Towards enhanced surface roughness modeling in machining: an analysis of data transformation techniques

Abstract

Data transformation methods are utilized to convert datasets into non-integer formats, potentially altering their distribution patterns. This implies that the variance and standard deviation of the dataset may be altered after the dataset undergoes data transformation operations. Improving model accuracy is a primary application of these methods. This study compares the efficacy of three data transformation techniques: square root transformation, logarithmic transformation, and inverse transformation. The comparison is conducted within the context of developing a surface roughness model for a turning process. Eighteen experiments are performed using the Box-Behnken method, with surface roughness chosen as the response variable. The surface roughness dataset undergoes transformation using the mentioned methods. Four surface roughness regression models are then built: one without transformation, one with square root transformation, one with logarithmic transformation, and one with inverse transformation. Evaluation metrics include coefficient of determination (R-Sq), adjusted coefficient of determination (R-Sq(adj)), Mean Absolute Error (%MAE), and Mean Squared Error (%MSE). Results indicate logarithmic transformation as the most effective, followed by square root transformation, in enhancing model accuracy. The surface roughness model utilizing data transformation exhibits high R-Sq and R-Sq(adj) values, at 0.8792 and 0.7434 respectively. On the other hand, this model has %MAE and %MSE values of only 10.33 and 2.05 respectively. Conversely, inverse transformation exhibits the least effectiveness among the three methods

Optimal Surface Grinding Regression Model Determination with the SRP Method

“…The formulas for each of the seven considered transformations are presented below [5,6]. Here, R a represents the surface roughness value in the experiment and y i (with i=2÷8) denotes the surface roughness value after performing the transformations.…”

“…A lower value indicates a better predictive performance of the model. The values of R 2 , R 2 (adj), R 2 (pred) range from 0 to 1, and higher values are preferable, whereas lower values of MAE and MSE are preferred [6]. However, if the regression model is directly constructed from experimental data, its accuracy might not be high, meaning R 2 , R 2 (adj), R 2 (pred) could have low values, and MAE and MSE could have high values.…”