Latent Variable Modeling with Slowness, Monotonicity, and Impulsivity Features
Creators: Chiplunkar, Ranjith Ravi Kumar
Publisher: name: University of Alberta Library
Year: 2022

<p>Data-driven modeling has been finding increasing prominence in process systems engineering in both academia and industries. Latent variable modeling forms an important component of data-driven modeling. Through latent variable modeling, not only can we deal with issues such as collinearity, noise, and high data dimensionality, but we can also impart the &quot;notions&quot; that we have regarding the process into the model. Imparting such notions makes the latent variables process-relevant and enhances the accuracy of the models. This thesis explores such ways of making the latent variables process-relevant by incorporating aspects such as slowness, monotonicity, and impulsivity that are commonly observed in various industrial processes. </p>

<pre><code>Many chemical engineering processes are typically characterized primarily by slow variations. The latent variables of such processes will be characterized by high temporal correlation or low velocities. This aspect is considered in slow feature analysis which is a latent variable method that aims to extract slowly varying features. Since the basic version of slow feature analysis is unsupervised, the first contribution of the thesis explores supervised learning of slow features through a linear model. In this case, the objective function of the slow feature analysis method is modified by adding a term that maximizes the correlation of the slow features with the output variables. Two such formulations are proposed to achieve the required objective and corresponding algorithms to achieve each objective are proposed. 

The second contribution extends the supervised slow feature extraction problem to a nonlinear case. The nonlinearity is achieved through the usage of Siamese neural networks. Siamese neural networks contain two identical networks that give them the ability to handle two samples at a time. Since the objective of slow feature analysis is to reduce the velocity of the latent variables, it needs to handle two samples simultaneously. Hence, this work uses the Siamese networks to perform supervised slow feature analysis. 

The third contribution of the thesis considers the monotonicity aspect in latent variable modeling for degrading processes. Processes that have degradation in either equipment or the quality of the process are overall non-stationarity in nature. Since degradation or damage usually evolves monotonically, latent variable modeling of such processes needs to include the monotonicity condition. This work proposes a state-space model to characterize such systems where the latent variable corresponding to the degrading component is modeled using a closed skew-normal random walk model, and other stationary variations are modeled by a Gaussian dynamic model. Here, the objective is to separate the monotonically degrading component of the data from other stationary variations for effective monitoring of the process. The resulting simultaneous state-and-parameter estimation problem is solved using the expectation-maximization approach and the smoothing algorithm is rigorously derived for a system defined by a closed skew-normal distribution random walk model. 

In the fourth contribution of the thesis, processes that are characterized by sudden or impulsive changes are studied. To characterize such behaviors the system is modeled using a state-space model with the dynamics of one of the states being defined by a Cauchy distribution. Since the Cauchy distribution has a fat tail, it can model the sudden jumps in a process. Hence, the resulting model has a mix of Cauchy and Gaussian latent variables, where the Cauchy latent variable models the sudden jumps and the Gaussian latent variables model other variations. The states and parameters of the resulting model are identified in a Bayesian manner using the variational Bayesian inference framework. The efficacy of all the contributions is verified through both numerical and relevant industrial case studies. 
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