A combination of computational fluid dynamics (CFD) and adaptive neuro-fuzzy system (ANFIS) for prediction of the bubble column hydrodynamics

Applications of ANFIS-Type Methods in Simulation of Systems in Marine Environments

ANFIS-type algorithms have been used in various modeling and simulation problems. With the help of algorithms with more accuracy and adaptability, it is possible to obtain better real-life emulating models. A critical environmental problem is the discharge of saline industrial effluents in the form of buoyant jets into water bodies. Given the potentially harmful effects of the discharge effluents from desalination plants on the marine environment and the coastal ecosystem, minimizing such an effect is crucial. Hence, it is important to design the outfall system properly to reduce these impacts. To the best of the authors’ knowledge, a study that formulates the effluent discharge to find an optimum numerical model under the conditions considered here using AI methods has not been completed before. In this study, submerged discharges, specifically, negatively buoyant jets are modeled. The objective of this study is to compare various artificial intelligence algorithms along with multivariate regression models to find the best fit model emulating effluent discharge and determine the model with less computational time. This is achieved by training and testing the Adaptive Neuro-Fuzzy Inference System (ANFIS), ANFIS-Genetic Algorithm (GA), ANFIS-Particle Swarm Optimization (PSO) and ANFIS-Firefly Algorithm (FFA) models with input parameters, which are obtained by using the realizable k-ε turbulence model, and simulated parameters, which are obtained after modeling the turbulent jet using the OpenFOAM simulation platform. A comparison of the realizable k-ε turbulence model outputs and AI algorithms’ outputs is conducted in this study. Statistical parameters such as least error, coefficient of determination (R2), Mean Absolute Error (MAE), and Average Absolute Deviation (AED) are measured to evaluate the performance of the models. In this work, it is found that ANFIS-PSO performs better compared to the other four models and the multivariate regression model. It is shown that this model provides better R2, MAE, and AED, however, the non-hybrid ANFIS model provides reasonably acceptable results with lower computational costs. The results of the study demonstrate an error of 6.908% as the best-case scenario in the AI models.

Numerical investigation of nanofluid flow using CFD and fuzzy-based particle swarm optimization

This paper is focused on the application and performance of artificial intelligence in the numerical modeling of nanofluid flows. Suspension of metallic nanoparticles in the fluids has shown potential in heat transfer enhancement of the based fluids. There are many numerical studies for the investigation of thermal and hydrodynamic characteristics of nanofluids. However, the optimization of the computational fluid dynamics (CFD) modeling by an artificial intelligence (AI) algorithm is not considered in any study. The CFD is a powerful technique from an accuracy point of view. However, it could be time and cost-consuming, especially in large-scale and complicated problems. It is expected that the machine learning technique of the AI algorithms could improve such CFD drawbacks by patterning the CFD data. Once the AI finds the CFD pattern intelligently, there is no need for CFD calculations. The particle swarm optimization-based fuzzy inference system (PSOFIS) is considered in this study to predict the velocity profile of Al₂O₃/water turbulent flow in a heated pipe. One of the challenging problems in CFD modeling is the lost data for a specific boundary condition. For example, the CFD data are available for wall heat fluxes of 75, 85, 105, and 125 w/m², but there is no data for the wall heat flux of 95 w/m². So, the PSOFIS learns the available CFD data, and it predicts the velocity profile for where the data is not available (i.e., wall heat flux of 95 w/m²). The intelligence of PSOFIS is checked by the coefficient of determination (R² pattern) for different values of accept ratio (AR) and inertia weight damping ratio (IWDR). The best intelligence is obtained for the AR and IWDR of 0.7 and 0.99, respectively. At this condition, the velocity profile predicted by both CFD and PSOFIS is compatible. As the performance of the PSOFIS, for learning time of 268 s, the prediction of the CFD data lost was negligible (~ 1 s). In contrast, the CFD calculation takes around 600 s for each simulation.

Bubble Column CFD Model with Effects of Forced Oscillations on Bubble Dynamics

Bubble size distribution has a significant effect on gas holdup, residence time distribution, and mass transfer in bubble column reactors (BCRs). The occurrence of small gas bubbles has potential advantages such as a limited residence time distribution and perfect gas‐liquid phase contact. Gas‐liquid mass transfer in bubble columns can be significantly enhanced by subjecting the liquid phase to low‐frequency vibrations. However, the effect of vibration frequency on bubble formation and hydrodynamic characteristics in BCRs is still not well understood. Herein, a 3D numerical model of a BCR was developed to study the effect of vibration frequency on bubble dynamics under different operating conditions. The Sauter mean bubble diameter was found to be approximately inversely proportional to the vibration frequency.

Prediction of gas velocity in two-phase flow using developed fuzzy logic system with differential evolution algorithm

In this investigation, differential evolution (DE) algorithm with the fuzzy inference system (FIS) are combined and the DE algorithm is employed in FIS training process. Considered data in this study were extracted from simulation of a 2D two-phase reactor in which gas was sparged from bottom of reactor, and the injected gas velocities were between 0.05 to 0.11 m/s. After doing a couple of training by making some changes in DE parameters and FIS parameters, the greatest percentage of FIS capacity was achieved. By applying the optimized model, the gas phase velocity in x direction inside the reactor was predicted when the injected gas velocity was 0.08 m/s.

Influence of machine learning membership functions and degree of membership function on each input parameter for simulation of reactors

To understand impact of input and output parameters during optimization and degree of complexity, in the current study we numerically designed a bubble column reactor with a single sparger in the middle of the reactor. After that, some input and output parameters were selected in the post-processing of the numerical method, and then the machine learning observation started to investigate the level of complexity and impact of each input on output parameters. The adaptive neuro-fuzzy inference system (ANFIS) method was exploited as a machine learning approach to analyze the gas-liquid flow in the reactor. The ANFIS method was used as a machine learning approach to simulate the flow of a 3D (three-dimensional) bubble column reactor. This model was also used to analyze the influence of input and output parameters together. More specifically, by analyzing the degree of membership functions as a function of each input, the level of complexity of gas fraction was investigated as a function of computing nodes (X, Y, and Z directions). The results showed that a higher number of membership functions results in a better understanding of the process and higher model accuracy and prediction capability. X and Y computing nodes have a similar impact on the gas fraction, while Z computing points (height of reactor) have a uniform distribution of membership function across the column. Four membership functions (MFs) in each input parameter are insufficient to predict the gas fraction in the 3D bubble column reactor. However, by adding two membership functions, all features of gas fraction in the 3D reactor can be captured by the machine learning algorithm. Indeed, the degree of MFs was considered as a function of each input parameter and the effective parameter was found based on the impact of MFs on the output.

Investigation on performance of particle swarm optimization (PSO) algorithm based fuzzy inference system (PSOFIS) in a combination of CFD modeling for prediction of fluid flow

Herein, a reactor of bubble column type with non-equilibrium thermal condition between air and water is mechanistically modeled and simulated by the CFD technique. Moreover, the combination of the adaptive network (AN) trainer with the fuzzy inference system (FIS) as the artificial intelligence method calling ANFIS has already shown potential in the optimization of CFD approach. Although the artificial intelligence method of particle swarm optimization (PSO) algorithm based fuzzy inference system (PSOFIS) has a good background for optimizing the other fields of research, there are not any investigations on the cooperation of this method with the CFD. The PSOFIS can reduce all the difficulties and simplify the investigation by elimination of the additional CFD simulations. In fact, after achieving the best intelligence, all the predictions can be done by the PSOFIS instead of the massive computational efforts needed for CFD modeling. The first aim of this study is to develop the PSOFIS for use in the CFD approach application. The second one is to make a comparison between the PSOFIS and ANFIS for the accurate prediction of the CFD results. In the present study, the CFD data are learned by the PSOFIS for prediction of the water velocity inside the bubble column. The values of input numbers, swarm sizes, and inertia weights are investigated for the best intelligence. Once the best intelligence is achieved, there is no need to mesh refinement in the CFD domain. The mesh density can be increased, and the newer predictions can be done in an easier way by the PSOFIS with much less computational efforts. For a strong verification, the results of the PSOFIS in the prediction of the liquid velocity are compared with those of the ANFIS. It was shown that for the same fuzzy set parameters, the PSOFIS predictions are closer to the CFD in comparison with the ANFIS. The regression number (R) of the PSOFIS (0.98) was a little more than that of the ANFIS (0.97). The PSOFIS showed a powerful potential in mesh density increment from 9477 to 774,468 and accurate predictions for the new nodes independent of the CFD modeling.

Thermal prediction of turbulent forced convection of nanofluid using computational fluid dynamics coupled genetic algorithm with fuzzy interface system

Computational fluid dynamics (CFD) simulating is a useful methodology for reduction of experiments and their associated costs. Although the CFD could predict all hydro-thermal parameters of fluid flows, the connections between such parameters with each other are impossible using this approach. Machine learning by the artificial intelligence (AI) algorithm has already shown the ability to intelligently record engineering data. However, there are no studies available to deeply investigate the implicit connections between the variables resulted from the CFD. The present investigation tries to conduct cooperation between the mechanistic CFD and the artificial algorithm. The genetic algorithm is combined with the fuzzy interface system (GAFIS). Turbulent forced convection of Al₂O₃/water nanofluid in a heated tube is simulated for inlet temperatures (i.e., 305, 310, 315, and 320 K). GAFIS learns nodes coordinates of the fluid, the inlet temperatures, and turbulent kinetic energy (TKE) as inputs. The fluid temperature is learned as output. The number of inputs, population size, and the component are checked for the best intelligence. Finally, at the best intelligence, a formula is developed to make a relationship between the output (i.e. nanofluid temperatures) and inputs (the coordinates of the nodes of the nanofluid, inlet temperature, and TKE). The results revealed that the GAFIS intelligence reaches the highest level when the input number, the population size, and the exponent are 5, 30, and 3, respectively. Adding the turbulent kinetic energy as the fifth input, the regression value increases from 0.95 to 0.98. This means that by considering the turbulent kinetic energy the GAFIS reaches a higher level of intelligence by distinguishing the more difference between the learned data. The CFD and GAFIS predicted the same values of the nanofluid temperature.

Performance and application analysis of ANFIS artificial intelligence for pressure prediction of nanofluid convective flow in a heated pipe

Heat transfer augmentation of the nanofluids is still an attractive concept for researchers due to rising demands for designing efficient heat transfer fluids. However, the pressure loss arisen from the suspension of nanoparticles in liquid is known as a drawback for developing such novel fluids. Therefore, prediction of the nanofluid pressure, especially in internal flows, has been focused on studies. Computational fluid dynamics (CFD) is a commonly used approach for such a prediction of fluid flow. The CFD tools are perfect and precise in prediction of the fluid flow parameters. But they might be time-consuming and expensive, especially for complex models such as 3-dimension modeling and turbulent flow. In addition, the CFD could just predict the pressure, and it is disabled for finding the relationship of such variables. This study is intended to show the performance of the artificial intelligence (AI) algorithm as an auxiliary method for cooperation with the CFD. The turbulent flow of Cu/water nanofluid warming up in a pipe is considered as a sample of a physical phenomenon. The AI algorithm learns the CFD results. Then, the relation between the CFD results is discovered by the AI algorithm. For this purpose, the adaptive network-based fuzzy inference system (ANFIS) is adopted as AI tool. The intelligence condition of the ANFIS is checked by benchmarking the CFD results. The paper outcomes indicated that the ANFIS intelligence is met by employing gauss2mf in the model as the membership function and x, y, and z coordinates, the nanoparticle volume fraction, and the temperature as the inputs. The pressure predicted by the ANFIS at this condition is the same as that predicted by the CFD. The artificial intelligence of ANFIS could find the relation of the nanofluid pressure to the nanoparticle fraction and the temperature. The CFD simulation took much more time (90-110 min) than the total time of the learning and the prediction of the ANFIS (369 s). The CFD modeling was done on a workstation computer, while the ANFIS method was run on a normal desktop.

Velocity prediction of nanofluid in a heated porous pipe: DEFIS learning of CFD results

Utilizing artificial intelligence algorithm of adaptive network-based fuzzy inference system (ANFIS) in combination with the computational lfuid dynamics (CFD) has recently revealed great potential as an auxiliary method for simulating challenging fluid mechnics problems. This research area is at the beginning, and needs sophisticated algorithms to be developed. No studies are available to consider the efficiency of the other trainers like differential evolution (DE) integrating with the FIS for capturing the pattern of the simulation results generated by CFD technique. Besides, the adjustment of the tuning parameters of the artificial intelligence (AI) algorithm for finding the highest level of intelligence is unavailable. The performance of AI algorithms in the meshing process has not been considered yet. Therfore, herein the Al₂O₃/water nanofluid flow in a porous pipe is simulated by a sophisticated hybrid approach combining mechnsitic model (CFD) and AI. The finite volume method (FVM) is employed as the CFD approach. Also, the differential evolution-based fuzzy inference system (DEFIS) is used for learning the CFD results. The DEFIS learns the nanofluid velocity in the y-direction, as output, and the nodes coordinates (i.e., x, y, and z), as inputs. The intelligence of the DEFIS is assessed by adjusting the methd's variables including input number, population number, and crossover. It was found that the DEFIS intelligence is related to the input number of 3, the crossover of 0.8, and the population number of 120. In addition, the nodes increment from 4833 to 774,468 was done by the DEFIS. The DEFIS predicted the velocity for the new dense mesh without using the CFD data. Finally, all CFD results were covered with the new predictions of the DEFIS.

Pressure and temperature predictions of Al2O3/water nanofluid flow in a porous pipe for different nanoparticles volume fractions: combination of CFD and ACOFIS

Artificial intelligence (AI) techniques have illustrated significant roles in finding general patterns of CFD (Computational fluid dynamics) results. This study is conducted to develop combination of the ant colony optimization (ACO) algorithm with the fuzzy inference system (ACOFIS) for learning the CFD results of a physical case study. This binary join of the ACOFIS and CFD was used for pressure and temperature predictions of Al₂O₃/water nanofluid flow in a heated porous pipe. The intelligence of ACOFIS is investigated for different input numbers and pheromone effects, as the ant colony tuning parameter. The results showed that the intelligence of the ACOFIS could be found for three inputs (x and y nodes coordinates and nanoparticles fraction) and the pheromone effect of 0.1. At the system intelligence, the ACOFIS could predict the pressure and temperature of the nanofluid on any values of the nanoparticles fraction between 0.5 and 2%. Comparing the ANFIS and the ACOFIS, it was shown that both methods could reach the same accuracy in predictions of the nanofluid pressure and temperature. The root mean square error (RMSE) of the ACOFIS (~ 1.3) was a little more than that of the ANFIS (~ 0.03), while the total process time of the ANFIS (~ 213 s) was a bit more than that of the ACOFIS (~ 198 s). The AI algorithms process time (less than 4 min) shows their ability in the reduction of CFD modeling calculations and expenses.

Liquid temperature prediction in bubbly flow using ant colony optimization algorithm in the fuzzy inference system as a trainer

In the current research paper a novel hybrid model combining first-principle and artificial intelligence (AI) was developed for simulation of a chemical reactor. We study a 2-dimensional reactor with heating sources inside it by using computational fluid dynamics (CFD). The type of considered reactor is bubble column reactor (BCR) in which a two-phase system is created. Results from CFD were analyzed in two different stages. The first stage, which is the learning stage, takes advantage of the swarm intelligence of the ant colony. The second stage results from the first stage, and in this stage, the predictions are according to the previous stage. This stage is related to the fuzzy logic system, and the ant colony optimization learning framework is build-up this part of the model. Ants movements or swarm intelligence of ants lead to the optimization of physical, chemical, or any kind of processes in nature. From point to point optimization, we can access a kind of group optimization, meaning that a group of data is studied and optimized. In the current study, the swarm intelligence of ants was used to learn the data from CFD in different parts of the BCR. The learning was also used to map the input and output data and find out the complex connection between the parameters. The results from mapping the input and output data show the full learning framework. By using the AI framework, the learning process was transferred into the fuzzy logic process through membership function specifications; therefore, the fuzzy logic system could predict a group of data. The results from the swarm intelligence of ants and fuzzy logic suitably adapt to CFD results. Also, the ant colony optimization fuzzy inference system (ACOFIS) model is employed to predict the temperature distribution in the reactor based on the CFD results. The results indicated that instead of solving Navier–Stokes equations and complex solving procedures, the swarm intelligence could be used to predict a process. For better comparisons and assessment of the ACOFIS model, this model is compared with the genetic algorithm fuzzy inference system (GAFIS) and Particle swarm optimization fuzzy inference system (PSOFIS) method with regards to model accuracy, pattern recognition, and prediction capability. All models are at a similar level of accuracy and prediction ability, and the prediction time for all models is less than one second. The results show that the model’s accuracy with low computational learning time can be achieved with the high number of CIR (0.5) when the number of inputs ≥ 4. However, this finding is vice versa, when the number of inputs < 4. In this case, the CIR number should be 0.2 to achieve the best accuracy of the model. This finding could also highlight the importance of sensitivity analysis of tuning parameters to achieve an accurate model with a cost-effective computational run.

Multidimensional machine learning algorithms to learn liquid velocity inside a cylindrical bubble column reactor

For understanding the complex behavior of fluids in a multiphase chemical bubble column reactor, a combination of the computational fluid dynamic (CFD) method and the adaptive network-based fuzzy inference system (ANFIS) method is used to predict bubble flow inside a reactor based on the function of column height. In this study, the Euler–Euler model is employed as a CFD method. In the Eulerian method, continuity and momentum governing equations are mathematically computed for each phase, while the equations are connected together by source terms. After calculating the flow pattern and turbulence flow in the reactor, all data sets are used to prepare a fully artificial method for further prediction. This algorithm contains different learning dimensions such as learning in different directions of reactor or large amount of input parameters and data set representing “big data”. The ANFIS method was evaluated in three steps by using one, two, and three inputs in each one to predict the liquid velocity in the x-direction (Ux). The x, y, and z coordinates of the location of the node of the liquid were considered as the inputs. Different percentages of data and various iterations and membership functions were used for training in the ANFIS method. The ANFIS method showed the best prediction using three inputs. This combination also shows the ability of computer science and computational methods in learning physical and chemical phenomena.

Computational Modeling of Transport in Porous Media Using an Adaptive Network-Based Fuzzy Inference System

This investigation is conducted to study the integration of the artificial intelligence (AI) method with computational fluid dynamics (CFD). The case study is hydrodynamic and heat-transfer analyses of water flow in a metal foam tube under a constant wall heat flux (i.e., 55 kW/m²). The adaptive network-based fuzzy inference system (ANFIS) is an AI method. A 3D CFD model is established in ANSYS-FLUENT software. The velocity of the fluid in the x-direction (Ux) is considered as an output of the ANFIS. The x, y, and z coordinates of the node's location are added to the ANFIS step-by-step to achieve the best intelligence. The number and type of membership functions (MFs) are changed in each step. The training process is done by the CFD results on the tube cross-sections at different lengths (i.e., z = 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 0.8, and 0.9), while all data (including z = 0.5) are selected for the testing process. The results showed that the ANFIS reaches the best intelligence with all three inputs, five MFs, and "gbellmf"-type MF. At this condition, the regression number is close to 1.

Simulation of liquid flow with a combination artificial intelligence flow field and Adams-Bashforth method

Direct numerical simulation (DNS) of particle hydrodynamics in the multiphase industrial process enables us to fully learn the process and optimize it on the industrial scale. However, using high-resolution computational calculations for particle movement and the interaction between the solid phase and other phases in fine timestep is limited to excellent computational resources. Solving the Eulerian flow field as a source of solid particle movement can be very time-consuming. However, by the revolution of the fast and accurate learning process, the Eulerian domain can be computed by smart modeling in a very short computational time. In this work, using the machine learning method, the flow field in the square shape cavity is trained, and then the Eulerian framework is replaced with a machine learning method to generate the artificial intelligence (AI) flow field. Then the Lagrangian framework is coupled with this AI flow field, and we simulate particle motion through the fully AI framework. The Adams–Bashforth finite element method is used as a conventional CFD method (Eulerian framework) to simulate the flow field in the cavity. After simulating fluid flow, the ANFIS method is used as an AI model to train the Eulerian data-set and represents AI fluid flow (framework). The Lagrangian framework is coupled with the AI method, and the particle freely migrates through this artificial framework. The results reveal that there is a great agreement between Euler-Lagrangian and AI- Lagrangian in the cavity. We also found that there is an excellent agreement between AI overview with the Adams–Bashforth approach, and the new combination of machine learning and CFD method can accelerate the calculation of the flow field in the square-shaped cavity. AI model can mimic the vortex structure in the cavity, where there is a zero-velocity structure in the center of the domain and maximum velocity near the moving walls.

Pattern recognition of the fluid flow in a 3D domain by combination of Lattice Boltzmann and ANFIS methods

Many numerical methods have been used to simulate the fluid flow pattern in different industrial devices. However, they are limited with modeling of complex geometries, numerical stability and expensive computational time for computing, and large hard drive. The evolution of artificial intelligence (AI) methods in learning large datasets with massive inputs and outputs of CFD results enables us to present completely artificial CFD results without existing numerical method problems. As AI methods can not feel barriers in numerical methods, they can be used as an assistance tool beside numerical methods to predict the process in complex geometries and unstable numerical regions within the short computational time. In this study, we use an adaptive neuro-fuzzy inference system (ANFIS) in the prediction of fluid flow pattern recognition in the 3D cavity. This prediction overview can reduce the computational time for visualization of fluid in the 3D domain. The method of ANFIS is used to predict the flow in the cavity and illustrates some artificial cavities for a different time. This method is also compared with the genetic algorithm fuzzy inference system (GAFIS) method for the assessment of numerical accuracy and prediction capability. The result shows that the ANFIS method is very successful in the estimation of flow compared with the GAFIS method. However, the GAFIS can provide faster training and prediction platform compared with the ANFIS method.

Prediction of Nanofluid Characteristics and Flow Pattern on Artificial Differential Evolution Learning Nodes and Fuzzy Framework

A combination of a fuzzy inference system (FIS) and a differential evolution (DE) algorithm, known as the differential evolution-based fuzzy inference system (DEFIS), is developed for the prediction of natural heat transfer in Cu-water nanofluid within a cavity. In the development of the hybrid model, the DE algorithm is used for the training process of FIS. For this purpose, first, the case study is simulated using the computational fluid dynamic (CFD) method. The CFD outputs, including velocity in the y-direction, the temperature of the nanofluid, and the nanoparticle content (Ø), are employed for the learning process of the DEFIS model. By choosing the optimum number of inputs and the number of population, the underlying DEFIS variable parameters are studied. After reaching the high value of DEFIS intelligence, in the learning step, a variety of Ø values (e.g., 0.5, 1, and 2) are reviewed. For the full intelligence of DEFIS, the velocity of the nanofluid is predicted in further nodes of the cavity domain. Finally, the velocity of the nanofluid is predicted by using the data at Ø = 0.15, which are absent in the DEFIS process.

Bubbly flow prediction with randomized neural cells artificial learning and fuzzy systems based on k-ε turbulence and Eulerian model data set

Computing gas and liquid interactions based on interfacial force models require a proper turbulence model that accurately resolve the turbulent scales such as turbulence kinetic energy and turbulence dissipation rate with cheap computational resources. The k − ε turbulence model can be a good turbulence predictive tool to simulate velocity components in different phases and approximately picture the turbulence eddy structure. However, even this average turbulence method can be expensive for very large domains of calculation, particularly when the number of phases and spices increases in the multi-size structure Eulerian approach. In this study, with the ability of artificial learning, we accelerate the simulation of gas and liquid interaction in the bubble column reactor. The artificial learning method is based on adaptive neuro-fuzzy inference system (ANFIS) method, which is a combination of neural cells and fuzzy structure for making decision or prediction. The learning method is specifically used in a cartesian coordinate such as Eulerian approach, while for the prediction process, the polar coordinate is applied on a fully meshless domain of calculations. During learning process all information at computing nodes is randomly chosen to remove natural pattern learning behavior of neural network cells. In addition, different \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}r and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}θ are used to test the ability of the learning stage during prediction. The results indicate that there is great agreement between ANFIS and turbulence modeling of bubbly flow within the Eulerian framework. ANFIS method shows that neural cells can grow in the domain to provide high-resolution results and they are not limited to the movement or deformation of source points such as Eulerian method. In addition, this study shows that mapping between two different geometrical structures is possible with the ANFIS method due to the meshless behavior of this algorithm. The meshless behavior causes the stability of the machine learning method, which is independent of CFD boundary conditions.

Changes in the Number of Membership Functions for Predicting the Gas Volume Fraction in Two-Phase Flow Using Grid Partition Clustering of the ANFIS Method

A 2D-bubble column reactor (BCR) including gas and liquid phases is simulated, and fluid characteristics such as gas-phase volume fraction and gas-phase turbulence are extracted from the CFD simulations. A type of heuristic algorithm called adaptive network-based fuzzy inference system (ANFIS) is applied here to simulate the gas-phase volume fraction in a physical system. Indeed, the x direction, the y direction, and gas-phase turbulence are considered as the ANFIS inputs. Changes in the number of inputs as well as membership functions are evaluated and studied to obtain a high level of ANFIS intelligence. By implementing the highest ANFIS intelligence, a surface is predicted, which suggests that the gas-phase volume fraction is based on x and y directions. It provides capability to achieve the amount of gas-phase volume fraction in different points of a 2D-BCR.

Prediction of Nanofluid Temperature Inside the Cavity by Integration of Grid Partition Clustering Categorization of a Learning Structure with the Fuzzy System

In this study, a quadratic cavity is simulated using computational fluid dynamics (CFD). The simulated cavity includes nanofluids containing copper (Cu) nanoparticles. The L-shaped thermal element exists in this cavity to produce heat distribution along with the domain. Results such as fluid velocity distribution in two dimensions and the fluid temperature field were generated as CFD simulation results. These outputs were evaluated using an adaptive neuro-fuzzy inference system (ANFIS) for learning and then the prediction process. In the training process related to the ANFIS method, x coordinates, y coordinates, and fluid temperature are three inputs, and the fluid velocity in line with Y is the output. During the learning process, the data have been classified using a clustering method called grid clustering. In line with the attempt to rise ANFIS intelligence, the alterations in the number of input parameters and of membership structure have been analyzed. After reaching the highest level of intelligence, the fluid velocity nodes were predicted to be in line with y, especially cavity nodes, which were absent in CFD simulations. The simulation findings indicated that there is a good agreement between CFD and clustering approach, while the total simulation time for learning and prediction is shorter than the time needed for calculation using the CFD method.

Robust Prediction of Filtrate Flux for Separation of Catalyst Particles from Wax Effluent of Fischer-Tropsch Bubble Column Reactor via Regularization Network

The effectiveness of an internal filtration system intended for separation of wax-catalyst from Fischer–Tropsch synthesis products is investigated in the present study. The generalization performances of in-house Regularization Network (RN) equipped with efficient training algorithm is recruited for prediction of filtrate flux. The network was trained by resorting several sets of experimental data obtained from a specific system of air/paraffin liquid phase/alumina oxide particle conducted in a slurry bubble column reactor. The RN is employed to explore the relationship between the slurry phase temperature (10–60 °C), pressure difference (0.3, 0.6 and 0.9 bar) and time (0–120 min) on the rate of outcome filtrate from various size of filter element (4, 8 and 12 microns). The superior recall and validation performances with different exemplars data points show that the optimally trained RN which has solid roots in multivariate regularization theory, is a reliable tool for prediction of filtrate flux. Faithful generalization performance of RN revels that around 66 % reduction in filtrate flux is observed by decreasing temperature from 60 {}_{}^ \circ C to10 {}_{}^ \circ C for filter pore size of 4 microns. Decreasing of slurry viscosity is the main reason of such behavior. Increasing pressure driving force has a significant effect on elevating filtrate flux. Due to cake formation, filtrate flux is decreased from 2 to 1.4 (ml/min.cm2) at constant temperature of 60 {}_{}^ \circ C for filter pore size of 8 microns. Furthermore, the backwashing process is more effective for smaller pore size filter and temperature variation does not have any considerable effect on filter recovery.

Performance Comparison of ANFIS Models by Input Space Partitioning Methods

In this paper, we compare the predictive performance of the adaptive neuro-fuzzy inference system (ANFIS) models according to the input space segmentation method. The ANFIS model can be divided into four types according to the method of dividing the input space. In general, the ANFIS1 model using grid partitioning method, ANFIS2 model using subtractive clustering (SC) method, and the ANFIS3 model using fuzzy C-means (FCM) clustering method exist. In this paper, we propose the ANFIS4 model using a context-based fuzzy C-means (CFCM) clustering method. Context-based fuzzy C-means clustering is a clustering method that considers the characteristics of the output space as well as the input space. Here, the symmetric Gaussian membership functions are obtained by the clusters produced from each context in the design of the ANFIS4. In order to evaluate the performance of the ANFIS models according to the input space segmentation method, a prediction experiment was conducted using the combined cycle power plant (CCPP) data and the auto-MPG (miles per gallon) data. As a result of the prediction experiment, we confirmed that the ANFIS4 model using the proposed input space segmentation method shows better prediction performance than the ANFIS model (ANFIS1, ANFIS2, ANFIS3) using the existing input space segmentation method.

Artificial Neural Network and Adaptive Neuro-Fuzzy Interface System Modeling of Supercritical CO2 Extraction of Glycyrrhizic Acid from Glycyrrhiza glabra L

In this study, the extraction of Glycyrrhizic acid (GA) from Glycyrrhiza glabra (licorice) root was investigated by Soxhlet extraction and modified supercritical CO2 with water as co-solvents and 30 min of static extraction time. The high performance liquid chromatography (HPLC) was used to identify and quantitatively determine the amount of extracted GA recovery of supercritical CO2 extraction of GA. The extraction recovery was modeled by adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN). Different ANFIS networks (by changing the type of membership functions) were compared with evaluation of networks accuracy in GA recovery prediction and subsequently the suitable network was determined. A three-layer artificial neural network was also developed for modeling of GA extraction from licorice plant root. In this regard, different networks (by changing the number of neurons in the hidden layer and algorithm of network training) were compared with evaluation of networks accuracy in extraction recovery prediction. One-step secant back propagation algorithm with six neurons in hidden layer was found to be the most suitable network and the coefficient of determination (R2) was 98.5 %. Gaussian combination membership function (gauss2mf) using 2 membership function to each input was obtained to be optimum ANFIS architecture with mean square error (MSE) of 0.05,0.17 and 0.07 for training, testing and checking data, respectively.