Modeling and Evaluation of the Permeate Flux in Forward Osmosis Process with Machine Learning

Abstract

Predicting the permeate flux is critical for evaluating and optimizing the performance of the forward osmosis (FO) process. However, the solution diffusion models have poor applicability in accessing the FO process. Recently, the data-driven eXtreme Gradient Boosting (XGBoost) algorithm has been proven to be effective in processing structure data in engineering problems and has not been utilized to assess the FO process. Herein, a combination of the XGBoost model with a genetic algorithm (GA) was first proposed to predict the permeate flux, highlighting its superiority in the FO process through comparison of the support vector regression (SVR) model, the artificial neural network (ANN), and the multiple linear regression (MLR). Moreover, the performance of these models was optimized by tuning hyperparameters with a genetic algorithm (GA) and compared via Taylor Diagram. Among these machine learning (ML) models, the GA-based XGBoost model is superior to the other three models in terms of mean square error (MSE, 2.7326) and coefficient of determination (R 2, 0.9721) on the test data, and its prediction power was compared to that of the solution diffusion (SD) model in the literature. Finally, further insight into the feature importance that affects the permeate flux in the FO process was examined by utilizing the SHapley Additive exPlanations (SHAP) to estimate the contribution value of various variables. The results demonstrated that the XGBoost model could predict the permeate flux in the FO system with high accuracy and good generalization ability for the given data set and even on the unseen data. Furthermore, the findings of the SHAP method show that the osmotic pressure difference, the osmotic pressure difference of draw solution and FS solution, the crossflow velocity of the feed solution and draw solution, and the water permeability coefficient have a significant impact on water flux.

On the evaluating membrane flux of forward osmosis systems: Data assessment and advanced intelligent modeling

“…The negative sign of FS concentration and the positive value of DS concentration align with this study's trend analysis result. The literature reports that osmotic pressure difference is the most influential factor on membrane flux (Jawad et al, 2021; Kim, Chang, et al, 2022; Shi et al, 2022). This is in line with our results because stating that DS concentration increases and FS concentration decreases is another way of presenting the increase in osmotic pressure difference.…”

Universal Model for Predicting Maximum Spreading of Drop Impact on a Smooth Surface Developed Using Boosting Machine Learning Models

“…CatBoost is trained by minimizing the expected loss function through gradient descent h t = arg nobreak0em.25em⁡ min nobreak0em.25em⁡ double-struckE h ∈ H ( prefix− ∂ L ( y , s ) ∂ s | s = F t − 1 false( x false) − ∑ j = 1 J b j double-struckl { x ∈ R j } ) where L is a smooth loss function, h is a gradient step function selected from H , R j denotes the disjoint regions ns corresponding the leaves of the tree, b j is the predictive value of the region, and double-struckE and double-struckl are the expectation and indicator functions. Further details on these ML methods can be found in previous references. − ,− …”

“…CatBoost is trained by minimizing the expected loss function through gradient descent where L is a smooth loss function, h is a gradient step function selected from H , R j denotes the disjoint regions ns corresponding the leaves of the tree, b j is the predictive value of the region, and and are the expectation and indicator functions. Further details on these ML methods can be found in previous references. − ,− …”

“…Despite numerous attempts, developing a universal model that can predict the maximum spreading of droplets of various liquids impacting on a smooth surface from low to high impact velocity accurately remains challenging due to the different and complex nonlinear characteristics exhibited by drop impact in viscous and capillary regimes. Recently, data-driven machine learning (ML) has been demonstrated to be a powerful technique for investigating fluid mechanics. − ML methods have been successful to predict various fluid phenomena, such as boiling, condensation, and multiphase flow. In recent studies by Yancheshme et al, the random forest method was utilized to predict β max by training their ML model with a database of 198 data points.…”

Data-Driven Optimization of High-Dimensional Variables in Proton Exchange Membrane Water Electrolysis Membrane Electrode Assembly Assisted by Machine Learning

“…Subsequently, we applied the GA to optimize the electrolytic voltage. In contrast to a comprehensive variable optimization, this method uses only 5 key features selected through the SHAP method − as decision variables. It yielded results comparable to those of full-variable optimization while substantially improving time efficiency.…”