Multiple machine learning models for prediction of CO2 solubility in potassium and sodium based amino acid salt solutions

Guanwei Yin; Fouad Jameel Ibrahim Alazzawi; Dmitry Bokov; Haydar Abdulameer Marhoon; A.S. El-Shafay; Md Lutfor Rahman; Chia-Hung Su; Yi-Ze Lu; Hoang Chinh Nguyen

doi:10.1016/j.arabjc.2021.103608

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Original article

03 2021

:15;

103608

doi:

10.1016/j.arabjc.2021.103608

Multiple machine learning models for prediction of CO₂ solubility in potassium and sodium based amino acid salt solutions

Guanwei Yin^{^a,⁎}, Fouad Jameel Ibrahim Alazzawi^{^b}, Dmitry Bokov^{^c,^d}, Haydar Abdulameer Marhoon^{^e,^f}, A.S. El-Shafay^{^g,^h}, Md Lutfor Rahman^ⁱ,⁎, Chia-Hung Su^{^j,⁎}, Yi-Ze Lu^{^j}, Hoang Chinh Nguyen^{^k}

a School of Chemistry and Chemical Engineering, Inner Mongolia University, Inner Mongolia Autonomous Region, Hohhot 010000, China

b Computer Engineering Department, Al-Rafidain University College, Baghdad, Iraq

c Institute of Pharmacy, Sechenov First Moscow State Medical University, 8 Trubetskaya St., bldg. 2, Moscow 119991, Russian Federation

d Laboratory of Food Chemistry, Federal Research Center of Nutrition, Biotechnology and Food Safety, 2/14 Ustyinsky pr., Moscow 109240, Russian Federation

e Information and Communication Technology Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar, Iraq

f College of Computer Sciences and Information Technology, University of Kerbala, Karbala, Iraq

g Department of Mechanical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

h Department of Mechanical Power Engineering, Faculty of Engineering, Mansoura University, Egypt

i Faculty of Science and Natural Resources, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah, Malaysia

j Department of Chemical Engineering, Ming Chi University of Technology, New Taipei City, Taiwan

k Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 700000, Viet Nam

⁎Corresponding authors. lotfor@ums.edu.my (Md Lutfor Rahman), chsu@mail.mcut.edu.tw (Chia-Hung Su)

Received: 2021-8-15, Accepted: 2021-12-2,

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

In this work, we developed artificial intelligence-based models for prediction and correlation of CO₂ solubility in amino acid solutions for the purpose of CO₂ capture. The models were used to correlate the process parameters to the CO₂ loading in the solvent. Indeed, CO₂ loading/solubility in the solvent was considered as the sole model’s output. The studied solvent in this work were potassium and sodium-based amino acid salt solutions. For the predictions, we tried three potential models, including Multi-layer Perceptron (MLP), Decision Tree (DT), and AdaBoost-DT. In order to discover the ideal hyperparameters for each model, we ran the method multiple times to find out the best model. R² scores for all three models exceeded 0.9 after optimization confirming the great prediction capabilities for all models. AdaBoost-DT indicated the highest R² Score of 0.998. With an R² of 0.98, Decision Tree was the second most accurate one, followed by MLP with an R² of 0.9.

Keywords

CO2 solubility

Artificial intelligence

Multi-layer Perceptron

Decision tree

AdaBoost

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1 Introduction

Development of models for prediction of CO₂ solubility in various solvents is a subject of great interest in order to develop efficient process for CO₂ capture (Nakhjiri and Heydarinasab, 2020; Pishnamazi, 2020; Nakhjiri, 2018; Nakhjiri, 2018; Marjani, 2020; Cao, 2021; Nakhjiri, 2018; Nakhjiri, 2020 ). From environmental point of view, it is crucial to implement proper engineered methodology as protective action for environment (Li, 2021; Shinde et al., 2021; Naddaf et al., 2021; Xu, 2021; Tjahjono, 2021; Ngafwan, 2021; Al-Shawi, 2021 ). Although various processes can be utilized for CO₂ capture from gas streams, absorption using chemical solvents is the attractive method for industrial applications due to its versatility and maturity of the process. Indeed, absorption is a gas–liquid operation which is driven based on mass transfer between gas and liquid phases with wide applications such as environment (Razzaq, 2021; Qaderi, 2020; Davoodnia, 2009 ). The mass transfer driving force can be enhanced by using a solvent which has great affinity towards the target component which is CO₂ (Wu, 2020; Wang, 2022; Won Lee, 2021; Geng, 2021 ). Indeed, mass transfer rate and consequently the separation efficiency can be enhanced by selection of a solvent by which the CO₂ solubility is high. However, examination and screening the appropriate solvents for a process is time consuming and costly, therefore predictive models can be employed for this purpose (Zajmi et al., 2018; Alsunki, 2020).

Predictive models have been already used in design and optimization of CO₂ capture processes such as membrane-based absorption systems in which the mass transfer and fluid dynamics of the process is simulated using mechanics or non-mechanistic models (Marjani, 2020; Rezakazemi et al., 2019; Dashti, 2018; Fadaei, 2012; Asadollahzadeh, 2018; Sohrabi, 2011; Dashti, 2020; Marjani, 2021; Razavi et al., 2015; Razavi et al., 2016; Shirazian et al., 2012; Razavi, 2016; Shirazian, 2017 ). Usually, mechanistic models based on computational fluid dynamics are used for simulation of CO₂ capture processes, however artificial intelligence-based models can be utilized in order to predict the solubility of CO₂ in a wide range of solvents. These artificial intelligence-based models rely on measured process data for fitting and training the model. Indeed, the data are used for training the network, and then validation is performed to assess the capability of the model in simulating the process data. Recently, combined and hybrid artificial intelligence-based algorithms have been developed and implemented to simulate chemical processing unit operations (Rezakazemi et al., 2019; Dashti, 2018; Ismail, 2019; Rezakazemi, 2018; Babanezhad, 2019; Cao, 2020; Nabipour, 2020; Soroush, 2019 ).

For prediction of CO₂ loading in chemical solvents, a number of machine learning methods have been implemented in which the model is used for screening the solvent and correlating the CO₂ solubility to process parameters. Soroush et al. (Alkawaz et al., 2020) predicted the solubility of CO₂ in various amino acid salt solutions via ANFIS method which is an artificial intelligence technique. The model indicated promising results with great accuracy in prediction of CO₂ loading as a function of input variables. Indeed, artificial intelligence models can be employed in this area to predict the solubility of CO₂ in different chemical and physical solvents. The results can be useful to choose the best solvent for a particular application. So, the cost and time of solvent selection and testing can be minimized by development of a robust predictive model for CO₂ loading. Machine learning (ML) techniques need measured data for simulation of processes and have attracted attention in wide areas of science and engineering (Dashti, 2018; Ismail, 2019; Rezakazemi, 2018; Wu, 2020; Deng et al., 2021; Wu, 2020; Farajnezhad, 2016; Rezakazemi et al., 2013; Khansary et al., 2017; Marjani et al., 2011; Rosenblatt, 1958 ).

In this work, we developed a comprehensive computational strategy for prediction of CO₂ solubility in various amino acid solutions. Three distinct artificial intelligence-based models are selected and implemented to the collected data of CO₂ solubility. We collected medium-sized numerical data on CO₂ solubility in potassium- and sodium-based amino acid salt solutions in this study. With six inputs: T (K), weight percent (wt.%), P_CO2 (kPa), M_W-am, MP_C, MW_C, and alpha (solubility/loading) as the only output, we have a complete system of data for simulation (Alkawaz et al., 2020). Because of this fact, we must choose the appropriate models for predicting that are accurate and proportional to these differences in size. As a result, MLP (Multi-layer Perceptron), k-nearest Neighbors, extreme random trees, AdaBoost, Bagging Regressors, and some other models can be used to achieve this goal for these datasets. This is because data with a reduced dimensionality may be more prone to over-fitting. We also need to be as precise as possible when defining the Hyper-parameters for each machine learning model. As a result, testing the data in various setups is a crucial stage in this investigation, and the results are interpreted and discussed to find out the best model for prediction of the dataset.

2 Modeling

In this study, a dataset consisting of the loading of CO₂ in solutions of amino acid salts versus input parameters were used for the modeling. The data are collected from literature and used in the artificial intelligence modeling (Alkawaz et al., 2020). Six inputs were considered in the model including temperature (T), solution concentration (wt%), CO₂ partial pressure (P_CO2), amino acid salt molecular weight (M_W-am), melting point of amino acid salt (MP_C), and molecular weight of cation (MW_C), while the CO₂ loading (alfa) was considered as the sole predicted output. Three different modeling approaches were employed which are defined in the following sections.

2.1

2.1 Multi-layer Perceptron (MLP) model

Frank Rosenblatt in (Agirre-Basurko et al., 2006) invented the Multi-Layer Perceptron (MLP), which is made up of several perceptrons or neurons. MLPs are generally arranged in three layers as it is shown in Fig. 1, known as the input layer, the hidden layer (which can contain more than one stack of neurons), and the output layer. Indeed, this type of configuration is known as an Artificial Neural Network (ANN). N neurons are located in the input layer, S neurons are in the hidden layer, and L neurons are located in the output layer as shown in Fig. 1.

A multilayer perceptron-based model (Ture, 2005).

Each input of the neurons $x_{i}$ is associated with a weight $w_{i}$ and calculated through Equation (1):

(1)

z = x_{1} w_{1} + \dots + x_{n} w_{n} = X^{T} W

The activation function is then computed as f(z), where f(z) can be any continuously differentiable function such as a linear function, sigmoid function, or even the newer ReLU frequently employed in deep learning. After the perceptron evaluates the inputs and activates the relevant activation functions, the results are transferred to a classifier, which generates a probability distribution and “guesses” the proper label for the data. After collecting results using backpropagation methods, the weights are then changed for future inputs.

2.2

2.2 Decision tree (DT) model

The second model that was employed in this study is Decision Tree (DT). Because of the expansion of data mining methods, decision trees are becoming increasingly prominent in data analytics. It's basically an algorithm for classification and regression of data according to a set of criteria. In order to fit the data, the conventional method is recursive partitioning, a top-down, greedy algorithm (Quinlan, 1986). Some of the most common Decision Tree algorithms are ID3 (Quinlan, 1993), C4.5 (Quinlan, 1993; Timofeev, 2004), CART (van Diepen and Franses, 2006), and the chi-squared automatic interaction detector tree (CHAID) (Perner et al., 2001). The decision tree has a significant advantage over other modeling techniques in that it generates a model that can represent interpretable rules or logic statements. An important feature is the ability to explain trees that produce axis parallel decision surfaces (Yang, 2017).

For example, in Fig. 2 we can see an example of decision tree for Energy Efficiency Heating. In this figure boxes indicate terminal leaf nodes with labels within, whereas circles represent other nodes with a symbol inside referring to the feature where the split occurs. On the corresponding pathways, the dividing rules are provided.

Example of DT for Energy Efficiency Heating (Freund and Schapire, 1997).

2.3

2.3 AdaBoost-DT model

AdaBoost (Adaptive Boosting) (Makni and Zine, 2016) is an ensemble method that boosts weak estimators (DT in this study) to make a strong and more accurate regressor. It begins by fitting a regressor on the original dataset, and then fits further copies of the regressor on the same dataset, but with weights of instances changed based to the error of current prediction. Regressors that come after them focus more on tough situations as a result of this [63]. Algorithm of this methods is shown in Fig. 3.

2.4

2.4 Accuracy criteria of models

Like any regression modeling project, we need to split whole data into test and train data. A quarter of all data is utilized for testing and not for training a model, hence test data is a quarter of all data. For the simulation of solubility data, the remaining three-fourth of the data are used in the training phase. For the sake of comparison and determining the best model and the accuracy of the final job, we employed several criteria. Both test and train data were used to determine the coefficient of determination (R²). Equation (2) calculates R², or the coefficient of determination:

(2)

R^{2} = 1 - \frac{u}{v}

where:

(3)

u = \sum_{i} {(Q_{i} - y_{i})}^{2}

(4)

v = \sum_{i} {(\bar{y} - y_{i})}^{2}

The k-fold cross-validation is the other requirement to implement the modeling of CO₂ solubility data. We employed the k-fold method to ensure that we don't run into the problem of overfitting. When it came time to find out how complex the model should be trained, we utilized three-fold cross-validation with k = 3. Finally, we also used MSE, RMSE and MAE metrics to compare the results of simulations generated by the models.

3 Results and discussions

3.1

3.1 Model selection

Besides comparing the models, we need to adjust certain other crucial hyper-parameters to gain better accuracy. A variety of configurations were used to test the data in order to optimize other parameters. To simulate using MLP, we need to tweak the hidden layer sizes, maximum iterations, and alpha values, among other things. As a result, we experimented with numerous values for these factors in order to find the optimum one. Table 1 lists some of the most accurate configurations employed in this study.

Table 1 Accuracy of different configs of MLP.

Max Depth	Hidden layer size	alpha	Train R²	Test R²	RMSE	MSE	Mean absolute error
1500	95	0.001	0.91088	0.89817	2.06E-01	4.23E-02	1.20E-01
1000	95	0.001	0.91088	0.89817	2.06E-01	4.23E-02	1.20E-01
2500	95	0.001	0.91088	0.89817	2.06E-01	4.23E-02	1.20E-01
2000	95	0.001	0.91088	0.89817	2.06E-01	4.23E-02	1.20E-01
3000	95	0.001	0.91088	0.89817	2.06E-01	4.23E-02	1.20E-01
1000	65	0.01	0.9078	0.89308	2.13E-01	4.56E-02	1.27E-01
3000	65	0.01	0.9078	0.89308	2.13E-01	4.56E-02	1.27E-01
2500	65	0.01	0.9078	0.89308	2.13E-01	4.56E-02	1.27E-01
1500	65	0.01	0.9078	0.89308	2.13E-01	4.56E-02	1.27E-01
2000	65	0.01	0.9078	0.89308	2.13E-01	4.56E-02	1.27E-01
1000	95	0.0001	0.89877	0.88487	2.12E-01	4.48E-02	1.20E-01
3000	95	0.0001	0.89877	0.88487	2.12E-01	4.48E-02	1.20E-01
1500	95	0.0001	0.89877	0.88487	2.12E-01	4.48E-02	1.20E-01
2000	95	0.0001	0.89877	0.88487	2.12E-01	4.48E-02	1.20E-01
2500	95	0.0001	0.89877	0.88487	2.12E-01	4.48E-02	1.20E-01
3000	95	0.01	0.88533	0.86868	2.24E-01	5.00E-02	1.24E-01

Changes of error rate on increasing hidden layer sizes are shown in Fig. 4. We can adjust this parameter near to 100 using this chart. Now we need tunning for alpha. A number of various values of this parameter have also been tried in the model based on available experimental data. These results suggest a value of 0.001 for alpha. After these tests, we will use the primary factors presented in Table 2 to create a final MLP model.

Error rate with Hidden Layer Size changes.

Table 2 Selected Parameters for MLP.

Parameter	Value
Hidden layer size	100
Max Iteration	1500
Alpha	0.001

For DT Model we need to do tunning for two important hyper-parameters: (1) maximum tree depth and criterion that is the function to measure the quality of a split. To do this, more than 300 different combinations were tested, some of the highest accuracy recorded in Table 3.

Table 3 Top Accurate Configurations for Decision Tree.

Criterion	Max Tree Depth	Train R²	Test R²	RMSE	MSE	Mean absolute error
Mae	9	0.98785	0.92622	2.09E-01	4.36E-02	1.45E-01
Mae	8	0.9759	0.9167	2.20E-01	4.83E-02	1.52E-01
Mse	9	0.99006	0.9089	2.09E-01	4.35E-02	1.38E-01
friedman_mse	9	0.99006	0.90693	2.11E-01	4.46E-02	1.39E-01
Mse	7	0.96771	0.90436	2.17E-01	4.69E-02	1.55E-01
friedman_mse	7	0.96771	0.90436	2.17E-01	4.69E-02	1.55E-01
friedman_mse	8	0.98237	0.90327	2.14E-01	4.60E-02	1.45E-01
Mse	8	0.98237	0.90321	2.15E-01	4.61E-02	1.45E-01
Mae	7	0.95507	0.89379	2.45E-01	6.02E-02	1.72E-01
Mse	6	0.94386	0.88197	2.38E-01	5.66E-02	1.71E-01

In Fig. 5 we show how error rate of DT changes on increasing maximum tree depth. According to these table and figure, following combination have chosen for final DT model: Criterion = mae, max_depth = 9.

Effect of maximum depth change on error rate in the decision tree model.

As the last step, Hyper-parameter selection for number of estimators employed in the third model, AdaBoost with DT as a weak learner, must also be improved along with maximum depth. It's all laid out in Table 4 and Fig. 6. The random AdaBoost-DT also uses the criteria mse, N estimators = 50, and Max Depth = 9 (see Fig. 7).

Table 4 Top Accurate Configurations for AdaBoost-DT.

Number of DTs	Max Depth	Train R²	Test R²	RMSE	MSE	Mean absolute error
40	9	0.99759	0.93888	1.70E-01	2.89E-02	1.07E-01
50	9	0.99765	0.93888	1.70E-01	2.90E-02	1.07E-01
60	9	0.99766	0.93846	1.71E-01	2.92E-02	1.08E-01
55	9	0.99765	0.93812	1.72E-01	2.94E-02	1.08E-01
45	9	0.99756	0.93757	1.72E-01	2.96E-02	1.08E-01
30	9	0.99729	0.93748	1.72E-01	2.95E-02	1.07E-01
35	9	0.99743	0.93695	1.72E-01	2.97E-02	1.08E-01
25	9	0.99727	0.9359	1.73E-01	3.00E-02	1.07E-01
20	9	0.99707	0.93587	1.74E-01	3.01E-02	1.06E-01
15	9	0.99671	0.93217	1.76E-01	3.11E-02	1.10E-01
70	8	0.99462	0.92923	1.82E-01	3.30E-02	1.15E-01
60	8	0.99436	0.92833	1.83E-01	3.34E-02	1.15E-01
80	9	0.99772	0.92363	1.88E-01	3.52E-02	1.09E-01
65	9	0.99771	0.92359	1.87E-01	3.51E-02	1.10E-01
130	9	0.99781	0.92347	1.88E-01	3.53E-02	1.08E-01
70	9	0.99767	0.92343	1.87E-01	3.51E-02	1.09E-01
85	9	0.99774	0.92324	1.88E-01	3.54E-02	1.09E-01
95	9	0.99782	0.92307	1.88E-01	3.55E-02	1.08E-01

Effect of Number of Estimators change on error rate in AdaBoost-DT.

Effect of Max Tree Depth change on error rate in AdaBoost-DT.

3.2

3.2 Model analysis

In this section, we test our data using the models specified in the previous section. Determining the importance of features is one of the comparative advantages of AdaBoost-DT, and some other tree-based models. So, after finding the best configuration of our AdaBoost-DT model, we can show importance of fractures on Fig. 8, and also on Fig. 9 we can see this importance. Furthermore, the final model results in terms of comparison are listed in Table 5. It is clearly observed that AdaBoost-DT indicated the best performance for fitting the solubility data.

Residuals on selected AdaBoost-DT model.

Table 5 Final Models results.

Model	MSE	RMSE	Mean absolute error	Train R²
MLP	5.5179E-02	2.3490E-05	2. 03467E-01	0.894
Decision Tree	4.9836E-02	2.2324E-01	1.47467E-01	0.988
AdaBoost-DT	3.6094E-02	1.8998E-01	1.10790E-01	0.998

A comparison between Figs. 8 and 9 shows the relative agreement of these values with two different models. Also, Figs. 10-15 indicate the comparisons of predicted and actual values for the training and testing stages for all three models used in this work. From Figs. 10 to 15 , it is clear that the AdaBoost-DT is more closely aligned with the expected outcome than either of the other two models.

Comparing Train prediction with true output (MLP Model).

Comparing Test prediction with true output (MLP Model).

Comparing Train prediction with true output (DT Model).

Comparing Test prediction with true output (DT Model).

Comparing Train prediction with true output (AdaBoost-DT Model).

Comparing Test prediction with true output (AdaBoot-DT Model).

The trained and tested models were then used to evaluate the importance of each parameter on the CO₂ loading, and the results for AdaBoost-DT and DT are represented in Figs. 16 and 17, respectively. It is seen that in AdaBoost-DT model, the weight percentage of solvent has the most important influence on the CO₂ loading, while the cation molecular weight shows the least importance effect. For both models, it is seen that CO₂ partial pressure and weight percentage are the most important parameters. Finally, the effect of P_CO2 (kPa) and weight% on the solubility of CO₂ shown in Fig. 18 depicts the AdaBoost model. Both P_CO2 (kPa) and weight percent have a considerable impact on CO₂ solubility.

The effect of PCO2(kPa) and weight% on CO2 solubility predicted by the AdaBoost-DT model.

4 Conclusion

We carried out a comprehensive simulation based on artificial intelligence to predict the solubility of CO₂ in amino acid salt solutions. In the simulation of CO₂ solubility, we created and analyzed a variety of supervised learning algorithms. The literature-sourced data on CO₂ solubility was incorporated into the simulations for training and validation. Instead of only employing these models, the Hyper-parameters were tuned to improve the anticipated results. The Mean absolute error criterion reduced the error to 1.10790E-01, and the R² score rose to 0.998 as a result. The results indicated that AdaBoost-DT showed the best performance in predicting CO₂ loading.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Quinlan, J.R., CHAPTER 5 - From Trees to Rules, in C4.5, J.R. Quinlan, Editor. 1993, Morgan Kaufmann: San Francisco (CA). p. 45-56.
Timofeev, R. Classification and Regression Trees(CART)Theory and Applications. 2004.
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Introduction

Modeling

Multi-layer Perceptron (MLP) model
Decision tree (DT) model
AdaBoost-DT model
Accuracy criteria of models

Results and discussions

Model selection
Model analysis

Conclusion

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[57] Timofeev, R. Classification and Regression Trees(CART)Theory and Applications. 2004.

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