Biosurfactants are a series of organic compounds that are composed of two parts, hydrophobic and hydrophilic, and since they have properties such as less toxicity and biodegradation, they are widely used in the food industry. Important applications include healthy products, oil recycling, and biological refining. In this research, to calculate the curves of rhamnolipid adsorption compared to Amberlite XAD-2, the least-squares vector machine algorithm has been used. Then, the obtained model is formed by 204 adsorption data points. Various graphical and statistical approaches are applied to ensure the correctness of the model output. The findings of this study are compared with studies that have used artificial neural network (ANN) and data group management method (GMDH) models. The model used in this study has a lower percentage of absolute mean deviation than ANN and GMDH models, which is estimated to be 1.71%.The least-squares support vector machine (LSSVM) is very valuable for investigating the breakthrough curve of rhamnolipid, and it can also be used to help chemists working on biosurfactants. Moreover, our graphical interface program can assist everyone to determine easily the curves of rhamnolipid adsorption on Amberlite XAD-2.
As mentioned above, biosurfactants are organic compounds that are produced by microorganisms and consist of two parts: hydrophilic and hydrophobic. They are often produced by bacteria on living surfaces. One of the reasons for attracting many industrial applications to biosurfactants is due to their amphiphilic properties. Among the usable and outstanding capabilities of biosurfactants used in various industries such as mines, fertilizers, petrochemicals, and petroleum, we can mention the environmental degradability and reduction of surface tension between interstitial and low toxicity. The reduction of the interfacial tension is due to the increase in the solubility of hydrophilic molecules when using biosurfactants. Capabilities such as surface modification and interfacial tension have made surfactants attractive to the industry. Rhamnolipids (RLs) are the most studied type of biosurfactants. According to the literature, rhamnolipids can reduce water surface tension by about 60% [
In this research, activated carbon is used for adsorbent in the process. The breakthrough curve of a packed column is a very significant attribute of this system. As a result, determining such curves will be useful for optimizing and understanding the performance of the column. To model the adsorption phenomena, the mass balance in liquid and solid phases is evaluated. It may also include modeling the porous and liquid film resistance and also axial dispersion. Finally, with a suitable software package, a set of differential equations can be solved.
Ill conditions and uncertainty in differential equations make using conventional mathematical models not suitable. Intelligent models have to be a powerful tool in solving process modeling problems. To predict the optimized targets, in various fields such as petroleum and gas fields, methods such as SVM, ANN, group method data manipulation (GMDH), fuzzy logic system, and adaptive fuzzy neural inference system can be used. Interactions between AI neurons are achieved by connecting different units. Artificial neurons’ interactions are achieved by connecting different units. Each weighted output is related to the sum of the output from the previous synaptic weight layer, and then it is used as an input for a specific neuron. Backpropagation ANNs are extensively applied, as they have shown to be a capable and powerful tool [
Due to the importance of predicting a trustworthy estimation of breakthrough curves, this research is aimed at predicting of breakthrough curves utilizing the LSSVM method for rhamnolipid (Figure
Chemical structure of the first identified rhamnolipid, symbolized as Rha-Rha-C10-C10.
In the present research, the LSSVM strategy was applied to calculate the curve to achieve rhamnolipid uptake relative to the Amberlite XAD-2 model resulting in a more simplified way [
The parameters of the above expression are as follows:
The input
Quadratic programming must be solved to determine the SVM parameters. The LSSVM eliminates deficiencies in the solving process of a quadratic programming problem [
The following constraints are applied to the cost function:
The Lagrangian of the LSSVM is expressed as
In the above phrase, the symbol
By solving the aforementioned equations, LSSVM parameters are obtained. LSSVM employs the kernel function in the same way that SVM strategy does. The most common applied kernel function is the radial basis function (RBF) which is given by
Schematic diagram of PSO-LSSVM strategy.
The adjusted parameters are
Different statistical error analyses such as mean absolute error (MAE), coefficient of determination (
The outlier is a set of data having a different behavior in comparison with the bulk of data. Finding outliers would improve the accuracy and reliability of a proposed model remarkably. To help to trace outliers, there are two procedures numerical and graphical procedures. One of the most powerful methods is the Leverage method in which the deviation of estimated values from the experimental ones is calculated. It also includes dealing with Hat matrix being made of experimental and predicted data. The equation below is used for calculating the Hat indices [
A reliable model would contain the majority of the predicted values by satisfying the following constraint:
Regardless of the value of
To create the LSSVM model, 75% of data points are considered as learning points, and the rest of them were used to examine the efficiency of the opposed model. Furthermore, data are normalized within the range of [-1,1] applying the equation below:
Here,
The predictive model’s accuracy is investigated employing different graphical and statistical methods. Figure
Plot of PSO-LSSVM model’s prediction vs. experimental data at training and testing stages.
Figure
Regression plot of suggested PSO-LSSVM model at training and testing stages.
Results of the current study are compared to the LSSVM, ANN, and GMDH models [ First layer:
Second layer:
Third layer:
Genome expression:
The ANN model based on these four input variables as mentioned as follows:
input layer hidden layer including six neurons output layer
Figure
Cross plot of predictions of different models for total data points: (a) ANN, (b) GMDH, and (c) LSSVM.
Compared to ANN and GMDH models, the less relative error is observed in the proposed LSSVM model. Figure
Absolute error for different models’ outcomes: (a) ANN, (b) GMDH, and (c) LSSVM.
Estimation accuracy is also investigated by applying the following statistical methods:
Table
Statistical parameters calculated for three models.
Analysis | LSSVM | ANN | GMDH | ||
---|---|---|---|---|---|
Train | Test | Total | Total | Total | |
MSE | 0.0001 | 0.0002 | 0.0001 | 0.0005 | 0.0047 |
AAD | 0.7293 | 0.8043 | 0.7481 | 1.9111 | 6.2395 |
0.9990 | 0.9990 | 0.9990 | 0.9946 | 0.9526 | |
STD | 0.0112 | 0.0122 | 0.0115 | 0.0271 | 0.0808 |
Predicted
Four different conditions of
In the last part of this research, the leverage approach is applied to find outliers, employing the Hat matrix, Williams plot, and residuals. As discussed, Eq. (
Diagnosis of the probable outlier data and applicability domain of the applied model.
Then LSSVM approach was employed to estimate breakthrough curves of rhamnolipid adsorption over Amberlite XAD-2 as a function of fixed bed height, flow velocity, runtime, and initial rhamnolipid concentration. The particle swarm optimization method was employed for the training process enhancing the accuracy of the proposed model. Various statistical and graphical methods were applied to evaluate the model’s reliability showing that the AAD% value for adsorption over activated carbon was 0.75%. For ANN and GMDH models that were developed by Padilha et al., AAD% of activated carbon is reported to be 1.9% and 6.2%. Based on the above evidence, we can find that the proposed LSSVM model is more reliable for the process of predicting the breakthrough curves.
A graphical user interface (GUI) version of the model is developed (Figure
GUI version of the developed LSSVM model.
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
The authors declare that they have no conflicts of interest.
The research presented in this paper was supported by the Funds of High-level Hospital Construction Research Project of Maoming People’s Hospital.
Table S1: experimental data points used in this study.