Gaussian process regression with levy flight optimization: Advanced AR66 adsorption studies

The coal fly ash (CFA), which is the residue generated by coal-fired power plants, was converted into a valuable zeolite material known as zeolite P (ZNa-P) through thermal and acid pretreatments followed by microwave radiation. Various analytical techniques were utilized to analyze the resulting zeolite, including X-ray diffraction, scanning electron microscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis, BET analysis, and zeta potential measurement. The efficiency of ZNa-P in eliminating anionic dyes from aqueous solutions was exhibited by successfully removing acid red dye 66 (AR66) from a solution composed of water. To optimize the removal process, Central Composite Design (CCD) was applied to investigate the impact of four main parameters: solution pH, initial dye concentration, adsorbent mass, and contact time. The generated CCD database was modeled using Gaussian process regression (GPR) with the Lévy flight distribution (LFD) optimization algorithm. The GPR model was then used to determine optimal conditions for maximum AR66 absorption (3405.3 mg/g), with a pH of 2, initial dye concentration of 1000 mg/L, adsorbent mass of 0.2 g/L, and contact time of 11 minutes. Furthermore, the GPR model exhibited significantly lower error (32.58 mg/g) in predicting the experimental values compared to the CCD model (204.92 mg/g), highlighting the efficiency and superiority of the GPR model in this study.