Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.

Analysis of patterns in mining time series using Qlucore

Raw measurement data does not always immediately convey useful information, but applying mathematical statistical analysis tools into measurement data can improve the situation. Data analysis can offer benefits like acquiring meaningful insight from the dataset, basing critical decisions on the findings, and ruling out human bias through proper statistical treatment. In this thesis we analyze data from an industrial mineral processing plant with the aim of studying the possibility of forecasting the quality of the final product, given by one variable, with a model based on the other variables. For the study mathematical tools like Qlucore Omics Explorer (QOE) and Sparse Bayesian regression (SB) are used. Later on, linear regression is used to build a model based on a subset of variables that seem to have most significant weights in the SB model. The results obtained from QOE show that the variable representing the desired final product does not correlate with other variables. For SB and linear regression, the results show that both SB and linear regression models built on 1-day averaged data seriously underestimate the variance of true data, whereas the two models built on 1-month averaged data are reliable and able to explain a larger proportion of variability in the available data, making them suitable for prediction purposes. However, it is concluded that no single model can fit well the whole available dataset and therefore, it is proposed for future work to make piecewise non linear regression models if the same available dataset is used, or the plant to provide another dataset that should be collected in a more systematic fashion than the present data for further analysis.