(375w) Symbolic Regression-Based Recursive Surrogate Model for a Manufacturing Process

Hybrid models are increasingly employed to model intricate physical processes by combining physics knowledge of a process with data obtained from measurements. This fusion of physics knowledge with data results in hybrid models that are more accurate and robust in capturing performance metrics of a physical process than purely data-driven or first-principle models [1]. Surrogate modeling is one of the hybrid modeling approaches that provides a simple mathematical representation of complex physical phenomena. Surrogate models are beneficial for modeling intricate processes or phenomena that are difficult to model from data directly, with less computational effort and low complexity [2]. Surrogate models can be developed by using symbolic regression. Symbolic regression provides a unique algebraic equation that can best represent the data. Symbolic regression forms initial expressions by randomly combining mathematical components such as analytic functions, constants, and state variables to find an explainable regression model, given the input variables and chosen basis functions. Genetic Programming Toolbox for the Identification of Physical Systems (GPTIPS) is a MATLAB toolbox that uses symbolic regression to develop models, based on genetic programming (GP). GP is a type of derivative-free optimization method that imitates how evolution works in nature [3]. GP first generates a random population of model structures and then builds a new population by mutating, selecting, and crossover of model structures with the best performance. This process is repeated until a model structure of desired complexity and accuracy is obtained.

This study demonstrates the use of symbolic regression using GPTIPS to develop generic recursive surrogate models for tool wear prediction in a manufacturing process. Tool wear is the degradation of the insert tip that performs machining and causes failures, faults, and inaccuracies in manufacturing. The in-process detection of tool wear is difficult and various contributors to tool wear, such as high interface temperatures, hard inclusions in the workpiece material, and high shear forces, are challenging to directly quantify [4]. Therefore, there is a need to find a model with which the tool wear can be inferred using quantifiable features. In this study, our objective is to use the symbolic regression framework to develop generic recursive models of health indicators and the tool wear in various machining processes, operating at varying conditions. We applied the developed framework to the NASA milling dataset [5], which comprises sixteen datasets of run-to-failure machining tests conducted with two different workpiece materials. We integrated physics knowledge into the model development. Analysis of data and understanding of the physics of the tool wear mechanism have identified that tool wear depends on the operating conditions, material type, and the state of the tool [6,7]. Using this insight, the state of a tool, the machine operating conditions (depth of cut and feed rate), material hardness, and cutting time were selected as input variables for symbolic regression. Moreover, considering the strong correlation between health indicators and the current state of a tool, to predict future tool wear, future values of health indicators were predicted using time dependent models of their progression.

A health indicator extracted from collected sensor signals should be responsive to changes in cutting conditions and tool wear, as the sensor signals do. If we have a feature model and design of experiments (or intended use in deployment) in the future, we can predict the health indicator in the future from the cutting conditions planned in the design of experiments. The health indicators that offer an accurate representation of the tool wear of different cases were first extracted from sensor signals and a recursive surrogate model of the health indicator was developed as a function of the operating conditions, material hardness, and the state of the indicator. Just as the progression of tool wear is dynamic depending on its state at any given time, the current state indicator is affected by the indicator value at a previous time. A recursive surrogate model of the tool wear was then developed. The inputs for the recursive tool wear model were the tool wear state, operating conditions, material hardness, cutting times, and health indicators predicted through the recursive health indicator model. As a result, the developed recursive tool wear model successfully captured the progression of tool wear of different 16 cases, with 0.955 R² value. Compared to other research methods developed using the NASA milling dataset, this study achieved a lower RMSE, demonstrating the accuracy and effectiveness of our symbolic regression framework over prior research.

References

[1] Yang,Q.,Pattipati,K.R.,Awasthi,U.,andBollas,G.M.,HybridData- Driven and Model-Informed Online Tool Wear Detection in Milling Machines, Journal of Manufacturing Systems 63 (2022) 329–43.

[2] Sansana,J.,Joswiak,M.N.,Castillo,I.,Wang,Z.,Rendall,R.,Chiang, L. H., and Reis, M. S., Recent Trends on Hybrid Modeling for Industry 4.0., Computers and Chemical Engineering 151 (2021) 107365.

[3] Searson, D.P., Leahy, D.E., Willis, M.J., GPTIPS: an open source genetic programming toolbox for multigene symbolic regression, Proceedings of the International MultiConference of Engineers and Computer Scientists 2010 (IMECS 2010), Hong Kong, 17-19 March, 2010.

[4] S. Han, Q. Yang, K. R. Pattipati, G. M. Bollas, Sensor selection and tool wear prediction with data-driven models for precision machining, Journal of Advanced Manufacturing and Processing (2022).

[5] K. Goebel, Management of Uncertainty in Sensor Validation, Sensor Fusion, and Diagnosis of Mechanical Systems Using Soft Computing Techniques, Ph.D. Thesis, Department of Mechanical Engineering, University of California at Berkeley, 1996.

[6] U. Awasthi, Z. Wang, N. Mannan, K. R. Pattipati, G. M. Bollas, Physics-based modeling and information-theoretic sensor and settings selection for tool wear detection in precision machining, Journal of Manufacturing Processes, 81 (2022) 127–140.

[7] S. Han, N. Mannan, D. C. Stein, K. R. Pattipati, G. M. Bollas, Classification and regression models of audio and vibration signals for machine state monitoring in precision machining systems, Journal of Manufacturing Systems, 61 (2021) 45–53.