Incorporating prior model into Gaussian processes regression for WEDM process modeling

Sufficient sampling is usually time-consuming and expensive but also is indispensable for supporting high precise data-driven modeling of wire-cut electrical discharge machining (WEDM) process. Considering the natural way to describe the behavior of a WEDM process by IF-THEN rules drawn from the field experts, engineering knowledge and experimental work, in this paper, the fuzzy logic model is chosen as prior knowledge to leverage the predictive performance. Focusing on the fusion between rough fuzzy system and very scarce noisy samples, a simple but effective re-sampling algorithm based on piecewise relational transfer interpolation is presented and it is integrated with Gaussian processes regression (GPR) for WEDM process modeling. First, by using re-sampling algorithm encoded derivative regularization, the prior model is translated into a pseudo training dataset, and then the dataset is trained by the Gaussian processes. An empirical study on two benchmark datasets intuitively demonstrates the feasibility and effectiveness of this approach. Experiments on high-speed WEDM (DK7725B) are conducted for validation of nonlinear relationship between the design variables (i.e., workpiece thickness, peak current, on-time and off-time) and the responses (i.e., material removal rate and surface roughness). The experimental result shows that combining very rough fuzzy prior model with training examples still significantly improves the predictive performance of WEDM process modeling, even with very limited training dataset. That is, given the generalized prior model, the samples needed by GPR model could be reduced greatly meanwhile keeping precise.