Closely correlating lower and upper bound plastic analysis of real slabs

An engineer assessing the load-carrying capacity of an existing reinforced concrete slab is likely to use elastic analysis to check the load at which the structure might be expected to fail in flexure or in shear. In practice, many reinforced concrete slabs are highly ductile in flexure, so an elastic analysis greatly underestimates the loads at which they fail in this mode. The use of conservative elastic analysis has led engineers to incorrectly condemn many slabs and therefore to specify unnecessary and wasteful flexural strengthening or replacement. The lower bound theorem is based on the same principles as the upper bound theorem used in yield line analysis, but any solution that rigorously satisfies the lower bound theorem is guaranteed to be a safe underestimate of the collapse load. Jackson presented a rigorous lower bound method that obtains very accurate results for complex real slabs.

Optimisation of passive and semi-active heavy vehicle suspensions

An investigation into the potential for reducing road damage by optimising the design of heavy vehicle suspensions is described. In the first part of the paper two simple mathematical models are used to study the optimisation of conventional passive suspensions. Simple modifications are made to the steel spring suspension of a tandem axle trailer and it is found experimentally that RMS dynamic tyre forces can be reduced by 15% and theoretical road damage by 5.2%. A mathematical model of an air-sprung articulated vehicle is validated, and its suspension is optimised according to the simple models. This vehicle generates about 9% less damage than the leaf-sprung vehicle in the unmodified state and it is predicted that, for the operating conditions examined, the road damage caused by this vehicle can be reduced by a further 5.4%. Finally, it is shown experimentally that computer-controlled semi-active dampers have the potential to reduce road damage by a further 5-6%, compared to an air suspension with optimum passive damping. © Copyright 1994 Society of Automotive Engineers, Inc.

A Bayesian framework to predict deformations during supported excavations based on a semi-empirical method

The ground movements induced by the construction of supported excavation systems are generally predicted by empirical/semi-empirical methods in the design stage. However, these methods cannot account for the site-specific conditions and for information that becomes available as an excavation proceeds. A Bayesian updating methodology is proposed to update the predictions of ground movements in the later stages of excavation based on recorded deformation measurements. As an application, the proposed framework is used to predict the three-dimensional deformation shapes at four incremental excavation stages of an actual supported excavation project. © 2011 Taylor & Francis Group, London.

Reliability analysis of deep excavation based on a semi-empirical approach

The design and construction of deep excavations in urban environment is often governed by serviceability limit state related to the risk of damage to adjacent buildings. In current practice, the assessment of excavation-induced building damage has focused on a deterministic approach. This paper presents a component/system reliability analysis framework to assess the probability that specified threshold design criteria for multiple serviceability limit states are exceeded. A recently developed Bayesian probabilistic framework is used to update the predictions of ground movements in the later stages of excavation based on the recorded deformation measurements. An example is presented to show how the serviceability performance for excavation problems can be assessed based on the component/system reliability analysis. © 2011 ASCE.

A Bayesian framework to predict deformations during supported excavations based on a semi-empirical method

The ground movements induced by the construction of supported excavation systems are generally predicted in the design stage by empirical/semi-empirical methods. However, these methods cannot account for the site-specific conditions and for information that become available as an excavation proceeds. A Bayesian updating methodology is proposed to update the predictions of ground movements in the later stages of excavation based on recorded deformation measurements. As an application, the proposed framework is used to predict the three-dimensional deformation shapes at four incremental excavation stages of an actual supported excavation project. Copyright © ASCE 2011.

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

Models for acoustic propagation through turbofan exhaust flows

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of previous solutions is that they do not allow for the jet nozzle to protrude a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). In this paper we use the matrix Wiener-Hopf technique, which will allow precisely the finite nacelle-jet nozzle separation to be included. The crucial step in our work is to factorise a certain matrix as a product of terms analytic and invertible in the upper/lower halves of the complex plane. The way we do this matrix factorisation is quite different in the buried and protruding nozzle cases. In the buried case our solution method is the so-called pole-removal technique. In the technically more demanding protruding case, however, we must first use Pade approximants to generate a uniformly-valid, meromorphic representation of a certain function, before the same pole-removal method can be applied. Sample results are presented, investigating in particular the effects of exit plane stagger. © 2007 by B Veitch and N Peake.