A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of interest depends discontinuously on the input parameters. As a remedy we propose an adaptive sampling algorithm based on minimum spanning trees combined with a domain decomposition method based on support vector machines. The minimum spanning tree determines new sample locations based on both the probability density of the input parameters and the gradient in the quantity of interest. The support vector machine efficiently decomposes the random space in multiple elements, avoiding the appearance of Gibbs phenomena near discontinuities. On each element, local approximations are constructed by means of least orthogonal interpolation, in order to produce stable interpolation on the unstructured sample set. The resulting minimum spanning tree multi-element method does not require initial knowledge of the behaviour of the quantity of interest and automatically detects whether discontinuities are present. We present several numerical examples that demonstrate accuracy, efficiency and generality of the method.
The aerodynamic performance of vehicles and animals, as well as the productivity of turbines and energy harvesters, depends on the turbulence intensity of the incoming flow. Previous studies have pointed at the potential benefits of active closed-loop turbulence control. However, it is unclear what the minimal sensory and algorithmic requirements are for realizing this control. Here we show that very low-bandwidth anemometers record sufficient information for an adaptive control algorithm to converge quickly. Our online Newton-Raphson algorithm tunes the turbulence in a recirculating wind tunnel by taking readings from an anemometer in the test section. After starting at 9% turbulence intensity, the algorithm converges on values ranging from 10% to 45% in less than 12 iterations within 1% accuracy. By down-sampling our measurements, we show that very-low-bandwidth anemometers record sufficient information for convergence. Furthermore, down-sampling accelerates convergence by smoothing gradients in turbulence intensity. Our results explain why low-bandwidth anemometers in engineering and mechanoreceptors in biology may be sufficient for adaptive control of turbulence intensity. Finally, our analysis suggests that, if certain turbulent eddy sizes are more important to control than others, frugal adaptive control schemes can be particularly computationally effective for improving performance.
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