This paper is a preliminary report on work done to explore the use of unsupervised machine learning methods to predict the onset of turbulent transitions in natural convection systems. The Lorenz system was chosen to test the machine learning methods due to the relative simplicity of the dynamic system. We developed a robust numerical solution to the Lorenz equations using a fourth order Runge-Kutta method with a time step of 0.001 seconds. We solved the Lorenz equations for a large range of Raleigh ratios from 1–1000 while keeping the geometry and Prandtl number constant. We calculated the spectral density, various descriptive statistics, and a cluster analysis using unsupervised machine learning. We examined the performance of the machine learning system for different Raleigh ratio ranges.
We found that the automated cluster analysis aligns well with well known key transition regions of the convection system. We determined that considering smaller ranges of Raleigh ratios may improve the performance of the machine learning tools. We also identified possible additional behaviors not shown in z-axis bifurcation plots. This unsupervised learning approach can be leveraged on other systems where numerical analysis is computationally intractable or more difficult.
The results are interesting and provide a foundation for expanding the study for Prandtl number and geometry variations. Future work will focus on applying the methods to more complex natural convection systems, including the development of new methods for Nusselt correlations.