Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Asymptotic Recovery for Discrete-Time Systems

An asymptotic recovery design procedure is proposed for square, discrete-time, linear, time-invariant multivariable systems, which allows a state-feedback design to be approximately recovered by a dynamic output feedback scheme. Both the case of negligible processing time (compared to the sampling interval) and of significant processing time are discussed. In the former case, it is possible to obtain perfect. © 1985 IEEE.

A discrete dislocation analysis of fatigue crack growth

Cyclic loading of a plane strain mode I crack under small scale yielding is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic solid. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a non-singular complementary solution that enforces the boundary conditions, which is obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. An irreversible relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, which permits crack growth to emerge naturally. It is found that crack growth can occur under cyclic loading conditions even when the peak stress intensity factor is smaller than the stress intensity required for crack growth under monotonic loading conditions; however below a certain threshold value of ΔKI no crack growth was seen.

Discrete dislocation plasticity analysis of crack-tip fields in polycrystalline materials

Small scale yielding around a mode I crack is analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. The polycrystalline material is taken to consist of two types of square grains, one of which has a bcc-like orientation and the other an fcc-like orientation. For both orientations there are three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains is used to construct the polycrystalline materials. Consistent with the increasing yield strength of the polycrystalline material with decreasing grain size, the calculations predict a decrease in both the plastic zone size and the crack-tip opening displacement for a given applied mode I stress intensity factor. Furthermore, slip-band and kink-band formation is inhibited by all grain arrangements and, with decreasing grain size, the stress and strain distributions more closely resemble the HRR fields with the crack-tip opening approximately inversely proportional to the yield strength of the polycrystalline materials. The calculations predict a reduction in fracture toughness with decreasing grain size associated with the grain boundaries acting as effective barriers to dislocation motion.

Using Discrete Event Simulation (DES) to manage theatre operations in healthcare: An audit-based case study

This paper discusses the application of Discrete Event Simulation (DES) in modelling the complex relationship between patient types, case-mix and operating theatre allocation in a large National Health Service (NHS) Trust in London. The simulation model that was constructed described the main features of nine theatres, focusing on operational processes and patient throughput times. The model was used to test three scenarios of case-mix and to demonstrate the potential of using simulation modelling as a cost effective method for understanding the issues of healthcare operations management and the role of simulation techniques in problem solving. The results indicated that removing all day cases will reduce patient throughput by 23.3% and the utilization of the orthopaedic theatre in particular by 6.5%. This represents a case example of how DES can be used by healthcare managers to inform decision making. © 2008 IEEE.

Natural versus artificial scene classification by ordering discrete fourier power spectra

Holistic representations of natural scenes is an effective and powerful source of information for semantic classification and analysis of arbitrary images. Recently, the frequency domain has been successfully exploited to holistically encode the content of natural scenes in order to obtain a robust representation for scene classification. In this paper, we present a new approach to naturalness classification of scenes using frequency domain. The proposed method is based on the ordering of the Discrete Fourier Power Spectra. Features extracted from this ordering are shown sufficient to build a robust holistic representation for Natural vs. Artificial scene classification. Experiments show that the proposed frequency domain method matches the accuracy of other state-of-the-art solutions. © 2008 Springer Berlin Heidelberg.

On the relationship between hidden Markov Models and convex functional transforms for simulating scanning probe Microscopy

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution.In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.©2009 SPIE.

Constrained discriminative mapping transforms for unsupervised speaker adaptation

Discriminative mapping transforms (DMTs) is an approach to robustly adding discriminative training to unsupervised linear adaptation transforms. In unsupervised adaptation DMTs are more robust to unreliable transcriptions than directly estimating adaptation transforms in a discriminative fashion. They were previously proposed for use with MLLR transforms with the associated need to explicitly transform the model parameters. In this work the DMT is extended to CMLLR transforms. As these operate in the feature space, it is only necessary to apply a different linear transform at the front-end rather than modifying the model parameters. This is useful for rapidly changing speakers/environments. The performance of DMTs with CMLLR was evaluated on the WSJ 20k task. Experimental results show that DMTs based on constrained linear transforms yield 3% to 6% relative gain over MLE transforms in unsupervised speaker adaptation. © 2011 IEEE.