A Prediction Method for Particle Collision Characteristics in Solid-State Additive Manufacturing Based on Machine Learning

Abstract

The present invention provides a method for predicting the particle collision characteristics in solid-state additive manufacturing based on machine learning. On the basis of multiple simulations, the existing data is sorted out, and an artificial neural network is established based on machine learning. By making full use of the existing simulation data, the prediction of the particle collision characteristics under unknown parameters is realized, saving time and computational costs and achieving rapid prediction; it is convenient to study the influence of multiple experimental parameters on the simulation results simultaneously.

Description

Technical Field

[0001] The present invention belongs to the fields of cold spray solid-state additive manufacturing and artificial intelligence, and particularly relates to a method for predicting the particle collision characteristics of solid-state additive manufacturing based on machine learning. Background Art

[0002] As a new type of solid-state additive manufacturing technology, cold spray drives powder particles to collide with a substrate at a temperature below the melting point of the material through a supersonic gas flow. A metallurgical or mechanical bond is formed between the particles and the substrate, thereby preparing a coating with high density and high bond strength. It has the advantages of high spraying rate, low residual stress of the coating, and small thermal impact on the substrate.

[0003] Studying the bonding mechanism between the coating and the substrate is of great significance for expanding the application scope of cold spray. However, under high-speed collisions, the collision characteristics of particles and the substrate are difficult to study under experimental conditions. Therefore, numerical simulation has become the main method for studying particle collision characteristics.

[0004] Currently, most models for studying particle collision characteristics are mostly based on the Lagrangian method and two-dimensional models, and cannot truly and effectively predict particle collisions. On this basis, the prediction accuracy is necessarily unable to meet the requirements. For a quarter three-dimensional model based on the Euler method, when the substrate radius is 100 μm, the particle size is 30 μm, the global mesh size is 1 μm, and the local size is 0.5 μm, the calculation time is more than 5 hours. When the global mesh size is 0.8 μm and the local size is 0.3 μm, the calculation time is 45 h.

[0005] When using finite element simulation for research, the factors affecting particle collision characteristics also include the modeling method, mesh division method, mesh size, etc. When any one of the above factors such as particle collision speed, particle or substrate temperature, model size, and mesh size changes, it is necessary to re-model or set relevant parameters and recalculate. It often takes 5 to 6 hours for the computer to obtain results under multi-core operation, and the time and material costs for each operation are relatively high.

[0006] Artificial neural networks have the abilities of self-learning, self-organization, fault tolerance, and self-repair, and have great potential in solving non-linear and severely uncertain systems. They have been applied to predict welding performance, hydrological conditions, boiler heating surface areas, etc. Compared with re-establishing a model for calculation, artificial neural networks can achieve rapid prediction, with an average time of within 10 minutes. Therefore, it is necessary to establish a three-dimensional solid-state additive manufacturing particle collision model using the Euler method, establish a relevant database, and realize the prediction of particle collision characteristics under different parameters through artificial neural networks, which greatly saves the calculation cost, is simple to operate, has high efficiency, and also effectively utilizes the existing calculation results. Summary of the Invention

[0007] The technical problem solved by the present invention is: to solve the technical problems that the existing simulation methods do not conform to the actual situation and the prediction methods are time-consuming and laborious. The present invention proposes a prediction method for the particle collision characteristics of solid-state additive manufacturing based on machine learning. A three-dimensional particle collision model is established by using the Euler method. On the basis of multiple simulations, the existing data is sorted out, and an artificial neural network is established based on machine learning, making full use of the existing simulation data to realize the prediction of the particle collision characteristics under unknown parameters, saving time and calculation costs, and achieving rapid prediction; it is convenient to study the influence of multiple experimental parameters on the simulation results at the same time.

[0008] The technical solution of the present invention is: a prediction method for the particle collision characteristics of solid-state additive manufacturing based on machine learning, comprising the following steps:

[0009] Step 1: Select input variables and output variables according to needs, and determine the number of nodes in the input layer and the number of nodes in the output layer of the neural network;

[0010] Step 2: Based on the Euler method, establish a three-dimensional solid-state additive manufacturing particle collision model, set parameters based on the input variables determined in Step 1, and integrate the calculation results of the corresponding parameters of the output variables to establish a data set;

[0011] Step 3: Create a neural network, use the data set established in Step 2 for training and testing, and optimize the neural network;

[0012] Step 4: Use the neural network optimized in Step 3, write in the values of any input variables, and obtain the corresponding values of the output variables, which are the obtained prediction values.

[0013] A further technical solution of the present invention is: the Step 2 includes the following sub-steps:

[0014] Step 2.1: Establish a three-dimensional finite element single-particle collision model, define the model angle, mesh type, mesh size, and perform local seeding on the particle part;

[0015] Step 2.2: After obtaining several groups of data according to Step 2.2, shuffle all the data of the input layer and the corresponding output layer before creating the artificial neural network, and at least 80% of the data is used as the training set, and the remaining data is used as the test set;

[0016] Step 2.3: Perform minimum-maximum normalization processing on the data of the input layer, and map the data set to [0,1] or [-1,1]:

[0017]

[0018] where x is the sample data, x * is the value of the sample data mapped to the data set mapped to [0,1] or [-1,1], xmax is the maximum value of the sample data, x min is the minimum value of the sample data.

[0019] A further technical solution of the present invention is that the optimization in step 3 includes the determination of the activation function, the number of hidden layer nodes, the number of iterations, and the learning rate.

[0020] A further technical solution of the present invention is that the activation function optimizes the neural network by adjusting three activation functions, namely Sigmoid, Tanh, and Rule, and their combined modes.

[0021] A further technical solution of the present invention is that the determination of the number of hidden layers is as follows:

[0022]

[0023] where m is the number of hidden layer nodes, n is the number of input layer nodes, l is the number of output layer nodes, and α is a constant between 1 and 10.

[0024] A further technical solution of the present invention is that the required initial number of iterations is 500.

[0025] A further technical solution of the present invention is that the learning rate is set to be 0.01 - 0.5.

[0026] Advantages of the Invention

[0027] The technical effect of the present invention is as follows: Compared with the prior art, the present invention has the following advantages:

[0028] 1. It realizes the rapid prediction of the particle collision characteristics in solid-state additive manufacturing, with high prediction efficiency and small error. The artificial neural network can perform batch prediction, and the time for each prediction is less than 10 minutes, greatly reducing the time cost. It can also be realized without a high-performance workstation, saving the material cost. From the verification set results of Example 1 and Example 2, such as Figure 4 and Figure 9 , it can be seen that the error can be controlled within 5%. Compared with re-establishing a model, setting parameters, and submitting working files for calculation, the artificial neural network of machine learning can perform prediction within a certain error range based on the existing data, improve the prediction accuracy through optimization, and reduce the calculation cost and time cost of re-simulation.

[0029] 2. Using the Euler method to establish a three-dimensional model is closer to the actual situation and improves the accuracy of predicting particle collision characteristics.

[0030] 2. Systematically study the influence of multiple independent variables on the particle collision characteristics in solid-state additive manufacturing. Since it takes a large amount of time to perform calculations using the reconstructed model, most previous particle collision simulations have studied the influence of several parameters, such as the material properties of the particles and the substrate, and the particle collision velocity, on the particle collision characteristics. By using the present invention, the prediction of the particle collision characteristics under the action of multiple factors and multiple parameters can be realized through the trained network, and a systematic study of multiple independent variables, such as the model angle, particle size, particle temperature, and substrate temperature, on the particle collision characteristics in solid-state additive manufacturing can be achieved.

[0031] 3. Provide a reference for predicting the critical deposition velocity of particles. When the particle collision velocity is greater than the critical deposition velocity, the particles can deposit on the substrate surface to form a coating. Currently, there are mainly two methods for predicting the critical deposition velocity of particles using finite element simulation. One is to take the collision velocity when a single particle shows a jet as the particle critical velocity; the other is to take the collision velocity when the equivalent plastic strain of the particle shows a mutation as the particle critical velocity. By using the present invention, the equivalent plastic strain of the particles can be effectively predicted, thereby obtaining the mutation position and predicting the critical velocity of the particles.

[0032] In summary, based on the existing simulation data, the present invention integrates the relevant data and performs prediction through a machine learning artificial neural network, and can efficiently and accurately obtain the output variable data under different input variables, realizing the effective prediction of the particle collision characteristics in solid-state additive manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flowchart of the present invention

[0034] Figure 2 It is a structure diagram of the artificial neural network in Embodiment 1

[0035] Figure 3 It is a curve diagram of the predicted value and the actual value of the test set in Embodiment 1

[0036] Figure 4 It is a relative error curve diagram of the predicted value and the actual value of the test set in Embodiment 1

[0037] Figure 5 It is a structure diagram of the artificial neural network in Embodiment 2

[0038] Figure 6 It is a curve diagram of the predicted value and the actual value of the particle equivalent plastic strain of the test set in Embodiment 2

[0039] Figure 7 It is a curve diagram of the predicted value and the actual value of the particle compression ratio of the test set in Embodiment 2

[0040] Figure 8 It is a curve diagram of the predicted value and the actual value of the substrate pit depth of the test set in Embodiment 2

[0041] Figure 9 The relative error curve graph of the predicted values and the actual values of the outputs of each item in the test set in Example 2 Specific implementation manners

[0042] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0043] See Figures 1-9 , a method for predicting the particle collision characteristics in cold spraying based on an artificial neural network, characterized by at least including the following steps:

[0044] Step 1: Based on the particle collision model and the research content, select the required input variables and output variables, and determine the number of nodes in the input layer and the number of nodes in the output layer of the neural network;

[0045] The input variables refer to the variable types that will cause changes in the results during the simulation process, which are equivalent to independent variables. Data such as particle size, collision speed, particle temperature, substrate temperature, particle collision angle, modeling method, and the size of the divided grid can all be used as the input parameters of the neural network. Generally, the number of nodes in the input layer is 3 to 10.

[0046] The output variables refer to the variable types that are meaningful for the research content included in the simulation results. Data such as particle flattening ratio, substrate pit depth, particle equivalent plastic strain, particle temperature, substrate temperature, etc. can all be used as the output parameters of the neural network. Generally, the number of nodes in the output layer is 1 to 6.

[0047] Step 2: Establish a solid-state additive manufacturing particle collision model, perform parameter settings based on the input variables determined in Step 1, and integrate the calculation results. Establish a data set for the machine learning artificial neural network, which is divided into input layer data and output layer data according to variables, and is divided into a training set and a test set according to usage requirements.

[0048] The model is a three-dimensional model based on the Euler method. The single-particle model can adjust the model angle size according to requirements, and the grid type is EC3D8RT, which can simultaneously analyze the stress field and the temperature field.

[0049] In order to avoid singularity, the data of the input layer needs to be normalized. The normalization method can be min-max normalization or mean-variance normalization depending on the sample data, and the dataset can be mapped within [0, 1] or [-1, 1].

[0050] Before the network training, the dataset needs to be shuffled and divided into a training set and a test set. It is required that at least 80% of the data is used as the training set, and the remaining data is used as the test set to test the reliability of the network.

[0051] Step 3: Create a neural network and use the dataset established in Step 2 for training and testing, and optimize the neural network according to the test accuracy requirements;

[0052] The optimization includes the optimization of activation functions, the number of hidden layer nodes, the number of iterations, the learning rate, etc.

[0053] The activation function optimizes and improves the neural network by adjusting three activation functions, namely Sigmoid, Tanh, and ReLU, and their combined modes.

[0054] The number of hidden layers is determined by the following empirical formula:

[0055]

[0056] where m is the number of hidden layer nodes, n is the number of input layer nodes, l is the number of output layer nodes, and α is a constant between 1 and 10.

[0057] The test accuracy is that the deviation between the predicted value and the target value is within 5%.

[0058] The number of iterations refers to the complete training times of the model from all data in the training set, which is adjusted according to the size of the dataset and the required accuracy. The initial number of iterations should be greater than 500 to avoid non-convergence due to too low number of iterations.

[0059] The learning rate refers to the magnitude of each parameter update. If the learning rate is too large, the parameter to be optimized will fluctuate near the minimum value and even non-convergence may occur; if the learning rate is too small, the convergence speed of the parameter to be optimized will be slow. Generally, the learning rate is set to 0.01 - 0.5.

[0060] The output data of the test set needs to be de-normalized to obtain the predicted value, and the de-normalization method corresponds to the normalization method of the input data.

[0061] Step 4: Obtain the expected output variable values under other input variables based on the neural network optimized in Step 3.

[0062] Write the input layer data corresponding to the data to be predicted into Matlab, perform normalization processing, and make predictions through the trained network to obtain the corresponding output layer data.

[0063] The following further illustrates the present invention with specific examples.

[0064] Example 1

[0065] Taking the collision of pure aluminum particles with a particle size of 30 μm against a copper substrate as an example, predict the stable maximum equivalent plastic strain of the particles at different collision speeds and particle preheating temperatures. The specific method of this example includes the following steps:

[0066] Step 1: Based on the particle collision model and research content, select the required input variables and output variables, and determine the number of input layer nodes and output layer nodes of the neural network;

[0067] In this example, the input variables are the particle collision speed and the particle preheating temperature, and the output variable is the stable maximum PEEQ of the particles. Therefore, the number of input layer nodes is 2, and the number of output layer nodes is 1.

[0068] Step 2: Establish a solid-state additive manufacturing particle collision model, set parameters based on the input variables determined in Step 1, and integrate the calculation results. Establish a data set for the machine learning artificial neural network;

[0069] In this embodiment, the ABAQUS software is used to establish a three-dimensional finite element single-particle collision model based on the Euler method. The model angle is 90°, the mesh type is EC3D8RT, the global mesh size is 0.1 μm, and local seeding is performed on the particle part with a size of 0.5 μm.

[0070] In this example, the existing data is organized into an excel file, and different positions are divided according to the input and output data for easy extraction in Matlab. Table 1 shows the numerical range of the input layer variables. The particle collision speed is between 700 m / s and 1010 m / s, and the particle preheating temperature is between 25 °C and 325 °C, with a total of 31 groups of data.

[0071] Table 1 Input layer variables for predicting Example 1

[0072]

[0073]

[0074] In this example, in order to further improve the accuracy of the neural network, all the input layer and corresponding output layer data are shuffled before creating the artificial neural network. Among them, 26 groups of data are used to train the network, and the remaining 5 groups of data are used as the test set.

[0075] In this example, the data of the input layer is normalized by the maximum and minimum values and mapped to [0, 1], which is convenient for reasonably predicting the weights of different input layer nodes. The normalization formula is as follows:

[0076]

[0077] where x is the sample data, and x * is the value of the sample data mapped to [0, 1], x max is the maximum value of the sample data, and x min is the minimum value of the sample data.

[0078] Step 3: Build a neural network and use the data set established in Step 2 for training and testing, and optimize the neural network according to the test accuracy requirements;

[0079] The activation function selected in this example is the Sigmoid function.

[0080] In this example, the number of hidden layer nodes is determined by the golden section method, and the formula is as follows:

[0081]

[0082] where m is the number of hidden layer nodes, n is the number of input layer nodes, l is the number of output layer nodes, and α is a constant between 1 and 10.

[0083] In this example, the number of hidden layer nodes is initially selected as 3, the number of iterations is 1000, and the learning rate is 0.02. The training ends when the root mean square error between the predicted value and the actual value in the test set is less than 1e-7. After learning, it is found that the current network can obtain predictions within the error range, so no further optimization is performed. The structure diagram of the constructed neural network is as Figure 2 shown.

[0084] The curve diagram of the predicted value and the actual value of the test set is as Figure 3 shown, and the relative error curve is as Figure 4 shown, both of which are less than 1%. After calculation, R 2 = 0.99, close to 1, and the prediction effect is good.

[0085] Step 4: Obtain the expected output variable values under other input variables based on the neural network optimized in Step 3;

[0086] Based on the above trained network, input the data to be measured: the particle collision speed is 955 m / s, and the particle preheating temperature is 25 °C, and the corresponding equivalent plastic strain of the particle is 2.9256.

[0087] Example 2

[0088] Taking the collision of pure aluminum particles with a copper substrate as an example, predict the maximum stable equivalent plastic strain, particle flattening ratio, and substrate pit depth of particles under different particle sizes, particle collision velocities, particle preheating temperatures, and model rotation angles. The steps are as follows:

[0089] Step 1: Based on the particle collision model and research content, select the required input variables and output variables, and determine the number of nodes in the input layer and output layer of the neural network;

[0090] The input variables in this example are particle size, particle collision velocity, particle preheating temperature, and model rotation angle, and the output variables are the maximum stable equivalent plastic strain of the particles, particle compression ratio, and substrate pit depth. Therefore, the number of nodes in the input layer is 4, and the number of nodes in the output layer is 3.

[0091] Step 2: Establish a solid-state additive manufacturing particle collision model, set parameters based on the input variables determined in Step 1, and integrate the calculation results. Establish a dataset for the machine learning artificial neural network;

[0092] In this embodiment, the mesh type and mesh size are the same as those in Embodiment 1. The difference is that the model angles in this embodiment are 5°, 10°, and 90°.

[0093] In this example, the existing data is stored in matlab in a.mat file, distinguished by different names for the input and output data, and the save function is called to save. Table 2 shows the numerical range of the input layer variables, with a total of 48 groups of data.

[0094] Table 2 is used to predict the input layer variables of Embodiment 2

[0095]

[0096] In this example, to further improve the accuracy of the neural network, the same as Embodiment 1, all the input layer and corresponding output layer data are shuffled before creating the artificial neural network. Among them, 44 groups of data are used to train the network, and the remaining 4 groups of data are used as the test set.

[0097] Perform the same normalization processing on the input data as in Embodiment 1

[0098] Step 3: Build a neural network and use the dataset established in Step 2 for training and testing, and optimize the neural network according to the test accuracy requirements;

[0099] The activation function selected in this example is the same as that in Embodiment 1, which is the Sigmoid function.

[0100] In this example, the determination of the number of hidden layer nodes is the same as that in Example 1. The golden section method is adopted, and the range is 4-13. Since the network in this example is more complex than the network in Example 1, the number of hidden layer nodes and the learning rate need to be determined through multiple trainings. After optimizing the network multiple times, finally, the number of hidden layer nodes is selected as 8, the number of iterations is 2000, and the learning rate is 0.01. The training ends when the root mean square error between the predicted value and the actual value in the test set is less than 1e-6, and the error of the test set is within 5%. The artificial neural network structure formed is as Figure 4 shown. The activation function is the same as that in Example 1.

[0101] The output layer data corresponding to the test set: particle equivalent plastic strain, particle compression rate, and substrate pit depth. The curve graphs of the predicted values and the actual values are respectively as Figure 6 , Figure 7 , Figure 8 shown. The relative error curve is as Figure 9 shown. After calculation, the R 2 corresponding to the three variables is 0.99, close to 1, and the prediction effect is good.

[0102] Step 4: Obtain the expected output variable values under other input variables based on the neural network optimized in Step 3.

[0103] Based on the above trained network, input the data to be measured: the particle size is 25 μm, the particle collision speed is 835 m / s, the particle preheating temperature is 125 °C, and the model angle is 70°. The corresponding particle equivalent plastic strain is 5.5246, the particle compression rate is 0.7838, and the substrate pit depth is 7.966.

Claims

1. A method for predicting particle collision characteristics in solid-state additive manufacturing based on machine learning, characterized in that, it includes the following steps: Step 1: Select input variables and output variables as needed, and determine the number of nodes in the input layer and output layer of the neural network; Step 2: Based on the Euler method, establish a three-dimensional solid-state additive manufacturing particle collision model, set parameters based on the input variables determined in Step 1, and integrate the calculation results of the corresponding parameters of the output variables to establish a data set, including the following sub-steps: Step 2.1: Establish a three-dimensional finite element single-particle collision model, define the model angle, mesh type, and mesh size, and perform local seeding on the particle part; Step 2.2: After obtaining several groups of data according to Step 2.2, shuffle all the data in the input layer and the corresponding output layer before creating the artificial neural network, where at least 80% of the data is used as the training set and the remaining data is used as the test set; Step 2.3: Perform minimum-maximum normalization processing on the data in the input layer and map the data set to [0,1] or [-1,1]; where x is the sample data, x * is the value obtained by mapping the sample data to map the data set within [0, 1] or [-1, 1], x max is the maximum value of the sample data, x min is the minimum value of the sample data; Step 3: Create a neural network, use the data set established in Step 2 for training and testing, and optimize the neural network; Step 4: Adopt the neural network optimized in Step 3, input the value of any input variable, and obtain the corresponding value of the output variable, which is the obtained predicted value.

2. A method for predicting particle collision characteristics in solid-state additive manufacturing based on machine learning according to claim 1, characterized in that, the optimization in Step 3 includes the determination of the activation function, the number of nodes in the hidden layer, the number of iterations, and the learning rate.

3. A method for predicting particle collision characteristics in solid-state additive manufacturing based on machine learning according to claim 2, characterized in that, the activation function optimizes the neural network by adjusting three activation functions, namely Sigmoid, Tanh, and Rule, and their combined modes.

4. A method for predicting particle collision characteristics in solid-state additive manufacturing based on machine learning according to claim 2, characterized in that, the determination of the number of hidden layers is as follows: where m is the number of nodes in the hidden layer, n is the number of nodes in the input layer, l is the number of nodes in the output layer, and α is a constant between 1 and 10.

5. A method for predicting particle collision characteristics in solid-state additive manufacturing based on machine learning according to claim 2, characterized in that, the initial number of iterations for the number of iterations is required to be 500.

6. A method for predicting particle collision characteristics in solid-state additive manufacturing based on machine learning according to claim 2, characterized in that, the learning rate is set to 0.01 - 0.5.

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