Efficient Approaches to Steady State Detection in Multivariate Systems
Steady state detection is critically important in many engineering fields such as fault detection and diagnosis, process monitoring and control. However, most of the existing methods are designed for univariate signals. In this dissertation, we proposed an efficient online steady state detection method for multivariate systems through a sequential Bayesian partitioning approach. The signal is modeled by a Bayesian piecewise constant mean and covariance model, and a recursive updating method is developed to calculate the posterior distributions analytically. The duration of the current segment is utilized to test the steady state. Insightful guidance is provided for hyperparameter selection. The effectiveness of the proposed method is demonstrated through thorough simulation and real-world case studies. Initial bias truncation is critically important for system performance assessment and warm- up length estimation in discrete-event simulations. Most of the existing methods are for univariate signals, while multivariate truncation has been rarely studied. To fill this gap, this dissertation proposes an efficient method, called adaptive minimal confidence region rule (AMCR) for multivariate initial bias truncation. It determines the truncation point by minimizing the modified confidence volume with a tuning parameter for the mean estimate. An elbow method is developed for adaptive selection of the tuning parameter. Theoretical properties of the AMCR rule have been derived for justification and practical guidance. The effectiveness and superiority of the AMCR rule over other existing approaches have been demonstrated through thorough numerical studies and real application. However, AMCR has some issues. First, if the covariance matrix is ill-conditioned matrix, we cannot get the sample generalized variance reliably. Second, AMCR is a division form. When the truncation point is very close to the sample size, it’s easy to become inaccurate. Third, AMCR has a time-consuming problem for high dimension and sample size. After applying bootstrap method, we can get the accurate estimates of sample generalized variance so as to improve the accuracy of initialization bias truncation. An efficient method named adaptive minimal confidence region rule with bootstrap (AMCR-B) has been developed for initial bias truncation of the multivariate systems. The basic idea of this method based on AMCR rule is to determine the optimal truncation point. The log-transformation is used to avoid the division form and the sample generalized variance is also recalculated. The bootstrap sampling method will be used to resample the data and then get the distribution of the sample generalized variance. Then, we need to select the quantile for bootstrap. The algorithm of sample generalized variance will be improved. The tuning parameter will be selected by elbow method automatically and directly. The performance of the proposed method was evaluated and compared with existing ones through numerical studies. The simulation results demonstrated that the proposed methods outperforms others for various types of signals. The evaluation and comparison results indicate that the proposed method can accurately estimate the truncation point for various multivariate output of different bias shapes and severity, and is superior to the existing methods in terms of truncation accuracy. The results of this research provide useful guidelines for establishing an online steady state detection scheme.
Industrial engineering|Computer Engineering|Statistics
Xu, Honglun, "Efficient Approaches to Steady State Detection in Multivariate Systems" (2022). ETD Collection for University of Texas, El Paso. AAI29323727.