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Calibri 83ffff̙̙3f3fff3f3f33333f33333.>TU Delft Repositoryg :uuidrepository linktitleauthorcontributorpublication yearabstract
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departmentresearch group programmeprojectcoordinates)uuid:f613079c90a147dcafcbf6833646ca5aDhttp://resolver.tudelft.nl/uuid:f613079c90a147dcafcbf6833646ca5aMLQG and Gaussian process techniques: For fixedstructure wind turbine control;Bijl, H.J. (TU Delft Numerics for Control & Identification)zVerhaegen, M.H.G. (promotor); van Wingerden, J.W. (promotor); Delft University of Technology (degree granting institution)^Wind turbines are growing bigger to becomemore costefficient. This does increase the severity of the vibrations that are present in the turbine blades, both due to predictable effects like wind shear and tower shadow, and due to less predictable effects like turbulence and flutter. If wind turbines are to become bigger and more costefficient, these vibrations need to be reduced. This can be done by installing trailingedge flaps to the blades. Because of the variety of circumstances which the turbine should operate in, this results in large uncertainties. As such, we need methods that can take stochastic effects into account. Preferably we develop an algorithmthat can learn from online data how the flaps affect the wind turbine and how to optimally control them. A simple prior analysis can be done using a linearized version of the system. In this case it is important to know not only the expected cost (damage) that will be incurred by the wind turbine in various situations, but also the spread of this cost. This can for instance be done by looking at the variance of the cost function. Various expressions are available to analytically calculate this variance. Alternatively, we can prescribe a degree of stability for the system. Due to the limitations of linear approximations of systems, it is more effective to apply nonlinear regression methods. A promising one is Gaussian Process (GP) regression. Given a training set (X, y) it can predict function values f (x) for test points x. It has its basis in Bayesian probability theory, which allows it to not only make this prediction, but also give information (the variance) about its accuracy. The usual way in which GP regression is applied has a few important limitations. Most importantly, it is computationally intensive, especially when applied to constantly growing data sets. In addition, it has difficulties dealing with noise present in the training input points x. There are methods to solve either of these issues, but these tricks generally do not work well together, or their combination requires many computational resources. However, by making the right approximations, like Taylor expansions and at times even linearizations, Gaussian process regression can be applied efficiently, in an online way, to data sets with noisy input points. This enables GP regression to be used for system identification problems like online nonlinear blackbox modeling. Another limitation is that it can be difficult to find the optimum of a Gaussian process. The reason is that the optimum of a Gaussian process is not a fixed point but a random variable. The distribution of this optimum cannot be calculated analytically, but we can use particle methods to approximate it. We can subsequently use this principle to efficiently explore an unknown nonlinear function, trying to locate its optimum. To do so, we sample a point x from the optimum distribution, measure what the function value f (x) at this point is, update the Gaussian process approximation of the function, update the optimum distribution and repeat this process until the distribution has converged. Finding the optimum of a function like this has shown to have competitive performance at keeping the cumulative regret low, compared to similar algorithms. In addition, it allows wind turbines to tune the gains of a fixedstructure controller so as to optimize a nonlinear cost function like the damage equiva<lent load. All these improvements are a step forward in the application of Gaussian process regression to wind turbine applications. But as is always the case with research, there are still many things left to improve further.Gaussian processes; regression; machine learning; optimization; system identification; automatic control; wind energy; smart rotorendoctoral thesis9789462995017%Numerics for Control & Identification)uuid:060d9f3e561c480687fbdd378cfaf3b0Dhttp://resolver.tudelft.nl/uuid:060d9f3e561c480687fbdd378cfaf3b0MAdaptive efficient global optimization of systems with independent components}Rehman, S.U. (TU Delft Structural Optimization and Mechanics); Langelaar, M. (TU Delft Structural Optimization and Mechanics)We present a novel approach for efficient optimization of systems consisting of expensive to simulate components and relatively inexpensive systemlevel simulations. We consider the types of problem in which the components of the system problem are independent in the sense that they do not exchange coupling variables, however, design variables can be shared across components. Component metamodels are constructed using Kriging. The metamodels are adaptively sampled based on a system level infill sampling criterion using Efficient Global Optimization. The effectiveness of the technique is demonstrated by applying it on numerical examples and an engineering case study. Results show steady and fast converge to the global deterministic optimum of the problems.vEfficient global optimization; Expected improvement; Gaussian processes; Infill sampling; Kriging; System optimizationjournal article%Structural Optimization and Mechanics)uuid:fbca8d52dfc242cfb64ce2403d603285Dhttp://resolver.tudelft.nl/uuid:fbca8d52dfc242cfb64ce2403d603285yTrajectory driven multidisciplinary design optimization of a suborbital spaceplane using nonstationary Gaussian process(Dufour, R.; De Meulenaere, J.; Elham, A.This paper presents the multidisciplinary optimization of an aircraft carried suborbital spaceplane. The optimization process focused on three disciplines: the aerodynamics, the structure and the trajectory. The optimization of the spaceplane geometry was coupled with the optimization of its trajectory. The structural weight was estimated using empirical formulas. The trajectory was optimized using a pseudospectral approach with an automated mesh refinement that allowed for increasing the sparsity of the Jacobian of the constraints. The aerodynamics of the spaceplane was computed using an Euler code and the results were used to create a surrogate model based on a nonstationary Gaussian process procedure that was specially developed for this study.bspaceplane multidisciplinary optimization; optimal control; surrogate modeling; Gaussian processesSpringerAerospace Engineering&Aerodynamics, Wind Energy & Propulsion)uuid:a8e5b498557e4c8ba05a77c5046a4493Dhttp://resolver.tudelft.nl/uuid:a8e5b498557e4c8ba05a77c5046a4493sCorrelation inequalities and applications to vectorvalued Gaussian random variables and fractional Brownian motion
Veraar, M.Correlation inequalities; Gebeleins inequality; Gaussian random variables; Maximal inequalities; Law of large numbers; Type and cotype; Gaussian processes; Fractional Brownian motion; BesovOrlicz spaces; Sample path; Nonseparable Banach space8Electrical Engineering, Mathematics and Computer Science
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