Robust frameworks for the observability and lie symmetries of structural dynamical systems

Thesis

System identification is an important technique in reconstructing and estimating dynamic states, unknown parameters and unmeasured inputs of dynamical systems using measured input-output signals, and in minimizing the gaps between real engineering systems and their mathematical models. Whether a system for a given setup of sensors can be, in theory, successfully identified is associated with its observability properties.

This thesis is overall devoted to two research directions: 1) developing efficient observability algorithms for handling large and complex dynamical systems and 2) incorporating unmeasured or unknown inputs into robust observability computation and tool. The research is motivated by the need to relax the computational limitation of the existing observability methods that is associated with their high physical memory requirements when used for large and complex real systems, as for example large civil infrastructures encountered in Structural Health Monitoring (SHM). Moreover robust observability computation with the consideration of unmeasured inputs is needed to account for joint state-parameter-input identification problems which have gained increasing attention in recent years.

In particular, two efficient and robust algorithms are proposed to test observability properties in Chapter 2 and Chapter 3. The first algorithm applies to large linear systems with unknown parameters, based on the efficient implementation of the Observability Rank Condition (ORC) method. The second algorithm applies to rational nonlinear systems with unmeasured inputs, based on the extended use of the extended Observability Rank Condition (EORC-DF) and a power series-based computational framework.

In Chapter 4, computational frameworks are developed for Lie symmetries of nonlinear systems with unmeasured inputs. The obtained Lie symmetries can provide an alternative path to approach the observability properties of a system for a given setup of sensors. More importantly, Lie symmetries imply the mathematical relationship between the true solutions of the system’s states, parameters and unmeasured inputs and their other possible solutions.

Finally in Chapter 5, the application of observability and Lie symmetry analyses is illustrated through a complex, nonlinear and non-smooth mechanical model. The model is successfully reduced and identified using suitably chosen identification methods.

Authors: Shi, X

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: System Identification; Structural Health Monitoring; Lie Symmetries; Observability/Identifiability
• Subjects: Structural health monitoring; System identification; Structural dynamics