A new approach using artificial neural network and support vector machine models to predict the permeate flux of a rotating disk membrane

doi:10.21203/rs.3.rs-1100319/v1

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A new approach using artificial neural network and support vector machine models to predict the permeate flux of a rotating disk membrane

https://doi.org/10.21203/rs.3.rs-1100319/v1

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The modeling of the permeate flux of a rotating disk membrane (RDM) filtration was investigated in this paper. Two computational intelligence techniques namely artificial neural networks (ANN) and support vector machine (SVM) were employed to model the permeate flux based on seven input variables including time of filtration, concentration of the feed fluid, transmembrane pressure, rotating velocity, dynamic velocity of the feed fluid, pore diameter of the membrane and, density of the feed fluid. The best-fit model was selected through the trial-error method and the two statistical parameters including the coefficient of determination (R²) and the average absolute relative deviation (AARD) between experimental and predicted data. The results obtained showed that the optimized ANN model can predict the permeate flux with R² = 0.999 and AARD% = 2.245 versus the SVM model with R² = 0.996 and AARD% = 4.09. Furthermore, the ANN model showed a high ability to predict the permeate flux in comparison with the SVM approach. The applicability domain of the ANN model was conducted to identify the outliers of the database and, the sensibility analysis of inputs on the output was employed for the determination of the relevant input variables.

Dynamic filtration

Rotating disk membrane

Flux

Modeling

ANN

SVM

To provide higher separation quality with lower maintenance costs and easier operational control, membrane filtration techniques, and in particular rotating disk membrane (RDM) filtration systems were commonly employed [1, 2]. However, the performance of such process is significantly affected by the fouling due to the cake build-up on the surface or in the pores of the membrane caused by the effluents disposal [3, 4]. So, the main objectives of RDM filtration are to increase the shear rate and reduce the cake build-up to improve the permeate flux [1, 5, 6].

Various investigations were carried out on the use of RDM for the filtration of many kinds of feed fluids, such as suspension yeast [7], suspension of calcium carbonate [7, 8], ferric hydroxide [9], and chicory juice [10, 11]. In all cases, it was found that RDM can improve the flux filtration by increasing the shear that reduces booth concentration polarization in nanofiltration, ultrafiltration, and cake build-up in microfiltration [5].

To preserve time and experimental cost, researchers have always tried to find an economical way to understand a phenomenon without experimenting, using modeling, simulation tools, and collected experimental databases [12, 13]. Therefore, there are many mathematical models in literature proposed to evaluate the effects of the shear rate on the membrane filtration by reducing the cake accumulation on the membrane surface [6, 14]. Nevertheless, these models could not simulate the membrane flux decline accurately because of the presence of several numbers of fitting parameters related to the membrane, feed fluid and quality in a membrane filtration mechanism [12].

In recent years, artificial neural networks (ANN) became one of the most powerful modeling tools in membrane filtration technology [12, 15]. In this context, several studies were realized and many models were proposed to deduce the flux using prediction methods and optimization algorithms [16]. To predict the flux decline and fouling resistance in oily wastewater treatment, Soleimani et al. [17] used ANN and GA (Genetic Algorithm) to optimize the operating conditions. Bowen et al. [18] developed an inaccurate ANN approach to model permeated flux of silica suspensions using three parameters (pH, ionic force, and pressure). Jawad et al. [19] employed ANN and MLR (Multi Linear Regression) to study the permeated ଂux in forwarding osmosis using several experimental data from literature with nine input parameters; they found that ANN is better in forming a relationship between input and output than MLR. Besides, Sahoo et al. [20] used genetic algorithms (GAs) to find the best geometry and values of an internal parameter of two learning algorithms of ANN. They used four parameters as an inlet (pH, feed water, particle diameters, and ionic strengths) and a flux decline as an outlet. Bagheri et al. [21], in their critical review, showed the performance of artificial intelligence (AI) and machine learning in controlling membrane fouling. They found that ANN can predict fouling with an R² = 0.99 and an error near zero. Liu et al. [22] used ANN to predict fouling in micro-filtration of water treatment. They employed five inputs to predict TMP (transmembrane pressure). Their results showed a good agreement with the experimental data. Furthermore, Wei et al. [23] investigated the modeling of permeate flux of colloidal suspensions making a comparison between the wavelet network (WN), back-forward back propagation neural network (BBNN), and MLR. Their results showed that WN is most predictable than MLR and BBNN.

The support vector machine (SVM) is a new promising technique which already showed good results in medical diagnostics, electric load prediction, and other domains [24]; it is a non-linear and nonparametric regression technique. To predict the clogging in a membrane bioreactor (MBR), Li and Tao [25] used first SA (simulated annealing algorithm) to optimize the three important parameters for SVM, and thereafter they employed the SVM to predict fooling in MBR. Gaoa et al. [26] applied the SVM model to predict the membrane permeate flux decline inside a sequencing batch reactor (SBR). They found a good agreement between the experimental data and predicted values of the SVM model.

Although many studies have been published on the modeling of dynamic membranes using ANN [15–17, 19–22], there were fewer researches about the use of the combination of SVM and ANN to model such systems. The aim of this study was to model the decrease of permeate flux in RDM using both ANN and SVM models. On the other hand and because of several experimental studies [10, 26, 27] that took place in the RDM and the existence of only few theoretical models, the main objective of this research was to identify the best approach between ANN and SVM models to predict the flux decline in RDM. For this, the main characteristics of ANN and SVM models were compared and validated with the experimental results of RDM.

The filtrate flux ‘‘J’’ can be written in the theoretical form by using Eq. 1:

$$J=\frac{1}{A}\frac{{d{V_p}}}{{dt}}$$

where A is the effective membrane surface, V_p is the total volume of permeate flux, and t is the filtration time.

The local pressure on the surface of the membrane and in the radial direction can be calculated as follows [8]:

$$P(r)={P_c}+\frac{1}{2}\rho {k^2}{\omega ^2}({r^2} - {R^2})$$

where ${P_c}$ is the peripheral pressure, $\rho$ is the density of the fluid, k is the constant of velocity factor (0.42, 0.84 for the disk without and with vanes, respectively) [13], and $\omega$is the angular velocity.

The mean transmembrane pressure (TMP) can be found by integrating the local pressure over the membrane surface with respect to r [28]:

$$\overline {{TMP}} ={p_c} - \frac{1}{4}\rho {k^2}{\omega ^2}{R^2}$$

The permeability of pure water L_p can be calculated from the water flux using Eq. 4:

$${L_p}=\frac{J}{{\overline {{TMP}} }}$$

The permeability of filtration in the case of the feed fluid varies with the resistance of cake ${R_c}$:

$${L_p}=\frac{1}{{\mu ({R_m}+{R_c})}}$$

where R represents the resistance of the membrane and µ represents the viscosity of the fluid.

The permeate flux can be deduced using Eq. 6:

$$J=\frac{{\overline {{TMP}} }}{{\mu ({R_m}+{R_c})}}=\frac{1}{A}\frac{{d{V_p}}}{{dt}}=\frac{Q}{A}$$

In this equation, the cake resistance is not constant; it varies over time. Consequently, estimating the decrease in permeate flux is so difficult on the RDM surface. Therefore, modeling by nonlinear methods using ANN or SVM is a real alternative method to model the flux decline.

The experimental data used in this work was collected from previously published works [7–11] summarized in Table 1. It regroups the maximum, minimum, mean and standard deviation (SD) of each parameter. The dataset consists of 1284 data points of different feed fluids such as chicory juice, carbonate suspension yeast, and ferric hydroxide solution. The results were chosen under different conditions and filtration parameters.

Table 1

Max, min, mean and values of standard deviation (SD) of collected base data
Variables Data values	Flux (L/h.m²)	Time (min)	TMP (kPa)	Rotating velocity Ω (rpm)	Fluid concentration (g/L)	Membrane Pore size (µm)	Fluid dynamic viscosity (Pa.s)	Fluid density (kg/m³)
Maximum	1397.65	360.00	129.77	2000	700.00	0.450	1.5400	2800.00
Minimum	16.57	0.22	25.62	750	3.00	0.002	0.0013	1001.07
Mean	292.60	89.58	64.01	1730.91	50.89	0.175	0.3027	1436.82
SD	340.21	91.27	24.23	384.91	119.20	0.082	0.4561	677.52

4.1. Model performances

The performance of the developed models was evaluated based on three statistical parameters, which are the correlation determination coefficient, and the average absolute relative deviation. The mathematical definition of the previous error types, R, R² and AARD% are given by Eq. 7 to Eq. 10, respectively.

$$R=\frac{{\sum\nolimits_{{i=1}}^{N} {\left( {y_{i}^{{\exp }} - {{\hat {y}}^{\exp }}} \right)\left( {y_{i}^{{cal}} - {{\hat {y}}^{cal}}} \right)} }}{{\sqrt {\sum\nolimits_{{i=1}}^{N} {{{\left( {y_{i}^{{\exp }} - {{\hat {y}}^{\exp }}} \right)}^2}} } \sum\nolimits_{{i=1}}^{N} {{{\left( {y_{i}^{{cal}} - {{\hat {y}}^{cal}}} \right)}^2}} }}$$

$${R^2}=1 - \frac{{\sum\nolimits_{{i=1}}^{N} {{{\left( {y_{i}^{{\exp }} - \hat {y}_{i}^{{cal}}} \right)}^2}} }}{{\sum\nolimits_{{i=1}}^{N} {{{\left( {y_{i}^{{\exp }} - {{\bar {y}}^{\exp }}} \right)}^2}} }}$$

With:

${\hat {y}^{cal}}=\sum\limits_{{i=1}}^{N} {\frac{{y_{i}^{{cal}}}}{N}}$ ${\hat {y}^{\exp }}=\sum\limits_{{i=1}}^{N} {\frac{{y_{i}^{{\exp }}}}{N}}$ (9)

And the average absolute-relative-deviation (AARD) is given as:

$$AARD\left( \% \right)=\frac{{100}}{N}\sum\limits_{n} {\frac{{\left| {{y^{cal}} - {y^{\exp }}} \right|}}{{{y^{\exp }}}}}$$

where N is the number of compounds in the dataset for each phase (training, test, or whole dataset), y^cal is the calculated (predicted) value of y; for training or test set, y^exp is the experimental (observed) value of y, ${\widehat{y}}^{cal}$ the average of calculated values of y, and ${\widehat{y}}^{exp}$ the average of experimental values of y.

4.2. Machine learning models for estimating permeate flux

4.2.1. Support vector regression

The support vector regression (SVM) is a robust tool to solve nonlinear regression problems. The gradient descent algorithm is the most widely applied algorithm to select SVM parameters. For this study with the use of the selected seven (07) inputs, a set of 1284 points were taken to build the SVM model. It was developed by writing a script in the MATLAB environment. To improve the forecasting accuracy of the SVM model, a gradient descent algorithm was used to find the optimal parameters namely the constant C (box-constraint), the epsilon (ε), and the parameter of the kernel function or Kernel-Scale (σ). The RBF, Gaussian, and polynomial Kernel functions were tested to select the most suitable model with better statistics performances. The developed model is carried out by the first SVM function of MATLAB® R2019b. For this, the cross-validation "holdout" method was selected, where 70% of the data was used randomly for learning, and 30% for testing. Since there is no rule to determine the appropriate parameter values of the SVM model; the optimized parameters were then determined using the trial-and-error method during the test stage (Table 2).

Table 2

Calculated parameters of SVM Model
Penalty parameter (C>0)	Kernel width parameter “σ”	Size of the insensitive zone (ε)	Kernel Function	Quantity Of support vectors (n)	Loss regression error
100	0.1	0.0448	Radial Basis Function (RBF)	856	5.1074 10⁻⁴

Figure 1 shows the regression analysis between the predicted values by SVM and the experimental permeate fluxes for the training, test, and global set. Therefore, the best SVM model can capture 99.84% of the variability of the permeate flux during the overall data set which is given in Fig. 1-c, 99.85% for the training stage (Fig. 1-a), and 99.83% for the test stage (Fig. 1-b). Consequently, the optimal SVM model was found with significant correlations during the different stages, which means that this model could accurately fit the permeate flux within the given interval of input variables employed through the training stage which corroborates the performance of the SVM model.

Table 3 summarizes the values obtained of the different statistical criteria and errors of the optimized SVM model. All the statistical criteria verify the conditions of acceptability (correlation close to the unit and errors close to zero).

Table 3

Comparison between the results predicted by SVM and experimental data
AARD%			R			R²
Train	Test	Global	Train	Test	Global	Train	Test	Global
0.963	4.093	2.006	0.9985	0.9983	0.9984	0.997	0.996	0.997

4.2.2. Artificial neural networks

In this work, a multi-layer feed-forward back propagation neural network (FFBP MLP-NN) was developed to model the permeate flux. The MLP-NN was trained with the Levenberg-Marquardt optimization algorithm. A different combination of MLP-NN parameters was then tested, including transfer function, number of hidden layers, and hidden neurons. These parameters were selected based on the trial-and-error method during the test stage and based on the above-cited statistical parameters. As described, a MLP with one hidden layer is capable to map the non-linear relationship between dependent and independent variables. Consequently, a MLP with one hidden layer was adopted with seven (07) input variables, one output variable, and the number of hidden neurons was changed from 1 to 30. Also, several transfer functions were tested with other parameters. The optimal conditions found for the best ANN model are summarized in Table 4.

Table 4

Structure of the optimized ANN model
Type of network	Training Algorithm	Input layer	Hidden layer		Output layer
FFBP NN (newff MTALAB function)	Bayesian regularization backpropagation algorithm (BRBP) (trainbr MATLAB function)	No. of neurons	No. of neurons	Transfer function	Number of neurons	Transfer function
FFBP NN (newff MTALAB function)		07	10	Hyperbolic tangent sigmoid (tansig MATLAB function)	01	Linear (purelin MATLAB function)

Figure 2 depicts the regression plots between experimental and predicted permeate fluxes using ANN for the four stages. The obtained results showed that the best model was found with a very low AARD and high regression coefficient. Since the obtained correlation coefficients were found superior to 0.99 for training, validation, tests, and the entire data set as depicted in Fig. 2-a, Fig. 2-b, and Fig. 2-c. Hence, the developed ANN with the selected architecture and parameters showed a high ability to quantify the correlation between the experimental and predicted permeate flux values.

Table 5 illustrates the different statistical errors and correlations for the four stages, where Fig. 3 gives a rapid comparison between ANN and SVM when estimating the permeate flux.

Table 5

Comparison between the experimental data and predicted values by ANN
AARD%				R				R²
Train	Test	Validation	Global	Train	Test	Validation	Global	Train	Test	Validation	Global
1.891	2.245	2.140	1.991	0.999	0.999	0.999	0.999	0.999	0.999	0.998	0.999

From Fig. 3, it was observed that the ANN and SVM models have almost the same correlation coefficient but the ANN yields the low AARD during the test stage. Consequently, ANN presents the best ability when predicting the permeate flux.

4.3. Comparison between experimental and ANN modeling of permeate flux

Another comparison between experimental (empty symbols) and predicted permeate flux using ANN (charged symbols) was made and the results were plotted for different operational conditions as shown in Fig. 4. For rotating velocity of 2000 rmp and TMP of 100 kPa (Fig. 4-a), the experimental data fit with high accuracy the ANN predictions with AARD = 1.126% alongside the total time cycle of filtration. However, for TMP values of 80 kPa and 49 kPa, the AARD was equal to 3.29 and 6.74%, respectively.

The comparison between experimental and ANN results versus time for the rotating velocity of 1500 rpm (Fig. 4-b) and under a TMP of 50 kPa showed a slight deviation in the time range of 0-300 min with a very acceptable AARD = 0.74%. However for the rotating velocity of 1000 rpm (Fig. 4-c), the ANN predictions showed the best performance when modeling the flux in the case of TMP equal to 27 kPa with an AARD = 0.70% in comparison with the values of TMP of 50 kPa and 80 kPa; in this case, the values of ARD are of 1.46% and 0.85%, respectively.

From the results presented in Table 6, it was noticed that the ANN model showed a very acceptable accuracy with an AARD of 0.7% under the operating conditions (Ω = 1000 rpm and TMP = 27 kPa), while it presents a considerable deviation with a high AARD of 6.74% for Ω = 2000 rpm and TMP = 49 kPa.

Table 6

Comparison between ANN and SVM models
Ω (rpm)	TMP (kPa)	AARD (%)
Ω (rpm)	TMP (kPa)	ANN		SVM
1000	27	0.70	1.00	9.49	7.46
	50	1.46		8.27
	80	0.85		4.61
1500	50	0.74	0.74	2.36	2.36
2000	49	6.74	3,72	2.66	1.88
	80	3.29		2.85
	100	1.13		0.14
MAARD (%)		1.82		3.90

For the generalization case, the ANN can be used to model permeate flux with the mean of AARD of 1.82% in comparison to the SVM model (Table 6).

4.4. Comparison between experimental and SVM modeling of permeate flux

Figure 5 illustrates the predicted values using SVM (charged symbols) versus experimental values of permeate flux (empty symbols) for different operational conditions.

It was shown that the SVM model followed accurately the trend of the experimental permeate flux with an AARD of 0.14% for Ω = 2000 rpm and TMP = 100 kPa, while it presented a higher deviation with an AARD of 9.49% for Ω = 1000 rpm and TMP = 279 kPa.

4.5. Applicability domain

The applicability domain using Williams’ plot of the ANN model was conducted to identify the dataset outliers. In the Williams diagram, the standardized residual parameter (δ) is plotted versus a distance called leverage (hi). These two parameters (δ and hi) can be calculated using Eq. 11 and Eq. 12, respectively:

$$\delta =\frac{{{y_i} - {{\hat {y}}_i}}}{{\sqrt {\frac{{\sum\nolimits_{{i=1}}^{n} {{{\left( {{y_i} - {{\hat {y}}_i}} \right)}^2}} }}{{\left( {n - A - 1} \right)}}} }}$$

where y_i and ${\widehat{y}}_{i}$are the experimental and the calculated values for the i-th compound, respectively, A is the number of descriptors and n is the number of compounds.

The leverage value (h_i) can be defined as [29]:

$${h_i}=x_{i}^{T}{\left( {{X^T}X} \right)^{ - 1}}{x_i}$$

where x_i is the descriptor vector of the i-th compound, ${x}_{i}^{T}$ is the transpose of x_i, X is the descriptor matrix and X^T is the transpose of X.

The warning leverage value (h^*) was calculated as:

$${h^ * }=\frac{{3\left( {k+1} \right)}}{n}$$

where k is the number of predictor variables included in the model and n is the number of data points.

The applicability domain of the ANN model was analyzed using a Williams plot (Fig. 6), where the vertical line is the critical leverage value (h*) and the horizontal lines ±3. From the results obtained, it was observed that only 67 points (5%) lie out the domain and most of the dataset belongs to the AD area, which is between the horizontal lines (limit of ± 3). This means that an average of 95% of the whole data set is covered.

4.6. Sensitivity analysis

The proposed model (ANN) can potentially provide a good dependency between the input and output parameters. To investigate how the inputs affect the outputs, a sensitivity analysis was undertaken. The most effective input can be recognized by the relevance factor (r), which is in the range of −1 to +1 and is stated by using Eq. 14 [30]:

$${r_k}=\frac{{\sum\nolimits_{{i=1}}^{n} {({X_{k,i}} - {{\bar {X}}_k})({Y_i} - \bar {Y})} }}{{\sqrt {\sum\nolimits_{{i=1}}^{n} {{{({X_{k,i}} - {{\bar {X}}_k})}^2}\sum\nolimits_{{i=1}}^{n} {{{({Y_i} - \bar {Y})}^2}} } } }}$$

where${X_{k,i}}$is the i-th value of the k-th input vector with its average${\bar {X}_k}$,${Y_i}$ is i-th output value and its average $\bar {Y}$and, n is the number of compounds.

The absolute value of the relevance factor has a direct relation with the output. As can be seen in Fig. 7, the permeate flux shows a straight dependency on the inputs (density, d_p, Ω, viscosity, TMP and concentration), and an opposite dependency on time. Also, the time and density are the most relevant input variables with a relevance factor of +0.56 and -0.14, respectively.

4.7. ANN interface of permeate flux calculation

A friendly and flexible Matlab user interface was designed based on the best ANN parameters (weights and baises) and the selected inputs to compute the permeate flux of the RDM (Fig. 8). This allows the user to make a quick and easy calculation of the permate flux without knowing any details about ANN, Matlab software or even the physical phenomena.

The conducted study aimed at modeling the non-linear behavior of the flux decline during the filtration process of a rotating disk membrane using ANN and SVM methods and under different operating conditions. The best ANN was found after trying different structures and the accuracy was assessed using different metrics namely, the regression coefficients and AARD%. The results obtained showed that the ANN with the architecture of 7-10-1, leads to R²> 0.99 and mean of AARD% of 1.82%, while the SVM model leads to a mean AARD of 3.96 and nearly the same correlations. This demonstrates the high accuracy of the optimal ANN model in predicting the permeate flux values in comparison to the SVM approach in the selected interval of input parameters. The applicability domain of the model was conducted proving that about 95% of the data set was covered. Also, a convivial graphical user interface was designed to facilitate the compute of the permeate flux by exploiting the obtained parameters and without learning about the phenomena. The sensitivity analysis of the best ANN model was done. The obtained results showed that the density has a high positive effect against time with a negative effect on the permute flux, followed by the other inputs with almost the same effect.

AARD : Average Absolute Relative Deviation.

ANN : Artificial Neural Networks.

BBNN : Back-forward Backpropagation Neural Network.

MLR : Multi Linear Regression.

RDM : Rotating Disk Membrane

SVM : Support Vector Machine

TMP : Transmembrane Pressure

WN : Wavelet Network

Nomenclature

A : Effective membrane area (m²)

d_p: Membrane pore size (µm)

J : Permeate ﬂux (Lm⁻² h⁻¹)

k : Velocity factor

L_p: Pure water permeability (Lm⁻² h⁻¹ bar⁻¹)

P_c: Peripheral pressure (bar)

Q : Permeate ﬂow rate (m³ h⁻¹)

R : Coefficient of correlation

R²: Coefficient of determination

T : Filtration time (min)

ρ : Fuid density (g L⁻¹)

µ : Fuid dynamic viscosity (Pa s)

ɷ : Angular velocity (rad s⁻¹)

Ω : Disk rotating velocity (rpm)

Acknowledgements

This work was supported by the Laboratory of Materials and Environment (LME, University of Medea, Algeria).

I. Ethical approval

Ethical approval for this study was not sought as my study does not require it. My study includes information that is freely available in the scientific literature.

II. Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

III. Conflict of interest

The Author declare that there are no conflicts of interest.

IV. Informed Consent

There is no informed consent to disclose or to declare.

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A new approach using artificial neural network and support vector machine models to predict the permeate flux of a rotating disk membrane

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Abstract

Figures

1. Introduction

2. Theoretical Background

3. Dataset Collection

4. Results And Discussion

4.1. Model performances

4.2. Machine learning models for estimating permeate flux

4.2.1. Support vector regression

4.2.2. Artificial neural networks

4.3. Comparison between experimental and ANN modeling of permeate flux

4.4. Comparison between experimental and SVM modeling of permeate flux

4.5. Applicability domain

4.6. Sensitivity analysis

4.7. ANN interface of permeate flux calculation

5. Conclusion

Abbreviations

Declarations

References

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