Effect of Lithium-Slag in the Performance of Slag Cement Mortar Based on Least-Squares Support Vector Machine Prediction

There is a universally accepted view that environmental pollution should be controlled while improving cement mortar natural abilities. The purpose of this study is to develop a green cement mortar that has better compressive strength and anti-chloride ion permeability. Two industrial wastes, lithium-slag and slag, were added to cement mortar, and the role of lithium-slag was to activate slag. In addition, to save economic and time costs, this paper also used the least-squares support vector machine (LS-SVM) method to predict the property changes of cementitious-based materials. Then multiple natural abilities of samples, including compressive strength, anti-chloride ion permeability, and fluidity, were tested. In addition, LS-SVM and traditional support vector machine (SVM) were used to train and forecast the performance, including compressive strength. The results show that lithium-slag can activate slag to improve the compressive strength, anti-chloride ion permeability of mortar, and LS-SVM sharpens accuracy by 11% compared to SVM.


Introduction
Cement mortar has a wide range of applications, and reinforcement for concrete structures is an important one [1]. The objective of this research is to develop a green cement mortar with better compressive strength and anti-chloride ion permeability. These are important performance parameters in the structural design of cementitious-based materials. Concrete reinforced by this proposed can improve the corrosion resistance and compressive strength of buildings. In recent years, studies have found that adding proper industrial waste to cement can sharpen the performance. Cement mortar containing silica fume can improve the compressive strength of cement, discovered by Zelić et al. [2] Tafraoui et al. [3] ascertained the good durability properties of Ultra-High-Performance Concrete (UHPC) containing metakaolin. Chi et al. [4] studied the effects of fly ash/slag ratio and liquid/binder ratio on the strength of alkali-activated fly ash/slag (AAFS) mortar. Luo et al. [5] established that lithium-slag can improve the compressive strength of alkali-activated slag concrete. However, many researchers only researched its compressive strength. This paper studies not only compressive strength, but also fluidity and anti-chloride ion permeability of cement containing lithium-slag and slag. In addition, if using conventional methods, such as property tests, there are disadvantages in the process that are long, costly, complicated, and highly variable for results. This paper used better methods to predict the properties.

Performance Test
There are many factors that affect the performance, such as the geometry of the sample, the curing method, the proportion of the admixture, and the amount of the admixture. Lithium-slag was first separately mixed into the cement to test compressive strength and fluidity of the cement. The water, sand and water-reducing agents were 210 g, 1350 g, and 2 g, respectively. The initial mass of cement was 450 g. After that, we substituted lithium-slag for slag, and water-reducing agent was used to control the volume of water. Each cement sample contained 2 g of water-reducing agent and 1350 g of sand. The curing temperature was 20 ± 2 • C and humidity above 90%. The ratio of ingredients is shown in Table 4. The 40 mm × 40 mm × 160 mm prism samples were casted for the cement mortar sample according to "Determinations for isotopes of lead, strontium, and neodymium in rock samples (Chinese Standard GB/T 17671-1999)" [17]. After the samples were cured and demolded, one set of samples was added to water for 7 days, and another for 28 days. Then, the compressive strength of cement was tested using the "YAW4206 microcomputer controlled automatic pressure testing machine" manufactured by SANS. The loading rate was (2400 ± 200) N/s. Compressive strength R c calculated in Newtons per square millimeter (MPa) as follows: where F c is the maximum load at break (N), A is the area of the compressed part (mm 2 ) (40 mm × 40 mm = 1600 mm 2 ).

Anti-Chloride Ion Permeability
Cylindrical samples with diameter of 100 ± 1 mm and a height of 50 ± 2 mm were prepared according to the "Standard for Test Methods of Long-Term Performance and Durability of Ordinary Concrete (Chinese Standard GB/T 50082-2009)" [18]. After being cured and demolded, the samples were added to water for 56 days. The anti-chloride ion permeability was tested using the electric flux method. After vacuum saturation, the samples were placed in the standard test environment. The electrical flux values were automatically recorded using "PER-6A chloride ion permeator" manufactured by Beijing Shourui Co. Ltd, Beijing, China.

Fluidity
Each group of cement mortar samples were prepared in accordance to the "Test method for fluidity of cement mortar (Chinese Standard GB/T 2419-2005)" [19]. Subsequently, the fluidity was tested using "NLD-3 cement mortar fluidity meter". The samples were lifted vertically and jolted 25 times. The test results took the arithmetic mean of the diameters in two perpendicular directions to the nearest 1 mm.

Methodology
The SVM [20] is a concrete realization of the principle of dimensionality and its optimization goal is to minimize the risk of structuring. It seeks the best compromise between model complexity and learning ability based on finite sample information, making itself a powerful non-linear estimation tool. The SVM is suitable for solving the practical problems of a small amount of data, non-linearity, overfitting, large number of input parameters, and local minimum points.
The LS-SVM further enhances these advantages of SVM. It uses the least-squares linear system as a loss function, replacing the traditional quadratic programming method of SVM [21]. In SVM, least-squares can convert inequality constraints into equality constraints, simplifying the solution of Lagrangian multiplier alpha. The quadratic programming problem is transformed into a solution to linear equations. Consequently, the solution speed and convergence accuracy of the problem are improved.
Let us assume that the training set (x i , y i ) N , where i varies from 1 to N, x i is the input vector, y i is the output vector, and N is the number of samples. In a regression problem, the goal is to find a hyperplane function. The linear function is expressed as follows [22]: where: ω is a normal vector; b is the intercept; φ(x) is a non-linear mapping from the input space to the output space. The next step is to minimize the Euclidean norm, which is 1 2 ||ω||. Then we introduce error variables e with regularization constant γ bigger than 0. γ acts as a noise term to avoid overfitting. So it can be written like this: We use the duality theory and introduce a Lagrangian operator to obtain the following formula [23].
The conditions for optimality are given by: as a symmetric function that satisfies Equation (5). Then we convert the optimization problem to solve linear equations, as follows: Finally, we use the LS-SVM to find α and b and obtain a non-linear prediction model: The three common kernel functions are as follows:

Polynomial kernel function
3. Radial basis function (RBF) kernel function

Model Development
In this study, there were models for predicting three properties, including compressive strength, fluidity, and electric flux. The input parameter X was the amount of cement, slag, lithium-slag, and water in the cement mortar, and the output parameter y was the compressive strength, fluidity, and electric flux.
The train-and-test technique [24] was used to develop the model, which is one of the most common ways to establish a learning algorithm for a given data set.
Combined with the actual situation of the data set, the data was divided into a training set and a test set following the ratio of 2:1. We used common statistical methods to evaluate the performance of the models, for instance: correlation coefficient (CC), coefficient of determination (R 2 ), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) [25]. Their formulae are as follows: where N is the total number of the data samples, y i represents each measurement data, f i is each prediction data, and y represents the average of all measurement data. The closer R 2 and CC are to 1, the more accurate and reliable the model is [9]. We perform normalization before training to eliminate the influence of different dimensions of the input parameters on the prediction results performed. We set the normalization interval to [0, 1]. The calculation formula is as follows: where X min , X max and X norm denote the minimum, maximum, and scaled value of the X data sample, respectively [26].
The SVM used in this study was implemented based on the Python3 sklearn library [27]. The parameters of the model were determined by the Gridsearch (GS) method. The training data in the data set was trained with the parameters in the parameter grid, and the cross-validation obtains the best parameters. Finally, retrained the model based on the best parameters. The specific flow is shown in Figure 1.
The modeling process includes the following steps: 1. Convert the data of each parameter into a dimensionless one in the range of [0, 1] through the normalization formula. 2. Divide the 33 samples into a training set and a test set in a 2:1 ratio randomly. 3. Use the GS to determine the optimal parameters of the three models. The parameters were the same for the SVM and LS-SVM. In addition, results are shown in Table 5. 4. Compare the results predicted by the three models. The outcome is shown in Table 6.

Data set
Training data Cross-valida¡on Parameter grid Best parameters Retrained model

Results and Discussion
From Figures 2-4, the compressive strength and fluidity of the cement will fall as the proportion of lithium-slag raises, when the lithium-slag was directly mixed with cement. The strength of cement mainly depends on the hydration reaction of mineral C 3 S and C 3 A in the cement clinker. Due to the incorporation of lithium-slag, the content of clinker minerals in the grit reduces, resulting in a decrease in strength. At the same time, the lithium-slag structure is loose and has many internal pores, so the water absorption is large. When the amount of lithium-slag in the cement goes up, the water demand will swell, and the fluidity will decrease.
In this study, performance prediction was done using SVM and LS-SVM. From Figures 5-7, the predicted values of the three performance indicators were compared with measured values. The results of the SVM are displayed on the left and the LS-SVM on the right. The scatter plot shows the predicted/measured value ratio and presents error measurements with R 2 coefficient. Table 7 shows the error measurements obtained by the models, including training set and test set.
An attempt was made to show the influence of lithium-slag and slag on compressive strength using the SVM and LS-SVM. The experimental results are presented in Table 6. The results showed that lithium-slag and slag influenced the compressive strengths. It can be seen from this table that as the proportion of lithium-slag instead of slag increases, the compressive strength would grow first, and then decrease. The filling value and chemical composition of the lithium-slag were maximized first, and the cement strength reached peak. After that, the incorporation of lithium-slag lowered the amount of cementitious material, and the excessive lithium-slag particles debased the gelation and the compressive strength of the samples.
Another goal was made to show the influence of lithium-slag and slag on fluidity and chloride ion permeation resistance using the SVM and LS-SVM. Experimental results are shown in Table 8. From the results, it can be found that lithium-slag and slag reduce the fluidity of cement and boost the anti-chloride ion permeability. The permeability was related to the compactness and void structure of cement. The incorporation of lithium-slag reduces the irregular capillary channels, which were connected to each other due to the formation of water. Simultaneously, the replacement of cement by lithium-slag shriveled the hydration speed in the early gelling system, making the structure development relatively perfect. In addition, the CSH gel produced by the secondary hydration of the lithium-slag made the internal structure of the concrete more compact and greatly enhanced the resistance to chloride ion penetration. Moreover, as the amount of lithium-slag continued to climb, the viscosity of the cement rose and the fluidity diminished, due to the large volume of water required for the lithium-slag itself.   Furthermore, the performance of the lithium-slag and slag cement mortar was predicted using the SVM and LS-SVM. It can be seen from Table 7 that the R 2 and CC values of the SVM and LS-SVM both were very close to 1. According to the scatter plot, it can be discovered that the variation between the measured and predicted values of LS-SVM was less than that of SVM in any case. The linear regression lines show that the performance predicted by these three models was basically in line with expectations. After comparing R 2 ,it can be seen that LS-SVM performed much better than SVM.
The performance of the two methods was calculated using the common benchmark. As can be seen from Tables 6 and 8, it can be determined that the model constructed by SVM and LS-SVM both can be used to assess the performance of the lithium-slag and slag cement mortar. In addition, the model built with LS-SVM was more accurate and robust.  Table 8. Comparison of electric flux and fluidity measured and predicted results.         In contrast, Zelić et al. [2] established that silica fume can improve the compressive strength of cement. This study found that the mixture of lithium-slag and slag not only has the same function, but also boosts the anti-chloride ion permeability of cement. The latter can enhance more performance and thus has a wider application scenario, even if the effect of increasing the compressive strength is not as obvious as the former. In addition, this research uses a more scientific and effective method, LS-SVM, to help the actual production. In general, LS-SVM accepts local optimal solutions, and the accuracy should be lower than SVM. However, both of them fit the data well in performance predictions in this study. Furthermore, LS-SVM has stronger generalization ability, and shows better performance for the dataset in this research.

Conclusions
This study aims to develop a green cement mortar with better performance, and forecast its changes with a better machine-learning method. In the present research, most studies have only studied the compressive strength properties of related cements. This paper not only studies the compressive strength of lithium-slag and slag cement, but also the fluidity and anti-chloride ion permeability, and used SVM and LS-SVM to predict these properties. We used common statistical methods to evaluate the performance of the models and compared the traditional SVM and LS-SVM.
The following conclusions could be drawn from this investigation: 1. Lithium-slag can activate slag and improve the compressive strength and anti-chloride ion permeability of cement. However, excessive lithium-slag will attenuate its fluidity and compressive strength. Therefore, this cement mortar can be used in special scenes with corrosion resistance and high compressive strength requirements, such as chemical plant floor, and chemical laboratory floor. 2. The LS-SVM can predict not just the compressive strength of this cement mortar, but the electric flux and fluidity. Comparing the three models comprehensively, it can be extracted that the LS-SVM used in this paper has an 11% improvement in accuracy compared to the previous SVM. 3. The study confirms the possibility of recycling lithium-slag and slag in cement production.
There is a new way to reduce the accumulation of lithium-slag, which scales back environmental pollution.
Combined with pre-designed ratio information, the performance of cement mortar can be predicted according to the model. Due to several factors affecting actual production, such as raw material quality and curing environment, engineers need to combine their practical experience to predict the performance of mortar based on the proportion of raw materials. For future work, cement mortar can be further blended with different types of industrial waste, to reduce the environmental pollution of industrial waste.

Conflicts of Interest:
The authors declare no conflict of interest.