Improved Shewhart Chart Using Multiscale Representation

Most univariate process monitoring techniques operate under three main assumptions, that the process residuals being evaluated are Gaussian, independent and contain a moderate level of noise. The performance of the conventional Shewhart chart, for example, is adversely affected when these assumptions are violated. Multiscale wavelet-based representation is a powerful data analysis tool that can help better satisfy these assumptions, i.e., decorrelate autocorrelated data, separate noise from features, and transform the data to better follow a Gaussian distribution at multiple scales. This research focused on developing an algorithm to extend the conventional Shewhart chart using multiscale representation to enhance its performance. Through simulated synthetic data, the developed multiscale Shewhart chart showed improved performance (with lower missed detection and false alarm rates) than the conventional Shewhart chart. The developed multiscale Shewhart chart was also applied to two real world applications, simulated distillation column data, and genomic copy number data, to illustrate the advantage of using the multiscale Shewhart chart for process monitoring over the conventional one

Enhanced Monitoring Using Multiscale Exponentially Weighted Moving Average Control Charts

The exponentially weighted moving average (EWMA) method is a widely used univariate process monitoring technique. This conventional EWMA technique is normally designed to optimize the out of control average run length (ARL1) specific to a fixed in control average run length (ARL0). This design procedure of EWMA technique is based on some assumptions – the evaluated process residuals are Gaussian, independent and contain moderate level of noise. Violation of these assumptions may adversely affect its fault detection abilities. Wavelet based multiscale representation of data is a powerful data analysis tool and has inherent properties that can help deal with these violations of assumptions, which thus improve the performance of EWMA through satisfying its assumptions. The main purpose of this work is to develop a multiscale EWMA technique with improved performance over the conventional technique and establish a design procedure for this method to optimize its parameters by minimizing the out of control average run length for different fault sizes and using a specified in control average run length assuming that the residuals are contaminated with zero mean Gaussian noise. Through several comparative studies using Monte Carlo simulations, it has been shown that the multiscale EWMA technique provides a better performance over the conventional method. Multiscale EWMA is shown to provide smaller ARL1 and missed detection rate with a slightly higher false alarm rate compared to the conventional EWMA technique not only when both the techniques are designed to perform optimally but also when data violate the assumptions of the EWMA chart. The advantages of the multiscale EWMA method over the conventional method are also illustrated through their application to monitor a simulated distillation column

Model-Based State Estimation for Fault Detection under Disturbance

The measurement of process states is critical for process monitoring, advanced process control, and process optimization. For chemical processes where state information cannot be measured directly, techniques such as state estimation need to be developed. Model-based state estimation is one of the most widely applied methods for estimation of unmeasured states basing on a high-fidelity process model. However, certain disturbances or unknown inputs not considered by process models will generate model-plant mismatch. In this dissertation, different model-based process monitoring techniques are developed and applied for state estimation under uncertainty and disturbance. Case studies are performed to demonstrate the proposed methods. The first case study estimates leak location from a natural gas pipeline. Non-isothermal state equations are derived for natural gas pipeline flow processes. A dual unscented Kalman filter is used for parameter estimation and flow rate estimation. To deal with sudden process disturbance in the natural gas pipeline, an unknown input observer is designed. The proposed design implements a linear unknown input observer with time-delays that considers changes of temperature and pressure as unknown inputs and includes measurement noise in the process. Simulation of a natural gas pipeline with time-variant consumer usage is performed. New optimization method for detection of simultaneous multiple leaks from a natural gas pipeline is demonstrated. Leak locations are estimated by solving a global optimization problem. The global optimization problem contains constraints of linear and partial differential equations, integer variable, and continuous variable. An adaptive discretization approach is designed to search for the leak locations. In a following case study, a new design of a nonlinear unknown input observer is proposed and applied to estimate states in a bioreactor. The design of such an observer is provided, and sufficient and necessary conditions of the observer are discussed. Experimental studies of batch and fed-batch operation of a bioreactor are performed using Saccharomyces cerevisiae strain mutant SM14 to produce β-carotene. The state estimation of the process from the designed observer is demonstrated to alleviate the model-plant mismatch and is compared to the experimental measurements