Strength mobilization in clays and silts

A large database of 115 triaxial, direct simple shear, and cyclic tests on 19 clays and silts is presented and analysed to develop an empirical framework for the prediction of the mobilization of the undrained shear strength, cu, of natural clays tested from an initially isotropic state of stress. The strain at half the peak undrained strength (γM=2) is used to normalize the shear strain data between mobilized strengths of 0.2cu and 0.8cu. A power law with an exponent of 0.6 is found to describe all the normalized data within a strain factor of 1.75 when a representative sample provides a value for γM=2. Multi-linear regression analysis shows that γM=2 is a function of cu, plasticity index Ip, and initial mean effective stress p′0. Of the 97 stress-strain curves for which cu, Ip, and p′0 were available, the observed values of γM=2 fell within a factor of three of the regression; this additional uncertainty should be acknowledged if a designer wished to limit immediate foundation settlements on the basis of an undrained strength profile and the plasticity index of the clay. The influence of stress history is also discussed. The application of these stress-strain relations to serviceability design calculations is portrayed through a worked example. The implications for geotechnical decision-making and codes of practice are considered.

Mathematical relationships between representations of structure in linear interconnected dynamical systems

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relationships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example. © 2011 AACC American Automatic Control Council.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Preloaded hopping with linear multi-modal actuation

For more dexterous and agile legged robot locomotion, alternative actuation has been one of the most long-awaited technologies. The goal of this paper is to investigate the use of newly developed actuator, the so-called Linear Multi-Modal Actuator (LMMA), in the context of legged robot locomotion, and analyze the behavioral performance of it. The LMMA consists of three discrete couplings which enable the system to switch between different mechanical dynamics such as instantaneous switches between series elastic and fully actuated dynamics. To test this actuator for legged locomotion, this paper introduces a one-legged robot platform we developed to implement the actuator, and explains a novel control strategy for hopping, i.e. 'preloaded hopping control'. This control strategy takes advantage of the coupling mechanism of the LMMA to preload the series elasticity during the flight phase to improve the energy efficiency of hopping locomotion. This paper shows a series of experimental results that compare the control strategy with a simple sinusoidal actuation strategy to discuss the benefits and challenges of the proposed approach. © 2013 IEEE.

Linear multi-modal actuation through discrete coupling

Due to technological limitations robot actuators are often designed for specific tasks with narrow performance goals, whereas a wide range of output and behaviours is necessary for robots to operate autonomously in uncertain complex environments. We present a design framework that employs dynamic couplings in the form of brakes and clutches to increase the performance and diversity of linear actuators. The couplings are used to switch between a diverse range of discrete modes of operation within a single actuator. We also provide a design solution for miniaturized couplings that use dry friction to produce rapid switching and high braking forces. The couplings are designed so that once engaged or disengaged no extra energy is consumed. We apply the design framework and coupling design to a linear series elastic actuator (SEA) and show that this relatively simple implementation increases the performance and adds new behaviours to the standard design. Through a number of performance tests we are able to show rapid switching between a high and a low impedance output mode; that the actuator's spring can be charged to produce short bursts of high output power; and that the actuator has additional passive and rigid modes that consume no power once activated. Robots using actuators from this design framework would see a vast increase in their behavioural diversity and improvements in their performance not yet possible with conventional actuator design. © 2012 IEEE.

Multi-channel signal separation

The separation of independent sources from mixed observed data is a fundamental and challenging problem. In many practical situations, observations may be modelled as linear mixtures of a number of source signals, i.e. a linear multi-input multi-output system. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include EEG signals, passive sonar applications and cross-talk in data communications. In this paper, we propose iterative algorithms to solve the n × n linear time invariant system under two different constraints. Some existing solutions for 2 × 2 systems are reviewed and compared.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Quantitative convergence analysis of multi-agent systems

We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions of contractiveness and (weak) connectedness (across an interval.) Convergence is shown to be exponential when either the system or the function characterizing the contraction is linear. Copyright © 2007 IFAC.

A self-adaptive genetic algorithm applied to multi-objective optimization of an airfoil

Genetic algorithms (GAs) have been used to tackle non-linear multi-objective optimization (MOO) problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the numbers of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimizing GA (MOGA) that uses self-adaptive mutation and crossover, and which is applied to optimization of an airfoil, for minimization of drag and maximization of lift coefficients. The MOGA is integrated with a Free-Form Deformation tool to manage the section geometry, and XFoil which evaluates each airfoil in terms of its aerodynamic efficiency. The performance is compared with those of the heuristic MOO algorithms, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this GA achieves better convergence.