LMS‐based structural health monitoring of a non‐linear rocking structure

A structure's health or level of damage can be monitored by identifying changes in structural or modal parameters. This research directly identifies changes in structural stiffness due to modelling error or damage for a post‐tensioned pre‐cast reinforced concrete frame building with rocking beam column connections and added damping and stiffness (ADAS) elements. A structural health monitoring (SHM) method based on adaptive least mean squares (LMS) filtering theory is presented that identifies changes from a simple baseline model of the structure. This method is able to track changes in the stiffness matrix, identifying when the building is (1) rocking, (2) moving in a hybrid rocking–elastic regime, or (3) responding linearly. Results are compared for two different LMS‐based SHM methods using an L ₂ error norm metric. In addition, two baseline models of the structure, one using tangential stiffness and the second a more accurate bi‐linear stiffness model, are employed. The impact of baseline model complexity is then delineated. The LMS‐based methods are able to track the non‐linearity of the system to within 15% using this metric, with the error due primarily to filter convergence rates as the structural response changes regimes while undergoing the El Centro ground motion record. The use of a bi‐linear baseline model for the SHM problem is shown to result in error metrics that are at least 50% lower than those for the tangential baseline model. Errors of 5–15% with this L ₂ error norm are fairly stringent compared to the greater than 2 × changes in stiffness undergone by the structure, however, in practice the usefulness of the results is dependent on the resolution required by the user. The impact of sampling rate is shown to be negligible over the range of 200–1000Hz, along with the choice of LMS‐based SHM method. The choice of baseline model and its level of knowledge about the actual structure is seen to be the dominant factor in achieving good results. The methods presented require 2.8–14.0 Mcycles of computation and therefore could easily be implemented in real time. Copyright © 2005 John Wiley & Sons, Ltd.     

An experimental study of temperature effect on modal parameters of the Alamosa Canyon Bridge

Damage detection techniques have been proposed to exploit changes in modal parameters and to identify the extent and location of damage in large structures. Most of such techniques, however, generally neglect the environmental effects on modal parameters. Such environmental effects include changes in loads, boundary conditions, temperature, and humidity. In fact, the changes due to environmental effects can often mask more subtle structural changes caused by damage. This paper examines a linear adaptive model to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. Data from the Alamosa Canyon Bridge in the state of New Mexico were used to demonstrate the effectiveness of the adaptive filter for this problem. Results indicate that a linear four-input (two time and two spatial dimensions) filter to temperature can reproduce the natural variability of the frequencies with respect to time of day. Using this simple model, we attempt to establish a confidence interval of the frequencies for a new temperature profile in order to discriminate the natural variation due to temperature. Copyright © 1999 John Wiley & Sons, Ltd.     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

Damage identification of a 3D full scale steel–concrete composite structure with partial‐strength joints at different pseudo‐dynamic load levels

Partial‐strength composite steel–concrete moment‐resisting (MR) frame structures represent an open research field in seismic design from both a theoretical and an experimental standpoint. Among experimental techniques, vibration testing is a well‐known and powerful technique for damage detection, localization and quantification, where actual modal parameters of a structure at different states can be determined from test data by using system identification methods. However, the identification of semi‐rigid connections in framed structures is limited, and hence this paper focuses on a series of vibration experiments that were carried out on a realistic MR frame structure, following the application of pseudo‐dynamic and quasi‐static cyclic loadings at the European laboratory for structural assessment of the Joint Research Centre at Ispra, Italy, with the scope of understanding the structural behaviour and identifying changes in the dynamic response. From the forced vibration response, natural frequencies, damping ratios, modal displacements and rotations were extracted using the circle fitting technique. These modal parameters were used for local and global damage identification by updating a 3D finite element model of the intact structure. The identified results were then correlated with observations performed on the structure to understand further the underlying damage mechanisms. Finally, the latin hypercube sampling technique, a variant of the Monte Carlo method, was employed in order to study the sensitivity of the updated parameters of the 3D model to noise on the modal inputs. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical significance of modal parameters of bridge systems identified from strong motion data

Modal parameters of structural systems have commonly been determined using system identification (SI) methods for damage detection and health monitoring. For determining the deterioration of the integrity of structural systems correctly, modal parameters of a healthy structure have to be obtained with adequate certainty so that these parameters can be used as reliable references for the healthy system to compare with those of the damaged system. In this study, the statistical significance of modal parameters identified using strong motion time histories recorded on two bridge structures is assessed. The confidence intervals of identified modal frequencies and damping ratios are obtained using Monte Carlo simulations and sensitivity analyses in conjunction with eigenrealization algorithm. The dependence of the statistical bounds on model parameters is examined. The effect of using different number of sensors on the statistical significance is evaluated using simulated time history data from a validated finite element model of a bridge. Copyright © 2005 John Wiley & Sons, Ltd.     

Structural complexity-guided predictive filtering

Random noise attenuation utilizing predictive filtering achieves great performance in denoising seismic data. Conventional predictive filtering methods are based on fixed filter operators and neglect the complexity of structures. In this way, the denoised data cannot meet the requirement of balancing the signal preservation and noise removal. In this study, we proposed a structural complexity-guided predictive filtering method that utilizes an adapted filter operator to adjust the changes of structural complexity. The proposed structural complexity-guided predictive filtering mainly consists of two stages. A slope field information is acquired according to plane-wave destruction to assess the structural complexity. In addition, an adaptive filter operator is obtained to denoise the seismic data according to the adaptive factor. Both synthetic data and real seismic profiles are employed to examine the denoising capacity and flexibility of the refined predictive filtering using adaptive lengths. The analysis of the predicted results shows that adaptive predictive filtering is powerful and has the ability to eliminate random noises with negligible distortions.     

Tracking modal parameters from building seismic response data using recursive subspace identification algorithm

Tracking modal parameters and estimating the current structural state of a building from seismic response measurements, particularly during strong earthquake excitations, can provide useful information for building safety assessment and the adaptive control of a structure. Therefore, online or recursive identification techniques need to be developed and implemented for building seismic response monitoring. This paper develops and examines different methods to track modal parameters from building seismic response data. The methods include recursive data‐driven subspace identification (RSI‐DATA) using Givens rotation algorithm, and RSI‐DATA using Bona fide algorithm. The question on how well the results of RSI‐DATA reflect the real condition is investigated and verified with a bilinear SDOF simulation study. Time‐varying modal parameters of a four‐story reinforced concrete school building are identified based on a series of earthquake excitations, including several seismic events, large and small. Discussions on the different methods' ability to track the time‐varying modal parameters are presented. The variation of the identified building modal frequencies and damping ratios from a series of event‐by‐event seismic responses, particularly before and after retrofitting of the building is also discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamic characterization of a long span bridge: A finite element based approach

Aging bridges coupled with increasing traffic loads are producing a severe toll on the nation's infrastructure. This has made it necessary to take a closer look at the health of existing bridges and develop automated damage identification methods if possible. Recent works in the field of structural dynamics have shown that damage detection techniques utilizing parameters like mode shapes, modal frequencies and damping ratios can be used to identify damage in structural systems. It is, however, important to be able to establish a baseline model for the structure first, and then a model updating technique can be utilized to evaluate the condition of the structure from time to time. It is with this goal in mind that the authors have decided to establish the process for obtaining a baseline model for a long span bridge. Based on the actual design drawings of a bridge, finite element (FE) models of the bridge in question are developed using SDRC-IDEAS. Three models of the bridge are simulated using Normal Mode Dynamics solver in SDRC-IDEAS to obtain the modal parameters of interest, in this case the modal frequencies and the mode shapes. A modal assurance criteria (MAC) is utilized to compare the different simulated mode shapes and, finally, the modal frequencies that have been obtained from the FE analysis are compared to frequencies that have been obtained from some preliminary field tests.     

Bridge health monitoring system based on vibration measurements

A bridge health monitoring system is presented based on vibration measurements collected from a network of acceleration sensors. Sophisticated structural identification methods, combining information from the sensor network with the theoretical information built into a finite element model for simulating bridge behavior, are incorporated into the system in order to monitor structural condition, track structural changes and identify the location, type and extent of damage. This work starts with a brief overview of the modal and model identification algorithms and software incorporated into the monitoring system and then presents details on a Bayesian inference framework for the identification of the location and the severity of damage using measured modal characteristics. The methodology for damage detection combines the information contained in a set of measurement modal data with the information provided by a family of competitive, parameterized, finite element model classes simulating plausible damage scenarios in the structure. The effectiveness of the damage detection algorithm is demonstrated and validated using simulated modal data from an instrumented R/C bridge of the Egnatia Odos motorway, as well as using experimental vibration data from a laboratory small-scaled bridge section.     

Evolution of modal characteristics of a mid-rise cold-formed steel building during construction and earthquake testing

Vibration-based structural identification is an essential technique for assessing structural conditions by inferring information from the dynamic characteristics of structures. However, the robustness of such techniques in monitoring the progressive damage of real structures has been validated with only a handful of research efforts, largely due to the paucity of monitoring data recorded from damaged structures. In a recent experimental program, a mid-rise cold-formed steel building was constructed at full scale atop a large shake table and subsequently subjected to a unique multi-hazard scenario including earthquake, post-earthquake fire, and finally post-fire earthquake loading. Complementing the simulated hazard events, low-amplitude vibration tests, including ambient vibrations and white noise base excitation tests, were conducted throughout the construction and the test phases. Using the vibration data collected during the multi-hazard test program, this paper focuses on understanding the modal characteristics of the cold-formed steel building in correlation with the construction and the structural damage progressively induced by the simulated hazard events. The modal parameters of the building (i.e., natural frequencies, damping ratios, and mode shapes) are estimated using two input–output and two output-only time-domain system identification techniques. Agreement between the evolution of modal parameters and the observations of the progression of physical damage demonstrates the effectiveness of the vibration-based system identification techniques for structural condition monitoring and damage assessment.     

Structural damage detection using empirical-mode decomposition and vector autoregressive moving average model

A method based on empirical-mode decomposition (EMD) and vector autoregressive moving average (VARMA) model is proposed for structural damage detection. The basic idea of the method is that the structural damages can be identified as the abrupt changes in energy distribution of structural responses at high frequencies. Using the time-varying VARMA model to represent the intrinsic mode functions (IMFs) obtained from the EMD of vibration signal, we define a damage index according to the VARMA coefficients. In the two examples given, the Imperial County Services Building and the Van Nuys hotel are used as the benchmark structures to verify the effectiveness and sensitivity of the damage index in real environments with the presence of actual noise. The analysis results show that the damage index can indicate the occurrence and relative severity of structural damages at multiple locations in an efficient manner. The damage index can also be potentially used for structural health monitoring, since it is based on the time-varying VARMA coefficients. Finally, some recommendations for future research are provided.     

环境激励下基于波动能量法的结构损伤识别

目前作为结构健康监测系统核心的损伤识别大多是基于模态参数变化而进行的,但模态参数对局部损坏不敏感,导致损伤识别精度不够。波在结构中的传播状态可以更好地反映局部损伤状况,波动能量可以作为损伤识别的有效指标。为了提高环境激励下结构损伤识别的精度,采用S变换分析了结构输出信号,建立波动能量指标,从而使波动能量指标的使用领域扩展到非平稳信号范围。最后通过三层钢框架试验及弹性分层剪切梁的数值模型对该方法进行了验证,结果表明:该方法不仅能够有效识别结构损伤位置,而且能够识别出损伤程度。     

基于自然激励技术和FT时移特性的模态阻尼比识别方法

基于环境激励下结构动力响应信号分析与处理识别结构的模态参数,是结构健康监测和损伤诊断的一个重要环节,目前为止,要得到较为可靠的识别结果仍有一定困难,尤其是模态阻尼比。基于自然激励技术和傅里叶变换的时移特性,提出了一种新的结构模态阻尼比估算方法,通过理论推导和仿真算例验证了该方法的可行性,进而利用一刚构-连续组合梁桥在环境激励下的动力测试数据,通过该方法对其阻尼比进行了识别,并将识别结果与数据驱动随机子空间法的识别结果进行了对比。结果表明:提出的方法可以减轻噪声影响,得到可接受的识别结果,可为大型工程结构阻尼比的识别提供一个方便和有效的途径。     

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.     

Development of basic technique to improve seismic response accuracy of tributary area-based lumped-mass stick models

Although a detailed finite element(FE) model provides more precise results, a lumped-mass stick(LMS) model is preferred because of its simplicity and rapid computational time. However, the reliability of LMS models has been questioned especially for structures dominated by higher modes and seismic inputs. Normally, the natural frequencies and dynamic responses of a LMS model based on tributary area mass consideration are different from the results of the FE model. This study proposes a basic updating technique to overcome these discrepancies; the technique employs the identical modal response, D(t), to the detailed FE model. The parameter D(t) is a time variable function in the dynamic response composition and it depends on frequency and damping ratio for each mode, independent of the structure's mode shapes. The identical response D(t) for each mode is obtained from the frequency adaptive LMS model; the adaptive LMS model which can provide identical modal frequencies as the detailed FE model. Theoretical backgrounds and formulations of the updating technique are proposed. To validate the updating technique, two types of structures(a symmetric straight column and an unsymmetric T-shaped structure) are considered. From the seismic response results including base shear and base moment, the updating technique considerably improves the seismic response accuracy of the tributary area-based LMS model.     

Damage detection of a thin plate using modal curvature via macrostrain measurement

Plate structures are employed as important structural components in many engineering applications. Hence, assessing the structural conditions of in-service plate structures is critical to monitoring global structural health. Modal curvature-based damage detection techniques have recently garnered considerable attention from the research community, and have become a promising vibration-based structural health monitoring solution. However, computing errors arise when calculating modal curvatures from lateral mode shapes, which result from unavoidable measurement errors in the mode shapes as identified from lateral vibration signals; this makes curvature-based algorithms that use a lateral measurement only theoretically feasible, but practically infeasible. Therefore, in this study, long-gauge fiber Bragg grating strain sensors are employed to obtain a modal curvature without a numerical differentiation procedure in order to circumvent the computing errors. Several damage indices based on modal curvatures that were developed to locate beam damage are employed. Both numerical and experimental studies are performed to validate the proposed approach. However, although previous studies have reported relative success with the application of these damage indices on a simple beam, only one damage index demonstrated the capability to locate damage when the stiffness of the local region changed near the sensor.     

APPLICATION OF OFF-LINE AND ON-LINE IDENTIFICATION TECHNIQUES TO BUILDING SEISMIC RESPONSE DATA

The objectives of this paper are to present a comparison of the dynamic characteristics of a seven-storey reinforced concrete building (Van Nuys–Holiday Inn) identified from four recorded strong-motion response data (Whittier earthquake, Landers earthquake, Big Bear earthquake and Northridge earthquake). In the analysis, time-domain methods for estimating the system parameters and the modal properties of the building are studied. Both off-line and on-line identification algorithms are applied to these seismic response data. Under the assumption of a linear time-invariant system the ARX model and ARMAX model are used. Comparison of the identification results using different models are made. In addition, recursive procedures are adapted as on-line identification and the time-varying modal parameters are estimated. For structural systems under strong earthquake excitation, a recursive identification method, adaptive forgetting through multiple models (AFMM), is introduced to identify systems with rapidly changing parameters. Through the analysis of the seismic response data of the building subjected to four earthquakes the identification algorithm and the identification results are discussed.     

基于损伤部位向量法的钢框架损伤识别研究

对损伤部位向量(DLV)法作了简单介绍,并用该方法对钢框架进行了损伤识别和损伤定位。该方法假定结构损伤前后为线性,对结构损伤前后柔度矩阵差进行奇异值分解,将奇异值为零所对应的向量,作为静荷载施加在无损结构的测点位置,则应力为零的单元为可能损伤的单元。对3种不同工况的钢框架进行了振动模态试验,用前3阶模态参数构造框架的柔度矩阵,按照DLV法对其进行了损伤识别,识别结果与已知损伤情况相一致。从测试自由度不完备、噪声和振型质量归一化系数这3个方面对识别效果进行了分析,结果表明:当损伤使结构动力特性有微小改变时,使用该方法不易定位损伤,应结合局部损伤识别方法进行判定;当损伤使结构动力特性有较大改变时,该方法能有效识别损伤的单元。DLV方法概念简单,理论明确,不受结构类型的限制,不需要结构的数学模型和模型缩聚或扩展技术,只需获得结构损伤前后的前几个低阶模态参数,即可识别结构一处或多处损伤,实际应用时可操作性强。     

Subspace system identification of support‐excited structures—part I: theory and black‐box system identification

This paper reviews the theoretical principles of subspace system identification as applied to the problem of estimating black‐box state‐space models of support‐excited structures (e.g., structures exposed to earthquakes). The work distinguishes itself from past studies by providing readers with a powerful geometric interpretation of subspace operations that relates directly to theoretical structural dynamics. To validate the performance of subspace system identification, a series of experiments are conducted on a multistory steel frame structure exposed to moderate seismic ground motions; structural response data is used off‐line to estimate black‐box state‐space models. Ground motions and structural response measurements are used by the subspace system identification method to derive a complete input–output state‐space model of the steel frame system. The modal parameters of the structure are extracted from the estimated input–output state‐space model. With the use of only structural response data, output‐only state‐space models of the system are also estimated by subspace system identification. The paper concludes with a comparison study of the modal parameters extracted from the input–output and output‐only state‐space models in order to quantify the uncertainties present in modal parameters extracted from output‐only models. Copyright © 2012 John Wiley & Sons, Ltd.     

Damage assessment through structural identification of a three‐story large‐scale precast concrete structure

This paper investigates the damage assessment of a three‐story half‐scale precast concrete building resembling a parking garage through structural identification. The structure was tested under earthquake‐type loading on the NEES large high‐performance outdoor shake table at the University of California San Diego in 2008. The tests provide a unique opportunity to capture the dynamic performance of precast concrete structures built under realistic boundary conditions. The effective modal parameters of the structure at different damage states have been identified from white‐noise and scaled earthquake test data with the assumption that the structure responded in a quasi‐linear manner. Modal identification has been performed using the deterministic‐stochastic subspace identification method based on the measured input–output data. The changes in the identified modal parameters are correlated to the observed damage. In general, the natural frequencies decrease, and the damping ratios increase as the structure is exposed to larger base excitations, indicating loss of stiffness, development/propagation of cracks, and failure in joint connections. The analysis of the modal rotations and curvatures allowed the localization of shear and flexural damages respectively and the checking of the effectiveness of repair actions. Copyright © 2013 John Wiley & Sons, Ltd.