Abstract. Guided wave ultrasound has the potential to detect relatively large defects in continuously welded rail track at long range. As monitoring can be performed in near real time it would be acceptable to only detect fairly large cracks provided this is achieved prior to complete rail breakage. Heavy haul rail lines are inspected periodically by conventional ultrasound and sections with even relatively small cracks are removed; therefore, no sizable defects are available to demonstrate monitoring in the presence of realistic environmental operating conditions. Instead, we glued a small mass to the rail to simulate reflection from a crack and monitored the guided wave signals as the glue joint deteriorated over time. Data was collected over a two week period on an operational heavy haul line. A piezoelectric transducer mounted under the head of the rail was used in pulse-echo mode to transmit and receive a mode of propagation with energy confined mainly in the head of the rail. The small mass was attached under the head of the rail, at a distance of 375m from the transducer, using a cyanoacrylate glue, which was not expected to remain intact for long. Pre-processing of the collected signals involved rejection of signals containing train noise, averaging, filtering and dispersion compensation. Reflections from aluminothermic welds were used to stretch and scale the signals to reduce the influence of temperature variations. Singular value decomposition and independent component analysis were then applied to the signals with the aim of separating the reflection caused by the artificial defect from the background signal. The performance of these techniques was compared for different time spans. The reflection from the artificial defect showed unanticipated fluctuations.

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Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) has become the most popular algorithm for aspect modeling. While sufficiently successful in text topic extraction from large corpora, VB is less successful in identifying aspects in the presence of limited data. We present a novel variational message passing algorithm as applied to Latent Dirichlet Allocation (LDA) and compare it with the gold standard VB and collapsed Gibbs sampling. In situations where marginalisation leads to non-conjugate messages, we use ideas from sampling to derive approximate update equations. In cases where conjugacy holds, Loopy Belief update (LBU) (also known as Lauritzen-Spiegelhalter) is used. Our algorithm, ALBU (approximate LBU), has strong similarities with Variational Message Passing (VMP) (which is the message passing variant of VB). To compare the performance of the algorithms in the presence of limited data, we use data sets consisting of tweets and news groups. Additionally, to perform more fine grained evaluations and comparisons, we use simulations that enable comparisons with the ground truth via Kullback-Leibler divergence (KLD). Using coherence measures for the text corpora and KLD with the simulations we show that ALBU learns latent distributions more accurately than does VB, especially for smaller data sets.

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