Numerical Substructure Research Articles

A shaking table real-time substructure experiment of an equipment–structure–soil interaction system

Based on branch substructure method, this article deduces motion equation of an equipment–structure–soil interaction system. The equation is converted and applied to a shaking table real-time substructure experiment. The equipment–structure system is adopted as experimental substructure loaded by the shaking table. Meanwhile, finite element model of soil is adopted as numerical substructure after modal reduction. An equipment–structure–soil interaction scale model is designed and tested using shaking table under different earthquake records. Comparison shows good agreement of results of experimental and finite element methods. This work also proves validity and accuracy of the proposed experimental method.

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

Real-time dynamic substructure testing of soil-adjacent structure system based on branch mode method

The concept of inertia coupling terms among substructures was proposed. Based on the branch mode method, the superstructures and foundation soil of one soil-adjacent structure system were divided into different branches. The branch mode method was effectively introduced to real-time dynamic substructure testing (RTDST) by decomposing and transforming the motion equation of the entire system. It was also applied for the interaction coupling terms to exchange data between the physical and numerical substructures. This method decreased the degree-of-freedom of the linear substructure effectively and considered the effects of foundation translation and rotation on the upper structures. One system composed of two adjacent four-story steel structures (S1 and S2, respectively) and foundation soil was presented in this study. S1 was applied on a shaking table as the physical substructure, whereas the foundation soil and S2 were set as two numerical substructures and simulated in a computer. The seismic response of the entire coupling system was analyzed by real-time data exchange among substructures. Test results agree with numerical solutions. The RTDST based on the branch mode method is a feasible and reliable method for the investigation of soil-adjacent structure interaction (SASI) problems, and provides a new way to consider SASI problems in the RTDST.

On‐line hybrid test method for evaluating the performance of structural details to failure

SummaryA test environment to evaluate the seismic performance of gusset plate connections intended for steel braced frames is proposed. The developed test method combines the substructuring techniques with finite element analysis methods in an on‐line hybrid scheme. Numerical substructure analysis is conducted on bracing members, while bracing connections are treated as experimental substructures. A force‐displacement combined control imposed with the aid of 2 jacks ensures physical continuity between the analysis and test. The rotational behavior of gusset plate connections subjected to large inelasticity and varying axial loading until fracture is investigated. Two gusset plate details were designed and tested to verify the efficiency of the proposed method. The test method is rational, and smooth operation is achieved. The test results revealed the advantage of the developed on‐line hybrid test method in exploring the ultimate capacity of bracing connections.

A dynamic load estimation method for nonlinear structures with unscented Kalman filter

Abstract A force estimation method is proposed for hysteretic nonlinear structures. The equation of motion for the nonlinear structure is represented in state space and the state variable is augmented by the unknown the time history of external force. Unscented Kalman filter (UKF) is improved for the force identification in state space considering the ill-condition characteristic in the computation of square roots for the covariance matrix. The proposed method is firstly validated by a numerical simulation study of a 3-storey nonlinear hysteretic frame excited by periodic force. Each storey is supposed to follow a nonlinear hysteretic model. The external force is identified and the measurement noise is considered in this case. Then a case of a seismically isolated building subjected to earthquake excitation and impact force is studied. The isolation layer performs nonlinearly during the earthquake excitation. Impact force between the seismically isolated structure and the retaining wall is estimated with the proposed method. Uncertainties such as measurement noise, model error in storey stiffness and unexpected environmental disturbances are considered. A real-time substructure testing of an isolated structure is conducted to verify the proposed method. In the experimental study, the linear main structure is taken as numerical substructure while the one of the isolations with additional mass is taken as the nonlinear physical substructure. The force applied by the actuator on the physical substructure is identified and compared with the measured value from the force transducer. The method proposed in this paper is also validated by shaking table test of a seismically isolated steel frame. The acceleration of the ground motion as the unknowns is identified by the proposed method. Results from both numerical simulation and experimental studies indicate that the UKF based force identification method can be used to identify external excitations effectively for the nonlinear structure with accurate results even with measurement noise, model error and environmental disturbances.

An improved equivalent force control algorithm for hybrid seismic testing of nonlinear systems

The equivalent force control (EFC) algorithm is a hybrid seismic testing method based on both an implicit integration algorithm and force feedback control. As it performs the computation of the numerical substructure with a fixed sampling number and some evaluations are not necessary, the EFC method is believed to be time-consuming for seismic testing of nonlinear systems with complicated numerical substructure model. In order to tackle this problem, the EFC method with varying sampling number (vEFC) has been conceived. The analysis of the vEFC method has shown that 2 traditional pseudodynamic testing (PDT) variants on the basis of implicit time integration schemes and numerical iteration, that is, the IPDT1 method and the IPDT2 method, can be recovered from the vEFC method. Moreover, the advantages of the vEFC method, such as fast response rate and compensation for control errors and possible slippage, are demonstrated.

Hybrid simulation of structural systems with online updating of concrete constitutive law parameters by unscented Kalman filter

Online model updating in hybrid simulation (HS) can represent an effective technique to reduce modeling errors of parts numerically simulated, that is, numerical substructures, especially when only a few critical components of a large system can be tested, that is, physical substructures. As a result, in an enhanced HS with online model updating, parameters of constitutive relationship can be identified based on experimental data provided by physical substructures and updated in numerical substructures. This paper proposes a novel method to identify constitutive parameters of concrete laws with unscented Kalman filter (UKF). In order to implement UKF, parts of the source codes of the OpenSEES software were modified to compute estimated measurements. Prior to experimental HS, a parametric study of UKF constitutive law parameters was conducted. As a result, the effectiveness of the UKF combined with OpenSEES was validated through numerical simulations, a monotonic loading test on a concrete column and real-time HSs of a reinforced concrete frame run with both standard and model-updating techniques based on UKF.

A practical numerical substructure method for seismic nonlinear analysis of tall building structures

SummaryIt is a challenging task to perform large‐scale nonlinear analysis for complicated tall building structures due to the trade‐off between computational efficiency and numerical accuracy. Existing methods cannot satisfactorily meet the demands of engineering practices because they require predetermining local yielded regions or adaptively refining models during the analysis. This paper presents a modified numerical substructure method (NSM) in which the difficult task is divided into seismic analysis of a linear elastic “master” structure and static nonlinear analyses of a limited quantity of substructures for local yielded regions. A “nonlinear force corrector” is calculated in the substructure and applied on the master structure to consider the contribution of the yielded region's nonlinearity. A 32‐story reinforced concrete frame shear‐wall building under earthquake is analyzed to verify the NSM and investigate its accuracy and efficiency. In addition, a reinforced concrete frame shake‐table test is simulated using the modified NSM, and local damage behaviors and improved accuracy can be obtained using the refined substructure model.

HyTest: Platform for Structural Hybrid Simulations with Finite Element Model Updating

Hybrid simulation has been demonstrated to be a powerful method to evaluate the system-level dynamic performance of structure. With the numerical substructure analyzed with finite element software and the difficult-to-model components tested with an experimental substructure, complex structures with sophisticated behaviors can readily be examined through a hybrid simulation. To coordinate and synchronize the substructures in hybrid simulation, software is required. In recent studies, model updating has been integrated into hybrid simulation to improve testing accuracy by updating the numerical model during the analysis. However, online model updating scheme requires some modifications in the typical hybrid simulation testing procedure, and this greater complexity is entailed in its implementation regarding the collaboration of identification algorithms with existing hybrid simulation software. To address this issue and broaden the utilization of hybrid simulation with model updating, an existing platform named HyTest originally for conventional hybrid simulation is extended for this purpose. This version of HyTest facilitates the online identification of material constitutive parameters using experimental measurements in its finite element based identification module. It also includes a data center with a uniform data transmission protocol to incorporate different substructures and modules. A numerical example is used to demonstrate the online identification of material parameters for concrete and steel models in a reinforced column, and to verify the accuracy of the identification module. Lastly the effectiveness of HyTest in conducting hybrid simulation with model updating is validated using actual hybrid tests on a steel frame.

Comparison of online model updating methods in pseudo-dynamic hybrid simulations of TADAS frames

Hybrid simulation is a cost-effective testing method to simulate responses of a structure under earthquake loads. In a conventional hybrid simulation, the structure is divided into experimental and numerical substructures. Experimental substructures represent the critical components that cannot be reliably simulated by numerical models. In the lack of enough number of testing equipment or budget deficit, only limited number of critical components can be modeled experimentally; others should be represented with numerical model. In the cases that critical components have common properties, the parameters in the numerically modeled components can be updated on the basis of measured response of the experimental specimen. The main objective of this research is to evaluate accuracy and computational time of two main methods for online model updating with component hysteretic behavior estimation scheme. In the first method, hysteretic parameters of numerical models get updated during the simulation. In the second method, weighted average of several hysteretic models 5 with pre-defined parameters shape the behavior of updating numerical models and weighting factor of each hysteretic model gets calibrated as simulation time proceeds. The employed structural model in this study is a 3-bay, 4-story moment resisting frame equipped with Triangular Added Damping and Stiffness dampers in all stories. It was observed that employing the second updating method results in more accurate responses.

Dynamic response and performance of cable-stayed bridges under blast load: Effects of pylon geometry

The air blast that is generated by the explosion of bombs or fuel tankers on or adjacent to a bridge can cause severe structural damage, and may result in partial or full collapse of the bridge. The dynamic response and structural performance of buildings under blast has been the subject of several studies, with considerably less attention being paid to the assessment of bridges under extreme blast loading scenarios. To reduce the computational expense of conducting blast analyses on large or complex bridges, the numerical sub-structuring technique is used in current practice. However, the simplifying assumptions adopted in these sub-structuring methods can lead to erroneous results. Accordingly, this study attempts to simulate numerically the dynamic response of an entire cable-stayed bridge subjected to blast loading using the LS-DYNA explicit finite element code. Based on best practice available in the literature, the blast load estimation, material modelling and detailed numerical simulation are carried out and the response of a cable-stayed steel bridge (designed according to minimum requirements of the Australian Bridge Standard) under blast loads ranging from a small to large detonation at different positions above the deck and near pylon are obtained. Furthermore, the potential effects of blast loads on different structural components with a focus on the cross-sectional geometry of the pylons are investigated.

Hybrid simulation of a carbon fibre–reinforced polymer-strengthened continuous reinforced concrete girder bridge

The behaviour of bridge columns strengthened using carbon fibre–reinforced polymer composites has been studied extensively. However, few investigations have been conducted regarding the influence of carbon fibre–reinforced polymer-strengthened columns on the seismic behaviour of reinforced concrete continuous girder bridges. This article details the hybrid simulations of a continuous reinforced concrete girder bridge whose columns are strengthened by carbon fibre–reinforced polymer jackets. In the hybrid simulations, one ductile column is selected as the experimental element, which is represented by a 1/2.5-scale specimen, and the remaining bridge parts are simultaneously modelled in OpenSees (the Open System for Earthquake Engineering Simulation). After combining the experimental element and the numerical substructure, the hybrid analysis model is developed with the established hybrid simulation system. The displacements of the bridge and the lateral force–displacement response of the experimental element in hybrid simulation are obtained. Compared with the results of numerical simulation, the stability and accuracy of the established hybrid simulation system are demonstrated. Meanwhile, the comparative hybrid simulation results of the as-built bridge and the carbon fibre–reinforced polymer-strengthened bridge also prove the effectiveness of the carbon fibre–reinforced polymer jackets’ confinement in the continuous reinforced concrete girder bridge.

Effect of Soil-Structure Interaction on Seismic Performance of Long-Span Bridge Tested by Dynamic Substructuring Method

Because of the limitations of testing facilities and techniques, the seismic performance of soil-structure interaction (SSI) system can only be tested in a quite small scale model in laboratory. Especially for long-span bridge, a smaller tested model is required when SSI phenomenon is considered in the physical test. The scale effect resulting from the small scale model is always coupled with the dynamic performance, so that the seismic performance of bridge considering SSI effect cannot be uncovered accurately by the traditional testing method. This paper presented the implementation of real-time dynamic substructuring (RTDS), involving the combined use of shake table array and computational engines for the seismic simulation of SSI. In RTDS system, the bridge with soil-foundation system is divided into physical and numerical substructures, in which the bridge is seen as physical substructures and the remaining part is seen as numerical substructures. The interface response between the physical and numerical substructures is imposed by shake table and resulting reaction force is fed back to the computational engine. The unique aspect of the method is to simulate the SSI systems subjected to multisupport excitation in terms of a larger physical model. The substructuring strategy and the control performance associated with the real-time substructuring testing for SSI were performed. And the influence of SSI on a long-span bridge was tested by this novel testing method.

Effects of Equipment-Structure-Soil Interaction on Seismic Response of Equipment and Structure via Real-Time Dynamic Substructuring Shaking Table Testing

Equation of motion for an equipment-structure-soil (ESS) interaction system was derived using the branch substructure method. After rearrangement, this equation was applied to real-time dynamic substructuring shaking table (RTDSST) testing of the ESS system. This method adopts the equipment-structure (ES) subsystem as the experimental substructure and a modal reduced soil model as the numerical substructure: the former is tested via the shaking table, and the latter is numerically simulated, while real-time data communication occurs between the two substructures during testing. A scale model of the ESS system was designed and underwent an RTDSST test. The experimental data were found to be consistent with the numerical calculation results, which corroborates the reliability and validity of the proposed testing method. A comparison of the experimental results from different earthquake stages implies that seismic responses of the equipment and structure decreased in general due to the intervention of soil, but the soil effect weakened with earthquake intensity.

Real-time hybrid simulation of the size effect of tuned liquid dampers

The use of tuned liquid dampers (TLDs) is an effective passive control technique to suppress structural vibration under wind and seismic loads. This paper investigates the size effect of TLDs on control efficiency. Given the advantages of real-time hybrid simulation, two issues affecting the control performance of TLD are addressed: (a) the geometric size and (b) the experimental model scale. A series of real-time hybrid simulations is performed, in which TLD devices with various sizes (including full-scale and small-scale) are experimentally modeled as physical substructures; the controlled structures are numerically simulated as numerical substructures. Results demonstrate that TLD performance is size dependent; a shallow liquid in TLD with lower relative liquid depth may be more efficient for both peak and root-mean-square response control. Scaled TLD models that are usually used in conventional shaking table tests generally overestimate the control performance of prototype TLD devices, indicating that full-scale TLD experiments should be pursued to ensure proper performance evaluation.

Real-time hybrid simulation technique for performance evaluation of full-scale sloshing dampers in wind turbines

As a variation of the pseudodynamic testing technique, the real-time hybrid simulation (RTHS) technique is executed in real time, thus allowing investigation of structural systems with rate-dependent components. In this paper, the RTHS is employed for performance evaluation of full-scale liquid sloshing dampers in multi-megawatt wind turbines, where the tuned liquid damper (TLD) is manufactured and tested as the physical substructure while the wind turbine is treated as the numerical substructure and modelled in the computer using a 13-degree-of-freedom (13-DOF) aeroelastic model. Wind turbines with 2 MW and 3 MW capacities have been considered under various turbulent wind conditions. Extensive parametric studies have been performed on the TLD, e.g., various tuning ratios by changing the water level, TLD without and with damping screens (various mesh sizes of the screen considered), and TLD with flat and sloped bottoms. The present study provides useful guidelines for employing sloshing dampers in large wind turbines, and indicates huge potentials of applying RTHS technique in the area of wind energy.

Dynamically Substructured System Testing for Railway Vehicle Pantographs

]The overall objective of this paper is to establish a dynamically substructured system (DSS) testing approach for railway vehicle pantographs. In this approach a pilot study quasi-pantograph (QP) is tested within a laboratory environment, where the catenary wire, contact wire and catenary support (abbreviated as ‘catenary’ in this paper) are modelled as a numerical substructure. This is simulated in real time and in parallel with the operation of the physical substructure, i.e. the QP rig itself. The entire DSS is driven by parametric excitation within the catenary model, whilst the numerical and physical substructures are synchronised at their interface via the DSS control technique of [1]. Simulation and physical experimental investigations of the pilot QP rig, constructed within the Advanced Control and Test Laboratory at the University of Bristol, UK, demonstrate the efficacy of the method when subjected to parametric variations, unknown parameter values and parametric excitation.

Synthesised H∞ / μ Control Design for Dynamically Substructured Systems

In the dynamically substructured system (DSS) testing technique, a controller that synchronises the responses of physical and numerical substructures is an essential part of the testing scheme to ensure synchronisation fidelity. This paper discusses a novel approach that generates a two-degree-of-freedom (2-DOF) output feedback controller for multi-input, multioutput (MIMO) DSS via control synthesis. This 2-DOF output feedback controller yields robust stability and robust performance of the physical/numerical substructure synchronisation and enables controller tuning in the frequency domain. Simulation and experimental results have been shown to validate the efficacy of the method.

Application of the nonlinear substructuring control method to nonlinear 2-degree-of-freedom systems

A nonlinear substructuring control (NLSC) method is developed as a more generalised form of linear substructuring control (LSC) by incorporating nonlinear signal-based control (NSBC) into a dynamical substructuring system (DSS). An advantage of NLSC is that it can be designed using the linearized models of the substructured systems without the need for accurate nonlinear dynamic models. In this study, the use of the NLSC method is demonstrated via substructured tests on nonlinear physical and numerical substructures.A series of substructuring tests were also conducted on a test rig, constructed within the ACTLab at the University of Bristol, which incorporated a pure time delay of 6.0 ms due to the presence of discrete-time elements. In the substructured tests, a trilinear hysteresis with piecewise linearity, commonly used in structural engineering, was embedded into the numerical substructure as the nonlinearity. The NLSC method was found to achieve stable and reliable substructured responses, even when the substructured systems had significant nonlinearity as well as the pure time delay term.

Real time hybrid simulation with online model updating: An analysis of accuracy

In conventional hybrid simulation (HS) and real time hybrid simulation (RTHS) applications, the information exchanged between the experimental substructure and numerical substructure is typically restricted to the interface boundary conditions (force, displacement, acceleration, etc.). With additional demands being placed on RTHS and recent advances in recursive system identification techniques, an opportunity arises to improve the fidelity by extracting information from the experimental substructure. Online model updating algorithms enable the numerical model of components (herein named the target model), that are similar to the physical specimen to be modified accordingly. This manuscript demonstrates the power of integrating a model updating algorithm into RTHS (RTHSMU) and explores the possible challenges of this approach through a practical simulation. Two Bouc–Wen models with varying levels of complexity are used as target models to validate the concept and evaluate the performance of this approach. The constrained unscented Kalman filter (CUKF) is selected for using in the model updating algorithm. The accuracy of RTHSMU is evaluated through an estimation output error indicator, a model updating output error indicator, and a system identification error indicator. The results illustrate that, under applicable constraints, by integrating model updating into RTHS, the global response accuracy can be improved when the target model is unknown. A discussion on model updating parameter sensitivity to updating accuracy is also presented to provide guidance for potential users.