Stability and Delay Compensation for Real-Time Substructure Testing

Real-time substructure testing is a method for establishing the dynamic behavior of structural systems. The method separates a complex structure into physical and numerically modeled substructures, which interact in real-time allowing time-dependent nonlinear behavior of the physical specimen to be accurately represented. Displacements are applied to the physical specimen using hydraulic actuators and the resulting measured forces are fed back to the numerical substructure. This feedback loop is implemented as a time-stepping routine. One of the key factors in obtaining reliable results using this method is the accurate compensation of the delayed response of the actuator. If this is not accounted for, instability of the feedback loop is likely to occur. This paper presents a method for estimating the delay while a test is in progress and accurately compensating for it during the test. The stability of both linear and nonlinear single-actuator systems is examined and the behavior of twin-actuator systems controlling two degrees-of-freedom at the substructure interface is presented. The effectiveness of the method is clearly demonstrated by comparisons between experimental and theoretical behavior.     

Impedance-Based Method for Nondestructive Damage Identification

A structural damage identification technique based on the impedance method is presented in this paper using smart piezoelectric transducer (PZT) patches. A modeling framework is developed to determine the structural impedance response and the dynamic output forces of PZT patches from the electric admittance measurements. A damage identification scheme for solving the nonlinear optimization problem is proposed to locate and quantify the structural damage through the minimization of the discrepancy between the structural impedance response and the numerically computed frequency response. The proposed technique does not use modal analysis or model reduction, and only the electric admittance measurements of PZT patches and the analytical system matrices are required. A beam example has been employed to illustrate the effectiveness of the proposed algorithm numerically. Furthermore, the influence of the measurement noise on the results has been investigated.     

Deterministic Excitation Forces for Simulation and Identification of Nonlinear Hysteretic SDOF Systems

This paper investigates how to design deterministic excitation forces in studying nonlinear single-degree-of-freedom systems, especially those with rate and path dependency and strength and stiffness degradation. One frequency-modulated periodic excitation and its amplitude-modulated counterpart are proposed as a solution, and a series of numerical exercises are carried out to show that these forces can be designed for sufficient forcing functions to study the complex nonlinear hysteresis. To rapidly reveal the underlying characteristics of the system and also to further lead to an effective system identification, four evaluation tools are proposed to be utilized together with the proposed excitation forces. These tools include the response curves, force-state map, intercycle drift, and intercycle pattern change, based on which some distinctive “patterns” are obtained to reveal the existence of nonlinearities, types of nonlinearities, existence of memory, and degradation. By using both Bouc-Wen and Bouc-Wen-Baber-Noori models for the system in all the simulations, the writers compare the commonly used forces with the proposed excitation forces to further demonstrate the advantages of the proposed excitation forces and evaluation tools. The writers also explore challenges in terms of implementing the proposed excitation forces. The results of this study are expected to benefit both physical testing and numerical simulation of complex nonlinear hysteretic systems in a time- and cost-effective manner, as well as leading to efficient schemes for system identification.     

Creep and Shrinkage Effect on Reinforced Concrete Slab-and-Beam Structures

In this paper a solution to the bending problem of reinforced concrete slab-and-beam structures including creep and shrinkage effect is presented. The adopted model takes into account the resulting in-plane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists of isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral deflection and in-plane deformation to the plate and lateral deflection and axial deformation to the beam, are established using continuity conditions at the interface. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the plate and the beams is taken into account. The solution of the arising plate and beam problems, which are nonlinearly coupled, is achieved using the analog equation method. The adopted model, compared with those ignoring the in-plane forces and deformations, describes better the actual response of the plate–beams system and permits the evaluation of the shear forces at the interfaces, the knowledge of which is very important in the design of prefabricated ribbed plates. The resulting deflections are considerably smaller than those obtained by other models.     

Displacement-Based and Two-Field Mixed Variational Formulations for Composite Beams with Shear Lag

Displacement-based and two-field mixed beam elements are proposed for the linear analysis of steel–concrete composite beams with shear lag and deformable shear connection. The kinematics of the shear lag relies on a parabolic shear warping function of uniform shape along the slab. These assumptions are verified by comparing a closed-form solution of the composite beam problem with the results provided by the ABAQUS code. Moreover, three displacement-based finite elements and two mixed elements where both variables, forces, and displacements are approximated within the elements are developed especially for very coarse discretizations. All models neglect uplift and consider shear connectors using distributed interface elements. Locking problems that arise in the 10 degrees-of-freedom (DOF) displacement-based element which ensures the lowest regularity required by the problem are detected. Then, a locking-free element which relies on a reduced integration and a scaling factor method is proposed and analyzed for fine mesh discretizations. Energy errors and convergence rates of the proposed elements are illustrated while numerical examples dealing with a fixed-end steel–concrete composite beam and a simply supported concrete Tee beam are considered to confirm the validity of the closed-form solution and illustrate the performance of the proposed elements, especially of the ones with 10 and 13 DOF.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Neural Networks for Decentralized Control of Cable-Stayed Bridge

The system identification and vibration control of a cable-stayed bridge are considered difficult to achieve due to the bridge’s structural complexity and system uncertainties. In this paper, based on the concept of decentralized information structures, a decentralized, nonparametric identification and control algorithm with neural networks is proposed for the purpose of suppressing the vibration of a documented six-cable-stayed bridge model induced by earthquake excitations. The control strategy proposed here uses the stay cables as active tendons to provide control forces through appropriate actuators. Each individual actuator is controlled by a decentralized neurocontroller that only uses local information. The feature of decentralized control simplifies the implementation of the control algorithms and makes decentralized control easy to practice and cost effective. The effectiveness of the decentralized identification and control algorithm based on neural networks is evaluated through numerical simulations. And the adaptability of the decentralized neurocontrollers for different kinds of earthquake excitations and for a damaged cable-stayed bridge model is demonstrated via numerical simulations.     

Engineering Approach for Predicting Fire Response of Restrained Steel Beams

Predicting the response of restrained beams under fire conditions is complex owing to the development of fire-induced forces and requires finite-element or finite-differences analysis. In this paper, a simplified approach is proposed for predicting the fire-induced forces and deflections of restrained steel beams. The method applies equilibrium equations for obtaining critical fire-induced forces and then utilizes compatibility principles for obtaining temperature-deflection history of the beam. Effect of end restraints, thermal gradient, location of axial restraint force, span length, and load intensity are accounted for in the proposed approach. The validation of the approach is established by comparing the predictions from the proposed approach with results obtained from rigorous finite-element analysis. The applicability of the proposed approach to practical design situations is illustrated through a numerical example.     

Real-Time Substructure Tests Using Hydraulic Actuator

A new real-time substructure method for testing systems under dynamic loading is described. The method separates a complex system into a physical, possibly nonlinear, subsystem (to be tested experimentally at large scale) and a surrounding linear system, modeled numerically. The two subsystems interact in real time allowing realistic time-dependent nonlinear behavior to take place. This behavior may be impossible to model computationally, and the method overcomes problems associated with scaling and time-dependent effects associated with current shaking table and pseudodynamic test methods. Dynamic forces are applied to the numerical model, and the resulting displacements at the interface between the two subsystems are applied to the physical system using servohydraulic actuators. The restoring forces are then measured and fed back to the numerical model, so that the response for the next time step can be calculated. The technique can be applied to a wide range of complex, linear∕nonlinear systems such as structures with localized plastic deformation, soil-structure interaction, or vehicle-suspension interaction. The method is demonstrated for both single and multi-degree-of-freedom systems, using a single actuator to apply displacements to a physical specimen. Comparisons between experimental and theoretical results show excellent agreement.     

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.     

Elastic Constants Identification of Composite Materials Using Single Angle-Ply Laminate

A method is presented for identification of elastic constants for composite materials using three measured strains of a single angle-ply laminate subjected to tensile testing. In the proposed method, the trial material constants of the angle-ply laminate are used to predict the corresponding strains in the laminate. An error function is established to measure the difference between the experimental and theoretical predictions of the strains. The identification of material constants is then formulated as a constrained minimization problem in which the material constants are determined to make the error function a global minimum. The accuracy and capability of the proposed method are demonstrated by means of a number of examples of the identification of material constants of angle-ply laminates with different lay-ups. Experimental data obtained from static tensile tests of several angle-ply laminates are used to identify the material constants of the laminates. The excellent results obtained in the experimental investigation have validated the applicability of the proposed method.     

Structural Damage Detection and Assessment from Modal Response

This paper presents a global damage detection and assessment algorithm based on a parameter estimation method using a finite-element model and the measured modal response of a structure. Damage is characterized as a reduction of the member constitutive parameter from a known baseline value. An optimization scheme is proposed to localize damaged parts of the structure. The algorithm accounts for the possibility of multiple solutions to the parameter estimation problem that arises from using spatially sparse measurements. Errors in parameter estimates caused by sensitivity to measurement noise are reduced by selecting a near-optimal measurement set from the data at each stage of the localization algorithm. Damage probability functions are computed upon completion of the localization process for candidate elements. Monte Carlo methods are used to compute the required probabilities based on the statistical distributions of the parameters for the damaged and the associated baseline structure. The algorithm is tested in a numerical simulation environment using a planar bridge truss as a model problem.     

Natural Excitation Technique and Eigensystem Realization Algorithm for Phase I of the IASC-ASCE Benchmark Problem: Simulated Data

A benchmark study in structural health monitoring based on simulated structural response data was developed by the joint IASC–ASCE Task Group on Structural Health Monitoring. This benchmark study was created to facilitate a comparison of various methods employed for the health monitoring of structures. The focus of the problem is simulated acceleration response data from an analytical model of an existing physical structure. Noise in the sensors is simulated in the benchmark problem by adding a stationary, broadband signal to the responses. A structural health monitoring method for determining the location and severity of damage is developed and implemented herein. The method uses the natural excitation technique in conjunction with the eigensystem realization algorithm for identification of modal parameters, and a least squares optimization to estimate the stiffness parameters. Applying this method to both undamaged and damaged response data, a comparison of results gives indication of the location and extent of damage. This method is then applied using the structural response data generated with two different models, different excitations, and various damage patterns. The proposed method is shown to be effective for damage identification. Additionally the method is found to be relatively insensitive to the simulated sensor noise.     

Structural Stability of Concrete Gravity Dams Strengthened by Rockfill Buttressing: Hydrostatic Load

Rockfill buttressing is often considered to strengthen existing gravity dams that have inadequate stability to resist the estimated hydrostatic and seismic loads. Various simplified methods for static stability analyses of composite concrete–rockfill dams, which represent the rockfill as equivalent forces, are discussed. Numerical analyses of composite dams using nonlinear rockfill and interface constitutive models are then considered. Hydrostatic stability analyses of a 35?m composite dam are carried out to compare the results obtained from simplified methods and numerical analyses. Parametric analyses are performed to investigate the effects of various modeling parameters such as the friction angle of the concrete–fill interface, the friction angle of the concrete–foundation interface, and the reservoir elevation during the fill placement. Numerical analyses results show that lowering the reservoir prior to construction of the rockfill does not have a significant effect on the stress response of the strengthened dam in the case analyzed. For design purpose, it is shown that the simplified minimum/maximum earth pressure method is always on the safe side irrespective of the concrete–rockfill friction angle.     

Numerical Modeling of Concrete-FRP Debonding Using a Crack Band Approach

In this study, numerical procedures are proposed to predict the structural behavior of concrete members strengthened with fiber-reinforced polymeric (FRP) sheets or plates. The concept of damage band or crack band is introduced and used for predicting the debonding failure of the concrete-epoxy interface formed when FRP sheets or plates are externally bonded to a concrete substrate. In the crack band approach, all the processes taking place during the failure of a concrete-epoxy interface are smeared in a band of fixed width. This makes the approach attractive from a modeling point of view since continuum theories, along with softening relations, can be used to model the damage which causes debonding of the interface. In order to validate this approach, numerical predictions, using the concept of crack band, are compared against experimental results obtained from tests of concrete blocks and reinforced concrete beams strengthened with FRP. In particular, the capability of the proposed numerical approach to predict the load-displacement response, strain distributions, failure sequences, damage distribution, and failure mechanisms experimentally observed is verified. Results presented in this study indicate that the concept of crack band is appropriate when modeling concrete-epoxy interfaces under general states of stresses.     

Estimation of Aeroelastic Parameters of Bridge Decks Using Neural Networks

A new method of estimating flutter derivatives using artificial neural networks is proposed. Unlike other computational fluid dynamics based numerical analyses, the proposed method estimates flutter derivatives utilizing previously measured experimental data. One of the advantages of the neural networks approach is that they can approximate a function of many dimensions. An efficient method has been developed to quantify the geometry of deck sections for neural network input. The output of the neural network is flutter derivatives. The flutter derivatives estimation network, which has been trained by the proposed methodology, is tested both for training sets and novel testing sets. The network shows reasonable performance for the novel sets, as well as outstanding performance for the training sets. Two variations of the proposed network are also presented, along with their estimation capability. The paper shows the potential of applying neural networks to wind force approximations.     

Temperature Prediction of Concrete-Filled Rectangular Hollow Sections in Fire Using Green’s Function Method

An efficient numerical approach using the Green’s function solutions of transient heat conduction for predictions of thermal response inside a concrete-filled rectangular hollow section subjected to fire is proposed in this paper. Thermal properties of construction materials are assumed to be isotropic and homogeneous. The Green’s function approach adopts different series expansions for small and large time solutions, therefore the desirable convergence properties can be achieved at any range of time by using the time partitioning strategy. A useful analytical relation in terms of step Green’s functions is derived in this paper to incorporate the multidimensional effect, in particular, for Neumann (prescribed flux) boundary conditions. A modified lumped capacitance method, together with an “orthogonal flux” concept, are employed to deal with spatially varying heat flux at the steel–concrete interface, where Duhamel’s theorem is applied in piecewise manner along the interface to incorporate the fire boundary conditions. No spatial discretization is required in the numerical algorithms based on the Green’s function approach.     

In-Plane Biaxial Crush Response of Polycarbonate Honeycombs

The crushing response of a polycarbonate circular cell honeycomb to inplane biaxial loading under displacement control is analyzed. The study involves a combination of experiment and numerical simulation. Experiments corresponding to several different biaxial loading conditions are carried out. In the first phase of the response, the material deforms in a uniform fashion. Next, a nonlinear phase caused by the progressive localization of deformation is characterized by the variation of overall (macroscopic) stiffness. The progressive localization causes the walls of each cell to contact. These periodic honeycomb materials show different collapsed modes under different biaxial loading histories. Experimental measurements indicate how the magnitude of the collapse load varies and how the load-displacement response changes as a function of load biaxiality. The experimental results are simulated through numerical analysis using the finite-element method.     

Adaptive Parametric Identification Scheme for a Class of Nondeteriorating and Deteriorating Nonlinear Hysteretic Behavior

The adaptive parametric identification of deteriorating and nondeteriorating nonlinear hysteretic phenomena is considered using a generalization of Masing model based on the observed memory behavior of distributed element models. The model permits a parametric identification to be performed using nonlinear optimization techniques for arbitrary response time histories. A changing objective function, defined as the normalized force estimation error over a shifting window of recent data, is employed so that classic nonlinear optimization techniques can be used for the adaptive identification problem. A variation of the steepest descent method is used with significant modifications. To achieve the best performance for any given problem, a set of a priori numeric tests are suggested to design the identification scheme. The design identification scheme exhibits a very good performance in identifying the correct values of the parameters and is rather robust in dealing with noise. The proposed approach has applications to adaptive identification of much wider types of nonlinear rate-dependent hysteretic behavior. Also, the set of guidelines proposed by the authors is a contribution toward having more effective autonomous identification schemes, using minimal information about the model and input.     

Multicrack Detection on Semirigidly Connected Beams Utilizing Dynamic Data

The problem of crack detection has been studied by many researchers, and many methods of approaching the problem have been developed. To quantify the crack extent, most methods follow the model updating approach. This approach treats the crack location and extent as model parameters, which are then identified by minimizing the discrepancy between the modeled and the measured dynamic responses. Most methods following this approach focus on the detection of a single crack or multicracks in situations in which the number of cracks is known. The main objective of this paper is to address the crack detection problem in a general situation in which the number of cracks is not known in advance. The crack detection methodology proposed in this paper consists of two phases. In the first phase, different classes of models are employed to model the beam with different numbers of cracks, and the Bayesian model class selection method is then employed to identify the most plausible class of models based on the set of measured dynamic data in order to identify the number of cracks on the beam. In the second phase, the posterior (updated) probability density function of the crack locations and the corresponding extents is calculated using the Bayesian statistical framework. As a result, the uncertainties that may have been introduced by measurement noise and modeling error can be explicitly dealt with. The methodology proposed herein has been verified by and demonstrated through a comprehensive series of numerical case studies, in which noisy data were generated by a Bernoulli–Euler beam with semirigid connections. The results of these studies show that the proposed methodology can correctly identify the number of cracks even when the crack extent is small. The effects of measurement noise, modeling error, and the complexity of the class of identification model on the crack detection results have also been studied and are discussed in this paper.