Knowing the pressure at all times in each node of a water distribution system (WDS) facilitates safe and efficient operation. Yet, complete measurement data cannot be collected due to the limited number of instruments in a real-life WDS. The data-driven methodology of reconstructing all the nodal pressures by observing only a limited number of nodes is presented in the paper.The reconstruction method is based on K-localized spectral graph filters, wherewith graph convolution on water networks is possible. The effect of the number of layers, layer depth and the degree of the Chebyshev-polynomial applied in the kernel is discussed taking into account the peculiarities of the application. In addition, a weighting method is shown, wherewith information on friction loss can be embed into the spectral graph filters through the adjacency matrix.The performance of the proposed model is presented on 3 WDSs at different number of nodes observed compared to the total number of nodes. The weighted connections prove no benefit over the binary connections, but the proposed model reconstructs the nodal pressure with at most 5% relative error on average at an observation ratio of 5% at least. The results are achieved with shallow graph neural networks by following the considerations discussed in the paper.
A novel technique to accelerate optimization-driven aerodynamic shape design is presented in the paper. The methodology of optimization-driven design is based on the automated evaluation of many similar shapes which are generated according to the output of an optimization algorithm. The vast amount of numerical simulations makes this process slow but the resource-intensive simulation part can be changed to so-called surrogate models or metamodels. However, there isn’t any guarantee of this solution’s accuracy.The motivation of this work was to develop an acceleration method to speedup optimization sessions without losing accuracy. Accordingly, the numerical simulation is kept in the pipeline but it is initialized with a velocity field that is close to the expected solution. This velocity field is generated by a predictive initializer that is based on a convolutional deep neural network. The network has to be trained before using it for initializing numerical simulations; the data generation, the training and the testing of the network are described in the paper as well.The performance of predictive initializing is presented through a test problem based on a deformable u-bend geometry. It has been found that the speedup in the convergence speed of the numerical simulation depends on the resolution of the predictive initializer and on the handling of velocities in the near-wall cells. A speedup of 13 % was achieved on a test set of 500 geometries that were not seen by the initializer before.
This paper describes a study based on computational fluid dynamics (CFD) and deep neural networks that focusing on predicting the flow field in differently distorted U-shaped pipes. The main motivation of this work was to get an insight about the justification of the deep learning paradigm in hydrodynamic hull optimisation processes that heavily depend on computing turbulent flow fields and that could be accelerated with models like the one presented. The speed-up can be even several orders of magnitude by surrogating the CFD model with a deep convolutional neural network.An automated geometry creation and evaluation process was set up to generate differently shaped two-dimensional U-bends and to carry out CFD simulation on them. This process resulted in a database with different geometries and the corresponding flow fields (2-dimensional velocity distribution), both represented on 128x128 equidistant grids. This database was used to train an encoder-decoder style deep convolutional neural network to predict the velocity distribution from the geometry.The effect of two different representations of the geometry (binary image and signed distance function) on the predictions was examined, both models gave acceptable predictions with a speed-up of two orders of magnitude.
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