Optimization and design of machine learning computational technique for prediction of physical separation process

Haiqing Li; Chairun Nasirin; Azher M. Abed; Dmitry Olegovich Bokov; Lakshmi Thangavelu; Haydar Abdulameer Marhoon; Md Lutfor Rahman

doi:10.1016/j.arabjc.2021.103680

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Original article

04 2021

:15;

103680

doi:

10.1016/j.arabjc.2021.103680

Optimization and design of machine learning computational technique for prediction of physical separation process

Haiqing Li^{^a,^b,⁎}, Chairun Nasirin^{^c}, Azher M. Abed^{^d}, Dmitry Olegovich Bokov^{^e,^f}, Lakshmi Thangavelu^{^g}, Haydar Abdulameer Marhoon^{^h,ⁱ}, Md Lutfor Rahman^{^j,⁎}

a College of Mechanical and Electrical Engineering, Zhejiang Industry Polytechnic College, Shaoxing, Zhejiang 312000, China

b College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou, Zhejiang 310014, China

c College of Health Sciences (STIKES) Mataram, Indonesia

d Department of Air conditioning and Refrigeration, Al-Mustaqbal University College, Babylon, Iraq

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

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

g Department of Pharmacology, Saveetha Dental College, Saveetha Institute of Medical and Technical Science, Saveetha University, Chennai, India

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

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

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

⁎Corresponding authors. proudchina2008@163.com (Haiqing Li), lotfor@ums.edu.my (Md Lutfor Rahman)

Received: 2021-7-23, Accepted: 2021-12-29,

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

Machine learning (ML) methods were developed and optimized for description and understanding a physical separation process. Indeed, this work indicates application of machine learning technique for a real physical system and optimization of process parameters to achieve the target. A bunch of datasets were extracted from resources for physical adsorption process in removal of impurities from water as a case study to test the developed machine learning model. The case study process is adsorption process which has extensive application in science and engineering. The machine learning (ML) method was developed, and the parameters were optimized in order to get the best simulation’s performance for adsorption process. The data are used to correlate the adsorption capacity of the material to the adsorption parameters including dosage and solution pH. Randomized training and validation were performed to predict the process’s output, and great agreement was obtained between the predicted values and the observed values with R² values greater than 0.9 for all cases of training and validation at the optimum conditions. Three different machine learning techniques including Random Forest (RF), Extra Tree (ET), and Gradient Boosting (GB) were employed for the adsorption data. Quantitatively, R² scores of 0.958, 0.998, and 0.999 were obtained for RF, GB, and ET, respectively. It was indicated that GB and ET models performed almost the same and better than RF in prediction of adsorption data.

Keywords

Machine learning

Artificial intelligence

Modeling

Optimization

Separation

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1 Introduction

Separation of a target component from a liquid mixture has extensive applications in science and engineering, for instance in chemical and biochemical industries. The target component is usually removed due to certain reasons. It could be either the unwanted component which must be removed from the solution, or the desire component for purification purposes (Chen, 2021a, 2021c, 2021d; Ghodke, 2020; Hasthavaram, 2020; Hu, 2021; Li, 2021; Qaderi, 2020; Shang, 2022; Yang, 2021 ). The purification can be performed on feed/raw materials or the final products in manufacturing industries. The separation is mainly governed by mass transfer which depends on the gradients of properties in the system such as concentration gradient (Aroon et al., 2020; Dong et al., 2021; Elgersma, 2022; Kumar Chaurasiya and Singh, 2021; Shirazian and Ashrafizadeh, 2011; Shirazian et al., 2009, 2012; Sohrabi, 2011 ). Basically, the rate of mass transfer for the target component determines the separation efficiency and performance of the unit operation used for separation (Ghadiri and Shirazian, 2013; Ghadiri et al., 2012; Marjani and Shirazian, 2012; Pishnamazi, 2020; Ranjbar, 2013; Riasat Harami, 2019; Shirazian and Ashrafizadeh, 2010, 2010, 2013, 2015; Shirazian, 2012, 2012 ). Indeed, improving the mass transfer is the key step in development of separation processes.

Separation can be conducted in different unit operations such as distillation, absorption, adsorption, membrane processes, etc. Depending on the degree of separation as well as the energy requirements, appropriate separation process can be selected and used for separation of target components. When the amount of target component concentration in the liquid phase is low, then adsorption is an attractive unit operation for the separation of target molecules from liquid mixture (Albadarin, 2017; Chachkov and Mikhailov, 2020; Chen, 2021b; Chupradit, 2021; Fatima et al., 2020; Khansary et al., 2017; Mengting, 2019; Shirazian and Ashrafizadeh, 2015; Shtamburg, 2020; Soltani et al., 2020; Soltani, 2020 ). This separation technique is based on selective removal of the target component from a mixture. Therefore, the affinity between the adsorbent and the target molecule is the key step in the adsorption process (Albadarin, 2017; Ghadiri, 2013; Mengting, 2019; Razavi et al., 2015; Rezakazemi and Shirazian, 2019; Shirazian and Ashrafizadeh, 2015; Soltani et al., 2020; Soltani, 2020, 2020 ). The design of the adsorbent should be carried out in a way to maximize its separation capacity for separation of the target molecules which can be achieved by enhancing the internal and external surface area of the adsorbent (Asadollahzadeh, 2018; Ghadiri et al., 2014; Harami, 2021; Hasanizadeh et al., 2018; Hemmati, 2015; Khansary et al., 2017; Nerlikar, 2020; Shirazian and Ashrafizadeh, 2015; Soltani et al., 2019; Soltani, 2019, 2020 ).

By development of computational technique, one can predict the adsorption capacity of a solid material for application in adsorption process. This computational task can be conducted by using different modeling approaches such as machine learning (ML) models which are suitable for fitting large datasets (Ding, 2020; Sajjia, 2017; Senthil et al., 2020; Singh, 2021; Tao, 2021; Wu, 2021; Zhang, 2021; Zhu et al., 2021 ). However, some machine learning models have been developed for small datasets (Babanezhad, 2020; Ismail, 2019, 2019, 2020; Liang, 2020; Shang, 2021 ). These models rely on training a dataset and fitting the model to the obtained data. Therefore, measured data are required to train the network (Cai, 2020; Chao, 2019; Meng, 2021; Wang et al., 2022; Wu, 2021; Yang, 2021; Zhang, 2021; Zhao, 2021; Zheng, 2021; Zhou, 2018 ). This method has been recently used in separation applications based on adsorption process to predict the performance of an adsorbent in removal of impurities from water (González, 2020; Syah, 2021a, 2021b ).

In this study, we implemented three different machine learning models for simulation of adsorption data. Indeed, the adsorption capacity of a composite material was predicted at different conditions using the developed models. Indeed, we deal with a regression problem with a very small number of data points which are the adsorption isotherms for a particular adsorbent. In such cases, we can use ensemble methods to build high-generality models. Ensembles, especially ensembles of tree-based models, are one of the most flexible and useful machine learning techniques. An ensemble is a collection of trained models with the goal of improving the predictive performance of a single model by combining their predictions. There are several methods in this class of machine learning algorithms, the most important and famous of which are bagging and boosting (Ding, 2021; Yin, 2021, 2021 ).

Bagging (short for “bootstrap aggregating”) approaches fit several considered learners independently of others, allowing them to be trained concurrently. The goal of this strategy is to create an ensemble model that is more robust than the individual models that comprise it.

In boosting at first, a subset is selected, and all data points are assigned equal weights. On this subset, a foundation model is built. This model is used to forecast the entire dataset. Errors are then determined using the actual and anticipated values. Higher weights are assigned to data that were mistakenly anticipated. A new model is built, and predictions are made on the dataset. Similarly, many models are developed, each one correcting the preceding model's flaws. The weighted mean of all the models is used to create the final model (strong learner).

Fig. 1 shows the difference between the bagging and boosting methods schematically. Based on these facts and figures, in this research, we have selected three different models consisting of two bagging models and a boosting model. In the following, we will discuss these methods and their results on the dataset of this research. These models include Random Forest (bagging), Gradient Boosting, and Extra Tree (boosting).

2 Dataset used

The dataset used in this study is similar (Soltani, 2021) which is taken from the literature (Cook, 1977). More information on how to collect this data set can be found in these two references. This dataset has 21 data points, which are shown in full in Table 1. In this regression problem, we have two inputs: adsorbent dosage [W(g] and solution pH, the first of which is floating point decimal number and the second of which is positive integer.

Table 1 The data used in our models.

W (g)	pH	Qe
0.05	3	15
0.05	4	28.83333
0.05	5	33.75
0.05	6	39.91667
0.05	7	39.41667
0.05	8	38.75
0.05	9	33.16667
0.03	3	10.83333
0.03	4	25
0.03	5	30.83333
0.03	6	37.41667
0.03	7	35.83333
0.03	8	33.33333
0.03	9	28.33333
0.01	3	7.5
0.01	4	21.66667
0.01	5	28.33333
0.01	6	35.5
0.01	7	33.75
0.01	8	28.33333
0.01	9	23.75

The relationship between the inputs as well as the output is shown in Fig. 2 as scatter plot matrix, which shows that there is no definite and linear relationship between these parameters.

3 Methodology

As mentioned before, 3 different models of bagging and boosting have been selected for modeling of the adsorption capacity of the adsorbent in this research. A simple framework shown in Fig. 3 is used to implement the exact models.

General architecture of the simulation method.

3.1

3.1 Preprocessing

Some of the steps shown in Fig. 3 are preprocessors that are needed to prepare the data for better modeling, including influential analysis and scaling. In order to carry out the influential analysis in this research, we have used the Cook's distance (Breiman, 2001). The latter has been done in order to find the influence of each data point on final model, and also for scaling we used standard scaling. The Standard Scaler scales data inside each feature so that the distribution is centered around 0 with a standard deviation of 1. Each feature is separately centered and scaled by computing the necessary statistics on the samples in the training set. If the data is not evenly distributed, this is not the best Scaler to utilize.

3.2

3.2 Random forest (RF) and extra tree (ET)

Random forest (RF) (Flach, 2012) is a bagging ensemble that attempts to average multiple noisy(weak), but fairly unbiased trees in order to reduce variance. When building a decision tree, RF first selects a set of features at random, and then continues the process of selecting the normal branch within the feature set.

Bootstrap aggregation (bagging) is the foundation of random forests. Instead of creating a single model, the approach generates a series of bootstrap samples, which are random subsets of the dataset generated with replacement. Each model will be unique because each sample is unique. As a result, rather than a regressor that is overfit to the training set, a robust regressor is produced. The algorithm then creates a model ensemble. The ensemble in a simple decision-tree model consists of decision trees that loop through all variables and split the sample based on the best variable at a time, as shown in the pseudocode in Algorithm 1 below.

Algorithm 1. select feature to split
Input: data D, feature list F.
Output: feature f to split on.
$I_{\min} \leftarrow 1$
For each $f \in F$ :
Split D into subsets D₁,…,D_L according to value of v_j of f:
If $Imp ($ D₁ $, \dots,$ D_L $) < I_{\min}$ then:
$I_{\min} \leftarrow I m p ($ D₁ $, \dots,$ D_L $)$
$f_{best} \leftarrow f$
End
End
Output: f_best

A splitting function Imp is used to make splits (usually a measure called the Gini index). A model (typically a simple weighted average) is generated at each resulting leaf node, and the algorithm subsequently constructs further splits along the tree until generating further branches yields a less reliable model than a parent node (Guo, 2011).

The random-forest model extends the decision-tree by employing a technique known as subspace sampling. The random forest splits depend on only a subset of the independent features at a time. By pushing differences between the models, this adds more variety to the ensemble. Additionally, especially in higher dimensional training sets, this step reduces computational cost.

In pseudocode, Algorithm 2 depicts the random forest ensemble creation algorithm.

Algorithm 2. train an ensemble of models from bootstrap samples
Input: data points D, ensemble size T, learning algorithm A.
Output: ensemble of the developed models.
For t = 0 to t = T:
create a bootstrap sample D_t from D by sampling \|D\| values with exchange.
choose d features.
train a tree network M_t on D_t with no pruning;
Finish
Output: $\{M_{t}\| 1 \leq t \leq T}$

When all of the bagged, subspaced decision tree models are completed, they are combined into a single super-model known as the ensemble regressor. The ensemble regressor then receives a forecast from each independent model and averages the findings to get a predicted value for the dependent variable. The random forest model can handle numerical features well, and unlike linear models, it can capture non-linear interactions between features and the target (Guo, 2011). Random Forests also provide a feature importance measure that is based on the permutation importance measure and is processed on OOB data (Geurts et al., 2006).

Assume the training sets are made up of $(x_{i}, l_{j})$ , where $x_{i}$ is an instance and $l_{j}$ is the true label.

The significance of a feature f per tree t is computed as follows (Geurts et al., 2006): ${F I}^{(t)} (f) = \frac{\sum_{x_{i} \in {B^{c}}^{(t)}} I (l_{j} = \overset{(t)}{\underset{i}{c}})}{| {B^{c}}^{(t)} |} - \frac{\sum_{x_{i} \in {B^{c}}^{(t)}} I (l_{j} = \overset{(t)}{\underset{i, π_{f}}{c}})}{| {B^{c}}^{(t)} |}$

For a random forest regression algorithm, there are several parameters to tune. Our random forest regression model's optimization method includes the following parameters:

Number of estimators
Maximum depth in each tree

Extra trees (Alswaina and Elleithy, 2018) (Extremely randomized trees) is other tree-based ensemble method similar to Random Forest. The ET is a recursively trained ensemble of Decision Trees, and the final model was produced using a big Decision Tree. Each one constructs the tree using the complete dataset, and the appropriate cut point for each split must be determined based on information gain (Xia, 2015). The ET model has two important innovations:

the nodes are divided randomly using the cut-point (Lin et al., 2012).
the whole training dataset was utilized to build the DT rather than the replica generation using the Bootstrap for other decision tree models, for the random forest model.

3.3

3.3 Gradient boosting (GB)

Instead of generating a single optimized model, Gradient Boosting (GB) improves the standard decision tree models using a statistical technique called boosting, whose main idea is to aggregate a series of weak or base models to generate a single strong consensus model (Bühlmann and Yu, 2003; Elith et al., 2008; Yang, 2020 ). Gradient boosting algorithm in shown in Algorithm 3.

Algorithm 3. gradient boosting algorithm
Input: Training set ${(x_{i}, y_{i})}_{i = 1}^{N}$ , loss function $L (y, F (x))$ , number of iterations M.
Output: The final regression function $F_{m} (x)$
Initialize: $F_{0} = {a r g m i n}_{ρ_{0}} \sum_{i = 1}^{N} L (y_{i}, ρ_{0})$
For m = 1 to M:
$r_{i} = - {[\frac{\partial L (y_{i}, F (x_{i}))}{\partial F (x_{i})}]}_{F (x) = F_{m - 1} (x)}, i = 1, \dots, N$
$α_{m} = {a r g m i n}_{α, β} \sum_{i = 1}^{N} {[r_{i} - β h (x_{i}; α)]}^{2}$
$ρ_{m} = {a r g m i n}_{ρ} \sum_{i = 1}^{N} L {[r_{i}, F_{m - 1} + ρ h (x_{i}; α_{m})]}^{2}$
$F_{m} (x) = F_{m - 1} (x) + ρ_{m} h (x; α_{m})$
End
Output: $F_{m} (x)$

In this algorithm

β

is weight factor,

r_{i}

is the negative gradient evaluated using the previous model. The GB framework starts with an initial model

F_{0} (x)

, assuming M decision trees would be built. Compensation of the residues is similar to optimizing the expansion coefficients

ρ_{m}

and

α_{m}

for each iteration

m = 1, 2, \dots, M

(Bühlmann and Yu, 2003):

(ρ_{m}, α_{m}) = {a r g m i n}_{ρ, α} \sum_{i = 1}^{N} L [y_{i}, F_{m - 1} + ρ h (x_{i}; α)],

And gets: $F_{m} (x) = F_{m - 1} (x) + ρ_{m} h (x; α_{m})$

The gradient boosting framework supports a variety of smooth loss functions, including AdaBoost, LogitBoost, and L2Boosting (Hamilton et al., 2015). For the regression issue, the squared loss function is utilized because of its simplicity and coherence: $L (y, F_{M} (x)) = \sum_{i = 1}^{N} {(y_{i} - F_{M} (x_{i}))}^{2} .$

3.4

3.4 Performance metrics

This study uses three metrics to assess each algorithm's performance:

R Squared (R²) is the percentage of the overall variance in the dependent variable that is accounted for by the independent variable [99]:

R^{2} = 1 - \frac{\sum_{i = 1}^{n} O_{i} - P_{i}^{2}}{\sum_{i = 1}^{n} O_{i} - O_{m}^{2}}

Mean Squared Error (MSE) is an estimator that assesses average squared errors:

MSE = \frac{1}{n} {\sum_{i = 1}^{n} | O_{i} - P_{i} |}^{1}

Rooted MSE (RMSE):

RMSE = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(O_{i} - P_{i})}^{2}}

In these equations $O_{i}$ are observed and $P_{i}$ are predicted values.

4 Results and discussion

The three models were implemented using the data listed in Table 1 in order to predict the adsorption data. To get the results, we first need to do the pre-processing steps. Fig. 4 shows the Cook distance diagram in the dataset used. According to this diagram, only one of the data points has an excessive effect on the final model. Therefore, this special point is removed from the learning stage.

To tune the hyperparameters of each of the models introduced in this study, different combinations of the values of these parameters were tested. Finally, we selected the set of values shown in Table 2 as the final values of these parameters.

Table 2 Final tuned hyper-parameters.

Hyper-Parameter	Random Forest	Extra Tree	Gradient Boosting
Number of Base Estimators	39	15	45
Maximum Tree Depth	13	6	2
Learning Rate	–	–	0.2
Criterion	Friedman_mse	MAE	–

Finally, these parameters were used for the final models, the results of which are shown in Table 3. The results of the residuals for the three models are indicated in Figs. 5–7 . Furthermore, the comparisons between the predicted and measured values for the three models are indicated in Figs. 8–13 . Based on these results, the ET model can be considered as the best model among these bagging and boosting algorithms. However, the performance of the ET and GB model are almost the same in terms of accuracy as listed in Table 3.

Table 3 Final results.

Metric	Random Forest	Extra Tree	Gradient Boosting
R² score	0.958	0.999	0.998
MSE	9.98	5.40	3.70
RMSE	3.15	2.33	1.92

5 Conclusion

In this study, due to the fact that we were faced with a very small data set, we decided to use bagging and boosting methods for prediction of adsorption capacity of an adsorbent in removal of impurity from water in adsorption process. We considered adsorbent dosage and solution pH as the model inputs, whereas the adsorption capacity was the only predicted output for the models. Three different machine learning models including RF, ET, and GB were considered in this study. Due to the nature of their algorithms, these methods can create highly generalized models in such situations. Fortunately, this hypothesis was confirmed in the practical results of the research. Finally, with R² criteria, scores of 0.958, 0.998, and 0.999 were obtained for RF, GB, and ET, respectively which is a good result. Also, due to the fact that the selected models are kept as simple as possible, there is the least possibility of over-fitting in them. As a result, we can introduce the ET model as the best predictor of this research. In future research, more parameters can be optimized, and the results can be examined and discussed.

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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Introduction

Dataset used

Methodology

Preprocessing
Random forest (RF) and extra tree (ET)
Gradient boosting (GB)
Performance metrics

Results and discussion

Conclusion

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Optimization and design of machine learning computational technique for prediction of physical separation process

Abstract

Keywords

Machine learning

Artificial intelligence

Modeling

Optimization

Separation

1 Introduction

2 Dataset used

3 Methodology

3.1 Preprocessing

3.2 Random forest (RF) and extra tree (ET)

3.3 Gradient boosting (GB)

3.4 Performance metrics

4 Results and discussion

5 Conclusion

Declaration of Competing Interest

References

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