The Quantitative Research on Atmospheric Environmental Corrosion of Aluminum Alloy Products

: In this paper, we conduct quantitative research on the atmospheric environmental corrosion of aluminum alloy based on the atmospheric environmental factors. we apply the elastic network regression method to construct a regression model for corrosion rates based on the identified damage factors, which allows us to calculate the dependent variable as long as we know the main environmental factors in a specific year. Finally, we introduce a measure of atmospheric environment corrosion based on the established regression which can characterize the severity of corrosion with different transformations.


Introduction
According to GJB 4239 "General Requirements for Equipment Environmental Engineering" [1] and GJB 6117-2007 "Equipment Environmental Engineering Terms"[2], environmental adaptability of a product refers to the ability of a product to maintain normal function and performance in all predetermined environments, and the requirements for environmental adaptability [3] are the requirements of a product's tolerance to environmental stress.An extensive analysis of typical cases of products' environmental adaptability shows that the environmental adaptability of different products varies with the environment, thus the environmental adaptability level of a product should be considered systematically when choosing the materials [4] . In this paper, A regression model for the corrosion of aluminum alloy in the atmospheric environment is constructed. we define a new measure of atmospheric corrosion to reflect the severity of environmental conditions.

Variable Selection
This paper selects seven aluminum alloy materials, 2B06-T4, 2D12-T4, 3A21-H24, 5A05-O, 7A09-T6, 7B04-T6 and 5A90-T3S. The environmental corrosion of aluminum alloy materials during storage is quantified based on the factors influencing the average corrosion rate. We define the independent variables 1 X (temperature), 2 X (relative humidity), 3 X (Cldeposition rate), 4 X (pH of rainwater), etc., to represent the environmental factors that have effect on the corrosion of aluminum alloy material. TABLE 1 gives the atmospheric average corrosion rates of the seven aluminum alloys in four typical environments (Jiangjin, Wanning, Mohe and Beijing). The dependent variable Y considered in this paper is the ratio of the average corrosion rate to the mean of each group. If the ratio is less than 1, it can be interpreted as "being averaged", while if the ratio is greater than 1, it indicates that the original average corrosion rate has made contributions to the final average. We construct a regression model of using the selected environmental factors as the independent variables. We finally construct an environmental corrosion measure H to characterize the severity of the environmental damage, which is a function of . The larger H , the more severe the environment will be, and thus the more severe corrosion will be if the aluminum alloy material is exposed to this environment. Table 1. Average corrosion rates of seven aluminum  alloys in different localities   Locality  Yea  r  2B06  -T4  2D12  -T4  3A21  -H24  5A05  -O  7A09-T6  7B04  -T6  5A90  -T3S  1 ( (2) where i x , i y are the i -th observation values of the independent variables and the response variable.
In this paper, we use 14 environmental variables excluding the chemical components as the independent variables for modeling, i.e., SO 2 deposition rate, temperature、relative humidity、pH of rainwater、solar radiation, Clof rainwater, rain days, atmospheric pressure, NH 3 , Cldeposition rate, snow days, average wind speed, fog days , and H 2 S。 The variance inflation factors given in Table 2 suggest that there is serious multicollinearity between independent variables. Therefore, if simple linear regression is performed directly, the estimation results are not reliable and the variance of the parameter estimators will be too large. Elastic Network Regression is another regularized regression method [4], which combines the L 1 and L 2 penalties of the lasso and ridge methods. Its loss function is as follows, where  is an important parameter to determine which regularization method dominates in the end. Elastic network regression is quite useful when there is a group of highly correlated variables. The value of  obtained by cross-validation [9] is 0.140766, which gives us the following model, For which, the mean square error is 0.16, and the goodness of fit is 97.80%.
Based on this model, the value of Y of a region can be obtained only based on the annual average values of temperature, relative humidity, pH of rainwater, average wind speed, and Cldeposition rate. The larger the value of Y , the more severe the corrosion of aluminum alloy products.
Based on the established model, we provide the values of Y in four different regions in Table 3 and plot the trend of each region in Figure 1.
In other words, for aluminum alloy materials, the environment in Wanning is the worst, followed by that in Jiang, Beijing. In addition, except for Mohe, the values in other regions show a decreasing trend year by year. This may be because the strengthening of environmental protection measures in China in recent years has improved the atmospheric environment.

Environmental Corrosion Measurement
According to the corrosion regression model of aluminum alloy material in the atmospheric environment provided in Eq (4), we can calculate Y of a region in a certain year when the independent variables are known, which allows us to give a general judgment of the severity of the environment. The larger the value of Y , the harsher the environmental conditions for the aluminum alloy products are. However, to have a more uniform and intuitive understanding, this paper constructs the environmental corrosion measurement based on the dependent variable. We consider using the quadratic fraction transformation [5,6]: (5) or the logit transformation [10] ： (6) to obtain a measurement of atmospheric environmental corrosion within [0,1], which allows us to better analyze the severity of the environment. A value of 0 indicates that the environment is the best for aluminum alloy products, and a value of 1 indicates that the environment is the harshest. Moreover, we introduce two undetermined parameters H Y   also indicates a harsh environment. Specifically, the measure is given by, or (8)

Quadratic fraction transformation
When applying the atmospheric environmental corrosion measurement, we hope that it can distinguish different typical environments as well as possible. Therefore, when determining the parameters 0  and 1  , this paper tries to maximize the difference between the two regions with the smallest difference in the measurement of atmospheric environmental corrosion among the four regions. Let the environmental corrosion measure in Jiangjin, Wanning, Mohe, and Beijing be denoted by Then the sequential quadratic programming method can be used to convert the problem into the following standard form: The results are given in Table 4.
Therefore, the measurement formula of atmospheric environmental corrosion under quadratic transformation is: These four regions represent four typical atmospheric environments in China, namely, the humid and hot marine atmospheric environment, the sub-humid and hot industrial atmospheric environment, the cold rural atmospheric environment, and the warm and semi-rural atmospheric environment. The atmospheric environmental corrosion measurements for the four regions are given in Table 5.

Logit transformation
Similarly, we establish the environmental corrosion measurement based on the Logit transformation [11,12] To determine the parameters 0  and 1  , we need to solve the following constrained non-linear programming problem. In

 
The sequential quadratic programming (SQP) algorithm [13,14] is used to solve the optimization problem (14), for which, we consider the following Lagrange function, Where  is Lagrange multiplier. Based on this operation, this paper transforms an optimization problem with two variables and one constraint condition into an extreme value problem of a system of equations with three variables without any constraints. Next, we consider the quadratic approximation of the Lagrange function to improve the similarity of the quadratic programming subproblem, which makes the optimization problem with strong nonlinearity can also be calculated.

H H H H   
. The results show that the environment of Wanning is the worst among the four regions, followed by Jiangjin, which is consistent with the results in Section 4.1.
The related reference [15] demonstrates that Jiangjin is perennial and cloudy. Long-term exposure of metal materials to a humid atmosphere increases the thickness of the surface water film, impeding the passage of oxygen, thus reducing the corrosion rate of the metal materials. While in Wanning where the measured value of the corrosion rate is the largest, the metal materials are exposed to the humid and hot marine atmospheric environment for a long time. The high temperature and humidity as well as the erosion of seawater will accelerate the corrosion of metal materials. Among the four regions, Mohe's atmospheric environmental corrosion measure is the smallest, where the metal materials are in the cold rural atmospheric environment. The low temperature and humidity will reduce the corrosion of metal materials. All these findings based on our model are in accordance with the objective law. As shown in Section 4, the atmospheric environmental corrosion measures constructed based on the quadratic power transformation or logit transformation can all be used to evaluate the effects of typical atmospheric environments on the corrosion of aluminum alloy material in China. In this section, we explored the corrosion measures of seven typical atmospheric environments, i.e., humid and hot marine atmospheric environment, humid and hot rainforest atmospheric environment, sub-humid and hot industrial atmospheric environment, cool plateau atmospheric environment, warm and semi-rural atmospheric environment, dry and hot desert atmospheric environment, and cold rural atmospheric environment.  The atmospheric corrosion measures for the seven typical atmospheric environments based on both the quadratic power and the logit transformations are given in TABLE  9 and TABLE 10, respectively.

Summary
From the results in the above two tables, we can see that in 2016, the corrosion severity of the seven typical atmospheric environments has the following relationship: Humid and hot marine atmospheric environment > Subhumid and hot industrial atmospheric environment > Warm and semi-rural atmospheric environment > Dry and hot desert atmospheric environment > Humid and hot rainforest atmospheric environment > Cold and warm plateau environment > Cold rural atmospheric environment. According to the long-term monitoring data of environmental factors and the field exposure test results of the seven environments[20], the order of environmental corrosion severity is: Marine atmospheric environment > Sub-humid and hot industrial environment > Dry and hot desert environment > Cold rural environment and Cold and warm plateau environment. So the results based on the atmospheric environment corrosion measurement in this paper are in line with the objective law.