Duranoğlu Dilek, Sinan Altın Esat, Küçük İlknur
Department of Chemical Engineering, Faculty of Chemical and Metallurgical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34220, Istanbul, Turkiye.
Heliyon. 2024 Feb 3;10(3):e25813. doi: 10.1016/j.heliyon.2024.e25813. eCollection 2024 Feb 15.
Prediction of adsorption via Adaptive Neuro-Fuzzy Inference System (ANFIS) can save the cost and time in practical applications. Chromium (VI) adsorption data obtained at different temperature, activated carbon dosage and pH values were evaluated by using MATLAB ANFIS. In order to achieve prediction of adsorption via ANFIS with acceptable error values, optimum membership function (MF) and optimum number of MF were determined by using Box-Behnken experimental design (BBD) method. In order to determine the optimum number of MF for each input, all combinations given in BBD matrix were examined via ANFIS, then, regression models for each MFs were developed between the root mean square error (RMSE) and MF numbers of each input. The most used five membership functions (triangular, trapezoidal, generalized bell shaped, Gaussian, Gaussian 2) were investigated. According to the analysis of variance (ANOVA), regression models developed for the test data with triangular and trapezoidal membership functions were significant in the 95 % confidence level. Predictions were employed via ANFIS by using optimum MF numbers of each inputs (6, 6, 3 for triangular MF and 8, 8, 2 for trapezoidal MF). Consequently, the best Cr(VI) adsorption percentage prediction (RMSE = 1.9084 and R = 0.992) was obtained by using triangular membership function with optimum MF numbers. Response surface plots, which gives the relationship between MF numbers and RMSE values for triangular MF were also evaluated. In this study, it was demonstrated that MF type and numbers, which are crucial for good prediction via ANFIS grid partition method, can be determined optimally by applying experimental design methodology.
通过自适应神经模糊推理系统（ANFIS）预测吸附可以在实际应用中节省成本和时间。利用MATLAB中的ANFIS对在不同温度、活性炭用量和pH值下获得的铬（VI）吸附数据进行了评估。为了通过ANFIS实现具有可接受误差值的吸附预测，采用Box-Behnken实验设计（BBD）方法确定了最佳隶属函数（MF）和最佳MF数量。为了确定每个输入的最佳MF数量，通过ANFIS检查了BBD矩阵中给出的所有组合，然后，在均方根误差（RMSE）和每个输入的MF数量之间建立了每个MF的回归模型。研究了最常用的五种隶属函数（三角形、梯形、广义钟形、高斯、高斯2）。根据方差分析（ANOVA），为具有三角形和梯形隶属函数的测试数据建立的回归模型在95%置信水平上具有显著性。通过使用每个输入的最佳MF数量（三角形MF为6、6、3，梯形MF为8、8、2），利用ANFIS进行预测。结果，通过使用具有最佳MF数量的三角形隶属函数获得了最佳的Cr（VI）吸附百分比预测（RMSE = 1.9084，R = 0.992）。还评估了给出三角形MF的MF数量与RMSE值之间关系的响应面图。在本研究中，证明了通过应用实验设计方法可以最优地确定对于通过ANFIS网格划分方法进行良好预测至关重要的MF类型和数量。
