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This paper presents a structural damage assessment method that relies on a cross-correlation-based damage sensitive feature known as Inner Product Vector (IPV). Such a feature is extracted from the dynamic response measured at different locations within a structure. Previous investigations on the use of the IPV in a damage detection framework were conducted through laboratory tests by manipulating the excitation source in an input-output approach. In this paper, a new output-only approach has been developed to extract the Inner Product Vector only from the structural response time histories without knowledge of the input excitation. This is a more realistic scenario in structural health monitoring applications where it is difficult (in some cases, impossible) to monitor the external forces. The new estimation of the IPV is accomplished by taking the cross-correlations between filtered contributions to the overall structural response. It is shown how the elements of the IPV are affected by changes of the structural properties induced by damage and how effective the proposed approach is in the presence of external disturbances. The proposed approach has been proven to be very effective in dealing with dense sensor networks requiring large computational efforts. Numerical and experimental tests have been performed to address the reliability of the proposed damage index as a damage sensitive feature in an output-only framework.

This paper proposes a novel method suitable for vibration-based damage identification of civil structures and infrastructures under ambient excitation. The damage-sensitive feature employed in the presented algorithm consists of a vector of multivariate autoregressive parameters estimated from the vibration responses collected at different locations of the analyzed structure. Outlier analysis and statistical pattern recognition are exploited for damage detection and localization. In particular, the Mahalanobis distance between a set of reference (i.e., “healthy”) and inspection parameters is evaluated. A threshold is then selected to determine whether the inspection vectors refer to damaged or undamaged conditions. The effectiveness of the proposed approach is proved using numerical simulations and experimental data from a benchmark test. The analysis results show that the largest values of Mahalanobis distance can be found in the proximity of those sensors closest to the damaged elements. Thus, the Mahalanobis distance applied to vectors of multivariate autoregressive parameters has proven to be a robust indicator for damage detection and localization.

Damage identification for structural health monitoring (SHM) is explored through applying the x-vector speaker recognition technique in the structural domain. Using the progressive damage tests from the Z24 Bridge Benchmark dataset, a time-delay neural network (TDNN) is trained as an acoustic model to classify the provided global damage scenarios. The outputs of a pre-final layer, called x-vectors, are used as damage-sensitive features for identification of damage presence and mechanisms. Since the developed TDNN has learned the underpinning dynamics of the damage mechanisms in the Z24 tests, we apply it as a basis for damage identification problems tangential to the Z24 progressive damage classification task. Transfer learning and domain transfer are investigated via application of the developed TDNN towards local damage identification of the Z24 Bridge, and global and local damage identification for the unseen LANL SHM Alamosa Canyon Bridge, UC-Irvine Bridge Column, and Bookshelf studies. Supervised and unsupervised classification techniques are explored to assess this method, and strong results in damage detection are obtained for these SHM problems.

Quantification of the mechanical properties of suspension bridge main cables during fire hazards is a vital part of holistic safety assessment of infrastructure. While some researchers hav...

none 5 si Modal flexibility-based methods are recognized in the literature as effective methods for detecting damage in structures using vibration measurements. However, the application of such methods with output-only data (as is the case of civil structures tested under ambient excitations) is challenging, because the mass normalization factors required for assembling the modal flexibility matrix cannot be estimated directly from the data. To address this issue, a method for output-only damage detection and localization in building structures that can be applied with minimal or no a-priori information about the structural masses has been proposed in a previous work by the authors. In the method, to estimate the mass distribution and to assemble the proportional flexibility matrices, the modal orthogonality relationships that involve the mode shapes and the structural masses are used to form a system of equations, and through that system of equations, an inverse problem is solved for the estimation of the mass distribution. Reducing the number of available modes, however, reduces the number of available equations, while the number of unknowns (i.e., the number of degrees of freedom) stay the same; hence, the approach cannot be applied when the modal space is severely truncated. This paper proposes a technique for estimating the mass distribution and assembling proportional flexibility matrices from output-only vibration data that overcomes the mentioned limitations and that can be applied for any number of identified modes, including the case in which the modal space is severely truncated. The proposed technique is then integrated into the above-mentioned method for output-only damage detection in building structures, to verify the applicability of the whole procedure when considering the case of severely truncated modal spaces. Numerical simulations and experimental vibration tests were used to demonstrate the validity and effectiveness of the approaches proposed in this paper. mixed Bernagozzi G.; Mukhopadhyay S.; Betti R.; Landi L.; Diotallevi P.P. Bernagozzi G.; Mukhopadhyay S.; Betti R.; Landi L.; Diotallevi P.P.

In recent years, a new research direction in structural condition assessment has been focusing on developing automated or semi-automated procedures to identify a structure’s modal parameters from its response measurements. This is because long-term structural monitoring systems rely on the implementation of system identification methodologies that often involve the intervention of an expert user with an acquired experience in the field. This paper aims to offer a semi-automated methodology for extracting the modal parameters independently of the chosen parametric system identification technique with minimum user involvement in the parameter selection process. Here, the framework is applied to two different parametric system identification algorithms: Data-Driven Stochastic Subspace Identification (DD-SSI) and Output Only Observer Kalman Filter (O/O OKID). The procedure can be represented as a multi-stage strategy where unsupervised tools and three clustering options are offered to the user to reach a reliable estimate of the modal parameters. The proposed procedure is validated with an application in the operational modal analysis of an existing hospital structure located in Italy. The results demonstrated excellent accuracy and robust performance of the methodology, even in the presence of closely spaced modes. The proposed procedure helps to improve the data analysis process in continuous monitoring, where usually, the algorithm’s parameters need to be constantly updated by the user.

This article presents the development and the results of three years of implementation of an automated vibration-based structural health monitoring system for modal tracking the dynamic characteristics of a concrete-masonry Civic Tower in Rieti (Italy) equipped with a passive vibration control system, a Non-Conventional Tuned Mass Damper. The system is based on the data recorded by a small number of high-sensitivity accelerometers set on remote automated modal parameters tracking. The analysis of monitoring data highlights the main characteristics of the response of the tower to operational vibrations and low-return period earthquakes. Despite the low levels of vibration in operational conditions, the system can track the evolution of the structural frequencies along time and successfully capture their dependence from temperature, both daily and seasonally. Moreover, the robustness of the modal identification procedure allowed the detection of anomalous variation from the validated reference dynamics of the structure.

Nowadays, long-term monitoring systems rely on the efficient implementation of automated methodologies to extract the modal parameters of buildings and bridges to assess their structural integrity. However, modal parameter estimation, usually, requires a certain level of user interaction, mainly when parametric system identification methods are used. Such procedures generally depend on the selection of a set of parameters, defined according to heuristic criteria, and kept constant during long monitoring campaigns. The main objective of this paper is to prove the necessity of abandoning identification approaches based on a single set of parameters for long-term monitoring campaigns and to propose a semi-automated modal identification tool, where the user-defined parameters vary within an established range of values, that can be set independently of the user’s expertise. The proposed method is validated with an application in the operational modal analysis of a historic civic tower, and its excellent results demonstrate the importance of considering multiple sets of parameters, mainly when dealing with complex structures and challenging monitoring conditions.

This paper presents a new approach for the identification of linear state-space models from input–output measurements in the presence of noise. In contrast to the original OKID/ERA algorithm, which works through the observer Markov parameters, the new approach uses the estimated observer output residuals to convert a stochastic identification problem into a virtually deterministic one. A system state-space model and an associated Kalman-filter gain can be then identified. Because the converted problem is virtually deterministic, any deterministic system-identification method can be used. The proposed stochastic-to-deterministic conversion enables these deterministic algorithms to produce the same performance level as the existing stochastic system-identification algorithms.

Suspension-bridge cables are constructed from strands of galvanized steel wire. They are failure-critical structural members, so a fundamental understanding of their mechanics is imminently important in quantifying suspension bridge safety. The load-carrying capabilities of such strands after local wire failures have been the subject of many theoretical studies utilizing analytical equations and finite-element analysis. Little experimental data, however, exists to validate these models.Over the past five years we have developed a methodology for measuring stress/strain transfer within parallel wire strands of suspension bridge cables using neutron diffraction [1,2]. In this paper we describe the design and verification of parallel cable strands used in our studies. We describe the neutron diffraction strain measurements performed on standard 7-wire and expanded 19-wire models in various configurations at both the Los Alamos National Laboratory Spectrometer for Materials Research at Temperature and Stress (LANL SMARTS) and at the Oak Ridge National Laboratory VULCAN Engineering Materials Diffractometer (ORNL VULCAN). Particular attention is placed on the challenges of aligning and measuring multibody systems with high strain gradients at body-to-body contact points.

We report the first direct measurements of clamping strains within individual wires of a 19 parallel wire strand constrained by a clamshell clamp. In these measurements neutron diffraction was used to determine the elastic strains along three orthogonal axes for all of the individual wires across the strand cross section underneath the clamp for various clamping loads. We observed that, while, for all clamping loads, the clamping strains within individual wires were heterogeneously distributed, increasing the clamping force significantly decreased the strain heterogeneity. In contrast, no strain heterogeneity was observed in a rigorous companion finite-element model of the strand unless dimensional variations in the wire diameters were introduced. Our results are in agreement with the hypothesis by Gjelsvik, which states that, within a parallel wire bridge cable, local variations in wire diameter due to manufacturing tolerances can lead to large variations in clamping constraint.

The heat transfer problem is often considered to be the kernel of a fire resistance analysis. In fact, one- or two-dimensional closed-form solutions have long laid the foundation for an eng...

The performance of suspension bridges exposed to fire hazards is severely under-studied – so much so that no experimental data exists to quantify the safety of a suspension bridge during or after a major fire event. Bridge performance and safety rely on the integrity of the main cable and its constituent high-strength steel wires. Due to the current lack of experimental high temperature data for wires, the theoretical models use properties and coefficients from data for other types of structural steel. No other structural steel undergoes the amount of cold-working that bridge wire does, and plastic strains from cold-working can be relieved at high temperature, drastically weakening the steel. As such, this work determines the elastic modulus, ultimate strength, and general thermo-mechanical profile of the high-strength steel wires in a range of elevated temperature environments. Specifically, these tests are conducted on a bundle of 61-wires (transient), and at the single wire level (steady-state) at a temperature range of approximately 20-700°C. The test results show an alarmingly high reduction in the elastic modulus and ultimate strength with increased temperature. The degradation shown by experiments is higher than predicted by current theoretical models, indicating that use of high-temperature properties of other types of steel is not sufficient. The test results also show scaling agreement between the single wire and the 61-wire bundle, implying that a full material work up at the single- wire level will accurately inform the failure characterization of the full cable.

Mel-Frequency Cepstral Coefficients (MFCCs) have been proved to be viable to detect damage-induced shifts in the frequency content of structures subjected to external forces. Nevertheless, the Melodic (Mel) Scale is a perceptual feature, roughly based on human perception and originally formulated to resemble the biological mechanisms of the auditory apparatus. Thus, its straight application to non-auditive acquisition systems may be misleading. However, the intrinsic basilar assumption – that is, a nonlinear, non-constant spacing between filters in the frequency domain – is promising for the time-frequency analysis of structural dynamic behaviour. Here, an ensemble of related techniques, developed departing from the original approach, is described; different features, filter types and filter spacing have been investigated. Candidates are compared to each other and benchmarked against the previous approaches present in Literature on the challenging Case Study of the Fossano Bell Tower, considering realistic damage scenarios.

The difficulties in dynamic system modeling and the recently developed machine learning tools have moved the attention of the structural damage assessment community towards a new direction. Attention is now placed on the immediate extraction of damage sensitive features directly from the monitored dynamic response of the structure, allowing engineers by-pass the creation of complex and sophisticated structural models. It is in this framework that the work presented in this paper has to be considered: the extraction of new damage sensitive features in the quefrency domain is discussed in the context of a vibration based analysis. Despite such a domain has been fully explored in acoustics, it represents an uncommon approach for the civil engineering community. In this paper, some variables characterizing the system dynamic response in the quefrency domain, referred to as cepstral coefficients, have been derived as functions of the structural characteristics and used in a damage assessment strategy. The main advantage of the quefrency domain over the frequency domain consists in a massive dimensionality reduction and, when dealing with real data, in a simplification of the extraction of cepstral coefficients versus that of natural frequencies. In this paper, the analytical expression of cepstral coefficients of the structural acceleration response has been derived and the statistical distribution of such coefficients has been investigated in a pattern recognition approach. In addition, a damage assessment strategy has been proposed by extracting, through a Principal Component Analysis (PCA), the projections of the cepstral coefficients with the lowest variances so to minimize the effect of external disturbances. The effectiveness of the proposed damage assessment strategy has been validated through numerical simulations and experimental data.

Since the publication of this article [1] we noticed the Greek characters are not properly properly converted due to a conversion error during the production process.

Recently, features and techniques from speech processing have started to gain increasing attention in the Structural Health Monitoring (SHM) community, in the context of vibration analysis. In particular, the Cepstral Coefficients (CCs) proved to be apt in discerning the response of a damaged structure with respect to a given undamaged baseline. Previous works relied on the Mel-Frequency Cepstral Coefficients (MFCCs). This approach, while efficient and still very common in applications, such as speech and speaker recognition, has been followed by other more advanced and competitive techniques for the same aims. The Teager-Kaiser Energy Cepstral Coefficients (TECCs) is one of these alternatives. These features are very closely related to MFCCs, but provide interesting and useful additional values, such as e.g., improved robustness with respect to noise. The goal of this paper is to introduce the use of TECCs for damage detection purposes, by highlighting their competitiveness with closely related features. Promising results from both numerical and experimental data were obtained.

The paper focuses on the time domain output-only technique called Data-Driven Stochastic Subspace Identification (DD-SSI); in order to identify modal models (frequencies, damping ratios and mode shapes), the role of its user-defined parameters is studied, and rules to determine their minimum values are proposed. Such investigation is carried out using, first, the time histories of structural responses to stationary excitations, with a large number of samples, satisfying the hypothesis on the input imposed by DD-SSI. Then, the case of non-stationary seismic excitations with a reduced number of samples is considered. In this paper, partitions of the data matrix different from the one proposed in the SSI literature are investigated, together with the influence of different choices of the weighting matrices. The study is carried out considering two different applications: (1) data obtained from vibration tests on a scaled structure and (2) in-situ tests on a reinforced concrete building. Referring to the former, the identification of a steel frame structure tested on a shaking table is performed using its responses in terms of absolute accelerations to a stationary (white noise) base excitation and to non-stationary seismic excitations of low intensity. Black-box and modal models are identified in both cases and the results are compared with those from an input-output subspace technique. With regards to the latter, the identification of a complex hospital building is conducted using data obtained from ambient vibration tests.

Methods based on the evaluation of structural deflections from experimental modal flexibility matrices are important tools in vibration-based damage detection, especially for building structures. Modal flexibility matrices, however, can not be directly estimated when dealing with output-only vibration data (e.g. in the important case of structures tested under ambient vibrations). One can use an a-priori estimate of the mass matrix of the structure or the added mass method to obtain the modal normalization constants needed to assemble the flexibility matrix, but these operations can be challenging for real-life civil structures. To address this problem, a modal flexibility-based approach for output-only damage detection and localization in building structures that can be applied with minimal or no a-priori information on the structural masses is proposed in this paper. This approach is also able to deal with the general case in which mass modifications, e.g. due to operational variability in structures, are present before and after damage. The approach is based on the estimation (directly from output-only data) of modal flexibility-based deflections of building structures that are proportional with respect to the corresponding true deflections. From analytical investigations it was found that the missing scaling factor between the two deflections can be made theoretically equal to the total mass of the structure, as proposed in the paper. Then, interstory drifts evaluated from the proportional deflections are used for damage detection and localization according to two proposed strategies. The first strategy can be applied with minimal a-priori information on the masses (i.e. using a parameter that quantifies an eventual relative modification of the total mass of the structure before and after damage). The second one is a more advantageous strategy that can be applied from output-only data without any a-priori information on the masses, even in the case in which the masses are varied before and after damage. The effectiveness of the proposed approach was demonstrated using both numerical simulations and experimental vibration tests on frame building structures.

This paper describes an algorithm that identifies a state-space model and an associated steady-state Kalman filter gain from noise-corrupted input–output data. The model structure involves two Kalman filters where a second Kalman filter accounts for the error in the estimated residual of the first Kalman filter. Both Kalman filter gains and the system state-space model are identified simultaneously. Knowledge of the noise covariances is not required.

Summary 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.

A hybrid optimization methodology is presented for the probabilistic finite element model up- dating of structural systems. The model updating pro- cess is formulated as an inverse problem, analyzed by Bayesian inference, and solved using a hybrid optimiza- tion algorithm. The proposed hybrid approach is a com- bination of a modified artificial bee colony (MABC) algorithm and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The MABC includes four modifica- tions compared to the standard ABC algorithm, which basically improve the global convergence of ABC in the solution phases of initialization, updating, selection, and rebirth. The BFGS is inserted to improve the finer solu- tion search ability aiming at a higher solution accuracy. In brief, a probabilistic framework based on Bayesian in- ference is first derived so to get a regularized objective function for optimization. Then the proposed MABC- BFGS algorithm is applied to determine the unknown system parameters by minimizing the newly defined objective function. System parameters as well as the pre- diction error covariance are updated iteratively in the optimization process. Posterior distributions of the iden- tified system parameters are determined using a weighted sum of Gaussian distributions. Finally, the effectiveness of the proposed approach is illustrated by the numer- ical data sets of the Phase I IASC-ASCE benchmark model and the experimental data sets of a three-storey frame structure (from the Los Alamos National Labo- ratory (LANL), New Mexico, United States).

Summary One of the most efficient ways to solve the damage detection problem using the statistical pattern recognition approach is that of exploiting the methods of outlier analysis. Cast within the pattern recognition framework, damage detection assesses whether the patterns of the damage-sensitive features extracted from the response of the system under unknown conditions depart from those drawn by the features extracted from the response of the system in a healthy state. The metric dominantly used to measure the testing feature's departure from the trained model is the Mahalanobis Squared Distance (MSD). Evaluation of the MSD requires the use of the inverse of the training population's covariance matrix. It is known that when the feature dimensions are comparable with the number of observations, the covariance matrix is ill-conditioned and numerically problematic to invert. When the number of observations is smaller than the feature dimensions, the covariance matrix is not even invertible. In this paper, four alternatives to the canonical damage detection procedure are investigated to address this issue: data compression through discrete cosine transform, use of pseudo-inverse of the covariance matrix, use of shrinkage estimate of the covariance matrix, and a combination of the three aforementioned techniques. The performance of the four methods is first studied on simulated data and then compared using the experimental data recorded on a four-story steel frame excited at the base by means of a shaking table available at the Carleton Laboratory at Columbia University. Copyright © 2015 John Wiley & Sons, Ltd.

This paper formulates optimal bilinear observers for bilinear state-space models. Observers in bilinear form, as opposed to other nonlinear forms, are required to develop an extension of observer/Kalman filter identification for simultaneous identification of a bilinear state-space model and an associated bilinear observer from noisy input–output measurements. The paper establishes the relationship between the bilinear observer gains and the interaction matrices which are used to convert the original bilinear state-space model to a form that simplifies the identification of such a model. Techniques to find the interaction matrices are developed. In the absence of noises, these matrices produce the gains of the fastest converging observer. In the presence of noises, they minimise the state estimation error in the same manner as a standard steady-state Kalman filter. Numerical examples illustrate both the theoretical and computational aspects of the proposed algorithms.

Summary Estimating the mass and stiffness parameters of a structural system via its vibration response measurements is the primary objective in the field of modal testing and structural health monitoring. The attainment of this objective, however, is hindered by various practical and theoretical issues. One such issue is incomplete instrumentation, leading to spatially incomplete mode shapes and often nonunique identification results. When the excitation is induced by ground motion, the problem is further complicated because of arbitrary normalization of mode shapes. This study attempts to address these issues for shear-building type structures. Mode shape normalization and expansion approaches are developed that utilize the topology of the structural matrices. Theoretical constraints regarding minimal instrumentation and the necessity for any a priori information are addressed vis-a-vis the requirements for global identifiability. Some practical implementation issues are discussed. The performance of the method is evaluated using numerical simulations and shake table experiments. Copyright © 2015 John Wiley & Sons, Ltd.

Summary This paper presents output-only observer/Kalman filter identification (O3KID), an effective method for the identification of the dynamic model of a structure and its underlying modal parameters using only output time histories measured on the field. The method is suitable for structural health monitoring based on modal parameters, in particular, for those civil infrastructures whose excitation is random in nature and in the way that it is applied to the structure (e.g., wind and traffic) and therefore is difficult to measure. O3KID is based on a linear-time-invariant state-space model and is derived from an established and successful approach for input–output system identification, known as observer/Kalman filter identification. The paper rigorously proves the applicability of the approach to the output-only case, presents the resulting new algorithms, and demonstrates them via examples on both numerical and experimental data. Copyright © 2014 John Wiley & Sons, Ltd.

This paper presents a generalization of observer/Kalman filter identification (OKID). OKID is a method for the simultaneous identification of a linear dynamical system and the associated Kalman filter from input-output measurements corrupted by noise. OKID was originally developed at NASA as the OKID/ERA algorithm. Recent work showed that ERA is not the only way to complete the OKID process and paved the way to the generalization of OKID as an approach to linear system identification. As opposed to other approaches, OKID is explicitly formulated via state observers providing an intuitive interpretation from a control theory perspective. The extension of the OKID framework to more complex identification problems, including nonlinear systems, is also discussed.

This paper is a brief introduction to the interaction matrices. Originally formulated as a parameter compression mechanism, the interaction matrices offer a unifying framework to treat a wide range of problems in system identification and control. We retrace the origin of the interaction matrices, and describe their applications in selected problems in system identification.