Optimal control with stochastic PDE constraints and uncertain controls

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

Optimal design of Functionally Graded Materials using a procedural model and Particle Swarm Optimization

A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples. © 2011 Elsevier Ltd. All rights reserved.

The use of centrifuge tests in the study of arching

The horizontal arching mechanism transfers horizontal earth pressures acting on flexible retaining wall panels to stiffer neighbouring elements via soil shear stresses. In this research, the horizontal arching mechanism and lateral displacements of fixed cantilever walls in a model basement are investigated using centrifuge tests. A series of six tests was carried out at 45 gravities where the panel widths and thicknesses around the model basement were varied, so that the effects of panel geometry and stiffness on horizontal arching could be studied. It is shown that panel crest displacements and base bending moments of the most flexible, narrow panels can be an order of magnitude smaller than conventional active earth pressure calculations would allow. It is suggested that the reduction of earth pressure acting on a panel is directly correlated to the mobilized soil shear strength and hence, soil shear strain. Earth pressure coefficients K are plotted against panel displacements normalized by the panel width, u/B, to simulate the reduction of K with increasing soil strain.An idealized K-u/B curve is introduced, characterised by a reference distortion (u/B) ref beyond which fully plastic soil arching can be inferred, and which is related to the corresponding reference shear strain γ ref at which soil strength is fully mobilized in element tests. © 2006 Taylor & Francis Group, London.

Case study on a deep excavation in soft ground by centrifuge model tests

This paper provides a case study on the deepest excavation carried out so far in the construction of the metro network in Shanghai, which typically features soft ground. The excavation is 38 m deep with retaining walls 65 m deep braced by 9 levels of concrete props. To obtain a quick and rough prediction, two centrifuge model tests were conducted, in which one is for the 'standard' section with green field surrounding and the other with an adjacent piled building. The tests were carried out in a run-stop-excavation-run style, in which excavation was conducted manually. By analyzing the lateral wall displacement, ground deformation, bending moment and earth pressure, the test results are shown to be reasonably convincing and the design and construction were validated. Such industry orientated centrifuge modeling was shown to be useful in understanding the performance of geotechnical processes, especially when engineers lack relevant field experience. © 2010 Taylor & Francis Group, London.

Dynamic centrifuge tests on shallow tunnel models in dry sand

In the framework of the Italian research project ReLUIS-DPC, a set of centrifuge tests were carried out at the Schofield Centre in Cambridge (UK) to investigate the seismic behaviour of tunnels. Four samples of dry sand were prepared at different densities, in which a small scale model of circular tunnel was inserted, instrumented with gauges measuring hoop and bending strains. Arrays of accelerometers in the soil and on the box allowed the amplification of ground motion to be evaluated; LVDTs measured the soil surface settlement. This paper describes the main results of this research, showing among others the evolution of the internal forces during the model earthquakes at significant locations along the tunnel lining. © 2010 Taylor & Francis Group, London.

Particle Image Velocimetry analysis in dynamic centrifuge tests

The Particle Image Velocimetry (PIV) technique is an image processing tool to obtain instantaneous velocity measurements during an experiment. The basic principle of PIV analysis is to divide the image into small patches and calculate the locations of the individual patches in consecutive images with the help of cross correlation functions. This paper focuses on the application of the PIV analysis in dynamic centrifuge tests on small scale tunnels in loose, dry sand. Digital images were captured during the application of the earthquake loading on tunnel models using a fast digital camera capable of taking digital images at 1000 frames per second at 1 Megapixel resolution. This paper discusses the effectiveness of the existing methods used to conduct PIV analyses on dynamic centrifuge tests. Results indicate that PIV analysis in dynamic testing requires special measures in order to obtain reasonable deformation data. Nevertheless, it was possible to obtain interesting mechanisms regarding the behaviour of the tunnels from PIV analyses. © 2010 Taylor & Francis Group, London.

Closing the gap: Improved bounds on optimal POMDP solutions

POMDP algorithms have made significant progress in recent years by allowing practitioners to find good solutions to increasingly large problems. Most approaches (including point-based and policy iteration techniques) operate by refining a lower bound of the optimal value function. Several approaches (e.g., HSVI2, SARSOP, grid-based approaches and online forward search) also refine an upper bound. However, approximating the optimal value function by an upper bound is computationally expensive and therefore tightness is often sacrificed to improve efficiency (e.g., sawtooth approximation). In this paper, we describe a new approach to efficiently compute tighter bounds by i) conducting a prioritized breadth first search over the reachable beliefs, ii) propagating upper bound improvements with an augmented POMDP and iii) using exact linear programming (instead of the sawtooth approximation) for upper bound interpolation. As a result, we can represent the bounds more compactly and significantly reduce the gap between upper and lower bounds on several benchmark problems. Copyright © 2011, Association for the Advancement of Artificial Intelligence. All rights reserved.