Rough-Fuzzy Modeling and Interpolation Reasoning with Application in Weld-Penetration Control

Weld-penetration control is a fundamental problem associated with welding automation. The pursuit of frontal molten-pool features that reflect the penetration information and the establishment of correspondence relationships between the molten state and the representative features of the molten pool are key procedures in achieving real-time penetration control. This article proposes a weld-penetration control method that combines variable-precision tolerance rough set (VPTRS) knowledge mining, fuzzy logic modeling, and interpolation reasoning techniques. A VPTRS model was constructed to address the shortcomings of classical rough sets, which handle continuous and noisy data poorly. A fast-reduction algorithm, which uses feature importance as heuristic information, was proposed. In addition, a rule-extraction algorithm was obtained by partitioning the universe of discourse through tolerance relations. Traditional fuzzy reasoning methods cannot effectively handle reasoning under incomplete rule-base conditions. To address this issue, a fuzzy interpolation reasoning algorithm was developed by extracting the geometric features of fuzzy-set membership functions and calculating feature distance and similarity ratios. Multiple welding experiments were conducted to establish a fusion decision information system. Correspondence relationships between the frontal molten-pool features and the penetration state were obtained from VPTRS feature reduction and rule extraction processes, and a weld-penetration control system was constructed based on fuzzy logic modeling and interpolation reasoning techniques. Welding experiments were also conducted to test the performance of the control system. The results indicated that the formed quality of the weld seam obtained by the proposed method was better than that obtained by ANN-fuzzy control, and that the system performance met the requirements of welding process specifications. The main contribution of this methodology is that it can extract a set of interpretable decision rules from the raw data set collected in the experiment, and then achieve real-time control of the welding penetration process through interpolation reasoning. By using the VPTRS modeling technology, it can be found that certain easily overlooked melt pool characteristics, such as tail width coefficient and tail area coefficient, are closely related to the melting state, which is crucial for achieving melting control with minimal controlled variables.