On the applicability of the lognormal distribution in random dynamical systems

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.

Shock dynamics of random structures.

Predicting the response of a structure following an impact is of interest in situations where parts of a complex assembly may come into contact. Standard approaches are based on the knowledge of the impulse response function, requiring the knowledge of the modes and the natural frequencies of the structure. In real engineering structures the statistics of higher natural frequencies follows those of the Gaussian Orthogonal Ensemble, this allows the application of random point process theory to get a mean impulse response function by the knowledge of the modal density of the structure. An ensemble averaged time history for both the response and the impact force can be predicted. Once the impact characteristics are known in the time domain, a simple Fourier Transform allows the frequency range of the impact excitation to be calculated. Experimental and numerical results for beams, plates, and cylinders are presented to confirm the validity of the method.

Using sub-word-level information for confidence estimation with conditional random field models

The task of word-level confidence estimation (CE) for automatic speech recognition (ASR) systems stands to benefit from the combination of suitably defined input features from multiple information sources. However, the information sources of interest may not necessarily operate at the same level of granularity as the underlying ASR system. The research described here builds on previous work on confidence estimation for ASR systems using features extracted from word-level recognition lattices, by incorporating information at the sub-word level. Furthermore, the use of Conditional Random Fields (CRFs) with hidden states is investigated as a technique to combine information for word-level CE. Performance improvements are shown using the sub-word-level information in linear-chain CRFs with appropriately engineered feature functions, as well as when applying the hidden-state CRF model at the word level.

Efficient numerical models for investigating the statistics of random dynamic systems

The study of random dynamic systems usually requires the definition of an ensemble of structures and the solution of the eigenproblem for each member of the ensemble. If the process is carried out using a conventional numerical approach, the computational cost becomes prohibitive for complex systems. In this work, an alternative numerical method is proposed. The results for the response statistics are compared with values obtained from a detailed stochastic FE analysis of plates. The proposed method seems to capture the statistical behaviour of the response with a reduced computational cost.

Low temperature growth of ultra-high mass density carbon nanotube forests on conductive supports

We grow ultra-high mass density carbon nanotube forests at 450°C on Ti-coated Cu supports using Co-Mo co-catalyst. X-ray photoelectron spectroscopy shows Mo strongly interacts with Ti and Co, suppressing both aggregation and lifting off of Co particles and, thus, promoting the root growth mechanism. The forests average a height of 0.38 μm and a mass density of 1.6 g cm -3. This mass density is the highest reported so far, even at higher temperatures or on insulators. The forests and Cu supports show ohmic conductivity (lowest resistance ∼22 kΩ), suggesting Co-Mo is useful for applications requiring forest growth on conductors. © 2013 AIP Publishing LLC.

Evaluation of bimetallic catalysts for the growth of carbon nanotube forests

We systematically study the growth of carbon nanotube forests by chemical vapor deposition using evaporated monometallic or bimetallic Ni, Co, or Fe films supported on alumina. Our results show two regimes of catalytic activity. When the total thickness of catalyst is larger than nominally 1nm, bimetallic catalysts tend to outperform the equivalent layers of a single metal, yielding taller forests of multi-walled carbon nanotubes (CNTs). In contrast, for layers thinner than ~1nm, bimetallic catalysts are notably less active than individually. However, the amount of small diameter and single-walled CNTs is significantly increased. This possible transition at ~1nm might be related to different catalyst composition after annealing, depending whether or not the films overlap during evaporation and alloy during catalyst formation. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Random Forest Kernel and other kernels for big data from random partitions

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random Forest. To demonstrate the potential of this method, we propose two new kernels, the Random Forest Kernel and the Fast Cluster Kernel, and show that these kernels consistently outperform standard kernels on problems involving real-world datasets. Finally, we show how the form of these kernels lend themselves to a natural approximation that is appropriate for certain big data problems, allowing $O(N)$ inference in methods such as Gaussian Processes, Support Vector Machines and Kernel PCA.