Research On Data Dimensionality Reduction And Re-lated Issues In Nonlinear Process Monitoring

Process monitoring based on measurement data is very useful for the maintenance of process safety and stability. While numerous variables are measured in modern indus-trial processes, there usually exist severe dependencies among them and high-dimensional process data is actually driven by fewer intrinsic free variables due to the underlying mass/energy balance and other operational constraints. How to effectively perform dimen-sionality reduction to discard redundancy and reveal intrinsic lower-dimensional structure in complex process data is a basic issue in process monitoring. Most traditional monitoring methods are based on linear multivariate statistical methods and not effective for prevalent nonlinear processes. From the perspective of data dimensionality reduction, this disserta-tion focuses on dealing with deficiencies in existing nonlinear process monitoring methods and proposing more effective monitoring methods, and the validity and superiority of the proposed methods are demonstrated on benchmark simulation and real world processes. The contribution of this dissertation is summarized as follows.Ⅰ. A new unsupervised dimensionality reduction method named maximum variance unfolding projections (MVUP) and MVUP-based nonlinear fault detection and iso-lation methods are proposed. MVUP approximates the underlying nonlinear dimen-sionality reduction mapping of the manifold learning method maximum variance un-folding (MVU) by linear projection, inheriting its nonlinear structure unfolding and distribution boundary preserving features. The MVUP-based monitoring method has very low online computational cost and comparable effectiveness to state-of-the-art nonlinear monitoring methods.Ⅱ. A kernel function learning method is proposed for kernel unsupervised dimensional-ity reduction (KUDR) (e.g. KPCA, KICA) methods which have been widely used in nonlinear fault detection. Nonlinear structure in data is unfolded to be linear in the kernel feature space corresponding to the learned optimal kernel. Therefore, KUDR using the optimal kernel can effectively explain data variation by performing a linear method in the kernel feature space, leading to improved detection performance.Ⅲ. A new KUDR method named kernel orthogonal locality preserving projections (KOLPP) and KOLPP-based fault detection method are proposed. KOLPP is the kernel gen-eralization of OLPP method and explicitly consider the underlying nonlinear struc-ture in data. KOLPP has more structure preserving power than other popular KUDR methods, leading to better detection performance.Ⅳ. To overcome the drawbacks of existing fault recognition methods due to using the Fisher's criterion, a new supervised dimensionality reduction method named local-ity preserving discriminant analysis (LPDA) and its kernel generalization KLPDA are proposed for nonlinear fault recognition. (K)LPDA directly target at minimizing local overlapping among different classes and can provide better recognition perfor-mance than existing methods.Ⅴ. To overcome the drawbacks of using extended vector for incorporating process dy-namic information, an extended matrix-based scheme is proposed. LPDA is extended to Tensor LPDA (TLPDA) which can deal with matrices directly. A dynamic fault recognition method based on extended matrix and TLPDA is proposed.Ⅵ. With theκ-nearest neighbor distance (dκ) as outlying measure which is effective for nonlinear data set, a fast outlier detection algorithm named NeighborHood Pruning (NHP) is proposed for preprocessing training data. NHP derives upper bounds of dk for other data points when performing each dκquery, which are used for pruning non-outliers and reducing the number of dκqueries. The searching order is optimized to increase the number of pruning and reduce the computational cost of each dκquery.