Observer-Based Parameter Estimation for Linear Uncertain Discrete-Time Systems

Presented is an observer-based parameter estimation solution for a class of linear, discrete-time systems. The proposed formulation embeds the problem of parameter estimation within a parametric uncertain observer formulation where the state and output matrices are expressed as and . The methodology is developed by creating general solutions for the uncertainty matrices and . A unique solution for each is recovered by parameterizing the general solution subject to a rank condition. The primary advantage of the proposed method is that individual parameters within the linear state equation matrices can be estimated using input/output data. The methodology is well suited for parameter estimation problems involving multi-energy-domain systems where intermediate measurements between fields are not available. Simulation examples are provided to demonstrate the utility of the proposed parameter estimation method. This result has broad applications to robust feedback solutions and system health monitoring (system diagnostics and prognostics). The methodology is applied to a double mass-spring-damper system with both constant and varying uncertainty cases. The approach is demonstrated to be able to adapt to the changes in parameters of the system in real-time. The observer-based parameter estimation method is applied to an adaptive model-based approach for structural health monitoring (SHM) of multistory buildings. Fault detection, isolation and estimation (FDIE) are accomplished through the integration of reduced-order physics models with the methodology that directly estimates changes in structural stiffness and damping. In the proposed method, each building floor is connected to its adjoining floors using springs and dampers (i.e., structure columns) to capture the planar motion of the system. The novelty in this method is that the structure features of stiffness and damping are directly estimated from the observer model states. To demonstrate the proposed method, a finite element analysis of a scaled digital building is used to generate dynamic structural data. The simulated data will be corrupted to emulate sensor noise. It will be shown that for this numerical study, a 15% stiffness change in one of the nine columns between the floors that produces 1.67% decrease in overall stiffness is detected. It will be also shown that the proposed approach is able to detect, isolate and estimate faults of different magnitudes at single and multiple locations. Finally, the identification approach is applied to a blowout preventer annular health-monitoring problem. The methodology is used to adapt the annular model coefficients and track their changes with cycles. The approach is able to separate graphically between early, middle, and aged cycles. Hence, health-monitoring decisions are achievable based on simple graphical representation of the results.