Technologies that predict the sources of substances diffused in the atmosphere, ocean, and chemical plants are being researched in various fields. The flows transporting such substances are typically in turbulent states, and several problems including the nonlinearity of turbulence must be overcome to enable accurate estimations of diffusion-source location from limited observation data. We studied the feasibility of machine learning, specifically convolutional neural networks (CNNs), to the problem of estimating the diffusion distance from a point source, based on two-dimensional, instantaneous information of diffused-substance distributions downstream of the source. The input image data for the learner are the concentration (or luminance of fluorescent dye) distributions affected by turbulent motions of the transport medium. In order to verify our approach, we employed experimental data of a fully developed turbulent channel flow with a dye nozzle, wherein we attempted to estimate the distances between the dye nozzle and downstream observation windows. The inference accuracy of four different CNN architectures were investigated, and some achieved an accuracy of more than 90%. We confirmed the independence of the inference accuracy on the anisotropy (or rotation) of the image. The trained CNN can recognize the turbulent characteristics for estimating the diffusion source distance without statistical processing. The learners have a strong dependency on the condition of learning images, such as window size and image noise, implying that learning images should be carefully handled for obtaining higher generalization performance.

For locating the source of leaking gas in various engineering fields, several issues remain in the immediate estimation of the location of diffusion sources from limited observation data, because of the nonlinearity of turbulence. This study investigated the practical applicability of diffusion source-location prediction using a convolutional neural network (CNN) from leaking gas instantaneous distribution images captured by infrared cameras. We performed direct numerical simulation of a turbulent flow past a cylinder to provide training and test images, which are scalar concentration distribution fields integrated along the view direction, mimicking actual camera images. We discussed the effects of the direction in which the leaking gas flows into the camera’s view and the distance between the camera and the leaking gas on the accuracy of inference. A single learner created by all images provided an inference accuracy exceeding 85%, regardless of the inflow direction or the distance between the camera and the leaking gas within the trained range. This indicated that, with sufficient training images, a high-inference accuracy can be achieved, regardless of the direction of gas leakage or the distance between the camera and the leaking gas.