Upstream flow geometries can be uniquely learnt from single-point turbulence signatures

Abstract

We test the hypothesis that the microscopic temporal structure of near-field turbulence downstream of a sudden contraction contains geometry-identifiable information pertaining to the shape of the upstream obstruction. We measure a set of spatially sparse velocity time-series data downstream of differently-shaped orifices. We then train random forest multiclass classifier models on a vector of invariants derived from this time-series. We test the above hypothesis with 25 somewhat similar orifice shapes to push the model to its extreme limits. Remarkably, the algorithm was able to identify the orifice shape with 100% accuracy and 100% precision. This outcome is enabled by the uniqueness in the downstream temporal evolution of turbulence structures in the flow past orifices, combined with the random forests' ability to learn subtle yet discerning features in the turbulence microstructure. We are also able to explain the underlying flow physics that enables such classification by listing the invariant measures in the order of increasing information entropy. We show that the temporal autocorrelation coefficients of the time-series are most sensitive to orifice shape and are therefore informative. The ability to identify changes in system geometry without the need for physical disassembly offers tremendous potential for flow control and system identification. Furthermore, the proposed approach could potentially have significant applications in other unrelated fields as well, by deploying the core methodology of training random forest classifiers on vectors of invariant measures obtained from time-series data.

Figures (1)

• Figure 1: $(a)$ Observation showing the difference in distance of the hot wire probing location from the edges of the square and circular geometry orifice plates. The orange dots in $(a)$ represent the $9$ probing points, labelled 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H' and 'I'. The results discussed in previous sections pertain to measurements from these $9$ locations. $(b)$ New locations assigned for hot wire measurements to investigate the edge effects on the performance of classifier models. The orange points in $(b)$ represent the probing locations immediately downstream of the orifice edge, labelled 'B0', 'H0', 'D0', and 'G0', and the blue points represent probing locations $5mm$ away from each edge location, towards the wall, labelled 'B5', 'H5', 'D5', and 'G5'.