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Hybrid Convolutional Neural Network and Whale Optimization Algorithm for Prediction of Permeate Flux in Nanofiltration Membranes.

Lima Hongou
Volume 5

Abstract

Nanofiltration (NF) membranes have become an important separation technology for water treatment, desalination pretreatment, wastewater reuse, hardness removal, organic micropollutant rejection, and selective ion separation. Permeate flux is one of the most critical performance indicators in nanofiltration systems because it directly reflects membrane productivity, hydraulic efficiency, fouling progression, and overall process stability. However, accurate prediction of permeate flux remains challenging due to the complex nonlinear interactions among operating pressure, feed concentration, temperature, pH, cross-flow velocity, membrane properties, solute characteristics, concentration polarization, scaling tendency, and fouling behavior. Conventional empirical models and manually tuned machine learning approaches often have limited ability to generalize across varying feedwater compositions and dynamic operating conditions. To address these limitations, this paper proposes a hybrid Convolutional Neural Network and Whale Optimization Algorithm framework for accurate prediction of permeate flux in nanofiltration membranes.

The proposed framework integrates the automatic feature extraction capability of Convolutional Neural Networks (CNNs) with the global optimization strength of the Whale Optimization Algorithm (WOA). The CNN model is designed to learn hidden patterns from structured membrane process data, including transmembrane pressure, feed flow rate, permeate flow rate, feed temperature, feed conductivity, total dissolved solids, solute concentration, membrane pore size, molecular weight cut-off, recovery ratio, pH, turbidity, and historical flux measurements. Input variables are transformed into one-dimensional or two-dimensional feature representations to allow convolutional filters to capture local relationships among operating parameters and temporal flux variations. The WOA component is employed to optimize critical CNN hyperparameters, including learning rate, number of convolutional filters, kernel size, number of dense neurons, dropout rate, batch size, optimizer configuration, and regularization coefficients. By reducing dependence on manual tuning, the WOA-enhanced CNN improves convergence efficiency, prediction accuracy, and robustness under diverse operating conditions.

A comprehensive preprocessing pipeline is applied to experimental and operational NF datasets, including missing value imputation, outlier removal, noise filtering, normalization, feature scaling, correlation analysis, and construction of lagged process variables. To improve model generalization, the framework considers variations in membrane material, feedwater quality, ion composition, organic matter concentration, pressure range, and fouling stage. The proposed model can be evaluated using laboratory-scale nanofiltration experiments, pilot plant monitoring data, or full-scale membrane process records. Performance is assessed using regression metrics such as Mean Absolute Error, Root Mean Square Error, Mean Absolute Percentage Error, normalized RMSE, coefficient of determination, and computational training time. Comparative analysis is conducted against empirical flux models, support vector regression, random forest, XGBoost, multilayer perceptron, standalone CNN, standalone WOA-optimized neural networks, and conventional artificial neural network baselines.

Experimental evaluation is expected to demonstrate that the proposed CNN-WOA model achieves superior permeate flux prediction performance by effectively capturing nonlinear relationships between membrane operating conditions and productivity. The optimized CNN architecture is anticipated to provide lower prediction error, faster convergence, and improved stability compared with manually configured deep learning models. In addition, sensitivity analysis and explainability techniques such as SHAP, permutation feature importance, and response surface visualization are incorporated to identify the most influential factors affecting permeate flux, including transmembrane pressure, feed temperature, solute concentration, cross-flow velocity, recovery ratio, and fouling-related indicators. These insights can help membrane operators understand process behavior and support evidence-based operational adjustment.

The proposed hybrid CNN-WOA framework provides a scalable, accurate, and computationally efficient solution for permeate flux prediction in nanofiltration membrane systems. By combining deep learning-based pattern recognition with metaheuristic optimization, the model can support real-time process monitoring, fouling-aware operation, energy-efficient control, and predictive maintenance. Its integration into smart membrane management platforms can improve water treatment efficiency, reduce operational uncertainty, optimize cleaning schedules, and enhance the long-term reliability of nanofiltration systems.

 

Keywords

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