Model-Based Learning of Turbulent Flows using Mobile Robots

Abstract--In this paper we consider the problem of modelbased learningof turbulent flows using mobile robots. The key idea is to use empirical data to improve on numerical estimates of time-averaged flow properties that can be obtained using Reynolds-Averaged Navier Stokes (RANS) models. RANS models are computationally efficient and provide global knowledge of the flow but they also rely on simplifying assumptions and require experimental validation. In this paper, we instead construct statistical models of the flow properties using Gaussian Processes (GPs) and rely on the numerical solutions obtained from RANS models to inform their mean. We then utilize Bayesian inference to incorporate empirical measurements of the flow into these GPs, specifically, measurements of the time-averaged velocity and turbulent intensity fields. Moreover, it accounts for measurement noise by systematically incorporating it in the GP models. To obtain the velocity and turbulent intensity measurements, we design a cost-effective mobile robot sensor that collects and analyzes instantaneous velocity readings. We control this mobile robot through a sequence of waypoints that maximize the information content of the corresponding measurements. The end result is a posterior distribution of the flow field that better approximates the real flow and also quantifies the uncertainty in the flow properties. We present experimental results that demonstrate considerable improvement in the prediction of the flow properties compared to pure numerical simulations. I. INTRODUCTION Knowledge of turbulent flow properties, e.g., velocity and turbulent intensity, is of paramount importance for many engineering applications.At larger scales, these properties are used for the study of ocean currents and their effects on aquatic life, [1], [2], [3], meteorology, [4], bathymetry, [5], and localization of atmospheric pollutants, [6], to name a few. At smaller scales, knowledge of flow fields is important in applications ranging from optimal HVAC of residential buildings for human comfort, [7], to design of drag-efficient bodies in aerospace and automotive industries, [8]. At even smaller scales, the characteristics of velocity fluctuations in vessels are important for vascular pathology and diagnosis, [9] or for the control of bacteria-inspired uniflagellar robots, [10]. Another important application that requires global knowledge of the velocity field is chemical source identification in advection-diffusion transport systems, [11], [12], [13].