Chapter 27 Incorporating Uncertainty in the Physical Substructure During Hybrid Substructuring Connor Ligeikis and Richard Christenson Abstract In hybrid substructuring, a structural system is partitioned into a numerical substructure and a physical substructure. Typically, the physical substructure consists of a system component whose behavior is difficult to model while the numerical substructure consists of a computational model of the remainder of the system. Hybrid substructuring has previously been shown to be an effective method to quantify the effect of parametric uncertainties in the numerical substructure on the response of the system. This paper proposes and implements a methodology where the effect of parametric uncertainty can also be incorporated into the physical substructure. This idea is implemented in a series of small-scale Real-Time Hybrid Substructuring (RTHS) tests on a magneto-rheological fluid damper used to control a two degree-of-freedom mass-spring system. The physical current supplied to the damper is treated as a random variable. Using the RTHS test results, a metamodel of the system’s frequency domain behavior is developed using Principal Component Analysis and Kriging. This metamodel is then used to evaluate probabilistic system performance. Keywords Real-time hybrid substructuring · Metamodeling · Kriging · Vibration control · Magneto-rheological dampers 27.1 Introduction Real-Time Hybrid Substructuring (RTHS) is a cyber-physical form of dynamic testing which interfaces numerical modeling with physical experiments in real time [1]. In RTHS, a system is partitioned into a numerical substructure and a physical substructure. The physical substructure is typically a rate-dependent physical component of the system which is difficult to model and the numerical substructure consists of a computational model of the remainder of the system. In a typical RTHS test, a simulated numerical loading is applied to the numerical substructure of the system. A numerical displacement is then computed and applied to the physical substructure via a transfer system such as a hydraulic actuator. Physical loading may also be applied directly to the physical substructure. Restoring forces produced by the physical substructure are measured using sensors and those forces are then fed back to the numerical substructure. This cycle repeats during each time step of the test. Thus, RTHS provides a cost-effective method to study the performance of the full system during the early stages of the design process while only physically testing a single component of that system. RTHS has been shown to be an effective way to evaluate structural system performance when that system contains parametric uncertainty in the numerical substructure. Abbiati et al. proposed a method called Adaptive Kriging-Hybrid Simulation (AK-HS) which combines a non-parametric statistical interpolation method called Kriging (Gaussian process regression), an adaptive machine learning algorithm, and hybrid substructuring to efficiently estimate a structural system’s probability of failure based on a given failure criteria [2]. In this method, a relatively small number of hybrid substructuring tests are used to build a computationally efficient metamodel of the system response. Monte Carlo (MC) simulations are then performed using this metamodel to quantify probabilistic system behavior. This proposed method was experimentally validated using RTHS tests on a system that consisted of two adjacent six degree-of-freedom (DOF) base-isolated structures connected with a viscous damper [3]. It was shown that probabilities of failure can be accurately estimated for a system containing up to 24 random variables using a reasonable number of RTHS tests. The authors propose an RTHS-based method which can be used to evaluate a structural system’s frequency domain behavior when parametric uncertainties are present in both the numerical and physical substructures. To demonstrate how C. Ligeikis · R. Christenson ( ) Department of Civil and Environmental Engineering, University of Connecticut, Storrs, CT, USA e-mail: rchriste@engr.uconn.edu © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_27 237
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