Vision-Assisted Probabilistic Inference of Milling Stability through Fully Bayesian Gaussian Process
Abstract
1. Introduction
2. Methodology
2.1. Parametric SLD
2.2. Likelihood Function for Stability Refinement
2.3. Bayesian Learning through Importance Sampling
2.4. Fully Bayesian Gaussian Process (FBGP)
2.5. Vision-Assisted Estimation of Tooling System Dimensions
3. Experimental Validations
- To predict the distribution of based on and .
- To predict the distribution of based on and .
- To predict the distribution of based on .
- To predict the distribution of based on .
4. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
DNN | Deep Neural Network; |
FBGP | Fully Bayesian Gaussian Process; |
GP | Gaussian Process; |
MCMC | Markov Chain Monte Carlo; |
RBF | Radial Basis Function; |
SDM | Semi-Discretization Method; |
STFT | Short-Time Fourier Transform; |
SLD | Stability Lobe Diagram; |
std | Standard Deviation; |
ZOS | Zero-Order Solution. |
References
- Altintaş, Y.; Budak, E. Analytical prediction of stability lobes in milling. CIRP Ann. 1995, 44, 357–362. [Google Scholar] [CrossRef]
- Budak, E.; Altintas, Y. Analytical prediction of chatter stability in milling—Part I: General formulation. J. Dyn. Sys. Meas. Control 1998, 120, 22–30. [Google Scholar] [CrossRef]
- Eynian, M. Chatter Stability of Turning and Milling with Process Damping. Ph.D. Thesis, University of British Columbia, Vancouver, BC, Canada, 2010. [Google Scholar]
- Insperger, T.; Stépán, G. Semi-discretization method for delayed systems. Int. J. Numer. Methods Eng. 2002, 55, 503–518. [Google Scholar] [CrossRef]
- Schmitz, T.L.; Donalson, R. Predicting high-speed machining dynamics by substructure analysis. CIRP Ann. 2000, 49, 303–308. [Google Scholar] [CrossRef]
- Ostad Ali Akbari, V.; Ahmadi, K. Substructure analysis of vibration-assisted drilling systems. Int. J. Adv. Manuf. Technol. 2021, 113, 2833–2848. [Google Scholar] [CrossRef]
- Cherukuri, H.; Perez-Bernabeu, E.; Selles, M.; Schmitz, T. Machining chatter prediction using a data learning model. J. Manuf. Mater. Process. 2019, 3, 45. [Google Scholar] [CrossRef]
- Postel, M.; Bugdayci, B.; Wegener, K. Ensemble transfer learning for refining stability predictions in milling using experimental stability states. Int. J. Adv. Manuf. Technol. 2020, 107, 4123–4139. [Google Scholar] [CrossRef]
- Akbari, V.O.A.; Kuffa, M.; Wegener, K. Physics-informed Bayesian machine learning for probabilistic inference and refinement of milling stability predictions. CIRP J. Manuf. Sci. Technol. 2023, 45, 225–239. [Google Scholar] [CrossRef]
- Akbari, V.O.A.; Postel, M.; Kuffa, M.; Wegener, K. Improving stability predictions in milling by incorporation of toolholder sound emissions. CIRP J. Manuf. Sci. Technol. 2022, 37, 359–369. [Google Scholar] [CrossRef]
- Namazi, M.; Altintas, Y.; Abe, T.; Rajapakse, N. Modeling and identification of tool holder–spindle interface dynamics. Int. J. Mach. Tools Manuf. 2007, 47, 1333–1341. [Google Scholar] [CrossRef]
- Akbari, V.O.A.; Mohammadi, Y.; Kuffa, M.; Wegener, K. Identification of in-process machine tool dynamics using forced vibrations in milling process. Int. J. Mech. Sci. 2023, 239, 107887. [Google Scholar] [CrossRef]
- Kyurkchiev, N.; Markov, S. Sigmoid Functions: Some Approximation and Modelling Aspects; AP LAMBERT Academic Publishing: Saarbrucken, Germany, 2015; Volume 4. [Google Scholar]
- Yuan, C.; Druzdzel, M.J. Importance sampling algorithms for Bayesian networks: Principles and performance. Math. Comput. Model. 2006, 43, 1189–1207. [Google Scholar] [CrossRef]
- Neal, R.M. Bayesian Learning for Neural Networks; Springer Science & Business Media: Berlin, Germany, 2012; Volume 118. [Google Scholar]
- Blundell, C.; Cornebise, J.; Kavukcuoglu, K.; Wierstra, D. Weight uncertainty in neural network. In Proceedings of the International Conference on Machine Learning, Lille, France, 6–11 July 2015; pp. 1613–1622. [Google Scholar]
- Brooks, S. Markov chain Monte Carlo method and its application. J. R. Stat. Soc. 1998, 47, 69–100. [Google Scholar] [CrossRef]
- Tokdar, S.T.; Kass, R.E. Importance sampling: A review. Wiley Interdiscip. Rev. Comput. Stat. 2010, 2, 54–60. [Google Scholar] [CrossRef]
- Rasmussen, C.E. Evaluation of Gaussian Processes and other Methods for Non-Linear Regression. Ph.D. Thesis, University of Toronto, Toronto, ON, Canada, 1997. [Google Scholar]
- Seeger, M. Gaussian processes for machine learning. Int. J. Neural Syst. 2004, 14, 69–106. [Google Scholar] [CrossRef] [PubMed]
- Wilson, A.G.; Knowles, D.A.; Ghahramani, Z. Gaussian process regression networks. arXiv 2011, arXiv:1110.4411. [Google Scholar]
- Wilson, A.; Nickisch, H. Kernel interpolation for scalable structured Gaussian processes (KISS-GP). In Proceedings of the International Conference on Machine Learning, Lille, France, 6–11 July 2015; pp. 1775–1784. [Google Scholar]
- Gardner, J.; Pleiss, G.; Weinberger, K.Q.; Bindel, D.; Wilson, A.G. Gpytorch: Blackbox matrix-matrix gaussian process inference with gpu acceleration. Adv. Neural Inf. Process. Syst. 2018, 31, 7576–7586. [Google Scholar]
- Riviére, E.; Stalon, V.; Van den Abeele, O.; Filippi, E.; Dehombreux, P. Chatter detection techniques using microphone. In Proceedings of the Seventh National Congress on Theoretical and Applied Mechanics, Mons, Belgium, 30–31 May 2006; Volume 2006. [Google Scholar]
- Huda, F.; Darman, D.; Rusli, M. Chatter detection in turning process using sound signal and simple microphone. IOP Conf. Ser. Mater. Sci. Eng. 2020, 830, 042027. [Google Scholar] [CrossRef]
- Wang, W.K.; Wan, M.; Zhang, W.H.; Yang, Y. Chatter detection methods in the machining processes: A review. J. Manuf. Process. 2022, 77, 240–259. [Google Scholar] [CrossRef]
Type | Designation | Specifications | Picture |
---|---|---|---|
Holder | REGO-FIX PG25x100H | Interface: HSK-A63 | |
Tool | Voha 0324 56 120 | Diameter: 12 mm | |
Length: 110 mm | |||
Flutes: 4 |
Case | [px] | Equivalent of in [mm] | [mm/Tooth] | [mm] |
---|---|---|---|---|
A | 531 | 60.9 | 0.05 | 12 |
B | 574 | 65.9 | 0.05 | 8.4 |
C | 596 | 68.4 | 0.05 | 10.8 |
D | 552 | 63.4 | 0.05 | 9.6 |
Case | Detected [px] | Equivalent of in [mm] | True [mm] | Error [%] |
---|---|---|---|---|
A | 531 | 60.9057 | 60.9 | 0.0094 |
B | 574 | 65.8316 | 65.9 | 0.1037 |
C | 596 | 68.3548 | 68.4 | 0.0661 |
D | 552 | 63.3085 | 63.4 | 0.1443 |
Case | Ω [rpm] | [mm] | s [-] |
---|---|---|---|
A | 13,500 | 0.25 | 0 |
A | 14,000 | 0.75 | 1 |
B | 13,000 | 1.00 | 0 |
C | 14,500 | 0.60 | 1 |
C | 10,750 | 0.80 | 0 |
Case | Distribution | [mm] | [mm] | [rpm] | [-] |
---|---|---|---|---|---|
Prior | mean | 0.200 | 3.000 | 20,000 | 0.600 |
std | 0.100 | 1.000 | 2000 | 0.050 | |
A | mean | 0.410 | 2.817 | 21,367.75 | 0.565 |
std | 0.176 | 1.044 | 1717.86 | 0.089 | |
B | mean | 0.438 | 2.848 | 2050.58 | 0.592 |
std | 0.226 | 1.012 | 1514.368 | 0.094 | |
C | mean | 0.593 | 3.132 | 20,114.61 | 0.600 |
std | 0.239 | 0.962 | 1788.36 | 0.092 |
[px] | [mm] | [mm] | [rpm] | [-] | [mm] | |
---|---|---|---|---|---|---|
Min. | 479 | 0.1 | 0.2 | 24,000 | 0.3 | 0 |
Max. | 654 | 2 | 4 | 16,000 | 0.8 | 12 |
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Ostad Ali Akbari, V.; Eichenberger, A.; Wegener, K. Vision-Assisted Probabilistic Inference of Milling Stability through Fully Bayesian Gaussian Process. Metals 2024, 14, 739. https://doi.org/10.3390/met14070739
Ostad Ali Akbari V, Eichenberger A, Wegener K. Vision-Assisted Probabilistic Inference of Milling Stability through Fully Bayesian Gaussian Process. Metals. 2024; 14(7):739. https://doi.org/10.3390/met14070739
Chicago/Turabian StyleOstad Ali Akbari, Vahid, Andrea Eichenberger, and Konrad Wegener. 2024. "Vision-Assisted Probabilistic Inference of Milling Stability through Fully Bayesian Gaussian Process" Metals 14, no. 7: 739. https://doi.org/10.3390/met14070739
APA StyleOstad Ali Akbari, V., Eichenberger, A., & Wegener, K. (2024). Vision-Assisted Probabilistic Inference of Milling Stability through Fully Bayesian Gaussian Process. Metals, 14(7), 739. https://doi.org/10.3390/met14070739