With widespread use of aluminum alloys, magnesium alloys, etc. in large thin-walled die-castings of new energy vehicles, requirements for their performance are increasing. Large thin-walled die-castings are prone to deformation after heat treatment, so research and development of aluminum alloys without heat treatment has become an important direction. Constructing a complete and accurate "composition-mechanical properties" relationship is an important theoretical basis for realizing rapid design and optimization of material composition. However, method based on "phase diagram calculation + trial and error" can only solve problems with few variables and simple relationships. It is only suitable for simple alloy design with fewer elements, composition design and optimization research with a small amount of trace elements added. Relationship between alloy composition and mechanical properties in practical industrial applications is often complex and high-dimensional. For commercial die-cast aluminum alloys, there are often about 10 alloying elements and impurity elements, and each alloying element has a certain influence on mechanical properties of material. Traditional trial-and-error method for composition design and optimization faces huge workload and cost, which limits development speed of new heat-treatment-free aluminum alloys to a certain extent.
With development of information technology, machine learning has become an important tool for building complex mapping relationship models between data. Researchers used random forest model to establish a mapping relationship model between 7 important components, process parameters and mechanical properties in ferrite/martensitic steel, achieved optimization of composition and process. Industrial big data database and random forest model were used to establish a big data model between element content, process parameters and mechanical performance indicators in steel, interior point method was used to optimize composition and process, and a new steel grade that meets requirements was developed. Gradient boosting tree (GBT) model was used to learn "composition-aging parameter-hardness" mapping relationship of Al-Cu-Mg-x (x is Zn, Zr, etc.) alloys, and finally an excellent prediction model with R2 of 0.94 was obtained. Mapping relationship model between Mn content, heat treatment temperature and mechanical properties in Ti-Al-Fe-Mn-based TRIP alloy was established through artificial neural network model, and based on this model, alloy composition and heat treatment conditions were optimized, so as to develop alloys with better mechanical properties. In addition, a number of machine learning studies on Al, Mg and Ti alloys have proved effectiveness of data-driven models in establishing mapping relationship model of "composition-process-performance" of light alloys.
Aiming at problem of efficient composition design and development of new heat-treatment-free aluminum alloys, this study constructed "composition-mechanical properties" relationship model of die-cast aluminum alloys containing 10 alloying elements through machine learning methods such as LASSO regression, BP neural network and random forest, analyzed influence of different alloying elements on mechanical properties, provided a reference for rapid iteration of alloy composition design and optimization.
Graphical results
"Composition-cast mechanical properties" data set of high-pressure casting aluminum alloys is shown in Table 1. Each data sample includes alloy composition and mechanical properties. Alloy elements include Si, Mg, Fe, Cu, Ni, Cr, Mn, Ti, Zn and Sr. Mechanical properties include yield strength (YS), tensile strength (UTS) and elongation (El).
From distribution characteristics of this group of data, it can be seen that composition of commercial aluminum alloys is complex and range of variation is small. This kind of local, dense, and high-dimensional data structure easily causes machine learning model to fall into an overfitting state and lose its generalization ability. To address this problem, 17 non-heat-treated aluminum alloy test bars of various compositions were prepared by high-pressure casting experiments using a test bar mold, and mechanical properties were tested. Alloy composition and mechanical properties are shown in samples 25 to 41 in Table 1. This group of aluminum alloys is prepared using high-purity aluminum ingots and intermediate alloys, in which only four key alloying elements, Si, Mg, Cu and Zn, are added. It has characteristics of sparseness, dispersion and low dimensionality, which makes up for shortcomings of samples 1 to 24 in data structure, can make prediction of machine learning model have stronger generalization ability and universality.

 

Table 1 Cast aluminum alloy composition-mechanical property data set
Linear regression is a simple mathematical model commonly used to establish linear mapping relationships, which can fit high-dimensional linear events. Composition range of samples 1 to 24 in data set is similar, and variation range is not large. It can be approximately considered that "composition-mechanical properties" relationship is a linear relationship, and a simple prediction model is established using linear regression. As can be seen from Figure 1, as penalty coefficient λ increases (−lgλ decreases), regression coefficient ωi will be converged and eventually converge to 0. Among them, regression coefficient of feature with lower importance in predicting mechanical properties will decay to 0 first, and regression coefficient of element with higher importance will decay to 0 later. Corresponding λ value is "contribution value" of element to mechanical properties. In this way, importance of each element can be ranked, and model dimension can be reduced, thereby reducing risk of overfitting and increasing generalization ability of model.

 

Figure 1 LASSO regression path
As can be seen from Figure 1a, five elements with the greatest influence on yield strength are: Mg, Cu, Si, Ni, and Fe, and their contributions to yield strength (regression coefficients) are all positive, and strengthening effect is: Mg>Cu>Si>Ni>Fe. This is because Mg and Si will form Mg2Si precipitation phase, Cu will form Al2Cu precipitation phase with Al, Fe and Al will form Al-Fe precipitation phase. These hard and brittle precipitation phases will produce precipitation strengthening, hinder dislocation movement, and lead to an increase in yield strength. Five elements with the largest positive contribution to tensile strength are: Cu, Si, Mg, Cr, and Sr, as shown in Figure 1b. Among them, precipitation phases formed by Mg, Cu, and Cr have precipitation strengthening effects, Sr element can refine eutectic Si as a modifier and improve mechanical properties. Five elements that contribute the most to elongation are: Fe, Si, Mg, Cu, and Ni, as shown in Figure 1c. Contribution values of these elements to elongation are all negative, because Fe, Cu, Mg, Al, Si form hard and brittle phases, which will reduce elongation while increasing strength. Two factors that contribute most to elongation are Sr and Mn content. Sr has a modification and refinement effect on eutectic Si, while Mn combined with Fe can change morphology and distribution of hard and brittle Al-Fe phase, thereby increasing plasticity of material. It can be seen that regression coefficient obtained by LASSO regression model is reasonable and explainable. LASSO regression can be used to quantitatively analyze influence and contribution of different elements on mechanical properties during composition design process.
After deleting features that contribute less to mechanical properties, number of elements involved in model prediction is reduced from 10 to 6, 8, and 5, respectively. Comparison of true value and predicted value of model is shown in Figure 2. Root mean square error (RMSE) of yield strength, tensile strength, and elongation are 8 MPa, 9 MPa, and 0.597 5%, respectively. It can be seen that mechanical property prediction model obtained by LASSO linear regression has high prediction accuracy and small error within composition range, and has certain prediction ability under small composition fluctuations. However, limitation of LASSO regression is that it can only predict mechanical properties within a small range of composition fluctuations. When composition changes greatly, contribution of elements to mechanical properties can no longer be approximated as a linear mapping relationship. It is necessary to use other machine learning models that can fit nonlinear mapping relationships for modeling and training.

 

Figure 2 Comparison of true value of mechanical properties and predicted value of LASSO linear regression model

 

Figure 3 Basic principle diagram of BP neural network, ensemble learning and support vector machine model
BP neural network model is currently the most widely used machine learning model and has important applications in establishment of material intrinsic relationship models. BP neural network used is a three-layer neural network, consisting of an input layer, a hidden layer, and an output layer. When learning rate is fixed at 0.01, main hyperparameter affecting model performance is number of hidden layer neurons. Figure 4 shows models of four methods. Mean square error of model corresponding to different numbers of hidden layer neurons is shown in Figure 4a. It can be seen that number of hidden layer neurons has an impact on prediction accuracy of model. Too few neurons cannot accurately fit mapping relationship, resulting in underfitting of model; too many neurons cause overfitting of model, which also leads to increased model error and longer model operation time. When number of neurons is 32, prediction error of BP neural network reaches minimum.

 

Figure 4 Relationship between prediction mean square error and hyperparameters of four nonlinear machine learning models
Both random forest and Adaboost models are ensemble learning methods. Basic principle is to integrate several weak learners into a strong learner through a certain ensemble method to enhance prediction ability, as shown in Figure 3b and Figure 4c. In this study, single weak learners of random forest and Adaboost algorithms are both decision tree models. Difference between the two lies in ensemble method of decision trees. Main hyperparameter of ensemble learning is number of weak learners. It can be seen from Figure 4b and Figure 4c that as number of decision trees increases, prediction errors of random forest model and Adaboost model generally show a downward trend. The more decision trees there are, the higher prediction accuracy. In random forest model, when number of decision trees is greater than 100, model prediction accuracy almost no longer decreases and enters a convergence state. Therefore, number of decision trees is 100 as final optimization result. In Adaboost model, when number of weak learners is greater than 50, model prediction error no longer decreases, so 50 is selected as final optimization result of hyperparameter.
Four machine learning models after hyperparameter optimization are used to train training set, prediction accuracy and generalization ability of model are tested and verified on test set that did not participate in training. Comparison between predicted value of mechanical properties and actual experimental value is shown in Figure 5. Mean absolute error (MAE) is used as criterion for judging accuracy of model prediction.

 

Figure 5 Comparison of prediction results of test set of four machine learning models

Table 2 Comparison of prediction errors of test set of four machine learning models
Conclusion
(1) Taking composition-mechanical properties dataset of as-cast die-cast aluminum alloy as research object, contribution value of each element to mechanical properties is analyzed by LASSO regression, and a rapid prediction model for mechanical properties of heat-free die-cast aluminum alloy within a small composition fluctuation range is established. Prediction errors of yield strength, tensile strength and elongation are 8 MPa, 9 MPa and 0.597 5% respectively.
(2) Four machine learning models were used to learn relationship between composition and mechanical properties of die-cast aluminum alloys. Optimal network parameters were obtained through hyperparameter optimization, and their prediction performance was compared. Results showed that BP neural network had the highest prediction accuracy for yield strength and elongation (MAE was 13 MPa and 0.67%), and random forest model had the highest prediction accuracy for tensile strength (MAE was 12 MPa). Combining neural network with random forest model can simultaneously achieve accurate prediction of three mechanical properties of yield strength, tensile strength, and elongation.