Output‐only structural identification in time domain: Numerical and experimental studies

By identifying changes in stiffness parameters, structural damage can be detected and monitored. Although considerable progress has been made in this research area, many challenges remain in achieving robust structural identification based on incomplete and noisy measurement signals. The identification task is made even more difficult if measurement of input force is to be eliminated. To this end, an output‐only structural identification strategy is proposed to identify unknown stiffness and damping parameters. A non‐classical approach based on genetic algorithms (GAs) is adopted. The proposed strategy makes use of the recently developed GA‐based method of search space reduction, which has shown to be able to accurately and reliably identify structural parameters from measured input and output signals. By modifying the numerical integration scheme, input can be computed as the parameter identification task is in progress, thereby eliminating the need to measure forces. Numerical and experimental results demonstrate the power of the strategy in accurate and efficient identification of structural parameters and damage using only incomplete acceleration measurements. Copyright © 2007 John Wiley & Sons, Ltd.     

Probabilistic approach for modal identification using non‐stationary noisy response measurements only

This paper addresses the problem of identification of the modal parameters for a structural system using measured non‐stationary response time histories only. A Bayesian time‐domain approach is presented which is based on an approximation of the probability distribution of the response to a non‐stationary stochastic excitation. It allows one to obtain not only the most probable values of the updated modal parameters and stochastic excitation parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centred at the most probable values of the parameters. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Structural identification with incomplete output‐only data and independence of measured information for shear‐type systems

Structural identification is the inverse problem of estimating physical parameters of a structural system from its vibration response measurements. Incomplete instrumentation and ambient vibration testing generally result in incomplete and arbitrarily normalized measured modal information, often leading to an ill‐conditioned inverse problem and non‐unique identification results. The identifiability of any parameter set of interest depends on the amount of independent available information. In this paper, we consider the identifiability of the mass and stiffness parameters of shear‐type systems in output‐only situations with incomplete instrumentation. A mode shape expansion‐cum‐mass normalization approach is presented to obtain the complete mass normalized mode shape matrix, starting from the incomplete non‐normalized modes identified using any operational modal analysis technique. An analysis is presented to determine the minimum independent information carried by any given sensor set‐up. This is used to determine the minimum necessary number and location of sensors from the point of view of minimum necessary information for identification. The different theoretical discussions are illustrated using numerical simulations and shake table experiments. It is shown that the proposed identification algorithm is able to obtain reliably accurate physical parameter estimates under the constraints of minimal instrumentation, minimal a priori information, and unmeasured input. The sensor placement rules can be used in experiment design to determine the necessary number and location of sensors on the monitored system. John Wiley & Sons, Ltd.     

Dual compensation strategy for real‐time hybrid testing

Real‐time hybrid testing is an experimental technique for evaluating the dynamic responses of structural systems under seismic loading. Servo‐hydraulic actuators, by nature, induce inevitable time delay between the command and the achieved displacements. This delay would lead to incorrect test results and even cause instability of the system; therefore, delay compensation is critical for stability and accuracy of hybrid simulations of structural dynamic response. In this paper, a dual delay compensation strategy is proposed by a combination of a phase lead compensator and a restoring force compensator. An outer‐loop feed‐forward phase lead compensator is derived by introducing the inverse model in the z domain. The adaptive law based on the gradient algorithm is used to estimate the system delay in the format of parametric model during the test. It is shown mathematically that the parameter in the delay estimator is guaranteed to converge. The restoring force compensator is adopted to improve the accuracy of experimental results especially when the structure is subjected to high frequency excitations. Finally, analytical simulations of an inelastic SDOF structure are conducted to investigate the feasibility of the proposed strategy. The accuracy of the dual compensation strategy is demonstrated through several shaking table tests. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimization approach to automatic first arrival picking for three‐component three‐dimensional vertical seismic profiling data

A new, adaptive multi‐criteria method for accurate estimation of three‐component three‐dimensional vertical seismic profiling of first breaks is proposed. Initially, we manually pick first breaks for the first gather of the three‐dimensional borehole set and adjust several coefficients to approximate the first breaks wave‐shape parameters. We then predict the first breaks for the next source point using the previous one, assuming the same average velocity. We follow this by calculating an objective function for a moving trace window to minimize it with respect to time shift and slope. This function combines four main properties that characterize first breaks on three‐component borehole data: linear polarization, signal/noise ratio, similarity in wave shapes for close shots and their stability in the time interval after the first break. We then adjust the coefficients by combining current and previous values. This approach uses adaptive parameters to follow smooth wave‐shape changes. Finally, we average the first breaks after they are determined in the overlapping windows. The method utilizes three components to calculate the objective function for the direct compressional wave projection. An adaptive multi‐criteria optimization approach with multi three‐component traces makes this method very robust, even for data contaminated with high noise. An example using actual data demonstrates the stability of this method.     

Tangential‐projection algorithm for manifold representation in unidentifiable model updating problems

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. In an identifiable case, the posterior probability density function (PDF) of the uncertain model parameters for given measured data can be approximated by a weighted sum of Gaussian distributions centered at a number of discrete optimal values of the parameters at which some positive measure‐of‐fit function is minimized. The present paper focuses on the problem of model updating in the general unidentifiable case for which certain simplifying assumptions available for identifiable cases are not valid. In this case, the PDF is distributed in the neighbourhood of an extended and usually highly complex manifold of the parameter space that cannot be calculated explicitly. The computational difficulties associated with calculating the highly complex posterior PDF are discussed and a new adaptive algorithm, referred to as the tangential‐projection (TP) algorithm, allowing for an efficient approximate representation of the above manifold and the posterior PDF is presented. Using this approximation, expressions for calculating the uncertain predictive response are established. A numerical example involving noisy data is presented to demonstrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Parameter identification for on‐line model updating in hybrid simulations using a gradient‐based method

To improve the efficiency of model fitting, parameter identification techniques have been actively investigated. Recently, the applications of parameter identification migrated from off‐line model fitting to on‐line model updating. The objective of this study is to develop a gradient‐based method for model updating to advance hybrid simulation also called hybrid test. A novel modification of the proposed method, which can reduce the number of design variables to improve the identification efficiency, is illustrated in detail. To investigate the model updating, simulated hybrid tests were conducted with a 5‐story steel frame equipped with buckling‐restrained braces (BRBs) utilized in the shaking table tests conducted in E‐Defense in Japan in 2009. The calibrated analytical model that was verified with the test results can serve as the reference model. In the simulated hybrid tests, the physical BRB substructure is numerically simulated by utilizing a truss element with the 2‐surface model identical to the part of the reference model. Such numerical verification allows simulation of measurement errors for investigation on the performance of the proposed method. Moreover, the feasibility of sharing the identified parameter values, which were obtained from the physical substructure responses, with the relevant numerical models is also verified with the artificial component responses derived from the physical experiments.     

Non‐stationary hydrological model parameters: a framework based on SOM‐B

The application of stationary parameters in conceptual hydrological models, even under changing boundary conditions, is a common yet unproven practice. This study investigates the impact of non‐stationary model parameters on model performance for different flow indices and time scales. Therefore, a Self‐Organizing Map based optimization approach, which links non‐stationary model parameters with climate indices, is presented and tested on seven meso‐scale catchments in northern Germany. The algorithm automatically groups sub‐periods with similar climate characteristics and allocates them to similar model parameter sets. The climate indices used for the classification of sub‐periods are based on (a) yearly means and (b) a moving average over the previous 61 days. Classification b supports the estimation of continuous non‐stationary parameters. The results show that (i) non‐stationary model parameters can improve the performance of hydrological models with an acceptable growth in parameter uncertainty; (ii) some model parameters are highly correlated to some climate indices; (iii) the model performance improves more for monthly means than yearly means; and (iv) in general low to medium flows improve more than high flows. It was further shown how the gained knowledge can be used to identify insufficiencies in the model structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Non‐linear system identification of the versatile‐typed structures by a novel signal processing technique

Non‐linear structural identification problems have raised considerable research efforts since decades, in which the Bouc–Wen model is generally utilized to simulate non‐linear structural constitutive characteristic. Support vector regression (SVR), a promising data processing method, is studied for versatile‐typed structural identification. First, a model selection strategy is utilized to determine the unknown power parameter of the Bouc–Wen model. Meanwhile, optimum SVR parameters are selected automatically, instead of tuning manually. Consequently, the non‐linear structural equation is rewritten in linear form, and is solved by the SVR technique. A five‐floor versatile‐type structure is studied to show the effectiveness of the proposed method, in which both power parameter known and unknown cases are investigated. Copyright © 2007 John Wiley & Sons, Ltd.     

An efficient algorithm for identifying pulse‐like ground motions based on significant velocity half‐cycles

Ground motions with strong velocity pulses are of particular interest to structural earthquake engineers because they have the potential to impose extreme seismic demands on structures. Accurate classification of records is essential in several earthquake engineering fields where pulse‐like ground motions should be distinguished from nonpulse‐like records, such as probabilistic seismic hazard analysis and seismic risk assessment of structures. This study proposes an effective method to identify pulse‐like ground motions having single, multiple, or irregular pulses. To effectively characterize the intrinsic pulse‐like features, the concept of an energy‐based significant velocity half‐cycle, which is visually identifiable, is first presented. Ground motions are classified into 6 categories according to the number of significant half‐cycles in the velocity time series. The pulse energy ratio is used as an indicator for quantitative identification, and then the energy threshold values for each type of ground motions are determined. Comprehensive comparisons of the proposed approach with 4 benchmark identification methods are conducted, and the results indicate that the methodology presented in this study can more accurately and efficiently distinguish pulse‐like and nonpulse‐like ground motions. Also presented are some insights into the reasons why many pulse‐like ground motions are not detected successfully by each of the benchmark methods.     

Damage detection of base‐isolated buildings using multi‐input multi‐output subspace identification

A damage detection algorithm of structural health monitoring systems for base‐isolated buildings is proposed. The algorithm consists of the multiple‐input multiple‐output subspace identification method and the complex modal analysis. The algorithm is applicable to linear and non‐linear systems. The story stiffness and damping as damage indices of a shear structure are identified by the algorithm. The algorithm is further tuned for base‐isolated buildings considering their unique dynamic characteristics by simplifying the systems to single‐degree‐of‐freedom systems. The isolation layer and the superstructure of a base‐isolated building are treated as separate substructures as they are distinctly different in their dynamic properties. The effectiveness of the algorithm is evaluated through the numerical analysis and experiment. Finally, the algorithm is applied to the existing 7‐story base‐isolated building that is equipped with an Internet‐based monitoring system. Copyright © 2004 John Wiley & Sons, Ltd.     

Algorithms for time synchronization of wireless structural monitoring sensors

Dense networks of wireless structural health monitoring systems can effectively remove the disadvantages associated with current wire‐based sparse sensing systems. However, recorded data sets may have relative time‐delays due to interference in radio transmission or inherent internal sensor clock errors. For structural system identification and damage detection purposes, sensor data require that they are time synchronized. The need for time synchronization of sensor data is illustrated through a series of tests on asynchronous data sets. Results from the identification of structural modal parameters show that frequencies and damping ratios are not influenced by the asynchronous data; however, the error in identifying structural mode shapes can be significant. The results from these tests are summarized in Appendix A. The objective of this paper is to present algorithms for measurement data synchronization. Two algorithms are proposed for this purpose. The first algorithm is applicable when the input signal to a structure can be measured. The time‐delay between an output measurement and the input is identified based on an ARX (auto‐regressive model with exogenous input) model for the input–output pair recordings. The second algorithm can be used for a structure subject to ambient excitation, where the excitation cannot be measured. An ARMAV (auto‐regressive moving average vector) model is constructed from two output signals and the time‐delay between them is evaluated. The proposed algorithms are verified with simulation data and recorded seismic response data from multi‐story buildings. The influence of noise on the time‐delay estimates is also assessed. Copyright © 2004 John Wiley & Sons, Ltd.     

Blind modal identification of output‐only structures in time‐domain based on complexity pursuit

Output‐only modal identification is needed when only structural responses are available. As a powerful unsupervised learning algorithm, blind source separation (BSS) technique is able to recover the hidden sources and the unknown mixing process using only the observed mixtures. This paper proposes a new time‐domain output‐only modal identification method based on a novel BSS learning algorithm, complexity pursuit (CP). The proposed concept—independent ‘physical systems’ living on the modal coordinates—connects the targeted constituent sources (and their mixing process) targeted by the CP learning rule and the modal responses (and the mode matrix), which can then be directly extracted by the CP algorithm from the measured free or ambient system responses. Numerical simulation results show that the CP method realizes accurate and robust modal identification even in the closely spaced mode and the highly damped mode cases subject to non‐stationary ambient excitation and provides excellent approximation to the non‐diagonalizable highly damped (complex) modes. Experimental and real‐world seismic‐excited structure examples are also presented to demonstrate its capability of blindly extracting modal information from system responses. The proposed CP is shown to yield clear physical interpretation in modal identification; it is computational efficient, user‐friendly, and automatic, requiring little expertise interactions for implementations. Copyright © 2013 John Wiley & Sons, Ltd.     

Application of subspace identification technique to long‐term seismic response monitoring of structures

This paper addresses the issue of structural system identification using earthquake‐induced structural response. The proposed methodology is based on the subspace identification algorithm to perform identification of structural dynamic characteristics using input–output seismic response data. Incorporated with subspace identification algorithm, a scheme to remove spurious modes is also used to identify real system poles. The efficiency of the proposed method is shown by the analysis of all measurement data from all measurement directly. The recorded seismic response data of three structures (one 7‐story RC building, one midisolation building, and one isolated bridge), under Taiwan Strong Motion Instrumentation Program, are analyzed during the past 15 years. The results present the variation of the identified fundamental modal frequencies and damping ratios from all the recorded seismic events that these three structures had encountered during their service life. Seismic assessment of the structures from the identified system dynamic characteristics during the period of their service is discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Structural impedance based damage diagnosis by piezo‐transducers

Although structural mechanical impedance is a direct representation of the structural parameters, its measurement is difficult at high frequencies owing to practical considerations. This paper presents a new method of damage diagnosis by means of changes in the structural mechanical impedance at high frequencies. The mechanical impedance is extracted from the electro‐mechanical admittance signatures of piezoelectric‐ceramic (PZT) patches surface bonded to the structure using the electro‐mechanical impedance (EMI) technique. The main feature of the newly developed approach is that both the real as well as the imaginary component of the admittance signature is used in damage quantification. A complex damage metric is proposed to quantify damage parametrically based on the extracted structural parameters, i.e. the equivalent single degree of freedom (SDOF) stiffness, the mass, and the damping associated with the drive point of the PZT patch. The proposed scheme eliminates the need for any a priori information about the phenomenological nature of the structure or any ‘model’ of the structural system. As proof of concept, the paper reports a damage diagnosis study conducted on a model reinforced concrete (RC) frame subjected to base vibrations on a shaking table. The proposed methodology was found to perform better than the existing damage quantification approaches, i.e. the low‐frequency vibration methods as well as the traditional raw‐signature based damage quantification in the EMI technique. Copyright © 2003 John Wiley & Sons, Ltd.     

A novel predictor–corrector algorithm for sub‐structure pseudo‐dynamic testing

A new predictor–corrector (P–C) method for multi‐site sub‐structure pseudo‐dynamic (PSD) test is proposed. This method is a mixed time integration method in which computational components separable from experimental components are solved by implicit time integration method (Newmark β method). The experiments are performed quasi‐statically based on explicit prediction of displacement. The proposed P–C method has an important advantage as it does not require the determination of the initial stiffness values of experimental components and is thus suitable for representing elastic and inelastic systems. A parameter relating to quality of displacement prediction at boundaries nodes is introduced. This parameter is determined such that P–C method can be applicable to many practical problems. Error‐propagation characteristics of P–C method are also presented. A series of examples including linear and non‐linear soil–foundation–structure interaction problem demonstrate the performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.     

System identification applied to long‐span cable‐supported bridges using seismic records

This paper presents the application of system identification (SI) to long‐span cable‐supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state‐space model. Numerical simulations using a benchmark cable‐stayed bridge demonstrate the advantages of this method in dealing with multiple‐input multiple‐output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu‐Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd.     

Scaling and self‐similarity in one‐dimensional unsteady open channel flow

The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial–boundary value problem, becomes self‐similar are investigated by utilizing one‐parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self‐similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self‐similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial–boundary value problem of a one‐dimensional unsteady open channel flow process in a prototype domain can be self‐similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal–horizontal and transverse–horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross‐section because the width‐to‐depth ratio and the inclination angles of the banks are conserved in a cross‐section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright © 2013 John Wiley & Sons, Ltd.     

Intelligent control for modelling of real‐time reservoir operation

This paper presents a new approach to improving real‐time reservoir operation. The approach combines two major procedures: the genetic algorithm (GA) and the adaptive network‐based fuzzy inference system (ANFIS). The GA is used to search the optimal reservoir operating histogram based on a given inflow series, which can be recognized as the base of input–output training patterns in the next step. The ANFIS is then built to create the fuzzy inference system, to construct the suitable structure and parameters, and to estimate the optimal water release according to the reservoir depth and inflow situation. The practicability and effectiveness of the approach proposed is tested on the operation of the Shihmen reservoir in Taiwan. The current M‐5 operating rule curves of the Shihmen reservoir are also evaluated. The simulation results demonstrate that this new approach, in comparison with the M‐5 rule curves, has superior performance with regard to the prediction of total water deficit and generalized shortage index (GSI). Copyright © 2001 John Wiley & Sons, Ltd.