Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

Condition monitoring and fault diagnosis of planetary gearboxes: A review

One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining class boundary just with the knowledge of positive class. The OCC problem has been considered and applied under many research themes, such as outlier/ novelty detection and concept learning. In this paper, we present a unified view of the general problem of OCC by presenting a taxonomy of study for OCC problems, which is based on the availability of training data, algorithms used and the application domains applied. We further delve into each of the categories of the proposed taxonomy and present a comprehensive literature review of the OCC algorithms, techniques and methodologies with a focus on their significance, limitations and applications. We conclude our paper by discussing some open research problems in the field of OCC and present our vision for future research.

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One-class classification: taxonomy of study and review of techniques

Vibration based condition monitoring and fault diagnosis of wind turbine planetary gearbox: A review

Two simple multivariate procedures for monitoring planetary gearboxes in non-stationary operating conditions

Spectral analysis is well-established analysis of vibrations used in diagnostics both in academia and industry. In general, one may identify components related to particular stages in the gearbox and analyze amplitudes of these components with a simple rule for decision-making: if amplitudes are increasing the condition becomes worse. However, usually one should analyze not single amplitude but at least several components, but: how to analyze them simultaneously? We have provided an example (case study) for planetary gearboxes in good and bad conditions (case B and case A). As diagnostic features we have used 15 amplitudes of spectral components related to fundamental planetary mesh frequency and its harmonics. Using Principal Component Analysis (PCA), it has been shown that amplitudes don't vary in the same way; change of condition affects not only amplitudes of all components in that sense, but also relation between them. We have investigated geometry of the data and it has been shown that the proportions of the explained total inertia of the three data sets (good, bad and mixed good/bad) are different. We claim that it may be a novel diagnostic approach to employ multidimensional analysis for accounting not only directly observed values but also interrelations both within and between the two groups of data. Different structure of the data is associated with different condition of the machines and such assumption is specified for the first time in the literature. Obviously it requires more studies.

https://iopscience.iop.org/article/10.1088/1742-6596/305/1/012075/pdf

Investigation on Spectral Structure of Gearbox Vibration Signals by Principal Component Analysis for Condition Monitoring Purposes

An application of outlier analysis for diagnosis of gearboxes working under non-stationary operating conditions is considered. The analysis is performed using quite large data characterizing (by 15 power spectrum amplitudes) two gearboxes, one in bad and the other in good condition. Analysis of Mahalanobis Distances in the two data sets shows that both of them are highly heterogeneous and non-Gaussian. A mapping of the data from the set 'good' to two dimensions by the non-linear Neuroscale method permits to visualize the data in a plane. Using the derived mapping, some decision boundaries (DBs) ? permitting to identify a given fraction alpha = 0.05 of low density outliers ? are constructed for the 'good' set. This is done using three methods: 1. Parzen kernel density, 2. mixture of Gaussians and 3. Suport Vector Data Description (SVDD). Each of the obtained DBs was tested using the bad data. For all 3 methods more than 98% of the bad data points were found outside the DBs constructed for the 'good' set.

https://iopscience.iop.org/article/10.1088/1742-6596/305/1/012031/pdf

Outliers analysis and one class classification approach for planetary gearbox diagnosis

http://labdiag.pwr.wroc.pl/radzim/papers/2014/aba.pdf

Dimensionality reduction via variables selection – Linear and nonlinear approaches with application to vibration-based condition monitoring of planetary gearbox

Anna Bartkowiak

Papers

Two simple multivariate procedures for monitoring planetary gearboxes in non-stationary operating conditions

Investigation on Spectral Structure of Gearbox Vibration Signals by Principal Component Analysis for Condition Monitoring Purposes

Outliers analysis and one class classification approach for planetary gearbox diagnosis

Dimensionality reduction via variables selection – Linear and nonlinear approaches with application to vibration-based condition monitoring of planetary gearbox

Novel method of informative frequency band selection for vibration signal using Nonnegative Matrix Factorization of spectrogram matrix