A computational framework for fast‐time hybrid simulation based on partitioned time integration and state‐space modeling

Abstract

Summary Hybrid simulation reproduces the experimental response of large‐ or even full‐scale structures subjected to a realistic excitation with reduced costs compared with shake table testing. A real‐time control system emulates the interaction between numerical substructures, which replace subparts having well‐established computational models, and physical substructures tested in the laboratory. In this context, state‐space modeling, which is quite popular in the community of automatic control, offers a computationally cheaper alternative to the finite‐element method for implementing nonlinear numerical substructures for fast‐time hybrid simulation, that is, with testing timescale close to one. This standpoint motivated the development of a computational framework based on partitioned time integration, which is well suited for hard real‐time implementations. Partitioned time integration, which relies on a dual assembly of substructures, enables coupling of state‐space equations discretized with heterogeneous time step sizes. In order to avoid actuators stopping at each simulation step, the physical substructure response is integrated with the same rate of control system, whereas a larger time step size is allowed on the numerical substructure compatibly with available computational resources. Fast‐time hybrid simulations of a two‐pier reinforced concrete bridge tested at the EUCENTRE Experimental Laboratory of Pavia, Italy, are presented as verification example.

Seismic Vulnerability Analysis of a Coupled Tank-Piping System by Means of Hybrid Simulation and Acoustic Emission

“…With regard to time integration adopted in HS, we relied on the Partitioned Generalized (PG-α) algorithm [11]. It allows to decouple the computation time between NS and PS and assures the compatibility of velocities between the two domains by means of Localized Lagrange Multipliers.…”

“…In order to carry out HSs, both mass and stiffness matrices were used to model the NS by means of the MATLAB/ Simulink code in the Host PC. The Host PC compiles the system of equations discretized in time by the Partitioned PG-α algorithm [11] which are then sent to an xPC target -a real time operating system installed in a target PC-via a LAN connection. During HS, the integration algorithm solves the equations of motion in the xPC target and estimates a displacement command for the PS.…”

“…Dimensions in mm ratio. Finally, a partitioned integration based on Localized Lagrange Multipliers (LLM) is used to enforce kinematic compatibility between velocities, at the interface between PS and NS [11].…”

“…Specifically, the hybrid model of the system under study combines numerical (NSs) and physical substructures (PSs). More precisely, following the approach of [10,11], the steel tank represents the NS and the piping network the PS. Furthermore, in order to both evaluate inelastic phenomena of the piping system and to detect and localize crack events, we employ a set of acoustic emission sensors.…”

Real-Time Hybrid Simulation Analysis of Moat Impacts in a Base-Isolated Structure

“…Despite the success of PDT, the extended time scale used for this technique prohibited accurate physical testing of rate-dependent components such as viscoelastic or friction dampers. To this end, a number of techniques have been used or developed to decrease the computational demand during testing including Frequency-Based Substructuring (Gordis, 1994), Convolution Integral Method (Kim et al, 2011), State Space Modeling (Su and Juang, 1994;Abbiati et al, 2019) and Partitioned Time Integration (Abbiati et al, 2019).…”