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.

Predicting the response of structures to transient shock loading.

This work concerns the prediction of the response of an uncertain structure to a load of short duration. Assuming an ensemble of structures with small random variations about a nominal form, a mean impulse response can be found using only the modal density of the structure. The mean impulse response turns out to be the same as the response of an infinite structure: the response is calculated by taking into account the direct field only, without reflections. Considering the short duration of an impulsive loading, the approach is reasonable before the effect of the reverberant field becomes important. The convolution between the mean impulse response and the shock loading is solved in discrete time to calculate the response at the driving point and at remote points. Experimental and numerical examples are presented to validate the theory presented for simple structures such as beams, plates, and cylinders.

Temporally adaptive estimation of logistic classifiers on data streams

Modern technology has allowed real-time data collection in a variety of domains, ranging from environmental monitoring to healthcare. Consequently, there is a growing need for algorithms capable of performing inferential tasks in an online manner, continuously revising their estimates to reflect the current status of the underlying process. In particular, we are interested in constructing online and temporally adaptive classifiers capable of handling the possibly drifting decision boundaries arising in streaming environments. We first make a quadratic approximation to the log-likelihood that yields a recursive algorithm for fitting logistic regression online. We then suggest a novel way of equipping this framework with self-tuning forgetting factors. The resulting scheme is capable of tracking changes in the underlying probability distribution, adapting the decision boundary appropriately and hence maintaining high classification accuracy in dynamic or unstable environments. We demonstrate the scheme's effectiveness in both real and simulated streaming environments. © Springer-Verlag 2009.

The ensemble statistics of the band-averaged energy of a random system

This paper is concerned with the response statistics of a dynamic system that has random properties. The frequency-band-averaged energy of the system is considered, and a closed form expression is derived for the relative variance of this quantity. The expression depends upon three parameters: the modal overlap factor m, a bandwidth parameter B, and a parameter α that defines the nature of the loading (for example single point forcing or rain-on-the-roof loading). The result is applicable to any single structural component or acoustic volume, and a comparison is made here with simulation results for a mass loaded plate. Good agreement is found between the simulations and the theory. © 2003 Published by Elsevier Ltd.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.