Symbolic Identification of Dynamical Systems: Theory and Experimental Validation
Open Access
- Author:
- Chakraborty, Subhadeep
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 03, 2010
- Committee Members:
- Asok Ray, Dissertation Advisor/Co-Advisor
Asok Ray, Committee Chair/Co-Chair
Matthew M Mench, Committee Member
Jeffrey Scott Mayer, Committee Member
Shashi Phoha, Committee Member - Keywords:
- Fault Detection and Isolation
Symbolic Dynamics
System Identification
Time Series Data Analysis
PMSM
C-MAPSS
Refractory Failure in Slagging Gasifiers - Abstract:
- This dissertation addresses some of the critical and practical issues in health monitoring of multi-component human-engineered systems. The inherent complexity and uncertainty in complex systems pose a challenging problem to health monitoring, since first principle models of these systems, are usually oversimplified, inaccurate, or may not be available at all. Human-engineered multi-component systems are usually interconnected physically as well as through the use of feedback control loops. Therefore, the degradation of a single component may affect the input streams to the remaining components. Furthermore, in most practical situations, the underlying system might need to operate in different operating regimes and under diverse input conditions. The purpose of the work reported in this dissertation is to develop a robust and computationally inexpensive system identification technique based on a formal language-theoretic formulation from the input/output characteristics. The objective here is to make the identification algorithm invariant with the input conditions, but it should be sensitive to changes in the parameters of the actual dynamical system. The proposed method involves abstraction of a qualitative description from a general dynamical system structure, using state space embedding of the output and input data-stream and discretization of the resultant pseudo-state and input spaces. The system identification is achieved through grammatical inference techniques, and the information is extracted in a compressed form as statistical patterns of evolving anomaly through usage of symbolic dynamic filtering (SDF) serving as the feature extractor. Support vector machines (SVM) have been used for classification between nominal and faulty cases with a rigorous mathematical framework of detection rates. Conditions for monotonicity of the symmetric Kullback-Leibler relative entropy with deteriorating fault conditions have been derived and a bound on the model likelihood has been proposed based on Lyapunov exponents. The proposed theory has been validated on several experimental and simulation test-beds. The first of these test-beds is a permanent magnet synchronous motor undergoing a gradual degradation of the magnetic flux linkage under diverse loading conditions. This concept has also been used for fault detection on a commercial-scale two-spool turbofan engine simulation model, provided by NASA. Another experiment involves development of an integrated computer simulation model of a generic entrained-bed slagging gasifier for real-time degradation monitoring and condition-based maintenance of refractory walls. The integrated simulation model yields: (a) quasi-steady-state spatial temperature profiles at any cross-section of the gasification system, and (b) dynamic response of the refractory wall temperature that is measured by an array of sensors installed at specified locations on the external surface of the gasifier wall. The information from dynamic response of refractory temperature is processed to characterize the health status of refractory walls in the gasification system.