Wavelet-Hybrid Feedback Linear Mean Squared Algorithm for Robust Control of Cable-Stayed Bridges

Cable-stayed bridges are flexible structures, and control of their vibrations is an important consideration and a challenging problem. In this paper, the wavelet-hybrid feedback least mean squared algorithm recently developed by the writers is used for vibration control of cable-stayed bridges under various seismic excitations. The effectiveness of the algorithm is investigated through numerical simulation using a benchmark control problem created based on an actual semifan-type cable-stayed bridge design. The performance of the algorithm is compared with that of a sample linear quadratic Gaussian (LQG) controller using three different earthquake records: the El Centro (California, 1940), Mexico City (Mexico, 1985), and Gebze (Turkey, 1999) earthquakes. Simulation results demonstrate that the new algorithm is consistently more effective than the sample LQG controller for all three earthquake records. Additional numerical simulations are performed to evaluate the sensitivity of the new control algorithm. It is concluded that the algorithm is robust against the uncertainties existing in modeling structures.     

Vibration Control of Wind-Excited Tall Buildings Using Sliding Mode Fuzzy Control

A sliding mode fuzzy control (SMFC) is proposed to design a controller for the third-generation benchmark problem on wind-excited buildings. A distinctive feature in vibration control of large civil infrastructure is the existence of large disturbances, such as wind, earthquake, and sea wave forces. Those disturbances govern the behavior of the structure; however, they cannot be precisely measured, especially for the case of wind excitations. Since the structural accelerations are measured only at a limited number of locations without the measurement of the wind forces, the structure of the conventional control may have the feedback loop only. The general structure of the SMFC, proposed herein, is composed of a compensation part and a convergent part. The compensation part prevents the system from diverging, and the convergent part directs the system to the sliding surface. The compensation part uses not only the structural response measurement but also the disturbance measurement, so the SMFC has a feedback loop and a feedforward loop. To realize the virtual feedforward loop for the wind-induced vibration control, a disturbance estimation filter is introduced. The structure of the filter is constructed based on an autoregressive model for the stochastic wind force. This filter estimates the wind force at each time instance based on the measured structural responses and the stochastic information of the wind force. For verification of the proposed algorithm, numerical simulation is carried out on the benchmark problem for wind-excited buildings. The results indicate that the present control algorithm is efficient for reducing the wind-induced vibration.     

Ground motion spatial variability effects on seismic response control of cable-stayed bridges

The spatial variability of input ground motion at supporting foundations plays a key role in the structural response of cable-stayed bridges (CSBs); therefore, spatial variation effects should be included in the analysis and design of effective vibration control systems. The control of CSBs represents a challenging and unique problem, with many complexities in modeling, control design and implementation, since the control system should be designed not only to mitigate the dynamic component of the structural response but also to counteract the effects of the pseudo-static component of the response. The spatial variability effects on the feasibility and efficiency of seismic control systems for the vibration control of CSBs are investigated in this paper. The assumption of uniform earthquake motion along the entire bridge may result in quantitative and qualitative differences in seismic response as compared with those produced by uniform motion at all supports. A systematic comparison of passive and active system performance in reducing the structural responses is performed, focusing on the effect of the spatially varying earthquake ground motion on the seismic response of a benchmark CSB model with different control strategies, and demonstrates the importance of accounting for the spatial variability of excitations.     

Semiactive Control Strategies for MR Dampers: Comparative Study

This paper presents the results of a study to evaluate the performance of a number of recently proposed semiactive control algorithms for use with multiple magnetorheological (MR) dampers. Various control algorithms used in recent semiactive control studies are considered including the Lyapunov controller, decentralized bang-bang controller, modulated homogeneous friction algorithm, and a clipped optimal controller. Each algorithm is formulated for use with the MR damper. Additionally, each algorithm uses measurements of the absolute acceleration and device displacements for determining the control action to ensure that the algorithms could be implemented on a physical structure. The performance of the algorithms is compared through a numerical example, and the advantages of each algorithm are discussed. The numerical example considers a six-story structure controlled with MR dampers on the lower two floors. In simulation, an El Centro earthquake is used to excite the system, and the reduction in the drifts, accelerations, and relative displacements throughout the structure is examined.     

Challenges in the Application of Stochastic Modal Identification Methods to a Cable-Stayed Bridge

This paper presents an analysis of the data collected in the ambient vibration test of the International Guadiana cable-stayed Bridge, which links Portugal and Spain, based on different output-only identification techniques: peak-picking, frequency domain decomposition, covariance-driven stochastic subspace identification, and data-driven stochastic subspace identification. The purpose of the analysis is to compare the performance of the four techniques and evaluate their efficiency in dealing with specific challenges involved in the modal identification of the tested cable-stayed bridge, namely the existence of closely spaced modes, the perturbation produced by the local vibration of stay-cables, and the variation of modal damping coefficients with wind velocity. The identified natural frequencies and mode shapes are compared with the corresponding modal parameters provided by a previously developed numerical model. Additionally, the variability of some modal damping coefficients is related with the variation of the wind characteristics and associated with a component of aerodynamic damping.     

Vibration Control of Stay Cables of the Shandong Binzhou Yellow River Highway Bridge Using Magnetorheological Fluid Dampers

The Shandong Binzhou Yellow River Highway Bridge is a three-tower, cable-stayed bridge in Shandong Province, China. Because the stay cables are prone to vibration, 40 magnetorheological (MR) fluid dampers were attached to the 20 longest cables of this bridge to suppress possible vibration. An innovative control algorithm for active and semiactive control of mass-distributed dynamic systems, e.g., stay cables, was proposed. The frequencies and modal damping ratios of the unimpeded tested cable were identified through an ambient vibration test and free vibration tests, respectively. Subsequently, a series of field tests were carried out to investigate the control efficacy of the free cable vibrations achieved by semiactive MR dampers, “Passive-off” MR dampers and “Passive-on” MR dampers. The first three modal damping ratios of the cable incorporated with the MR dampers were also identified from the in situ experiments. The field experiment results indicated that the semiactive MR dampers can provide significantly greater supplemental damping for the cable than either the Passive-off or the Passive-on MR dampers because of the pseudonegative stiffness generated by the semiactive MR dampers.     

Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges

This paper investigates the elastic-plastic seismic behavior of long span cable-stayed steel bridges through the plane finite-element model. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the stay cable sag effect, axial force-bending moment interaction, and large displacements. Material nonlinearity arises when the stiffening steel girder yields. The example bridge is a cable-stayed bridge with a central span length of 605 m. The seismic response analyses have been conducted from the deformed equilibrium configuration due to dead loads. Three strong earthquake records of the Great Hanshin earthquake of 1995 in Japan are used in the analysis. These earthquake records are input in the bridge longitudinal direction, vertical direction, and combined longitudinal and vertical directions. To evaluate the residual elastic-plastic seismic response, a new kind of seismic damage index called the maximum equivalent plastic strain ratio is proposed. The results show that the elastic-plastic effect tends to reduce the seismic response of long span cable-stayed steel bridges. The elastic and elastic-plastic seismic response behavior depends highly on the characteristics of input earthquake records. The earthquake record with the largest peak ground acceleration value does not necessarily induce the greatest elastic-plastic seismic damage.     

Quick Seismic Response Estimation of Prestressed Concrete Bridges Using Artificial Neural Networks

Seismic early warning has been very important and has become feasible in Taiwan. Perhaps because of the lack of quick and reliable estimations of the induced structural response, however, the triggering criteria of almost all of the existing earthquake protection or early warning systems in the world are merely based on the collected or estimated data of the ground motion, without any information regarding the structural response. This paper presents a methodology of generating quick seismic response estimations of a prestressed concrete (PC) bridge using artificial neural networks (ANNs), which may be incorporated in a seismic early warning system for the bridge. In the methodology ANNs were applied to model the critical structural response of a PC bridge subjected to earthquake excitation of various magnitudes along various directions. The objective was to implement a well-trained network that is capable of providing a quick prediction for the critical response of the target bridge. The well-known multilayer perception (MLP) networks with back propagation algorithm were employed. A simple augmented form of MLP that can be quantitatively determined was proposed. These networks were trained and tested based on the analytical data obtained from the nonlinear dynamic finite fiber element analyses of the target PC bridge. The augmented MLPs were found to be much more efficient than the MLPs in modeling the critical bending moments of the piers and girder of the PC bridge.     

General Approach for Training Back-Propagation Neural Networks in Vibration Control of Multidegree-of-Freedom Structures

A general approach is proposed for back-propagation training of multilayer feed-forward (MLFF) neural networks for active control of earthquake-induced vibrations in multidegree-of-freedom structures. The training functions for adjustment of connection weights of the neural network controller are formulated in the proposed approach by minimizing a general cost function using the steepest gradient descent scheme. The proposed method can be applied for training an MLFF neural network controller in vibration control of building structures both in the pattern (online) and batch (off-line) mode. The method can be implemented in structural control systems with more than one control action. Case studies are presented to demonstrate the feasibility of implementing the training approach for effective vibration control of structures subjected to earthquake ground motions.     

On-Line Learning Failure-Tolerant Neural-Aided Controller for Earthquake Excited Structures

This paper presents an on-line learning failure-tolerant neural controller capable of controlling buildings subjected to severe earthquake ground motions. In the proposed scheme the neural controller aids a conventional H∞ controller designed to reduce the response of buildings under earthquake excitations. The conventional H∞ controller is designed to reduce the structural responses for a suite of severe earthquake excitations using specially designed frequency domain weighting filters. The neural controller uses a sequential learning radial basis function neural network architecture called extended minimal resource allocating network. The parameters of the neural network are adapted on-line with no off-line training. The performance of the proposed neural-aided controller is illustrated using simulation studies for a two degree of freedom structure equipped with one actuator on each floor. Results are presented for the cases of no failure and failure of the actuator on each of the two floors under several earthquake excitations. The study indicates that the performance of the proposed neural-aided controller is superior to that of the H∞ controller under no actuator failure conditions. In the presence of actuator failures, the performance of the primary H∞ controller degrades considerably, since actuator failures have not been considered for the design. Under these circumstances, the neural-aided controller is capable of controlling the acceleration and displacement structural responses. In many cases, using the neural-aided controller, the response magnitudes under failure conditions are comparable to the performance of the H∞ controller under no-failure conditions.     

Instantaneous Optimal Wilson-Θ Control Method

A control algorithm based on the instantaneous optimal control method, is presented for on-line control of the civil engineering structures subjected to earthquake excitations. This algorithm employs the unconditionally stable Wilson-θ method to discretize the continuous second-order form of the dynamical equation of motion, and uses a new performance index having an acceleration term as well as velocity and displacement terms. This method is named the instantaneous optimal Wilson-θ method. An eight-story shear-type building frame using one active mass damper/driver mechanism installed on the roof is used to demonstrate the efficiency of the proposed control algorithm in comparison to the other optimal control methods. Behavior of different combinations of weighting matrices related to displacement, velocity, and acceleration response vectors of the entire building are examined, and compared with the complete feedback control of the response vectors.     

Sliding Mode Control of Cable-Stayed Bridge Subjected to Seismic Excitation

The working group on bridge control within the ASCE Committee on Structural Control recently initiated a first-generation benchmark problem addressing the control of a cable-stayed bridge subjected to seismic excitation. Previous research examined the applicability of a LQG-based semiactive control system using magnetorheological (MR) dampers to reduce the structural response of the benchmark bridge and confirmed the capability of the MR damper-based system for seismic response reduction. In this paper, sliding mode control (SMC) is applied in lieu of the LQG formulation to the benchmark bridge problem. The performance and robustness of the SMC-based semiactive control system using MR dampers (SMC/MR) is investigated through a series of numerical simulations, and it is confirmed that SMC/MR can be very effectively applied to the benchmark cable-stayed bridge, subjected to a wide range of seismic loading conditions.     

Linking Nonlinear System Identification with Nonlinear Dynamic Simulation under OpenSees: Some Justifications and Implementations

This study seeks to bridge the gap between nonlinear system identification and nonlinear dynamic finite-element analysis. Motivated by the needs in earthquake simulation, it is first investigated under which conditions and to what degree the prediction of maximum lateral drift and base shear requires accurate nonlinear hysteretic moment-rotation joint models. A series of simulations is carried out using a simple but typical steel frame under two different earthquake ground motion time histories scaled up to various levels. As one of the two major classes of models in nonlinear system identification, nonparametric models are proposed to be implemented into OpenSees. A methodology with details is provided to effectively implement feedforward neural networks with one hidden layer as a new one-dimensional nonlinear smooth material model directly from a MATLAB environment to OpenSees. The same methodology can be applied to benefit the implementation of other parametric and nonparametric models with linear parameterization. Numerical examples are provided. Challenges are discussed and future work is identified.     

Bridge Structural Condition Assessment Based on Vibration and Traffic Monitoring

A stochastic model of traffic excitation on bridges is developed assuming that the arrival of vehicles traversing a bridge (modeled as an elastic beam) follows a Poisson process, and that the contact force of a vehicle on the bridge deck can be converted to equivalent dynamic loads at the nodes of the beam elements. The parameters in this model, such as the Poisson arrival rate and the stochastic distribution of vehicle speeds, are obtained by image processing of traffic video data. The model reveals that traffic excitations on bridges are spatially correlated. This important characteristic is usually incorrectly ignored in most output-only methods for the identification of bridge structural properties using traffic-induced vibration measurement data. In this study, the stochastic traffic excitation model with partial traffic information is incorporated in a Bayesian framework, to evaluate the structural properties and update their uncertainty for condition assessment of the bridge superstructure. The vehicle weights are also estimated simultaneously in this procedure. The proposed structural assessment methodology is validated on an instrumented highway bridge.     

Dynamic Analysis of Nonlinear Frames by Prandtl Neural Networks

A new type of activation function, based on the use of the Prandtl–Ishlinskii operator, has been developed and used in the feed forward neural networks in order to improve their capabilities in learning to identify and analyze nonlinear structures subject to dynamic loading. The genetic algorithm has been used in its training. The neural network, which is referred to as the Prandtl neural network here, has been trained and used in the analysis of two shear frames, a single degree of freedom (SDOF) and a 3DOF, both subjected to earthquake excitations. To assess the capabilities of the Prandtl neural network under ideal situations, the data on the response of the frames have been obtained through the integration of their governing nonlinear equations of motion. The training has been based on the white noise while the strong earthquakes of 200% El Centro in 1940 and Gilroy have been used for testing. Results have shown the high precision of the Prandtl neural network in solving highly hysteretic problems. The issue is important for two main applications in structural dynamics and control: (1) analysis of highly nonlinear structures where it is desired to train a neural network to directly learn the behavior of a structure from experimental data; and (2) intelligent active control of structures where neural network emulators are designed to provide as precise predictions about the future response of the structures as possible, in order to be used in the determination of the required control forces.     

Energy Damage Detection Strategy Based on Strain Responses for Long-Span Bridge Structures

An energy damage detection strategy through disposing strain responses has been developed. First, the strain-based energy dynamic indexes for a system with multiple degrees of freedom were derived from the frequency response function (FRF) of strain responses and energy spectra density. Then, the traditional mode-shape curvature strategy and the proposed strain-based energy damage detection strategy were both used to analyze a long-span cable-stayed bridge, and it was found through comparison that the proposed strain-based energy damage detection strategy solved the shortcomings of the traditional mode-shape curvature strategy. Finally, damage location, damage quantification, and noise pollution resistance analysis for a long-span cable-stayed bridge with different degrees of damage were carried out to verify the effectiveness of the proposed strain-based energy damage detection strategy. The numerical analysis showed that the proposed strain-based energy damage detection strategy can locate damage positions accurately, and it also has good damage quantification and noise pollution resistance abilities.     

Optimal Structural Control Using Neural Networks

An optimal control algorithm using neural networks is proposed. The controller neural network is trained by a training rule developed to minimize cost function. Both the linear structure and the nonlinear structure can be controlled by the proposed neurocontroller. A bilinear hysteretic model is used to simulate nonlinear structural behavior. Three main advantages of the neurocontroller can be summarized as follows. First, it can control a structure with unknown dynamics. Second, it can easily be applied to nonlinear structural control. Third, external disturbances can be considered in the optimal control. Examples show that structural vibration can be controlled successfully.     

Fault Classification Using Pseudomodal Energies and Probabilistic Neural Networks

This paper introduces a new fault identification method that uses pseudomodal energies to train probabilistic neural networks (PNNs). The proposed procedure is tested on a population of 20 cylindrical shells and its performance is compared to the procedure which uses modal properties to train probabilistic neural networks. The PNNs trained using pseudomodal energies provide better classification of faults than the PNNs trained using the conventional modal properties.     

Model-Based Damage Identification in a Continuous Bridge Using Vibration Data

Damage often causes changes in the dynamic characteristics of a structure such as frequencies and mode shapes. Vibration-based damage identification techniques utilize the changes in the dynamic characteristics of a structure to determine the location and extent of damage in the structure. Such techniques are applied in this study to the Crowchild Bridge, a steel-free deck continuous bridge located in western Canada. While the numerical models of the bridge are correlated with the measured dynamic characteristics, computer simulation is used to study the identification of a number of different damage patterns, and the effects of measurement errors and incomplete mode shapes on the quality of results are evaluated. The effectiveness of some selected damage identification techniques is examined; the potential difficulties in identifying the damage are outlined; and areas of further research are suggested. A three-dimensional finite-element model and a simple two-dimensional girder model of the bridge have been constructed to study the usefulness of the selected damage identification methods. Another promising damage detection method proposed here is based on the application of neural networks that combines a vibration-based method.     

Wavelet Network for Semi-Active Control

This paper proposes a wavelet neurocontroller capable of self-adaptation and self-organization for uncertain systems controlled with semiactive devices that are ideal candidates for control of large-scale civil structures. A condition on the sliding surface for cantilever-like structures is defined. The issue of applicability of the control solution to large-scale civil structures is made the central theme throughout the text, as this topic has not been extensively discussed in the literature. Stability and convergence of the proposed neurocontroller are assessed through various numerical simulations for harmonic, earthquake, and wind excitations. The simulations consist of semiactive dampers installed as a replacement for the current viscous damping system in an existing structure. The controller uses only localized measurements. Results show that the controller is stable for both active and semiactive control using limited measurements and that it is capable of outperforming passive control strategies for earthquake and wind loads. In the case of wind loads, the neurocontroller is found to also outperform a linear quadratic regulator (LQR) controller designed using full knowledge of the states and system dynamics.