A method and system for rapidly predicting a creep stress exponent of a tin-based solder alloy using an integrated model

Abstract

The application discloses a method and system for rapidly predicting a creep stress index of a tin-based solder alloy by integrating a model, collects element compositions, test temperatures and creep stress index values of the tin-based solder alloy from literature, and adds experimental data as dataset samples; the element compositions and test temperatures of the tin-based solder alloy are sorted out and used as features for modeling; the dataset is randomly divided into a training set and a test set in a 4:1 ratio; the collected creep stress index values of the tin-based solder alloy are used as target variables, and the features are used as independent variables; based on the divided training set, the independent variables are scaled by using RobustScaler, three learners are trained and integrated to obtain an R-X-L integrated model; and the R-X-L integrated model is used to rapidly predict the creep stress index of the test set samples and four independent experimental samples. The prediction model for the creep stress index of the tin-based solder alloy is simple, fast, low-cost, pollution-free and the like based on reliable literature data and a modeling method.

Description

Technical Field

[0001] This invention relates to the field of creep properties of tin-based solder alloys, and in particular to a method for rapidly predicting the creep stress index of tin-based solder alloys using an integrated model. Technical Background

[0002] Tin-based solder alloys are the most commonly used solder alloy system for soft soldering, possessing excellent mechanical strength and hardness properties, and have been identified as a promising material in the microelectronics industry. However, the application of this alloy is hindered by the severe creep deformation that electronic devices undergo during operation or when the environment heats up. Therefore, there is a need to design tin-based solder alloys with even better creep resistance.

[0003] Traditional trial-and-error methods for designing tin-based solder alloys with high creep resistance are time-consuming and labor-intensive. Therefore, machine learning methods, such as Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), have been widely used in predicting target material properties. Using existing creep stress indices to study the creep resistance of tin-based solder alloys can significantly improve the speed of material design and is of great importance for designing high-performance tin-based solder alloys. Therefore, how to design an RXL ensemble model to quickly predict the creep stress index of tin-based solder alloys has become an urgent technical problem to be solved. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies in the testing of creep performance of tin-based solder alloys, namely high cost and low prediction accuracy. It provides a simple, fast, low-cost, and highly generalizable integrated model for rapidly predicting the creep stress index of tin-based solder alloys. This invention's integrated model completes the learning task by constructing and combining multiple learners. Compared with a single learner, it improves the accuracy and stability of prediction results, solves the overfitting problem, and improves parameter selection. This invention uses an RXL integrated model that integrates three high-performance learners to rapidly predict the creep stress index of tin-based solder alloys, significantly improving efficiency.

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

[0006] A method for rapidly predicting the creep stress index of tin-based solder alloys using an integrated model includes the following steps:

[0007] 1) Collect the elemental composition, test temperature and creep stress index values ​​of tin-based solder alloys from the literature, and add new relevant experimental data as a dataset sample;

[0008] 2) Compile the elemental composition and test temperature data of the tin-based solder alloy for use as features in the modeling;

[0009] 3) Randomly divide the dataset into training and test sets in a 4:1 ratio;

[0010] 4) Using the creep stress index values ​​of tin-based solder alloys collected in step 1) as the target variable and the features in step 2) as the independent variables, based on the training set divided in step 3), the independent variables are scaled using RobustScaler to train three learners and integrated to obtain the RXL ensemble model.

[0011] 5) Using the RXL ensemble model established in step 4), the creep stress index of the test set samples and the four independent experimental samples in step 3) is quickly predicted.

[0012] Preferably, in step 4), the specific steps for training the RXL ensemble model are as follows:

[0013] 4-1) Using the Bootstrap resampling method, multiple subsamples T are randomly selected from the overall training sample set S. TS In utilizing each T TS During model training, several attribute values ​​are randomly selected for node splitting to generate multiple regression trees to the maximum extent without pruning, ultimately forming a multivariate nonlinear regression combined learner1.

[0014] 4-2) Based on the loss function, the complexity constraint of the tree model is considered, and the loss function and complexity are combined into the objective function; the objective function of the m-th decision tree can be written as:

[0015]

[0016] Among them, y i Let F be the observation value of the i-th sample, where i = 1, ..., n, and N represents the number of samples in the dataset. m (x) represents the predicted value of the first m decision trees for this sample, x is the input value of this sample, and l is the deviation between the observed value and the predicted value calculated by the loss function for this sample; the first term of the objective function is the loss function of the original m-th decision tree, and the second term... Let T be the model complexity of the m-th decision tree, and let ω be the weights learned smoothly to avoid overfitting. Here, T is the number of leaf nodes, ω is the weight of the leaf nodes, and f is the weight of the leaf node. m This represents the predicted value of the sample within the leaf node, where γ and λ are hyperparameters.

[0017] Continuously add decision trees to the original decision tree until the objective function is minimized, then stop iterative training to obtain learner 2;

[0018] 4-3) Given a dataset {x1, ..., x...} n}, where x i For input space χ s In this context, we have a vector of dimension s; in each iteration of gradient boosting, the negative gradient of the loss function output by the model is denoted as {g1, ..., g...}. n The training samples are sorted in descending order of the absolute value of their gradients. The first a% of samples with larger gradients are set as subset A, and the remaining (1-a)% of samples with smaller gradients are set as subset A. c and from A c b% of the samples are randomly selected as subset B;

[0019] Calculate the variance gain on A∪B Select To segment the sample nodes. The definition is as follows:

[0020]

[0021] Among them, A l ={x i ∈A:x ij ≤d},A r ={x i ∈A:x ij >d}, B l ={x i ∈B:x ij ≤d},B r ={x i ∈B:x ij >d}, coefficient Used to normalize the gradient on B to A c The size of the dataset; n is the number of samples in the dataset, d is the number of sample nodes, x i For input space χ s In the vector of dimension s, g i Let A be the negative gradient of the loss function output by the model; A is the subset of samples with larger gradients selected from the top a% after sorting the training samples in descending order of the absolute value of their gradients. c B is the remaining (1-a)% small gradient sample subset, and B is the subset of samples from A. c b% of the sample size is randomly selected. Represented as x i ∈A:x ij The number of sample nodes d > d For x i ∈A:x ijThe number of sample nodes d > d, x ij Let be the j-th dimension feature of the i-th sample, i = 1, ..., n, j = 1, ..., s;

[0022] Select the corresponding sample nodes and determine the corresponding output values; repeat the above steps until the fitting accuracy threshold is reached or the upper limit of the number of trees is reached, and finally learner 3 is obtained;

[0023] 4-4) Integrate the three learners obtained in steps 4-1), 4-2), and 4-3) above to obtain the RXL ensemble model.

[0024] A system for rapidly predicting the creep stress index of tin-based solder alloys includes a memory and a processor. The memory stores computer programs, input data, and output data. The processor executes the computer program corresponding to the method for rapidly predicting the creep stress index of tin-based solder alloys using the integrated model of the present invention.

[0025] Compared with the prior art, the present invention has the following obvious and prominent substantive features and significant advantages:

[0026] 1. The method of the present invention for predicting the creep stress index of tin-based solder alloys is simple and quick. The collected tin-based solder alloy data can be imported into the established integrated model, and the calculation results can be obtained in just a few seconds.

[0027] 2. The method of the present invention can provide a method for constructing a quantitative relationship between tin-based solder alloy composition, test temperature and creep stress index, and can also be used to map a qualitative relationship between tin-based solder alloy composition, test temperature and creep stress index;

[0028] 3. The method of the present invention can effectively improve the design efficiency of tin-based solder alloys with higher creep resistance; by designing reasonable virtual samples, the method can predict the chemical formula of candidate tin-based solder alloys with higher performance, avoiding continuous trial and error and overcoming the shortcomings of traditional experimental trial and error methods.

[0029] 4. The method of this invention uses an integrated model to predict the creep stress index of tin-based solder alloys. The entire process does not involve experiments or chemicals, which is in line with the concept of green environmental protection and has low cost. Attached image description:

[0030] Figure 1 This is a diagram showing the leave-one-out method results of the training set for the RXL ensemble model of the creep stress index of the tin-based solder alloy in Embodiment 3 of the present invention.

[0031] Figure 2 The figure shows the test results of the RXL integrated model of the creep stress index of the tin-based solder alloy in Embodiment 4 of the present invention. Detailed implementation method:

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0033] Example 1

[0034] A method for rapidly predicting the creep stress index of tin-based solder alloys using an integrated model includes the following steps:

[0035] 1) Collect the elemental composition, test temperature and creep stress index values ​​of tin-based solder alloys from the literature, and add new relevant experimental data as a dataset sample;

[0036] 2) Compile the elemental composition and test temperature data of the tin-based solder alloy for use as features in the modeling;

[0037] 3) Randomly divide the dataset into training and test sets in a 4:1 ratio;

[0038] 4) Using the creep stress index values ​​of tin-based solder alloys collected in step 1) as the target variable and the features in step 2) as the independent variables, based on the training set divided in step 3), the independent variables are scaled using RobustScaler to train three learners and integrated to obtain the RXL ensemble model.

[0039] 5) Using the RXL ensemble model established in step 4), the creep stress index of the test set samples and the four independent experimental samples in step 3) is quickly predicted.

[0040] This embodiment of the integrated model completes the learning task by constructing and combining multiple learners. Compared with a single learner, it can improve the accuracy and stability of prediction results, solve the overfitting problem, and improve the selection of parameters.

[0041] Example 2

[0042] In step 4), the specific steps for training the RXL ensemble model are as follows:

[0043] 4-1) Using the Bootstrap resampling method, multiple subsamples T are randomly selected from the overall training sample set S. TS In utilizing each T TS During model training, several attribute values ​​are randomly selected for node splitting to generate multiple regression trees to the maximum extent without pruning, ultimately forming a multivariate nonlinear regression combined learner1.

[0044] 4-2) Based on the loss function, the complexity constraint of the tree model is considered, and the loss function and complexity are combined into the objective function; the objective function of the m-th decision tree can be written as:

[0045]

[0046] Among them, y i Let F be the observation value of the i-th sample, where i = 1, ..., n, and N represents the number of samples in the dataset. m (x) represents the predicted value of the first m decision trees for this sample, x is the input value of this sample, and l is the deviation between the observed value and the predicted value calculated by the loss function for this sample; the first term of the objective function is the loss function of the original m-th decision tree, and the second term... Let T be the model complexity of the m-th decision tree, and let ω be the weights learned smoothly to avoid overfitting. Here, T is the number of leaf nodes, ω is the weight of the leaf nodes, and f is the weight of the leaf node. m This represents the predicted value of the sample within the leaf node, where γ and λ are hyperparameters.

[0047] Continuously add decision trees to the original decision tree until the objective function is minimized, then stop iterative training to obtain learner 2;

[0048] 4-3) Given a dataset {x1, ..., x...} n}, where x i For input space χ s In this context, we have a vector of dimension s; in each iteration of gradient boosting, the negative gradient of the loss function output by the model is denoted as {g1, ..., g...}. n The training samples are sorted in descending order of the absolute value of their gradients. The first a% of samples with larger gradients are set as subset A, and the remaining (1-a)% of samples with smaller gradients are set as subset A. c and from A c b% of the samples are randomly selected as subset B;

[0049] Calculate the variance gain on A∪B Select To segment the sample nodes. The definition is as follows:

[0050]

[0051] Among them, A l ={x i ∈A:x ij ≤d},A r ={x i ∈A:x ij >d}, B l ={x i ∈B:x ij ≤d},B r ={x i ∈B:x ij >d}, coefficient Used to normalize the gradient on B to A c The size of the dataset; n is the number of samples in the dataset, d is the number of sample nodes, x i For input space χ s In the vector of dimension s, g i Let A be the negative gradient of the loss function output by the model; A is the subset of samples with larger gradients selected from the top a% after sorting the training samples in descending order of the absolute value of their gradients. c B is the remaining (1-a)% small gradient sample subset, and B is the subset of samples from A. c b% of the sample size is randomly selected. Represented as x i ∈A:x ij The number of sample nodes d > d For x i ∈A:x ij The number of sample nodes d > d, x ij Let be the j-th dimension feature of the i-th sample, i = 1, ..., n, j = 1, ..., s;

[0052] Select the corresponding sample nodes and determine the corresponding output values; repeat the above steps until the fitting accuracy threshold is reached or the upper limit of the number of trees is reached, and finally learner 3 is obtained;

[0053] 4-4) Integrate the three learners obtained in steps 4-1), 4-2), and 4-3) above to obtain the RXL ensemble model.

[0054] This embodiment uses an RXL ensemble model that integrates three high-performance learners to quickly predict the creep stress index of tin-based solder alloys, significantly improving efficiency. The method in this embodiment for predicting the creep stress index of tin-based solder alloys is simple and fast; by importing the collected tin-based solder alloy data into the established ensemble model, the calculation results can be obtained in just a few seconds.

[0055] Example 3

[0056] This embodiment is basically the same as the above embodiments, except that:

[0057] In this embodiment, the creep stress index of tin-based solder alloys is rapidly predicted using an integrated model, including the following steps:

[0058] (1) Chemical formulas, test temperatures, and creep stress index experimental values ​​of tin-based solder alloys were collected from the literature, resulting in 78 samples. Thirteen new experimental data points were added, bringing the total to 91 samples used as the dataset. Some of the chemical formulas, test temperatures, and creep stress index experimental values ​​of tin-based solder alloys are shown in Table 1.

[0059] Table 1. Chemical formulas, test temperatures, and experimental values ​​of creep stress index for some tin-based solder alloys of the present invention.

[0060]

[0061] (2) Organize the elemental composition of the samples in the dataset and convert the mass fractions into atomic fractions. Use the 14 elemental components and 1 test condition (temperature) as modeling features.

[0062] (3) The dataset is randomly divided into a training set and a test set in a ratio of 4:1, with 72 and 19 samples in the training set and the test set, respectively.

[0063] (4) Using the experimental values ​​of the creep stress index of the tin-based solder alloy collected in step 1) as the target variable, and the features in step 2) as the independent variables, based on the training set divided in step 3), the data is scaled using RobustScaler to train three learners and ensemble them to obtain the RXL ensemble model; the specific steps for training the RXL ensemble model are as follows:

[0064] 4-1) Use the Bootstrap resampling method to randomly select multiple subsamples T from the overall training sample set S. TS In utilizing each T TS During model training, several attribute values ​​are randomly selected for node splitting to generate multiple regression trees to the maximum extent without pruning, ultimately forming a multivariate nonlinear regression combined learner1.

[0065] 4-2) Considering the complexity constraints of the tree model based on the loss function, the loss function and complexity are combined and referred to as the objective function. The objective function of the m-th decision tree can be written as:

[0066]

[0067] Among them, y i Let F be the observation value of the i-th sample, where i = 1, ..., n, and N represents the number of samples in the dataset. m (x) represents the predicted value of the first m decision trees for this sample, x is the input value of this sample, and l is the deviation between the observed value and the predicted value calculated by the loss function for this sample; the first term of the objective function is the loss function of the original m-th decision tree, and the second term... Let T be the model complexity of the m-th decision tree, and let ω be the weights learned smoothly to avoid overfitting. Here, T is the number of leaf nodes, ω is the weight of the leaf nodes, and f is the weight of the leaf node. m This represents the predicted value of the sample within the leaf node, where γ and λ are hyperparameters.

[0068] Continuously add decision trees to the original decision tree until the objective function is minimized, then stop iterative training to obtain learner 2.

[0069] 4-3) Given a dataset {x1, ..., x...} n}, where x i For input space χ s The vector in the model is of dimension s. In each iteration of gradient boosting, the negative gradient of the loss function output by the model is denoted as {g1, ..., g...}. n The training samples are sorted in descending order of the absolute value of their gradients. The first a% of samples with larger gradients are set as subset A, and the remaining (1-a)% of samples with smaller gradients are set as subset A. c and from A c b% of the samples are randomly selected as subset B.

[0070] Calculate the variance gain on A∪B Select To segment the sample nodes. The definition is as follows:

[0071]

[0072] Among them, A l ={x i ∈A:x ij ≤d},A r ={x i ∈A:x ij >d}, B l ={x i ∈B:x ij ≤d},B r ={x i ∈B:x ij >d}, coefficient Used to normalize the gradient on B to A c The size of the dataset. n is the number of samples in the dataset, d is the number of sample nodes, and x... i For input space χ s In the vector of dimension s, g i Let A be the negative gradient of the loss function output by the model; A is the subset of samples with larger gradients selected from the top a% after sorting the training samples in descending order of the absolute value of their gradients. c B is the remaining (1-a)% small gradient sample subset, and B is the subset of samples from A. c b% of the sample size is randomly selected. Represented as x i ∈A:x ij The number of sample nodes d > d For x i ∈A:x ijThe number of sample nodes d > d, x ij Let be the j-th dimension feature of the i-th sample, i = 1, ..., n, j = 1, ..., s;

[0073] Select the corresponding sample nodes and determine the corresponding output values. Repeat the above steps until the fitting accuracy threshold or the upper limit of the number of trees is reached, finally obtaining learner 3.

[0074] 4-4) Integrate the three learners mentioned above to obtain the RXL ensemble model.

[0075] (5) Use the RXL integrated model established in step 4) to quickly predict the creep stress index of the test set samples and the four independent experimental samples in step 3).

[0076] In this embodiment, the leave-one-out method results of the creep stress index prediction model training set, based on 72 tin-based solder alloy samples and the RXL ensemble model, are as follows: Figure 1 As shown.

[0077] The leave-one-out method was used to perform internal cross-validation on the creep stress index prediction model of tin-based solder alloys established with 72 sample data. The correlation coefficient R between the predicted values ​​of the creep stress index model of tin-based solder alloys and the experimental values ​​in the literature was 0.857, and the root mean square error RMSE was 1.598.

[0078] Example 4

[0079] This embodiment is basically the same as Embodiment 3, except that:

[0080] In this embodiment, the prediction results of the predictable model test set based on 72 tin-based solder alloy samples combined with the RXL integrated model are as follows: Figure 2 As shown.

[0081] The established RXL integrated model for predicting the creep stress index of tin-based solder alloys was used to predict 19 samples in the test set, and good results were obtained. The correlation coefficient R between the model-predicted creep stress index of tin-based solder alloys and the experimental values ​​in the literature was 0.922, and the root mean square error RMSE was 1.281.

[0082] Example 5

[0083] This embodiment is basically the same as the above embodiments, except that:

[0084] In this embodiment, the prediction results of the predictable creep stress index test set based on 72 tin-based solder alloy samples, three learners, and an integrated model are compared, as shown in Table 2:

[0085] Table 2. Comparison of prediction results of the three learners and the ensemble model on the test set of the present invention.

[0086]

[0087] In summary, the ensemble model outperforms the three learners in generalization. This embodiment uses an RXL ensemble model that integrates three high-performing learners to quickly predict the creep stress exponent of tin-based solder alloys, significantly improving efficiency.

[0088] Example 6

[0089] This embodiment is basically the same as the above embodiments, except that:

[0090] In this embodiment, the predictable creep stress index model established based on 72 tin-based solder alloy samples, combined with three learners and an ensemble model, includes prediction results for an independent test set of four samples, as shown in Table 3:

[0091] Table 3. Prediction results of the three learners and the ensemble model on the independent test set of the present invention.

[0092]

[0093] An integrated model of creep stress index of tin-based solder alloy was used to predict four samples in an independent test set. Compared with three learners, the prediction results were closer to the true values.

[0094] The present invention describes a method for rapidly predicting the creep stress index of tin-based solder alloys using an integrated model. First, it collects elemental composition, test temperature, and creep stress index values ​​of tin-based solder alloys from literature, and adds new experimental data as a dataset sample. Then, it organizes the elemental composition and test temperature of the tin-based solder alloys as features for modeling. Next, it randomly divides the dataset into training and test sets at a 4:1 ratio. Then, using the collected creep stress index values ​​of tin-based solder alloys as the target variable and the constructed features as independent variables, it trains three learners based on the partitioned training set by scaling the independent variables using RobustScaler, and integrates them to obtain an RXL ensemble model. The above embodiments utilize the RXL ensemble model to rapidly predict the creep stress index of the test set samples and four independent experimental samples. Based on reliable literature data and modeling methods, the above embodiments of the present invention provide a tin-based solder alloy creep stress index prediction model with advantages such as simplicity, speed, low cost, and no pollution.

[0095] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any changes, modifications, substitutions, combinations or simplifications made based on the spirit and principle of the technical solution of the present invention shall be equivalent substitutions. As long as they meet the purpose of the invention and do not deviate from the technical principle and inventive concept of the present invention, they shall fall within the protection scope of the present invention.

Claims

1. A method of integrated model fast prediction of creep stress exponent of tin-based solder alloys, characterized by, Includes the following steps: 1) Collect the elemental composition, test temperature and creep stress index values ​​of tin-based solder alloys from the literature, and add new relevant experimental data as a dataset sample; 2) Compile the elemental composition and test temperature data of the tin-based solder alloy for use as features in the modeling; 3) Randomly divide the dataset into training and test sets in a 4:1 ratio; 4) Using the creep stress index values ​​of tin-based solder alloys collected in step 1) as the target variable and the features in step 2) as the independent variables, based on the training set divided in step 3), the independent variables are scaled using RobustScaler to train three learners and integrated to obtain the RXL ensemble model. 5) Using the RXL ensemble model established in step 4), quickly predict the creep stress index of the test set samples and the four independent experimental samples in step 3); In step 4), the specific steps for training the RXL ensemble model are as follows: 4-1) Using the Bootstrap resampling method, from the overall training sample set... S Multiple subsamples are randomly selected from the middle In utilizing each During model training, several attribute values ​​are randomly selected for node splitting to generate multiple regression trees to the maximum extent without pruning, ultimately forming a multivariate nonlinear regression combined learner1. 4-2) On the basis of the loss function, the restriction of the complexity of the tree model is considered, and the loss function and the complexity are collectively referred to as the objective function; the first m The objective function of a decision tree can be written as: ;in, For the first i Observations of a sample , N This indicates the number of samples in the dataset. It is the first of the samples m The predicted values ​​of each decision tree. x For the input value of this sample, l It is the deviation between the observed and predicted values ​​of this sample calculated by the loss function; the first term of the objective function is the original value of the first term. m The loss function of a decision tree, the second term For the first m The model complexity of decision trees can be reduced by smoothly learning weights to avoid overfitting. T For the number of leaf nodes, The weights of the leaf nodes are... This represents the predicted value of the sample within that leaf node. γ and λ For hyperparameters; Continuously add decision trees to the original decision tree until the objective function is minimized, then stop iterative training to obtain learner 2; 4-3) Given a dataset ,in For input space The dimension of is s The vector; in each iteration of gradient boosting, the negative gradient of the loss function output by the model is denoted as . The training samples are sorted in descending order of the absolute value of their gradients. The first a% of samples with larger gradients are set as subset A, and the remaining (1-a)% of samples with smaller gradients are set as subset B. and from b% of the samples are randomly selected as subset B; Computing the variance gain on , selecting to split the sample node; Select the corresponding sample nodes and determine the corresponding output values; repeat the above steps until the fitting accuracy threshold is reached or the upper limit of the number of trees is reached, and finally learner 3 is obtained; 4-4) Integrate the three learners obtained in steps 4-1), 4-2), and 4-3) above to obtain the RXL ensemble model.

2. The method for rapid prediction of creep stress exponent of tin-based solder alloys using integrated model as claimed in claim 1 wherein, In the step 4-3), are defined as follows: ;in, , , , ,coefficient Used to normalize the gradient on B to Size; n The number of samples in the dataset. d For sample nodes, For input space The dimension of is s The vector, Let be the negative gradient of the loss function output by the model; A is the subset of samples with larger gradients selected from the top a% after sorting the training samples in descending order of the absolute value of their gradients. B is the remaining (1-a)% small gradient sample subset, where B is from Randomly select b% of the sample size; Represented as The number of sample nodes d, for The number of sample nodes d, For the first i The first sample j dimensional features, , .

3. A system for rapidly predicting the creep stress index of tin-based solder alloys, comprising a memory and a processor, wherein the memory is used to store computer programs, input data, and output data, characterized in that: The processor is used to execute the method for rapidly predicting the creep stress index of tin-based solder alloys using the integrated model of claim 1 or 2.

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