Towards identification of a general model of damping

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.

The modified Kanerva model for automatic speech recognition

A parallel processing network derived from Kanerva's associative memory theory Kanerva 1984 is shown to be able to train rapidly on connected speech data and recognize further speech data with a label error rate of 0·68%. This modified Kanerva model can be trained substantially faster than other networks with comparable pattern discrimination properties. Kanerva presented his theory of a self-propagating search in 1984, and showed theoretically that large-scale versions of his model would have powerful pattern matching properties. This paper describes how the design for the modified Kanerva model is derived from Kanerva's original theory. Several designs are tested to discover which form may be implemented fastest while still maintaining versatile recognition performance. A method is developed to deal with the time varying nature of the speech signal by recognizing static patterns together with a fixed quantity of contextual information. In order to recognize speech features in different contexts it is necessary for a network to be able to model disjoint pattern classes. This type of modelling cannot be performed by a single layer of links. Network research was once held back by the inability of single-layer networks to solve this sort of problem, and the lack of a training algorithm for multi-layer networks. Rumelhart, Hinton & Williams 1985 provided one solution by demonstrating the "back propagation" training algorithm for multi-layer networks. A second alternative is used in the modified Kanerva model. A non-linear fixed transformation maps the pattern space into a space of higher dimensionality in which the speech features are linearly separable. A single-layer network may then be used to perform the recognition. The advantage of this solution over the other using multi-layer networks lies in the greater power and speed of the single-layer network training algorithm. © 1989.

A model for nonlinear viscoelastic mechanical responses of collagenous soft tissues

Experimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasi-linear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and time-dependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasi-linear viscoelastic approach. © 2006 Materials Research Society.

Surface excavation with model predictive control

This paper describes the application of variable-horizon model predictive control to trajectory generation in surface excavation. A nonlinear dynamic model of a surface mining machine digging in oil sand is developed as a test platform. This model is then stabilised with an inner-loop controller before being linearised to generate a prediction model. The linear model is used to design a predictive controller for trajectory generation. A variable horizon formulation is augmented with extra terms in the cost function to allow more control over digging, whilst still preserving the guarantee of finite-time completion. Simulations show the generation of realistic trajectories, motivating new applications of variable horizon MPC for autonomy that go beyond the realm of vehicle path planning. ©2010 IEEE.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

Application of the fixed point method for solution in time stepping finite element analysis using the inverse vector Jiles-Atherton model

An implementation of the inverse vector Jiles-Atherton model for the solution of non-linear hysteretic finite element problems is presented. The implementation applies the fixed point method with differential reluctivity values obtained from the Jiles-Atherton model. Differential reluctivities are usually computed using numerical differentiation, which is ill-posed and amplifies small perturbations causing large sudden increases or decreases of differential reluctivity values, which may cause numerical problems. A rule based algorithm for conditioning differential reluctivity values is presented. Unwanted perturbations on the computed differential reluctivity values are eliminated or reduced with the aim to guarantee convergence. Details of the algorithm are presented together with an evaluation of the algorithm by a numerical example. The algorithm is shown to guarantee convergence, although the rate of convergence depends on the choice of algorithm parameters. © 2011 IEEE.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

Convex approaches to model wavelet sparsity patterns

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso. © 2011 IEEE.

A model for diffusive and displacive phase transitions: Thermo-chemo-mechanical coupling effects

A diffuse interface phase field model is proposed for the unified analysis of diffusive and displacive phase transitions under nonisothermal conditions. Two order parameters are used for the description of the phenomena: one is related to the solute mass fraction and the other to the strain. The model governing equations come from the balance of linear momentum, the solute mass balance (which will lead to the Cahn-Hilliard equation) and the balance of internal energy. Thermodynamic restrictions allow to define constitutive relations for the thermodynamic forces and for the mechanical and chemical dissipations. Numerical tests carried out at different values of the initial temperature show that the model is able to describe the main features of both the displacive and the diffusive phase transitions, as well as their effect on the temperature. © 2010, Advanced Engineering Solutions.

Shape Recognition of Linear Construction Entities from Construction Site Images

The capability to automatically identify shapes, objects and materials from the image content through direct and indirect methodologies has enabled the development of several civil engineering related applications that assist in the design, construction and maintenance of construction projects. This capability is a product of the technological breakthroughs in the area of Image Processing that has allowed for the development of a large number of digital imaging applications in all industries. In this paper, an automated and content based shape recognition model is presented. This model was devised to enhance the recognition capabilities of our existing material based image retrieval model. The shape recognition model is based on clustering techniques, and specifically those related with material and object segmentation. The model detects the borders of each previously detected material depicted in the image, examines its linearity (length/width ratio) and detects its orientation (horizontal/vertical). The results emonstrate the suitability of this model for construction site image retrieval purposes and reveal the capability of existing clustering technologies to accurately identify the shape of a wealth of materials from construction site images.

Combustion rumble prediction with integrated computational-fluid-dynamics/ low-order-model methods

The pressure oscillation within combustion chambers of aeroengines and industrial gas turbines is a major technical challenge to the development of high-performance and low-emission propulsion systems. In this paper, an approach integrating computational fluid dynamics and one-dimensional linear stability analysis is developed to predict the modes of oscillation in a combustor and their frequencies and growth rates. Linear acoustic theory was used to describe the acoustic waves propagating upstream and downstream of the combustion zone, which enables the computational fluid dynamics calculation to be efficiently concentrated on the combustion zone. A combustion oscillation was found to occur with its predicted frequency in agreement with experimental measurements. Furthermore, results from the computational fluid dynamics calculation provide the flame transfer function to describe unsteady heat release rate. Departures from ideal one-dimensional flows are described by shape factors. Combined with this information, low-order models can work out the possible oscillation modes and their initial growth rates. The approach developed here can be used in more general situations for the analysis of combustion oscillations. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

Thermal modelling of a tubular linear machine for marine renewable generation

A lumped parameter thermal model has been constructed for a tubular linear machine that has been designed for use in a marine environment. It shows good correlation to both steady state and transient experimental tests on the machine. The model has been developed for a stationary machine in a laboratory environment - the modelling techniques used and enhancements to enable the application of the model directly to marine scenarios are discussed.

Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

Optimal constraint tightening policies for robust variable horizon model predictive control

This paper develops a technique for improving the region of attraction of a robust variable horizon model predictive controller. It considers a constrained discrete-time linear system acted upon by a bounded, but unknown time-varying state disturbance. Using constraint tightening for robustness, it is shown how the tightening policy, parameterised as direct feedback on the disturbance, can be optimised to increase the volume of an inner approximation to the controller's true region of attraction. Numerical examples demonstrate the benefits of the policy in increasing region of attraction volume and decreasing the maximum prediction horizon length. © 2012 IEEE.