitivity test is carried out, and the final result is that the mesh size of the wall is 0.01 mm to ensure the accuracy of the simulation results.

[0030] The fluid-structure interaction implicit dynamics analysis is carried out using the finite element simulation software ANSYS Fluent, and the VOF model is set; when setting the boundary conditions, the material surface boundary is set as a fixed boundary, and at the same time the contact angle of the material surface is set to simulate the droplet impact and spreading conditions. The material properties of the droplet are created. The fluid material is: an incompressible fluid with a viscosity of 0.02 Pa·s and a density of 1.45 g / cm 3 , and the surface tension is 0.05 N·m -1 . A droplet region is created, and at the same time the diameter and height of the droplet are set. The model is initialized, and the values in the region are set to 1, representing that the inside of the region is the droplet, and the outside of the region is set as the air domain, and the initial velocity of the droplet is set in the Y-axis direction. A finite element model is constructed for each group of data, and finite element simulations are carried out according to different initial states. The volume fraction cloud map after the simulation of each model is obtained, and the maximum spreading diameter and the central thickness are calculated through the built-in algorithm of the software after extracting the features, and a dataset of droplet impact and spreading is constructed.

[0031] The collected data is entered into the software Minitab for range analysis, and the range analysis is used to quantify the weights of the influence of various factors on the experimental evaluation index, so as to obtain the influence law of various factors on the dynamic characteristics of droplet impact and spreading.

[0032] Step 2: Adopt the Taguchi orthogonal experiment. 25 groups of parameter configurations with balanced representativeness are generated through the orthogonal table, and 5 groups of extreme value combinations are supplemented to form 30 groups of full-factor experimental data. Based on the principle of orthogonal experiment, the data in the dataset is divided into a training set and a test set at a ratio of 5:1;

[0033] Specifically, the Taguchi orthogonal array method is adopted to generate 4 factors with 5 different levels of system parameter combinations. 25 groups of parameter configurations are generated through matrix row vector mapping to ensure that the different levels of each parameter appear with equal frequency (each level appears 5 times), and the interaction of any two parameters is evenly distributed in the experiment. On the basis of the orthogonal test matrix, 5 additional extreme combinations containing parameter boundary values are added to form a complete data set containing 30 groups of parameters. This design not only maintains the balance of the orthogonal test but also enhances the coverage ability of the system's extreme working conditions. The first 25 groups are used as the training set, and the last 5 groups are used as the test set, ensuring that: the training set completely contains the standard orthogonal combinations of all parameter levels; the test set covers the key areas of the parameter space boundary; the training / test set maintains projection balance in the parameter dimension (each parameter level appears once in the test set); compared with the random division method, this strategy enables the test set to have better parameter space coverage and verification effectiveness of the model generalization ability, while avoiding evaluation biases caused by random sampling.

[0034] Step 3: Use the training set to construct a neural network model. The initial diameter of the droplet, the initial velocity, the height, and the contact angle of the material surface are used as input parameters. The maximum spreading diameter and the central thickness are calculated through the ELM-IGWO neural network model, and the accuracy of the ELM-IGWO neural network prediction model is evaluated by evaluation indexes. The generalization ability of the ELM-IGWO neural network prediction model is evaluated using the test set.

[0035] Specifically, use the training set to construct a neural network model as Figure 2 shown. The initial diameter of the droplet (d), the height (h), the initial velocity (u), and the contact angle of the material surface (α) are used as input parameters. The maximum spreading diameter and the central thickness are predicted through the ELM-IGWO neural network model. The accuracy of the ELM-IGWO neural network prediction model is evaluated by indexes, and the generalization ability of the ELM-IGWO neural network prediction model is evaluated using the test set.

[0036] The evaluation indexes are the coefficient of determination R 2 , the root mean square error RMSE, and the mean absolute error MAE. The calculation formulas for the coefficient of determination R 2 , the root mean square error RMSE, and the mean absolute error MAE are as follows:

[0037]

[0038]

[0039]

[0040] In the formula, N is the total number of samples, , and They are the experimental values, the predicted outputs, and the average of the predicted outputs, respectively.

[0041] Step 4: Use the test set to test and verify the accuracy of the machine learning prediction model and evaluate it with evaluation metrics. When the accuracy meets the standard, output the ELM-IGWO neural network prediction model. When the accuracy does not meet the standard, repeat Step 3 until the accuracy meets the standard. After the accuracy meets the standard, output the ELM-IGWO neural network prediction model, which is the prediction model for the maximum spreading diameter and the central thickness of the droplet collision and diffusion system.

[0042] Step 5: Based on the neural network prediction of the maximum spreading diameter and the central thickness of the droplet, deduce whether the application requirements are met and determine the initial droplet parameters that meet the droplet collision and diffusion system.

[0043] The specific finite element analysis method for the droplet impact and spreading process in Step 1 includes:

[0044] S1.1: Preprocessing: The droplet is spherical, and during the droplet impact and spreading process, the shape of the droplet always remains centrally symmetric. Its three-dimensional model can be replaced by an axial section to simplify the three-dimensional simulation into a two-dimensional simulation.

[0045] S1.2: Finite element analysis: When setting the boundary conditions, set the material surface boundary as a fixed boundary and set the contact angle of the material surface at the same time. Set the pressure outlet and the initial conditions of the VOF model. Define the height and initial diameter of the droplet by creating a region. Initialize the droplet, set the created region as 1, representing that the region is liquid, and the velocity in the Y direction is the initial velocity of the droplet, and conduct a finite element simulation analysis on the droplet impact and spreading process.

[0046] S1.3: In the post-processing stage, create an isosurface, record the spreading diameter and thickness during the droplet impact and spreading process, and calculate the maximum spreading diameter and the central thickness of the droplet.

[0047] The dataset in Step 2 specifically includes: the initial diameter, velocity, height of the droplet in the droplet collision and diffusion system, and 4 dimensional parameters of the contact angle of the material surface, as well as 2 output parameters of the maximum spreading diameter and the central thickness. Through the Taguchi orthogonal experimental design method, 30 different finite element models are established, and the specific values are as follows:

[0048] Initial diameter of the droplet (d / mm): 0.5, 0.75, 1, 1.25, 1.5.

[0049] Initial velocity of the droplet (u / ms^-2): 1, 2, 3, 4, 5.

[0050] Initial height of the droplet (h / mm): 5, 10, 15, 20, 25.

[0051] Contact angle of the material surface (α / °): 30, 60, 90, 120, 150.

[0052] In step 3, the neural network model selects the ELM-IGWO neural network; there is a complex non-linear relationship between the input and output, and the ELM-IGWO neural network can avoid falling into the local optimal problem and is more likely to find the global optimal solution; the number of input parameters is 4, the number of output parameters is 2, the number of neurons in the hidden layer is 7, the maximum number of iteration steps is 1000, and the learning rate is set to 0.1.

[0053] The present invention uses finite element simulation to construct a dataset of droplet impact and spreading, preprocesses the data in the dataset, divides it into a training set and a test set according to a certain ratio, uses the ELM-IGWO neural network to construct a prediction model for the maximum spreading diameter and central thickness of the droplet, uses the test set to test the reliability of the model, and uses numerical indicators such as the correlation coefficient R2 and the root mean square error RMSE to evaluate the accuracy of the model, and finally obtains the best prediction model. This prediction model can predict the maximum spreading diameter and central thickness during the droplet collision and diffusion process, so as to obtain the morphology of the droplet after collision and diffusion with different initial states. Using this prediction method can improve the calculation efficiency and shorten the time cost.

[0054] The embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principle and spirit of the present invention, various changes, modifications, substitutions, and variations to these embodiments still fall within the protection scope of the present invention.

Claims

1. A dynamic behavior prediction method for droplet collision and diffusion based on ELM-IGWO, characterized in that: It includes the following steps: Step 1: Use finite element simulation software to refine the mesh of the droplet's dripping path and the spreading part of the droplet, conduct finite element analysis on the droplet impact and spreading process, obtain the spreading conditions of droplets with different initial states after simulation, extract features, and calculate the droplet shape parameters during the spreading process: the maximum spreading diameter and the central thickness, and construct a dataset of droplet impact and spreading; Step 2: Through orthogonal experiments, divide the data in the dataset into a training set and a test set; Step 3: Use the training set to construct a neural network model. The initial diameter, initial velocity, height of the droplet, and the contact angle of the material surface are used as input parameters. Calculate the maximum spreading diameter and the central thickness through the ELM-IGWO neural network model, evaluate the accuracy of the ELM-IGWO neural network prediction model with evaluation indicators, and use the test set to evaluate the generalization ability of the ELM-IGWO neural network prediction model; Step 4: Use the test set to test and verify the accuracy of the machine learning prediction model and evaluate it with evaluation indicators. When the accuracy meets the standard, output the ELM-IGWO neural network prediction model. When the accuracy does not meet the standard, repeat Step 3 until the accuracy meets the standard; after the accuracy meets the standard, output the ELM-IGWO neural network prediction model, which is the prediction model of the maximum spreading diameter and the central thickness of the droplet collision and diffusion system; Step 5: Based on the neural network prediction of the maximum spreading diameter and the central thickness of the droplet, deduce whether it meets the application requirements and determine the initial droplet parameters that conform to the droplet collision and diffusion system.

2. The dynamic behavior prediction method for droplet collision and diffusion based on ELM-IGWO according to claim 1, characterized in that: The specific method for finite element analysis of the droplet impact and spreading process in Step 1 includes: S1.1: Preprocessing: The droplet is spherical, and during the droplet impact and spreading process, the shape of the droplet always remains centrally symmetric. Its three-dimensional model can be replaced by an axial section to simplify the three-dimensional simulation into a two-dimensional simulation; S1.2: Finite element analysis: When setting the boundary conditions, set the material surface boundary as a fixed boundary and simultaneously set the contact angle of the material surface; set the pressure outlet and the initial conditions of the VOF model; define the height and initial diameter of the droplet by creating a region; initialize the droplet, set the created region as 1, representing that the region is liquid, and the velocity in the Y direction is the initial velocity of the droplet, and conduct finite element simulation analysis on the droplet impact and spreading process; S1.3: Post-processing stage: Create an isosurface, record the spreading diameter and thickness during the droplet impact and spreading process, and calculate the maximum spreading diameter and the central thickness of the droplet.

3. The dynamic behavior prediction method for droplet collision and diffusion based on ELM-IGWO according to claim 1, characterized in that: The data in the dataset in Step 2 specifically includes: the initial diameter, velocity, height of the droplet, and the contact angle of the material surface in the droplet collision and diffusion system, which are 4 dimensional parameters, and the maximum spreading diameter and the central thickness, which are 2 output parameters. Different finite element models are constructed by changing the sizes of these parameters, and the output parameters are the maximum spreading diameter and the central thickness.

4. The dynamic behavior prediction method for droplet collision and diffusion based on ELM-IGWO according to claim 1, wherein: In step 3, the neural network model selects the ELM-IGWO neural network; there is a complex non-linear relationship between the input and output. The ELM-IGWO neural network can avoid falling into the local optimal problem and easily find the global optimal solution; the number of input parameters is 4, the number of output parameters is 2, the number of neurons in the hidden layer is 7, the maximum number of iteration steps is 1000, and the learning rate is set to 0.

1.

5. The dynamic behavior prediction method of droplet collision and diffusion based on ELM-IGWO according to claim 1, characterized in that: In step 1, constructing the droplet impact and spreading dataset includes: entering the collected dataset into the software Minitab for range analysis, and quantifying the weights of the influence of various factors on the experimental evaluation index through range analysis to obtain the influence law of various factors on the dynamic characteristics of droplet impact and spreading.

6. The dynamic behavior prediction method for droplet collision and diffusion based on ELM-IGWO according to claim 1, characterized in that: In the third step, the evaluation indicators are the coefficient of determination R 2 , root mean square error RMSE, and mean absolute error MAE. The calculation formulas for the coefficient of determination R 2 , root mean square error RMSE, and mean absolute error MAE are as follows: ； ； ； where N is the total number of samples, , and are the experimental value, the predicted output, and the average value of the predicted output, respectively.

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