Structural Health Monitoring by Recursive Bayesian Filtering

A new vision of structural health monitoring (SHM) is presented, in which the ultimate goal of SHM is not limited to damage identification, but to describe the structure by a probabilistic model, whose parameters and uncertainty are periodically updated using measured data in a recursive Bayesian filtering (RBF) approach. Such a model of a structure is essential in evaluating its current condition and predicting its future performance in a probabilistic context. RBF is conventionally implemented by the extended Kalman filter, which suffers from its intrinsic drawbacks. Recent progress on high-fidelity propagation of a probability distribution through nonlinear functions has revived RBF as a promising tool for SHM. The central difference filter, as an example of the new versions of RBF, is implemented in this study, with the adaptation of a convergence and consistency improvement technique. Two numerical examples are presented to demonstrate the superior capacity of RBF for a SHM purpose. The proposed method is also validated by large-scale shake table tests on a reinforced concrete two-span three-bent bridge specimen.     

Two-Stage Structural Health Monitoring Approach for Phase I Benchmark Studies

This paper presents a two-stage structural health monitoring methodology and applies it to the Phase I benchmark study sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. In the first stage, modal parameters are identified using measured structural response from the undamaged system and then from the (possibly) damaged system. In the second stage, these data are used to update a parametrized structural model of the system using Bayesian system identification. The approach allows one to obtain not only estimates of the stiffness parameters but also the probability that damage in any substructure exceeds any specified threshold expressed in terms of a fractional stiffness loss. It successfully identifies the location and severity of damage in all cases of the benchmark problem.     

Model Selection Using Response Measurements: Bayesian Probabilistic Approach

A Bayesian probabilistic approach is presented for selecting the most plausible class of models for a structural or mechanical system within some specified set of model classes, based on system response data. The crux of the approach is to rank the classes of models based on their probabilities conditional on the response data which can be calculated based on Bayes’ theorem and an asymptotic expansion for the evidence for each model class. The approach provides a quantitative expression of a principle of model parsimony or of Ockham’s razor which in this context can be stated as “simpler models are to be preferred over unnecessarily complicated ones.” Examples are presented to illustrate the method using a single-degree-of-freedom bilinear hysteretic system, a linear two-story frame, and a ten-story shear building, all of which are subjected to seismic excitation.     

Application of Wavelet Approach for ASCE Structural Health Monitoring Benchmark Studies

This paper presents an application of wavelet analysis for damage detection and locating damage region(s) for the ASCE structural health monitoring benchmark data. The response simulation data were generated basically by a FEM program provided by the ASCE Task Group on Health Monitoring for a four-story prototype building structure subjected to simulated stochastic wind loading. Damage was introduced in the middle of response by breaking one or more structure elements such as interstory braces. Wavelets were used to analyze the simulation data. It was found that structural damage due to sudden breakage of structural elements and the time when it occurred can be clearly detected by spikes in the wavelet details. The damaged region can be determined by the spatial distribution pattern of the observed spikes. The effects of measurement noise and the severity of damage were investigated. The results in this paper illustrate a great promise of wavelet analysis for structural health monitoring, especially for an on-line application.     

Bayesian Analysis of the Phase II IASC–ASCE Structural Health Monitoring Experimental Benchmark Data

A two-step probabilistic structural health monitoring approach is used to analyze the Phase II experimental benchmark studies sponsored by the IASC–ASCE Task Group on Structural Health Monitoring. This study involves damage detection and assessment of the test structure using experimental data generated by hammer impact and ambient vibrations. The two-step approach involves modal identification followed by damage assessment using the pre- and postdamage modal parameters based on the Bayesian updating methodology. An Expectation–Maximization algorithm is proposed to find the most probable values of the parameters. It is shown that the brace damage can be successfully detected and assessed from either the hammer or ambient vibration data. The connection damage is much more difficult to reliably detect and assess because the identified modal parameters are less sensitive to connection damage, allowing the modeling errors to have more influence on the results.     

Bayesian Probabilistic Approach for the Correlations of Compression Index for Marine Clays

The compression index is an important soil property that is essential to many geotechnical designs. Over the decades, a number of empirical correlations have been proposed to relate the compressibility to other soil index properties, such as the liquid limit, plasticity index, in situ water content, void ratio, specific gravity, etc. The reliability and thus predictability of these correlations are always being questioned. Moreover, selection between simple and complicated models is a difficult task and often depends on subjective judgments. A more complicated model obviously provides “better fit” to the data but not necessarily offers an acceptable degree of robustness to measurement noise and modeling error. In the present study, the Bayesian probabilistic approach for model class selection is used to revisit the empirical multivariate linear regression formula of the compression index. The criterion in the formula structure selection is based on the plausibility of a class of formulas conditional on the measurement, instead of considering the likelihood only. The plausibility balances between the data fitting capability and sensitivity to measurement and modeling error, which is quantified by the Ockham factor. The Bayesian method is applied to analyze a data set of 795 records, including the compression index and other well-known geotechnical index properties of marine clay samples collected from various sites in South Korea. It turns out that the correlation formula linking the compression index to the initial void ratio and liquid limit possesses the highest plausibility among a total of 18 candidate classes of formulas. The physical significance of this most plausible correlation is addressed. It turns out to be consistent with previous studies and the Bayesian method provides the confirmation from another angle.     

Probabilistic Models for Modulus of Elasticity of Self-Consolidated Concrete: Bayesian Approach

Current models of the modulus of elasticity, E, of concrete recommended by the American Concrete Institute and the American Association of State Highway and Transportation Officials are derived for normally vibrated concrete (NVC). Because self-consolidated concrete (SCC) mixtures differ from NVC in the quantities and types of constituent materials, supplementary cementing materials, and chemical admixtures, the current models, may not take into consideration the complexity of SCC, and thus they may predict the E of SCC inaccurately. Although some authors recommend specific models to predict E of SCC, they include only a single variable of assumed importance, namely, the design compressive strength of concrete, fc′. However, there are other parameters that may need to be accounted for while developing a prediction model for E of SCC. In this paper, a Bayesian variable selection method is used to identify the significant parameters in predicting the E of SCC, and more accurate models for E are generated using these variables. The models have a parsimonious parametrization for ease of use in practice and properly account for the prevailing uncertainties.     

Electromechanical Impedance-Based Structural Health Monitoring with Evolutionary Programming

An impedance-based structural health monitoring technique is presented. By analyzing the in-plane vibration of a thin lead–zirconate–titanate (PZT) patch, the electromechanical impedance of the PZT patch is predicted. The force impedances of a beam and a plate with damage are calculated by Ritz method using polynomial as shape functions. The damage is then identified from the changes of the impedance spectra caused by the appearance of damage. A hybrid evolutionary programming is employed as a global search technique to back-calculate the damage. A specially designed fitness function is proposed, which is able to effectively reduce the inaccuracy in representing the real structure using analytical or numerical models. Experiments are carried out on a beam and a plate to verify the numerical predictions. The results demonstrate that the proposed method is able to effectively and reliably locate and quantify the damage in the beam and the plate.     

Quantitative Structural Health Monitoring by Ultrasonic Guided Waves

This paper presents a global-local (GL) method to simulate the interaction of ultrasonic guided waves with structural defects in isotropic and multilayered composite platelike structures. The GL method uses a full finite-element (FE) discretization of the defected region to properly represent wave diffraction phenomena and a suitable set of wave functions to simulate regions away from the joint. Displacement and stress continuity conditions are imposed at the boundary between the global and the local regions. The radiated wave field can be then calculated by using standard techniques (least-squares method). The novelty of the proposed approach over previous GL techniques is the use of semianalytical FE (SAFE) modeling for the “global” simulation. The SAFE method, which only requires the discretization of the waveguide’s cross section, allows handling complex structures (multilayered composites, arbitrary cross sections, etc.) in a computationally efficient manner. Applications of the GL method to damage quantification will be shown for the cases of notches in aluminum plates and delaminationlike defects in aircraft composite panels.     

Application of a Statistical Model Updating Approach on Phase I of the IASC-ASCE Structural Health Monitoring Benchmark Study

This paper addresses the problem of structural health monitoring (SHM) and damage detection based on a statistical model updating methodology which utilizes the measured vibration responses of the structure without any knowledge of the input excitation. The emphasis in this paper is on the application of the proposed methodology in Phase I of the benchmark study set up by the IASC–ASCE Task Group on structural health monitoring. Details of this SHM benchmark study are available on the Task Group web site at 〈http://wusceel.cive.wustl.edu/asce.shm〉. The benchmark study focuses on important issues, such as: (1) measurement noise; (2) modeling error; (3) lack of input measurements; and (4) limited number of sensors. A statistical methodology for model updating is adopted in this paper to establish stiffness reductions due to damage. This methodology allows for an explicit treatment of the measurement noise, modeling error, and possible nonuniqueness issues characterizing this inverse problem. The paper briefly describes the methodology and reports on the results obtained in detecting damage in all six cases of Phase I of the benchmark study assuming unknown (ambient) data. The performance, limitations, and difficulties encountered by the proposed statistical methodology are discussed.     

Long-Term Structural Health Monitoring of the San Ysidro Bridge

As part of the Lifecycle Innovative Financing Evaluation initiative, the San Ysidro Bridge along U.S. Route 550 will be monitored throughout a 10?year warranty period to determine changes in deflection, stiffness, and load-carrying capacity. This paper discusses an initial live-load test on the San Ysidro Bridge as well as a subsequent load test on a full-scale single lane test bridge. The two load tests in conjunction with finite element modeling were used to determine the load rating for both shear and moment of the San Ysidro Bridge. This load rating was then compared with the load rating using the distribution factors from the American Association of State Highway and Transportation Officials (AASHTO) Standard and Load and Resistance Factor Design Specifications. According to both AASHTO specifications, the interior girder shear controlled the load rating of the San Ysidro Bridge. Using the finite element modeling scheme of frame and shell elements the interior girder moment was found to control the design. This load rating will be used as a baseline for comparison with future load ratings throughout the warranty period.     

Application of Structural Health Monitoring Techniques to Track Structural Changes in a Retrofitted Building Based on Ambient Vibration

One of the issues complicating the reliability assessment of structural health monitoring (SHM) methodologies slated for implementation under field conditions for damage detection in conjunction with typical infrastructure systems, is the paucity of experimental measurements from such structures. Particularly lacking is the availability of experimental data from physical structures, where quantifiable changes are made in the structure while SHM studies are being performed. That is precisely the focus of this paper. As a result of the 1994 Northridge Earthquake, a critical six-story building in the metropolitan Los Angeles region was found to need significant seismic mitigation measures. The building was instrumented with 14 state-of-the-art strong-motion accelerometers that were placed at various locations and in different orientations throughout the building. The instrumentation network was used to acquire extensive ambient vibration data sets at regular intervals that covered the whole construction phase, during which the building evolved from its original condition to the retrofitted status. This paper evaluates the usefulness of the natural excitation technique (NExT) in conjunction with the eigensystem realization algorithm (ERA) to determine the evolution of the modal properties of the subject building during the various phases of its retrofit process. Further, an assessment is made of the influence on the system identification results of significant user-selectable parameters such as: data window size and overlap; reference degree-of-freedom; and the dimensions of the associated Hankel matrix. In spite of the very low levels of ambient excitation, and the low spatial resolution of the sensors, use of the NExT/ERA algorithm yielded excellent identification results of the dominant modes of the building. Changes in the identified structural frequencies are correlated with the time that specific structural changes were made. It is shown that this unique collection of data can be extremely useful in calibrating the accuracy and sensitivity of various SHM schemes, as well as in providing useful identification parameter guidelines that can assist in the planning and deployment of sensor networks and associated data collection schemes for SHM applications.     

Long-Term Wireless Structural Health Monitoring of the Ferriby Road Bridge

As part of an effective bridge management system, sensor networks can provide data to support both inspection and assessment. Wireless sensor networks (WSNs) have the potential to offer significant advantages over traditional wired monitoring systems in terms of sensor, cabling, and installation costs as well as expandability. However, there are drawbacks with WSNs relating to power, data bandwidth, and robustness. To evaluate the potential of WSNs for use in bridge management, a network of seven sensor nodes was installed on the Ferriby Road Bridge, a three-span reinforced concrete bridge. Three displacement transducer nodes were placed across cracks on the soffit of the bridge to measure the change in crack width. Three inclinometer sensor nodes were mounted on two of the elastomeric bearing pads to measure the change in inclination of the bearing pads while a final node monitored temperature in the box that contained the gateway. The installation of the WSN is discussed and data from this network is analyzed. Finally, the use of sensor networks to support inspection and assessment is discussed.     

Structural Health Monitoring by Piezo-Impedance Transducers. I: Modeling

The electromechanical impedance (EMI) technique, which employs piezoelectric–ceramic lead–zirconate–titarate (PZT) patches as impedance transducers, has emerged as a powerful nondestructive evaluation technique during the last few years. This series of two papers present a new simplified methodology to diagnose structural damages by means of surface bonded piezo-impedance transducers. The first part introduces a new PZT–structure electroelastic interaction model based on the concept of “effective impedance.” The proposed formulations can be conveniently employed to extract the mechanical impedance of any “unknown” structural system from the admittance signatures of a surface bonded PZT patch. This is an improvement over the existing models, whose complexity prohibits direct application in similar practical scenarios. This also eliminates the requirement of any a priori information concerning the phenomenological nature of the structure. The proposed model is experimentally verified by means of test on a smart system comprising an aluminum block with a PZT patch instrumented on it. Part II of this paper outlines a new methodology to evaluate structural damages using the extracted impedance spectra. The proposed approach is found to be suitable for diagnosing damages in structures ranging from miniature precision machine and aerospace components to large civil structures.     

Sensor Network for Structural Health Monitoring of a Highway Bridge

A bridge monitoring TestBed is developed as a research environment for sensor networks and related decision-support technologies. A continuous monitoring system, capable of handling a large number of sensor data channels and three video signals, is deployed on a four-span, 90-m long, reinforced concrete highway bridge. Of interest is the integration of the image and sensor data acquisition into a single computer, thereby providing accurate time synchronization between the response and corresponding traffic loads. Currently, video and acceleration records corresponding to traffic induced vibration are being recorded. All systems operate online via a high-speed wireless Internet network, allowing real-time data transmission. Elements of the above health monitoring framework are presented herein. Integration of these elements into an automated functional system is emphasized. The recorded data are currently being employed for structural system identification via a model-free technique. Effort is also underway to correlate the moving traffic loads with the recorded accelerations. Finally, the TestBed is available as a resource for verification of new sensor technologies, data acquisition/transmission algorithms, data mining strategies, and for decision-support applications.     

Overview of Vibrational Structural Health Monitoring with Representative Case Studies

In the field of nondestructive evaluation and damage detection, there is continued interest in the utilization of vibrational techniques. Structural damage will result in permanent changes in the distribution of structural stiffness. These changes may be detected through structural monitoring. Because of the direct relationship of stiffness, mass, and damping of a multi-degree-of-freedom system to the natural frequencies, mode shapes, and modal damping values, many studies have been directed at using these dynamic properties for the purpose of structural health monitoring. The use of vibrational monitoring is a developing field of structural analysis and is capable of assisting in both detecting and locating structural damage. Vibrational data have been shown to be most useful when used in conjunction with other monitoring systems if a remote and robust damage detection scheme is desired. This paper includes a literature review that summarizes the basic approaches to vibrational monitoring, suggested guidelines for sensor selection and monitoring, and concludes with three example case studies.     

Probabilistic Approach to Predict Cracking in Lightly Reinforced Microconcrete Panels

The ultimate strength of structures made of brittle materials—such as microconcrete—strongly depends on microstructural defects, the structure size, and the loading pattern. Probabilistic approaches allow one to take account of such dependencies. By using a Weibull model, cracking of ferrocement panels is analyzed. Provided the behavior of the reinforcement remains elastic, it is shown that the Weibull parameters identified on unreinforced microconcrete samples tested in flexure may be used to predict multiple cracking in ferrocement panels tested in tension. A key aspect of the analysis is related to the understanding and modeling of the stress heterogeneity effect on the local failure probability of unreinforced as well as reinforced microconcrete by the use of a so-called Weibull stress.     

Unified Approach to Probabilistic and Possibilistic Analysis of Uncertain Systems

Various methods exist for assessing the safety of a structural or mechanical system that has uncertain parameters. These methods are either statistical (probabilistic), in which case the probability of failure is sought, or deterministic (possibilistic), in which case bounds on the response are sought. Well-known statistical methods include the first-order reliability method (FORM) and the second-order reliability method (SORM), while deterministic methods include interval analysis, convex modeling, and fuzzy set theory (although the categorization of the latter approach as a deterministic method is debatable). The development of probabilistic and possibilistic methods has tended to occur independently, with specialized algorithms being developed for the implementation of each technique. It is shown here that a wide range of probabilistic and possibilistic methods can be encompassed by a single mathematical algorithm, so that, for example, existing codes for FORM and SORM can potentially be employed for other methods, thus allowing the designer to readily choose the method most suited to the available data. A second common algorithm is also derived, and the analysis is illustrated by application to a simple system composed of N structural components in series.     

Approach to Designing Structural Slurry Walls

Some of the deepest structural slurry walls in the world were designed for permanent training walls at the Dam No. 2 Hydropower Project on the Arkansas River. Each of the 152 wall panels had to be optimized for embedment, length, section type, and restraining system. Compatibility for deflection and load transfer of adjacent panels was an integral part in designing individual structural slurry wall panels to behave as a system of panels. Design of the structural slurry walls utilized the computer program RIDO to analyze the deflection, shear, and moment under construction and operation conditions. Structural requirements for the design based on the RIDO analyses were checked using STAAD-III. A third program (SOILSTRUCT) was used to verify the 2D global deformation of the proposed structural slurry wall system. Analyses and design had to be completed in a short 9-month time frame. This paper presents the design methodology, approach, and procedures for optimization of the structural slurry wall system required to make this project a reality.