Enhanced Probabilistic Slow Feature Analysis - Dealing with Complexities in Industrial Process Data
Creators: Puli, Vamsi Krishna
Publisher: name: University of Alberta Library
Year: 2023

<p>In modern industrial processes, the measurement and storage of thousands of correlated process variables have become commonplace. Dimensionality reduction techniques are often employed to extract underlying informative patterns called features by discarding redundant information. Slow feature analysis is one such technique that focuses on extracting slowly varying patterns. A probabilistic extension was proposed to address data corruption caused by measurement noise. However, industrial process data is fraught with additional complexities, including periodic patterns from plant-wide oscillations, non-stationarity due to aging equipment, non-linearities, skewed noise distribution etc. The estimated parameter error will be large when a conventional probabilistic slow feature model is applied to complex industrial data. Hence, this thesis focuses on enhancing the probabilistic slow feature model to accommodate various industrial complexities.   Oscillatory behavior commonly arises in measured data as a result of poor controller tuning, stiction, and external oscillatory disturbances. Identifying and analyzing these oscillatory patterns is vital for monitoring control loops and diagnosing faults. Unfortunately, the presence of significant measurement noise prevents the conventional slow feature analysis from effectively extracting these patterns due to limitations in the model structure. Therefore, the primary contribution of this thesis is to develop an enhanced slow feature model that overcomes this limitation by relaxing the diagonal structure of the state-transition matrix and incorporating a block-diagonal matrix structure to accommodate complex poles. As a result, the enhanced slow feature analysis is called complex slow feature analysis in this thesis. Further, the drift-type non-stationary characteristics in measured variables also pose significant challenges for conventional slow feature extraction methods as the corresponding slow features are assumed stationary. Consequently, the second contribution of this thesis is to address this issue by introducing an additional latent variable that compensates for the drift-type non-stationary behaviour, thereby ensuring the stationarity of the extracted slow features. Due to the inherent non-linearity observed in complex industrial processes, we enhance the second contribution by incorporating an extended gated recurrent neural network architecture.         Process data commonly suffer from measurement issues like outliers and asymmetric noise distributions, impacting the quality and performance of extracted slow features. Our fourth contribution proposes a robust complex slow feature model that assumes a skewed t-distribution for measurement noise, rather than a Gaussian distribution. Model parameters are jointly estimated using the expectation-maximization algorithm. Additionally, high-dimensional datasets often stem from a low-dimensional latent space, and not all latent features influence all measured variables. Hence, it is crucial to ensure that only a subset of latent variables influences each measured variable. To address this, our fifth contribution introduces a novel model that automatically determines the optimal latent space dimension by employing a Laplace distribution to model the emission matrix, resulting in a sparse model. The conventional black-box nature of the slow feature model and its numerous extensions may lead to inconsistent or unacceptable results at the physical boundaries. Therefore, the final contribution integrates process knowledge into the probabilistic slow feature model to extract features that adhere to physical laws/limits.      The efficiency of all contributions is demonstrated through simulations and industrial/experimental case studies in which they are compared to state-of-the-art methods. This comparison yields conclusive evidence of their effectiveness.</p>