Least-Squares Estimation with Unknown Excitations for Damage Identification of Structures

System identification and damage detection for structural health monitoring of civil infrastructures have received considerable attention recently. Time domain analysis methodologies based on measured vibration data, such as the least-squares estimation and the extended Kalman filter, have been studied and shown to be useful. The traditional least-squares estimation method requires that all the external excitation data (input data) be available, which may not be the case for many structures. In this paper, a recursive least-squares estimation with unknown inputs (RLSE-UI) approach is proposed to identify the structural parameters, such as the stiffness, damping, and other nonlinear parameters, as well as the unmeasured excitations. Analytical recursive solutions for the proposed RLSE-UI are derived and presented. This analytical recursive solution for RLSE-UI is not available in the previous literature. An adaptive tracking technique recently developed is also implemented in the proposed approach to track the variations of structural parameters due to damages. Simulation results demonstrate that the proposed approach is capable of identifying the structural parameters, their variations due to damages, and unknown excitations.     

On neural blind separation with noise suppression and redundancy reduction

Noise is an unavoidable factor in real sensor signals. We study how additive and convolutive noise can be reduced or even eliminated in the blind source separation (BSS) problem. Particular attention is paid to cases in which the number of sensors is larger than the number of sources. We propose various methods and associated adaptive learning algorithms for such an extended BSS problem. Performance and validity of the proposed approaches are demonstrated by extensive computer simulations.     

Hilbert-Huang Based Approach for Structural Damage Detection

When measured data contain damage events of the structure, it is important to extract the information of damage as much as possible from the data. In this paper, two methods are proposed for such a purpose. The first method, based on the empirical mode decomposition (EMD), is intended to extract damage spikes due to a sudden change of structural stiffness from the measured data thereby detecting the damage time instants and damage locations. The second method, based on EMD and Hilbert transform is capable of (1) detecting the damage time instants, and (2) determining the natural frequencies and damping ratios of the structure before and after damage. The two proposed methods are applied to a benchmark problem established by the ASCE Task Group on Structural Health Monitoring. Simulation results demonstrate that the proposed methods provide new and useful tools for the damage detection and evaluation of structures.     

Dynamic Field Test, System Identification, and Modal Validation of an RC Minaret: Preprocessing and Postprocessing the Wind-Induced Ambient Vibration Data

The investigation of dynamic response for civil engineering structures largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. Dynamic characteristics of structures may be obtained numerically and experimentally. The finite-element method is widely used to model structural systems numerically. However, there are some uncertainties in numerical models. Material properties and boundary conditions may not be modeled correctly. There may be some microcracks in the structures, and these cracks may directly affect the modeling parameters. Modal testing gives correct uncertain modeling parameters that lead to better predictions of the dynamic behavior of a target structure. Therefore, dynamic behavior of special structures, such as minarets, should be determined with ambient vibration tests. The vibration test results may be used to update numerical models and to detect microcracks distributed along the structure. The operational modal analysis procedure consists of several phases. First, vibration tests are carried out, spectral functions are produced from raw measured acceleration records, dynamic characteristics are determined by analyzing processed spectral functions, and finally analytical models are calibrated or updated depending on experimental analysis results. In this study, an ambient vibration test is conducted on the minaret under natural excitations, such as wind effects and human movement. The dynamic response of the minaret is measured through an array of four trixial force-balanced accelerometers deployed along the whole length of the minaret. The raw measured data obtained from ambient vibration testing are analyzed with the SignalCAD program, which was developed in MATLAB. The employed system identification procedures are based on output-only measurements because the forcing functions are not available during ambient vibration tests. The ModalCAD program developed in MATLAB is used for dynamic characteristic identification. A three-dimensional model of the minaret is constructed, and its modal analysis is performed to obtain analytical frequencies and mode shapes by using the ANSYS finite-element program. The obtained system identification results have very good agreement, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure, which can be used to calibrate finite-element models and as a baseline in health monitoring studies.     

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.     

Optimal Control: Basis for Performance Comparison of Passive and Semiactive Isolation Systems

Passive damping in shock and vibration isolation systems reduces the deformation of the isolation system but can increase the acceleration sustained by the isolated object. Semiactive (i.e., controllable) damping systems offer a solution to the problem of increased vibration transmissibility at high frequencies. Semiactive damping is especially relevant to protecting acceleration-sensitive components to the effects of large impulsive earthquakes. In this paper, we compare three semiactive control policies, i.e., pseudonegative-stiffness control, continuous pseudoskyhook-damping control, and bang-bang pseudoskyhook-damping control, in terms of their effectiveness in addressing the deficiencies of passive isolation damping. In order to establish a performance goal for these suboptimal semiactive control rules, we present a method for true optimization of the response of dynamically excited, semiactively controlled structures subjected to constraints imposed by the dynamics of a particular semiactive device. The optimization procedure involves solving Euler–Lagrange equations. The closed-loop dynamics of structures with semiactive control systems are nonlinear due to the parametric nature of the control actions. These nonlinearities preclude an analytical evaluation of Laplace transforms. In this paper, frequency response functions for semiactively controlled structural systems are compiled from the computed time history responses to sinusoidal and pulse-like base excitations. For control devices with no saturation forces, the closed-loop frequency response functions are independent of the excitation amplitude. We make use of this homogeneity of the solution of semiactive control systems and present results in dimensionless form.     

Enhanced Realization∕Identification of Physical Modes

Physical structures are often sufficiently complicated to preclude constructing an accurate mathematical model of the system dynamics from simple analysis using the laws of physics. Consequently, determination of an accurate model requires utilization of (generally noisy) output measurements from dynamic tests. In this paper, we present a robust method for constructing accurate, structural‐dynamic models from discrete time‐domain measurements. The method processes the measurements in order to determine the number of modes present, the damping and frequency of each mode, and the mode shape. The structure may be highly damped. Although the mode‐shape identification is more sensitive to measurement noise than the order, frequency, and damping identification, the method is considerably less sensitive to noise than other leading methods. Accurate detection of the modal parameters and mode shapes is demonstrated for modes with damping ratios exceeding 15%.     

Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data

An accurate prediction for the response of tall buildings subject to strong wind gusts or earthquakes requires the information of in situ dynamic properties of the building, including natural frequencies and damping ratios. This paper presents a method of identifying natural frequencies and damping ratios of in situ tall buildings using ambient wind vibration data. Our approach is based on the empirical mode decomposition (EMD) method, the random decrement technique (RDT), and the Hilbert–Huang transform. Our method requires only one acceleration sensor. The noisy measurement of the building acceleration is first processed through the EMD method to determine the response of each mode. Then, RDT is used to obtain the free vibration modal response. Finally, the Hilbert transform is applied to each free vibration modal response to identify natural frequencies and damping ratios of in situ tall buildings. The application of the proposed methodology is demonstrated in detail using simulated response data of a 76-story benchmark building polluted by noise. Both the along-wind and across-wind vibration measurements have been illustrated. Simulation results demonstrate that the accuracy of the proposed method in identifying natural frequencies and damping ratios is remarkable. The methodology proposed herein provides a new and effective tool for the parametric identification of in situ tall buildings.     

Seismic Fragility Analysis of Structural Systems

A method is presented for the evaluation of the seismic fragility function of realistic structural systems. The method is based on a preliminary, limited, simulation involving nonlinear dynamic analyses performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of a general system reliability problem with correlated demands and capacities. The results compare favorably with the fragility obtained by plain Monte Carlo simulation, while the associated computational effort is orders of magnitude lower. The method is demonstrated with two applications, a steel-concrete box girder viaduct with RC piers subjected to both uniform and nonuniform excitations, and a three-dimensional RC building structure subjected to bidirectional excitation.     

Identification of Structural Systems Using an Evolutionary Strategy

The problem of system identification is an inverse problem of difficult solution. Currently, difficulties lie in the development of algorithms that use measured data from the system to characterize it without significant a priori knowledge of the system. In this paper, a parameter estimation technique based on an evolution strategy (an optimization algorithm inspired by natural evolution) is presented to overcome some of the difficulties encountered in the field. Using this method, a set of direct problems is solved instead of directly tackling the inverse problem. If the uniqueness of the identification solution is guaranteed for the assumed model and the available data, this heuristic method is able to find a solution without incurring restrictions of other classical optimization methods, like the need for reliable initial estimates and convergence to local optima. Some results obtained with this algorithm are presented for the identification of 3 degrees of freedom (DOF) and a 10?DOF structural system under conditions including limited input/output data, noise polluted signals, and no prior knowledge of mass, damping, or stiffness of the system.     

Dynamic Ratcheting in Elastoplastic Single-Degree-of-Freedom Systems

In dynamic analysis, hysteretic damping often provides a reasonable model of the inelastic behavior of a structure. Nonlinearity presented by hysteretic damping, however, introduces the possibility of developing complicated motions not expected in linear dynamics. In this study, motions of a single-degree-of-freedom system with hysteretic damping under dual-frequency sinusoidal excitations are investigated through numerical simulation. Hysteretic damping behavior is represented by three different plasticity models: the elasto-perfectly-plastic model; the linear kinematic hardening model; and the two-surface model. Under certain conditions, the resultant motions from the elasto-perfectly-plastic model and the two-surface model exhibit a continual increment of plastic deformation in successive cycles. Parametric study shows that this dynamic ratcheting develops when applied frequencies are commensurable (i.e., related to each other with integer ratio), and the product of terms comprising the ratio is an even number. In the Poincaré section, motion from commensurable frequencies shows limit cycle behavior, whereas the boundedness of motion for incommensurable frequencies is depicted by having quasi-periodicity. On the other hand, the response of the linear kinematic hardening model is qualitatively different and, in particular, dynamic ratcheting does not develop, irrespective of the frequency commensurability. These findings suggest that model selection may have unanticipated consequences for the analysis and design of structural systems subjected to severe dynamic loadings, such as major earthquakes.     

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.     

Equivalent Modal Damping of Short-Span Bridges Subjected to Strong Motion

In this paper four different methods are investigated for estimating the equivalent modal damping ratios of a short-span bridge under strong ground motion by considering the energy dissipation at the boundary. The Painter Street Overcrossing (PSO) is investigated because of seismic data availability. Computed responses using the response-spectrum method with the equivalent damping ratios estimates are compared with the recorded responses. The results show that the four methods provide reasonable estimation of equivalent modal damping ratios and that neglecting off-diagonal elements in the damping matrix is the most efficient and practical method. The equivalent damping ratio of the PSO was nearly 25% under an earthquake with peak ground acceleration of 0.55g, which is much higher than the conventional assumption of 5%.     

Linear Predictor-Based Lossless Compression of Vibration Sensor Data: Systems Approach

This paper presents a novel systems approach to compressing sensor network data. Unlike previous data compression methods, the proposed lossless linear predictor-based sensor data compression method utilizes structural system information to minimize the signal correlation in sensor network data. In the proposed method, linear predictor is derived in a system identification framework in which auto-regressive (AR) model is used as its model structure and the instrumental variables (IV) method is used to calculate the predictor parameters. A parametric study was carried out to study the effects of changes in system property, number of sensors, and sensor noise level on the compression performance of the proposed method. Both numerical simulation and experimental results show that the proposed sensor data compression method has a better compression performance than conventional linear predictor-based data compression method for single sensor.     

Ars Moriendi: illuminations on ''the good death'' from the arts and humanities

This paper presents a method for the identification of the dynamics of non-linear systems by learning from data. The key idea which underlies our approach consists of the integration of qualitative modeling techniques with fuzzy logic systems. The resulting hybrid method exploits the a priori structural knowledge on the system to initialize a fuzzy inference procedure which determines, from the available experimental data, a functional approximation of the system dynamics that can be used as a reasonable predictor of the patient's future state. The major advantage which results from such an integrated framework lies in a significant improvement of both efficiency and robustness of identification methods based on fuzzy models which learn an input output relation from data. As a benchmark of our method, we have considered the problem of identifying the response to the insulin therapy from insulin-dependent diabetic patients: the results obtained are presented and discussed in the paper.     

Vascularized fascial patch for repair of suboccipital dural defect

The capabilities of current protein structure prediction methods have been assessed from the outcome of a set of blind tests. In comparative modeling, many of the numerical methods did not perform as well as expected, although the resulting structures are still of great practical use. The new methods of fold identification ('threading') were partially successful, and show considerable promise for the future. Except for secondary structure data, results from traditional ab initio methods were poor. A second blind prediction experiment is underway, and progress in all areas is expected.     

Design of Mechanical Viscous Dampers for Stay Cables

External dampers have been utilized in a number of cable-stayed bridges to suppress transverse cable vibrations. However, simple and accurate damper design recommendations that concurrently consider all important cable parameters are lacking. Previous efforts have been based on the idealization of cables as taut strings. In this paper, the governing differential equation for vibration of cables containing a viscous damper was first converted to a complex eigenvalue problem containing nondimensional cable parameters. Then, a parametric study was conducted involving repeated solutions of the eigenvalue problem for a wide range of nondimensional parameters. Based on the results of the parametric study, the effects of dampers on first mode vibration frequencies and first mode cable damping ratios were presented in nondimensional format. It is shown that for the range of parameters involved in most stay cables, the influence of cable sag is insignificant, whereas the cable bending stiffness can have a significant influence on the resulting cable damping ratios. Simplified nondimensional relationships are proposed for calculating damper-induced changes in the first mode cable damping ratios. Results of laboratory tests on a scaled model cable are compared with the estimated values using the formulation presented. Finally, example problems are presented for comparison with other relationships, and for the design of mechanical viscous dampers for suppression of cable vibrations including rain-wind induced vibrations.     

Bayesian Model Updating Using Hybrid Monte Carlo Simulation with Application to Structural Dynamic Models with Many Uncertain Parameters

In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.     

Semi-Implicit Integration Algorithm for Stochastic Analysis of Multi-Degree-of-Freedom Structures

This paper presents a semi-implicit integration algorithm for random vibration problems that is appropriate for analyzing large structures, nonlinear hysteretic systems, and structural control problems. This semi-implicit approach results in a recursive expression for the mean and covariance response. A state-space representation of the equations of motion is adopted for deriving the algorithm. The solution of the state-space equations is first obtained, after which the expected value of the resulting equations is taken so as to obtain the first two moments. A stability condition for the method is also derived. Three numerical examples, a linear oscillator, a Duffing oscillator, and a multi-degree-of-freedom system with hysteretic supplemental damping devices, are provided to illustrate the effectiveness of the proposed method. Results compare well with Monte Carlo simulation, indicating that the semi-implicit integration algorithm is accurate and stable.     

Experimental Investigation of Static and Dynamic Properties of Steel–Rubber,Cast Iron–Rubber and Epoxy Granite–Rubber as IC Engine Mount

The effective way of reducing the vibration transmitted from the engine to the supporting structures is use of mounts. The mounts are used not only to isolate the vibration but also to withstand the static and dynamic loads of the engine. In this work, the mount structural materials are prepared from steel, cast iron and epoxy granite and tested for the structural properties and damping ratio. The mounts manufactured using these materials and natural rubber are tested using the experimental setup for the dynamic behavior with harmonic excitations. The results of the reaction forces exerted and the respective phase angles during the harmonic excitations showed that the epoxy granite–rubber mount has improved natural frequency and vibration isolation.