Modelling and control of nonlinear systems using Gaussian processes with partial model information

Gaussian processes are gaining increasing popularity among the control community, in particular for the modelling of discrete time state space systems. However, it has not been clear how to incorporate model information, in the form of known state relationships, when using a Gaussian process as a predictive model. An obvious example of known prior information is position and velocity related states. Incorporation of such information would be beneficial both computationally and for faster dynamics learning. This paper introduces a method of achieving this, yielding faster dynamics learning and a reduction in computational effort from O(Dn2) to O((D - F)n2) in the prediction stage for a system with D states, F known state relationships and n observations. The effectiveness of the method is demonstrated through its inclusion in the PILCO learning algorithm with application to the swing-up and balance of a torque-limited pendulum and the balancing of a robotic unicycle in simulation. © 2012 IEEE.

Kernel conditional quantile estimation via reduction revisited

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches. © 2009 IEEE.

Gaussian Processes for Machine Learning

The code provided here originally demonstrated the main algorithms from Rasmussen and Williams: Gaussian Processes for Machine Learning. It has since grown to allow more likelihood functions, further inference methods and a flexible framework for specifying GPs.

Trailing edge noise theory for rotating blades in uniform flow

This paper presents a new formulation for trailing edge noise radiation from rotating blades based on an analytical solution of the convective wave equation. It accounts for distributed loading and the effect of mean flow and spanwise wavenumber. A commonly used theory due to Schlinker and Amiet (1981) predicts trailing edge noise radiation from rotating blades. However, different versions of the theory exist; it is not known which version is the correct one and what the range of validity of the theory is. This paper addresses both questions by deriving Schlinker and Amiet's theory in a simple way and by comparing it to the new formulation, using model blade elements representative of a wind turbine, a cooling fan and an aircraft propeller. The correct form of Schlinker and Amiet's theory (1981) is identified. It is valid at high enough frequency, i.e. for a Helmholtz number relative to chord greater than one and a rotational frequency much smaller than the angular frequency of the noise sources.

Airfoil flow and noise computation using monotonically integrated large eddy simulation and acoustic analogy: Effect of the grid resolution.

A new scalable Monotonically Integrated Large Eddy Simulation (MILES) method based on the Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) has been applied for the simulation of unsteady flow around NACA0012 airfoil at Re = 400,000 and M = 0.058. The flow solution is coupled with the Ffowcs Williams-Hawkings formulation for far-field noise prediction. The computational modeling results are presented for several computational grid resolutions: 8, 16, and 32 million grid cells and compared with the experimental data available.