GTM through time

The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (iid) vectors. For time series, however, the iid assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.

Acoustic emission and yield in sand

An experimental investigation into the Acoustic Emission (AE) response of sand has been undertaken, and the use of AE as a method of yield point identification has been assessed. Dense, saturated samples of sand were tested in conventional triaxial apparatus. The measurements of stresses and strains were carried out according to current research practice. The AE monitoring system was integrated with the soil mechanics equipment in such a way that sample disturbance was minimised. During monotonically loaded, constant cell pressure tests the total number of events recorded was found to increase at an increasing rate in a manner which may be approximated by a power law. The AE response of the sand was found to be both stress level and stress path dependent. Undrained constant cell pressure tests showed that, unlike drained tests, the AE event rate increased at an increasing rate; this was shown to correlate with the mean effective stress variation. The stress path dependence was most noticeable in extension tests, where the number of events recorded was an order of magnitude less than that recorded in comparable compression tests. This stress path dependence was shown to be due to the differences in the work done by the external stresses. In constant cell pressure tests containing unload/reload cycles it was found that yield could be identified from a discontinuity in the event rate/time curve which occurred during reloading. Further tests involving complex stress paths showed that AE was a useful method of yield point identification. Some tests involving large stress reversals were carried out, and AE identified the inverse yield points more distinctly than conventional methods of yield point identification.