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.

Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Discriminative spoken language understanding using word confusion networks

Current commercial dialogue systems typically use hand-crafted grammars for Spoken Language Understanding (SLU) operating on the top one or two hypotheses output by the speech recogniser. These systems are expensive to develop and they suffer from significant degradation in performance when faced with recognition errors. This paper presents a robust method for SLU based on features extracted from the full posterior distribution of recognition hypotheses encoded in the form of word confusion networks. Following [1], the system uses SVM classifiers operating on n-gram features, trained on unaligned input/output pairs. Performance is evaluated on both an off-line corpus and on-line in a live user trial. It is shown that a statistical discriminative approach to SLU operating on the full posterior ASR output distribution can substantially improve performance both in terms of accuracy and overall dialogue reward. Furthermore, additional gains can be obtained by incorporating features from the previous system output. © 2012 IEEE.

Dynamical structure function identifiability conditions enabling signal structure reconstruction

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars. © 2012 IEEE.

Dissipativity characterization of a class of oscillators and networks of oscillators

This paper uses dissipativity theory to provide the system-theoretic description of a basic oscillation mechanism. Elementary input-output tools are then used to prove the existence and stability of limit cycles in these "oscillators". The main benefit of the proposed approach is that it is well suited for the analysis and design of interconnections, thus providing a valuable mathematical tool for the study of networks of coupled oscillators.

A framework for the analysis of thermal losses in reciprocating compressors and expanders

This article presents a framework that describes formally the underlying unsteady and conjugate heat transfer processes that are undergone in thermodynamic systems, along with results from its application to the characterization of thermodynamic losses due to irreversible heat transfer during reciprocating compression and expansion processes in a gas spring. Specifically, a heat transfer model is proposed that solves the one-dimensional unsteady heat conduction equation in the solid simultaneously with the first law in the gas phase, with an imposed heat transfer coefficient taken from suitable experiments in gas springs. Even at low volumetric compression ratios (of 2.5), notable effects of unsteady heat transfer to the solid walls are revealed, with thermally induced thermodynamic cycle (work) losses of up to 14% (relative to the work input/output in equivalent adiabatic and reversible compression/expansion processes) at intermediate Péclet numbers (i.e., normalized frequencies) when unfavorable solid and gas materials are selected, and closer to 10-12% for more common material choices. The contribution of the solid toward these values, through the conjugate variations attributed to the thickness of the cylinder wall, is about 8% and 2% points, respectively, showing a maximum at intermediate thicknesses. At higher compression ratios (of 6) a 19% worst-case loss is reported for common materials. These results suggest strongly that in designing high-efficiency reciprocating machines the full conjugate and unsteady problem must be considered and that the role of the solid in determining performance cannot, in general, be neglected. © 2014 Richard Mathie, Christos N. Markides, and Alexander J. White. Published with License by Taylor & Francis.

Linear dimensionality reduction: Survey, insights, and generalizations

© 2015 John P. Cunningham and Zoubin Ghahramani. Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.

Engineering design and mechatronics: The schemebuilder project

The paper describes the development of a software design aid for use at the conceptual stage of engineering design. It is intended for use in the design of mechatronic products but has wider potential uses. Early approaches were based on function structures and tables of options and the system that evolved allows the assembly of schemes linked by matching their input and output ports. A database of components is provided which can be accessed via different indexes and the designer can easily create and compare alternative schemes at the concept stage. A bond graph approach is used to define the interconnections between components. This allows correct port matching but also provides for future development such as constraint propagation through the design and links to simulation tools. © 1993 Springer-Verlag New York Inc.

Recurrent input transformations for Hidden Markov models

This paper presents a new architecture which integrates recurrent input transformations (RIT) and continuous density HMMs. The basic HMM structure is extended to accommodate recurrent neural networks which transform the input observations before they enter the Gaussian output distributions associated with the states of the HMM. During training the parameters of both HMM and RIT are simultaneously optimized according to the Maximum Mutual Information (MMI) criterion. Results are presented for the E-set recognition task which demonstrate the ability of recurrent input transformations to exploit longer term correlations in the speech signal and to give improved discrimination.

Gaussian Process training with input noise

In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d. Gaussian noise. To make computations tractable we use a local linear expansion about each input point. This allows the input noise to be recast as output noise proportional to the squared gradient of the GP posterior mean. The input noise variances are inferred from the data as extra hyperparameters. They are trained alongside other hyperparameters by the usual method of maximisation of the marginal likelihood. Training uses an iterative scheme, which alternates between optimising the hyperparameters and calculating the posterior gradient. Analytic predictive moments can then be found for Gaussian distributed test points. We compare our model to others over a range of different regression problems and show that it improves over current methods.