Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Bayesian and L1 Approaches to Sparse Unsupervised Learning

The use of L1 regularisation for sparse learning has generated immense research interest, with successful application in such diverse areas as signal acquisition, image coding, genomics and collaborative filtering. While existing work highlights the many advantages of L1 methods, in this paper we find that L1 regularisation often dramatically underperforms in terms of predictive performance when compared with other methods for inferring sparsity. We focus on unsupervised latent variable models, and develop L1 minimising factor models, Bayesian variants of "L1", and Bayesian models with a stronger L0-like sparsity induced through spike-and-slab distributions. These spike-and-slab Bayesian factor models encourage sparsity while accounting for uncertainty in a principled manner and avoiding unnecessary shrinkage of non-zero values. We demonstrate on a number of data sets that in practice spike-and-slab Bayesian methods outperform L1 minimisation, even on a computational budget. We thus highlight the need to re-assess the wide use of L1 methods in sparsity-reliant applications, particularly when we care about generalising to previously unseen data, and provide an alternative that, over many varying conditions, provides improved generalisation performance.

Model based learning of sigma points in unscented Kalman filtering

The unscented Kalman filter (UKF) is a widely used method in control and time series applications. The UKF suffers from arbitrary parameters necessary for a step known as sigma point placement, causing it to perform poorly in nonlinear problems. We show how to treat sigma point placement in a UKF as a learning problem in a model based view. We demonstrate that learning to place the sigma points correctly from data can make sigma point collapse much less likely. Learning can result in a significant increase in predictive performance over default settings of the parameters in the UKF and other filters designed to avoid the problems of the UKF, such as the GP-ADF. At the same time, we maintain a lower computational complexity than the other methods. We call our method UKF-L. ©2010 IEEE.

Model based learning of sigma points in unscented Kalman filtering

The unscented Kalman filter (UKF) is a widely used method in control and time series applications. The UKF suffers from arbitrary parameters necessary for sigma point placement, potentially causing it to perform poorly in nonlinear problems. We show how to treat sigma point placement in a UKF as a learning problem in a model based view. We demonstrate that learning to place the sigma points correctly from data can make sigma point collapse much less likely. Learning can result in a significant increase in predictive performance over default settings of the parameters in the UKF and other filters designed to avoid the problems of the UKF, such as the GP-ADF. At the same time, we maintain a lower computational complexity than the other methods. We call our method UKF-L. © 2011 Elsevier B.V.

An Infinite Latent Attribute Model for Network Data

Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes then depends only on their cluster assignment. Currently available models can be classified by whether clusters are disjoint or are allowed to overlap. These models can explain a "flat" clustering structure. Hierarchical Bayesian models provide a natural approach to capture more complex dependencies. We propose a model in which objects are characterised by a latent feature vector. Each feature is itself partitioned into disjoint groups (subclusters), corresponding to a second layer of hierarchy. In experimental comparisons, the model achieves significantly improved predictive performance on social and biological link prediction tasks. The results indicate that models with a single layer hierarchy over-simplify real networks.

Avoiding pathologies in very deep networks

Choosing appropriate architectures and regularization strategies of deep networks is crucial to good predictive performance. To shed light on this problem, we analyze the analogous problem of constructing useful priors on compositions of functions. Specifically, we study the deep Gaussian process, a type of infinitely-wide, deep neural network. We show that in standard architectures, the representational capacity of the network tends to capture fewer degrees of freedom as the number of layers increases, retaining only a single degree of freedom in the limit. We propose an alternate network architecture which does not suffer from this pathology. We also examine deep covariance functions, obtained by composing infinitely many feature transforms. Lastly, we characterize the class of models obtained by performing dropout on Gaussian processes.

Improving the consensus performance via predictive mechanisms

Considering some predictive mechanisms, we show that ultrafast average-consensus can be achieved in networks of interconnected agents. More specifically, by predicting the dynamics of the network several steps ahead and using this information in the design of the consensus protocol of each agent, drastic improvements can be achieved in terms of the speed of consensus convergence, without changing the topology of the network. Moreover, using these predictive mechanisms, the range of sampling periods leading to consensus convergence is greatly expanded compared with the routine consensus protocol. This study provides a mathematical basis for the idea that some predictive mechanisms exist in widely-spread biological swarms, flocks, and networks. From the industrial engineering point of view, inclusion of an efficient predictive mechanism allows for a significant increase in the speed of consensus convergence and also a reduction of the communication energy required to achieve a predefined consensus performance.

Performance evaluation of multiplexed model predictive control for a large airliner in nominal and contingency scenarios

Model predictive control allows systematic handling of physical and operational constraints through the use of constrained optimisation. It has also been shown to successfully exploit plant redundancy to maintain a level of control in scenarios when faults are present. Unfortunately, the computational complexity of each individual iteration of the algorithm to solve the optimisation problem scales cubically with the number of plant inputs, so the computational demands are high for large MIMO plants. Multiplexed MPC only calculates changes in a subset of the plant inputs at each sampling instant, thus reducing the complexity of the optimisation. This paper demonstrates the application of multiplexed model predictive control to a large transport airliner in a nominal and a contingency scenario. The performance is compared to that obtained with a conventional synchronous model predictive controller, designed using an equivalent cost function. © 2012 AACC American Automatic Control Council).

Robust multiplexed model predictive control

This paper extends the recently developed multiplexed model predictive control (MMPC) concept to ensure satisfaction of hard constraints despite the action of persistent, unknown but bounded disturbances. MMPC uses asynchronous control moves on each input channel instead of synchronised moves on all channels. It offers reduced computation, by dividing the online optimisation into a smaller problem for each channel, and potential performance improvements, as the response to a disturbance is quicker, albeit via only one channel. Robustness to disturbances is introduced using the constraint tightening approach, tailored to suit the asynchronous updates of MMPC and the resulting time-varying optimisations. Numerical results are presented, involving a simple mechanical example and an aircraft control example, showing the potential computational and performance benefits of the new robust MMPC.

Hybrid model predictive control applied to switching control of burner load for a compact marine boi

This paper discusses the application of hybrid model predictive control to control switching between different burner modes in a novel compact marine boiler design. A further purpose of the present work is to point out problems with finite horizon model predictive control applied to systems for which the optimal solution is a limit cycle. Regarding the marine boiler control the aim is to find an optimal control strategy which minimizes a trade-off between deviations in boiler pressure and water level from their respective setpoints while limiting burner switches.The approach taken is based on the Mixed Logic Dynamical framework. The whole boiler systems is modelled in this framework and a model predictive controller is designed. However to facilitate on-line implementation only a small part of the search tree in the mixed integer optimization is evaluated to find out whether a switch should occur or not. The strategy is verified on a simulation model of the compact marine boiler for control of low/high burner load switches. It is shown that even though performance is adequate for some disturbance levels it becomes deteriorated when the optimal solution is a limit cycle. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

Multiplexed model predictive control

Most academic control schemes for MIMO systems assume all the control variables are updated simultaneously. MPC outperforms other control strategies through its ability to deal with constraints. This requires on-line optimization, hence computational complexity can become an issue when applying MPC to complex systems with fast response times. The multiplexed MPC scheme described in this paper solves the MPC problem for each subsystem sequentially, and updates subsystem controls as soon as the solution is available, thus distributing the control moves over a complete update cycle. The resulting computational speed-up allows faster response to disturbances, and hence improved performance, despite finding sub-optimal solutions to the original problem. The multiplexed MPC scheme is also closer to industrial practice in many cases. This paper presents initial stability results for two variants of multiplexed MPC, and illustrates the performance benefit by an example. Copyright copy; 2005 IFAC. Copyright © 2005 IFAC.