| Process data suffers from many different types of imperfections, for example, bad data due to sensor problems, multi-rate data, outliers, data compression etc. Since most modeling and data analysis methods are developed to analyze regularly sampled and well conditioned data sets there is a need for pre-treatment of data. Traditionally these imperfections have been viewed as unrelated problems and dealt individually. In this thesis we treat these diverse problems under the general framework of 'treatment of missing data'. A vast amount of literature on the statistical analysis of data with missing values has flourished over last three decades mainly dealing with statistical surveys and biomedical data analysis. Therefore, the objectives of this study are to: (i) establish the link between the missing data literature and the process data analysis, so that the process engineering community can take advantage of these methods, (ii) extend some of the commonly used process data analysis tools using these formal methods for building models from data matrix with missing values and (iii) implement novel applications of missing data handling techniques in solving problems which may not appear as missing data problem directly.; This thesis has two main parts. Part-I of this thesis deals with 'off-line' modeling of 'latent variable models'. Principal Component Analysis (PCA), Iterative-PCA (IPCA) and Maximum Likelihood Factor Analysis (MLFA) are extended to the Data Augmentation framework for dealing with missing values. Missing data handling techniques have been applied to synchronize uneven length batch process data and recover the correlation between compressed signals. Data pre-processing issues other than missing values have been dealt with in relation to an industrial case study where PCA was used to detect sheet-breaks in a paper mill.; Part-II of the thesis deals with the 'on-line' filtering problem. The Sequential Monte Carlo (SMC) filter is extended to a Multiple Imputation framework for updating the filter with multi-rate measurements.; The improved performance of the proposed methods have been demonstrated using simulated examples, experimental data and industrial case study. |
