Date of Completion


Embargo Period



Richard Christenson, Arash Zaghi, Wei Zhang

Field of Study

Civil Engineering


Master of Science

Open Access

Open Access


Real-time hybrid substructuring (RTHS) is a cyber-physical vibration testing method that partitions a structural system into numerical and physical substructures. RTHS incorporates sensing, actuation, and computing technologies to couple these substructures in real time. RTHS can be used to realistically examine the performance of structural systems with rate-dependent structural components that may be difficult to accurately model. However, uncertainty can be found in many aspects of RTHS testing including noise in sensor measurements, actuator performance and tracking, non-linearities in the physical test specimen, and numerical modeling assumptions. In the numerical substructure, uncertainty in material properties, stiffness, damping, or geometry may be considered random variables. Certain physical substructure characteristics may also be similarly parameterized. This thesis aims to develop and experimentally validate techniques that incorporate these parametric uncertainties into RTHS testing protocols, thereby improving the robustness of the RTHS method. This goal was accomplished through two studies.

First, a study was performed to extend and experimentally validate a proposed structural reliability method called Adaptive Kriging-Hybrid Simulation (AK-HS). The method combines a metamodeling technique known as Kriging, an adaptive learning algorithm, the Monte Carlo method, and RTHS testing to iteratively estimate a structural system’s probability of failure given random parameters in the numerical substructure. The method was validated with a series of bench-scale RTHS tests of a Taylor Devices, Inc. viscous damper connecting two adjacent 6-degree-of-freedom rigid body structures. The AK-HS method was found to accurately predict probabilities of failure for systems with up to 24 random variables using a reasonable number of RTHS tests.

The second study proposed and validated a method that can be used to develop metamodels of a system’s frequency response functions using Principal Component Analysis, Kriging, and RTHS. The proposed method was experimentally validated through a series of bench-scale RTHS tests of a Lord Corporation magnetorheological fluid damper controlling vibrations in a 2-degree-of-freedom mass-spring system subjected to an input ground acceleration. Uncertainty was introduced to the system by treating the numerical substructure spring stiffnesses and the physical damper current as random variables. It is shown that accurate, statistical metamodels can be created using a small number of RTHS tests. These metamodels may then be used to conduct Monte Carlo simulations to obtain distributions of the system’s frequency domain response behavior.

Major Advisor

Richard Christenson