KEYWORDS: Earthquakes, Damage detection, Data modeling, Finite element methods, Chemical elements, Civil engineering, System identification, Sensors, Complex systems, Matrices
Civil engineering structures, such as reinforced concrete frames, exhibit nonlinear hysteretic behavior when subject to
dynamic loads, such as earthquakes. The ability to detect damages in structures after a major earthquake will ensure their
reliability and safety. Innovative analysis techniques for damage detection of structures have been extensively studied
recently. However, practical and effective damage identification techniques remain to be developed for nonlinear
structures, in particular hysteretic reinforced concrete (RC) structures. In this paper, a smooth hysteretic model with
stiffness and strength degradations and with the pinching effect is used to represent the dynamic characteristics of
reinforced concrete (RC) frames. A system identification method capable of detecting damages in nonlinear structures,
referred to as the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI), is used to detect damages in
hysteretic RC frames. The performance of the AQSSE-UI technique is demonstrated by the experimental data.
A 1/3 scale 2-story RC frame has been tested experimentally on the shake table at NCREE, Taiwan. This 2-story RC
frame was subject to different levels of ground excitations back to back. The RC frame is firstly considered as a linear
model with rotational springs and the tracking of the degradation of the stiffness parameters is carried out using the
AQSSE-UI technique. Then the same RC frame is considered as a nonlinear structure with plastic hinges following a
smooth hysteretic model. Experimental results show that the AQSSE-UI technique is quite effective for tracking of : (i)
the stiffness degradation of linear structures, and (ii) the non-linear hysteretic parameters with stiffness and strength
degradations.
An objective of the structural health monitoring system is to identify the state of the structure and to detect its damages
after a major event, such as the earthquake, to ensure the reliability and safety of structures. Innovative analysis
techniques for the damage detection of structures have been extensively studied recently. However, practical and
effective damage identification techniques remain to be developed for nonlinear structures, in particular nonlinear
hysteretic reinforced concrete (RC) structures. In this paper, in addition to the equivalent time-varying linear model, a
smooth hysteretic model with stiffness and strength degradations and with the pinching effect is used to represent the
dynamic characteristics of reinforced concrete (RC) frames. A system identification technique capable of detecting
damages in nonlinear structures, referred to as the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI),
is used to track the degradation of the time-varying parameters of nonlinear RC frames. The performance of the
AQSSE-UI technique is also demonstrated by the experimental data.
Six identical 1/2-scale one-story two-bay RC frames have been designed and tested on the shake table at NCREE,
Taiwan. Each RC frame was subject to different levels of seismic excitations followed by cyclic loads until failure. Test
data were used to verify the capability of the AQSSE-UI technique in detecting structural damages. Experimental results
demonstrate that the AQSSE-UI technique is quite effective in tracking (i) the stiffness degradation of equivalent linear
time-varying structure, and (ii) the non-linear hysteretic parameters with stiffness and strength degradations.
KEYWORDS: Earthquakes, Damage detection, Finite element methods, Chemical elements, Complex systems, Sensors, Data modeling, Systems modeling, Lithium, System identification
Many civil and mechanical engineering structures exhibit nonlinear hysteretic behavior when subject to dynamic loads,
such as earthquakes. The modeling and identification of non-linear hysteretic systems with stiffness and strength
degradations is a practical but challenging problem encountered in the engineering field. A recently developed
technique, referred to as the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI), is capable of
identifying time dependant parameters of nonlinear hysteretic structures. In this paper, the AQSSE-UI technique is
applied to the parametric identification of nonlinear hysteretic reinforced concrete structures with stiffness and strength
degradations, and the performance of the AQSSE technique is demonstrated by the experimental test data. A 1/3 scaled
2-story RC frame has been tested experimentally on the shake table at NCREE, Taiwan. This 2-story RC frame was
subject to different levels of ground excitations back to back. The structure is firstly considered as an equivalent linear
model with time-varying stiffness parameters, and the tracking of the degradation of the stiffness parameters is carried
out using the AQSSE-UI technique. Then the same RC frame is considered as a nonlinear hysteretic model with inelastic
hinges following the generalized Bouc-Wen model, and the time-varying nonlinear parameters are identified again using
the AQSSE-UI technique. Experimental results demonstrate that the AQSSE technique is quite effective for the tracking
of: (i) the stiffness degradation of linear structures, and (ii) the non-linear hysteretic parameters with stiffness and
strength degradations.
It is well-known that the damage in a structure is a local phenomenon. Based on measured vibration data from sensors,
the detection of a structural damage requires the finite-element formulation for the equations of motion, so that a change
of any stiffness in a structural element can be identified. However, the finite-element model (FEM) of a complex
structure involves a large number of degree-of-freedom (DOFs), which requires a large number of sensors and involves a
heavy computational effort for the identification of structural damages. To overcome such a challenge, we propose the
application of a reduced-order model in conjunction with a recently proposed damage detection technique, referred to as
the adaptive quadratic sum-square error with unknown inputs (AQSSE-UI). Experimental data for the shake table tests
of a 1/4-scal 6-story steel frame structure, in which the damages of the joints were simulated by loosening the connection
bolts, have been available recently. Based on these experimental data, it is demonstrated that the proposed combination
of the reduced-order finite-element model and the adaptive quadratic sum-square error with unknown inputs is quite
effective for the damage assessment of joints in the frame structure. The proposed method not only can detect the
damage locations but also can quantify the damage severities.
KEYWORDS: Sensors, Error analysis, Matrices, Signal to noise ratio, Structural health monitoring, Earthquakes, Damage detection, Finite element methods, Interference (communication), Complex systems
The detection of structural damages, either on-line or almost on-line, based on vibration data measured from sensors,
is essential for the structural health monitoring system. The problem is quite challenging, in particular when the external
excitations are not completely measured and when the structural system is complex. In practical applications, external
excitations (inputs), such as seismic excitations, wind loads, traffic loads, etc., may not be measured or may not be
measurable, and the structure may not always be shear-beam type which can be easily represented as spring-mass
system. In this paper, a newly proposed damage detection method, referred to as the adaptive quadratic sum-squares
error with unknown inputs (AQSSE-UI), is used for the detection of structural damages of a plane steel truss with finite
element model. In this approach, external excitations and some structural responses may not be measured. Analytical
recursive solution for the proposed AQSSE-UI method will be presented. The accuracy and effectiveness of the
proposed approach will be demonstrated by numerical simulations where the structure is excited by different external
loads. The simulation results indicate that the proposed approach is a viable damage detection technique capable of: (i)
identifying structural parameters, (ii) tracking the changes of parameters leading to the detection of structural damages,
and (iii) identifying the unknown external excitations.
Recently, an adaptive extended Kalman filter (AEKF) approach has been proposed for the damage identification and
tracking of structures. Simulation and experimental studies have demonstrated that this AEKF approach is capable of
tracking the damages for linear structures. In this paper, an experimental study is conducted and presented to verify the
capability of the adaptive extended Kalman filter (AEKF) approach for identifying and tracking the damages in
nonlinear structures. A base-isolated building model, consisting of a scaled building model mounted on a rubber-bearing
isolation system, has been tested experimentally in the laboratory. The non-linear behavior of the base isolators is
modeled by the Bouc-Wen model. To simulate the structural damages during the test, an innovative device, referred to as
the stiffness element device (SED), is proposed to reduce the stiffness of either the upper story of the structure or the
base isolator. Two earthquake excitations have been used to drive the test model, including the El Centro and Kobe
earthquakes. Various damage scenarios have been simulated and tested. Measured acceleration response data and the
AEKF approach are used to track the variation of the stiffness during the test. The tracking results for the stiffness
variations correlate well with that of the referenced values. It is concluded that the AEKF approach is capable of tracking
the variation of structural parameters leading to the detection of structural damages.
An objective of the structural health monitoring system is to identify the state of the structure and to detect the
damage when it occurs. Analysis techniques for the damage identification of structures, based on vibration data
measured from sensors, have received considerable attention. Recently, a new damage tracking technique, referred to as
the adaptive quadratic sum-square error (AQSSE) technique, has been proposed, and simulation studies demonstrated
that the AQSSE technique is quite effective in identifying structural damages. In this paper, the adaptive quadratic sumsquare
error (AQSSE) along with the reduced-order finite-element method is proposed to identify the damages of
complex structures. Experimental tests were conducted to verify the capability of the proposed damage detection
approach. A series of experimental tests were performed using a scaled cantilever beam subject to the white noise and
sinusoidal excitations. The capability of the proposed reduced-order finite-element based adaptive quadratic sum-square
error (AQSSE) method in detecting the structural damage is demonstrated by the experimental results.
An early detection of structural damages is critical for the decision making of repair and replacement maintenance in
order to guarantee a specified structural reliability. Consequently, the structural damage detection, based on vibration
data measured from the structural health monitoring (SHM) system, has received considerable attention recently. The
traditional time-domain analysis techniques, such as the least square estimation (LSE) method and the extended Kalman
filter (EKF) approach, require that all the external excitations (inputs) be available, which may not be the case for some
SHM systems. Recently, these two approaches have been extended to cover the general case where some of the external
excitations (inputs) are not measured, referred to as the LSE with unknown inputs (LSE-UI) and the EKF with unknown
inputs (EKF-UI). Also, new analysis methods, referred to as the sequential non-linear least-square estimation with
unknown inputs and unknown outputs (SNLSE-UI-UO) and the quadratic sum-square error with unknown inputs
(QSSE-UI), have been proposed for the damage tracking of structures when some of the acceleration responses are not
measured and the external excitations are not available. In this paper, these newly proposed analysis methods will be
compared in terms of accuracy, convergence and efficiency, for damage identification of structures based on
experimental data obtained through a series of experimental tests using a small-scale 3-story building model with white
noise excitation. The capability of the LSE-UI, EKF-UI, SNLSE-UI-UO and QSSE-UI approaches in tracking the
structural damages will be demonstrated.
Critical non-structural equipment, including life-saving equipment in hospitals, circuit breakers, computers, high technology instrumentations, etc., are venerable tostrong earthquakes, and the failure of these equipments may result in a heavy economic loss. In this connection, innovative control systems and strategies are needed for their seismic protections. This paper presents the performance evaluation of passive and semi-active control in the equipment isolation system for earthquake protection. Through shaking table tests of a 3-story steel frame with equipment on the 1nd floor, a MR-damper together with a sliding friction pendulum isolation system is placed between the equipment and floor to reduce the vibration of the equipment. Various control algorithms are used for this semi-active control studies, including the decentralized sliding mode control (DSMC) and LQR control. The passive-on and passive-off control of MR damper is used as a reference for the discussion on the control effectiveness.
This paper presents the structural control results of shaking table tests for a steel frame structure in order to evaluate
the performance of a number of proposed semi-active control algorithms using multiple magnetorheological (MR) dampers. The test structure is a six-story steel frame equipped with MR-dampers. Four different cases of damper arrangement in the structure are selected for the control study. In experimental tests, an EL Centro earthquake, a Kobe earthquake and a Chi-Chi earthquake (station TCU067) are used as ground excitations. Various control algorithms are used for this semi-active control studies, including the Decentralized Sliding Mode Control (DSMC), LQR control and passive-on and passive-off control. Each algorithm is formulated specifically for the use of MR-dampers. Additionally, each algorithm uses measurements of the absolute acceleration and the device velocity for the determination of the control action to ensure that the algorithm can be implemented on a physical structure. The performance of each algorithm is evaluated based on the results of shaking table tests, and the advantages of each algorithm is compared and discussed. The reduction of the story drift and acceleration throughout the structure is examined.
Damage identification of structures is an important task of a health monitoring system. The ability to detect damages
on-line or almost on-line will ensure the reliability and safety of structures. Analysis methodologies for structural
damage identification based on measured vibration data have received considerable attention, including the least-square
estimation (LSE), extended Kalman filter (EKF), etc. Recently, new analysis methods, referred to as the sequential non-linear
least-square estimation (SNLSE) and quadratic sum-squares error (QSSE), have been proposed for the damage
tracking of structures. In this paper, these newly proposed analysis methods will be compared with the LSE and EKF
approaches, in terms of accuracy, convergence and efficiency, for damage identification of structures based on
experimental data. A series of experimental tests using a small-scale 3-story building model have been conducted. In
these experimental tests, white noise excitations were applied to the model, and different damage scenarios were
simulated and tested. Here, the capability of the adaptive LSE, EKF, SNLSE and QSSE approaches in tracking the
structural damage are demonstrated using experimental data. The tracking results for the stiffness of all stories, based on
each approach, are compared with the stiffness predicted by the finite-element method. The advantages and drawbacks
for each damage tracking approach will be evaluated in terms of the accuracy, efficiency and practicality.
An identification method for estimating the time varying excitation force acting on a structural system based on its response measurement is presented in this study. The method employs the simple Kalman filter to establish a regression model between the residual innovation and the input excitation forces. Based on the regression model, a recursive least-squares estimator is proposed to identify the input excitation forces incorporating with the measurement noise and the modeling error. In applying the method, the ambient vibration measurement of a structural system was used first. The stochastic subspace identification is applied to estimate the system matrix "A" and the measurement matrix "C". Then the Kalman filter with a recursive estimator is applied to determine the input excitation forces. The dynamic excitation forces are estimated from the measured structural responses by an inverse algorithm while least-square method with a recursive estimator is employed to update the estimation in the sense of real-time computation. Verification of the method with numerical simulation through MIMO system is conducted first. Identification of soil forces during the shaking table test of soil-pile interaction is also demonstrated.
KEYWORDS: Sensors, Matrices, Damage detection, Structural health monitoring, Chemical elements, Signal to noise ratio, Solids, Information operations, Earthquakes, Velocity measurements
A challenging problem in structural damage detection based on vibration data is the requirement of a large number
of sensors and the numerical difficulty in obtaining reasonably accurate results when the system is large. To address
this issue, the substructure identification approach may be used. Due to practical limitations, the response data are not
available at all degrees of freedom of the structure and the external excitations may not be measured (or available). In
this paper, an adaptive damage tracking technique, referred to as the sequential nonlinear least-square estimation with
unknown inputs and unknown outputs (SNLSE-UI-UO) along with the sub-structure approach will be used to identify
damages at critical locations (hot spots) of the complex structure. In our approach, only a limited number of response
data are needed and the external excitations may not be measured, thus significantly reducing the number of sensors
required and computational efforts. The accuracy of the proposed approach is illustrated using a long-span truss with
finite-element formulation. Simulation results demonstrate that the proposed approach is capable of tracking the local
damages and it is suitable for local structural health monitoring.
KEYWORDS: Surface conduction electron emitter displays, Sensors, Error analysis, Solids, Finite element methods, Chemical elements, Data analysis, Structural health monitoring, Motion models, Aerospace engineering
The detection of structural damage is an important objective of structural health monitoring systems. Analysis
techniques for the damage detection of structures, based on vibration data measured from sensors, have been studied
without experimental verifications. In this paper, a newly proposed data analysis method for structural damage
identifications, referred to as the adaptive quadratic sum squares error (AQSSE), will be verified experimentally. A
series of experimental tests using a scaled 3-story building model have been conducted recently. In the experimental
tests, white noise excitations were applied to the top floor of the model, and different damage scenarios were simulated
and tested. These experimental data will be used to verify the capability of the AQSSE approach in tracking the
structural damage. The tracking results for the stiffness of all stories, based on the AQSSE approach, are compared with
the stiffness predicted by the finite-element method. Experimental results demonstrate that the AQSSE approach is
capable of tracking the structural damage with reasonable accuracy.
Base isolation systems have been used in buildings and bridges as protective systems against earthquakes, and the health monitoring of base isolators is of great importance. The ability to detect damages on-line, based on vibration data measured from the health monitoring system, will ensure the reliability and safety of base-isolated structures. When a base-isolated structure is subject to strong earthquakes, it is important to be able to determine the damage of isolators from the seismic response data either on-line or almost on-line. The problem is quite challenging because the restoring force of the base isolator is inelastic, and only a limited number of sensors can be installed in the structural health monitoring system, indicating that the response data may not be available at all degrees of freedom of the structure and that the external excitations may not be measured. In this paper, we propose a new data analysis method, referred to as the sequential nonlinear least-square estimation with unknown inputs and unknown outputs (SNLSE-UI-UO), for the real time on-line identification of structural damages, including the nonlinear base isolators. In this approach, only a limited number of response data are needed and the external excitations may not be measured. Analytical recursive solutions are derived and presented, which are not available in previous literature. The Bou-Wen model is used for the nonlinear base-isolation system, and the accuracy of the new approach is demonstrated using a base-isolated building. Simulation results demonstrate that the proposed approach is capable of tracking on-line the changes of structural parameters, such as the parameters of base isolators, leading to the identification of structural damages.
KEYWORDS: Filtering (signal processing), Earthquakes, Structural health monitoring, Complex systems, System identification, Reliability, Damage detection, Chemical elements, Error analysis, Signal to noise ratio
An early detection of structural damage is an important goal of any structural health monitoring system. In particular, the ability to detect damages on-line, based on vibration data measured from sensors, will ensure the reliability and safety of the structures. Innovative data analysis techniques for the on-line damage detection of structures have received considerable attentions recently. The problem is quite challenging, in particular when the structure is nonlinear. In this paper, we proposed a new data analysis method, referred to as the sequential nonlinear least square estimation (SNLSE), for the on-line identification of nonlinear structural parameters. This new approach has significant advantages over the extended Kalman filter (EKF) approach in terms of the stability and convergence of the solution as well as the computational efforts involved. Further, an adaptive tracking technique recently proposed has been implemented in the proposed SNLSE to identify on-line the time-varying system parameters of nonlinear structures. The accuracy and effectiveness of the proposed approach has been demonstrated using a nonlinear elastic structure and nonlinear hysteretic structures. Simulation results indicate that the proposed approach is capable of tracking on-line the changes of structural parameters leading to the identification of structural damages.
An important objective of health monitoring systems for civil infrastructures is to identify the state of the structure and to detect the damage when it occurs. System identification and damage detection based on measured vibration data have received considerable attention recently. Frequently, the damage of a structure may be reflected by a change of some system parameters, such as a degradation of the stiffness. In this paper, we propose an adaptive tracking technique, based on the extended Kalman filter approach, to identify the structural parameters and their changes. The proposed technique is capable of tracking the abrupt change of system parameters from which the event and severity of structural damages can be detected. Our adaptive filtering technique is based on the current measured data to determine the parametric variation so that the residual error of the estimated parameters is contributed only by noises. The proposed technique is applicable to linear and nonlinear structures. Simulation results for tracking the parametric changes of linear and nonlinear hysteretic structures are presented to demonstrate the application and effectiveness of the proposed technique in detecting the structural damages using vibration data from the health monitoring system.
In this paper, we present two control strategies for applications to civil engineering structures, referred to as the generalized H2 control and L1 control, respectively. Both control strategies are capable of addressing the performance-based design of structures, in the sense that the design requirements for the peak response quantities, such as peak interstory drifts, peak shear forces, peak floor accelerations, etc., can be satisfied. Likewise, these two controllers minimize the upper bound of the peak response of the controlled output vector. The design procedures for these two controllers are formulated in the framework of linear matrix inequalities (LMIs) so that the LMI toolbox in MATLAB can be used effectively and conveniently for the controller design. These control strategies are applied herein to the wind-excited benchmark problem to demonstrate their applicability to practical problems as well as their control performances. Simulation results illustrate that the performances of both the generalized H2 controller and the L1 controller are very plausible in comparison with the LQG control method.
KEYWORDS: Earthquakes, Buildings, Near field, Switching, Control systems, Electroluminescence, Numerical simulations, Electromagnetism, Bismuth, Information operations
The near-field earthquake ground motion is characterized by high peak accelerations and velocity pulses with long period components as well as large ground displacements. Such characteristics are responsible for severe damages to flexible structures. The peak ground acceleration occurs in the form of a shock, rather than a gradual build-up. As a result, passive dampers may not dissipate energies quick enough to prevent a serious damage to structures. Recently, a resetting or switching semi-active stiffness damper (RSASD or SSASD) and a semi-active electromagnetic friction damper (SAEMFD) have been shown to be effective in reducing the structural response due to dynamic loads. In this paper, the performance and effectiveness of these two semi-active hybrid isolation systems are studied extensively for base-isolated buildings subject to near-field earthquakes. Numerical results clearly demonstrate that these two semi-active dampers are effective in protecting the integrity of base-isolated structures during near-field earthquakes.
KEYWORDS: Matrices, Signal processing, Time metrology, Numerical simulations, System identification, Chemical elements, Solids, Frequency modulation, Civil engineering, Smart materials
Recently, the method of Hilbert transform has been used successfully by the authors to identify parameters of linear structures with real eigenvalues and eigenvectors, e.g., structures with proportional damping. Frequently, linear structures may not have proportional damping so that normal modes do not exist. In this case, all the eigenvalues, eigenvectors and modeshapes are complex. In this paper, the Hilbert transform and the method of Empirical Mode Decomposition are used to identify the parameters of structures with nonproportional damping using the impulse response data. Measured impulse response signals are first decomposed into Intrinsic Mode Functions using the method of Empirical Mode Decomposition with intermittency criteria. An Intrinsic Mode Function (IMF) contains only one characteristic time scale (frequency), which may involve the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio, referred to as the modal response. It is shown that all the modal responses can be obtained from IMFs. Then, each modal response is decomposed in the frequency-time domain to yield instantaneous phase angle and amplitude as functions of time using the Hilbert transform. Based on only a single measurement of the impulse response time history at one location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex modeshapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the methodology presented are demonstrated through numerical simulations. It is shown that complete dynamic characteristics of linear structures with nonproportional damping can be identified effectively using the Hilbert transform and the Empirical Mode Decomposition method.
The design of passive dampers involves the determination of the required capacity of each damper installed at selected locations. Generally, dampers with identical capacities are installed in various story units of a building. However, installing identical dampers in various story units does not achieve the optimal performance for the building and it may result in a conservative and more expensive design. In this paper, a design method, based on the concepts of active control theories, is proposed for the design of the capacities of passive dampers. For most of the passive dampers, the force applied to the structure depends on the drift and velocity across the dampers. From the standpoint of active control, the control force depends only on the local measurements of the displacement (i.e., drift across the damper) and velocity. Controllers of the form described above are designed by decentralized control theories. For this purpose, the method of static output optimal control is modified and applied to the design of passive dampers. Advantages of the proposed method for different types of passive dampers are demonstrated through numerical simulations.
A 310 m Nanjing TV transmission tower in China will be installed with an active mass driver on the upper observation deck in order to reduce the acceleration responses under strong winds. The wind-induced structural responses considered in this paper include the coupling effect of lateral and torsional motions. The along-wind and across-wind components of the wind velocity are modeled as random processes defined by the Davenport cross-power spectra. The structural responses, in particular the acceleration, increase due to the coupling effect of lateral and torsional motions. This paper presents the Linear Quadratic Gaussian (LQG) control strategy using accelerations as the feedback quantities to reduce the tower response. Emphasis is placed on the practical applications, such as the limitations on actuator peak force and stroke, limited number of sensors, noise pollution, etc. A state reduced-order system has been established to design the dynamic output feedback controllers. The power spectral density and rms of acceleration responses of the TV transmission tower equipped with an active mass driver have been computed. Simulation results demonstrate that the LQG strategy is remarkable in reducing the lateral and torsional motions of the tower and it is suitable for the full-scale implementation of active mass driver on Nanjing Tower.
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