Linear Nonlinear Regression Analysis Research Articles

Prediction Modeling for the Estimation of Dynamic Elastic Young’s Modulus of Thermally Treated Sedimentary Rocks Using Linear–Nonlinear Regression Analysis, Regularization, and ANFIS

Thermal cracking significantly affects the dynamic and mechanical stability of rock mass. This study first focuses on the evaluation of dynamic-mechanical behavior of thermally deteriorated rocks in terms of their dynamic elastic Young’s modulus (Ed), quality factor (Q-factor), resonance frequency (Fr), unconfined compressive strength (UCS) and tensile strength (BTS). Secondly, it focuses on the comparison of the performance of different statistical data modeling techniques. The overall reduction in the values of Ed, Q-factor, Fr, UCS, and BTS for all thermally treated rock samples was recorded as 23–49%, 6–28%, 7–21%, 10–38%, and 14–56%, respectively. The previous studies do not show any significant correlation between the strength parameters of thermally deteriorated rocks. In this study, a total of 7 predictive models were developed to estimate Ed for thermally deteriorated rocks using linear-nonlinear regression analysis, regularization, and adaptive-neuro fuzzy inference system (ANFIS). Results of hypothesis testing showed that the linear-nonlinear regression equations were statistically significant. Similarly, outcomes of neuro-fuzzy logic analysis, based on the degree of thermal cracking of rocks satisfied the statistical significance of the ANFIS model. Among all prediction models, the ANFIS model has the lowest value of root mean square error (RMSE) and the highest value of the Nash–Sutcliffe coefficient (E). Based on the results of model quality indices, these statistical modeling techniques are arranged in the following order; ANFIS > Nonlinear Regression > Regularization > Linear Regression. The outcomes of this study can provide references to solve complex problems in geostatistics.

Stochastic modeling approaches based on neural network and linear–nonlinear regression techniques for the determination of single droplet collection efficiency of countercurrent spray towers

This paper presents a new mathematical model and a two-layer neural network approach to predict the single droplet collection efficiency (SDCE), hd, of countercurrent spray towers. SDCE values were calculated using MATLAB \ algorithm for 205 different artificial scenarios given in a large range of operating conditions. Theoretical results were com- pared with outputs obtained from a two-layer neural network and DataFit \ scientific software. The predic- ted model developed from linear-nonlinear regression analysis and network outputs agreed with the theoret- ical data, and all predictions proved to be satisfactory with a correlation coefficient of about 0.921 and 0.99, respectively. By using the proposed model, iterations between Reynolds number (Re), drag coefficient (CD) and terminal velocity values (vT) were neglected for a large range of operating conditions. SDCE values were also obtained speedily and practically for five main operating inputs used in the model.