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Sustaining the serviceability of civil structures is a significant issue for inhabitants of seismic zones, since structures get damaged while exposed earthquakes. The weakened stiffness as a consequence causes change in its natural frequencies. The natural frequency is a dynamic feature that belongs to the global signature of the structure, and reveals merely the overall structural health condition. Over the last two decades, civil engineers have taken their efforts to structural health monitoring (SHM) with the help of the development of dynamic analysis. Still, we have diffculties in localizing damage and in assessing the damage level in the structure using natural frequencies and the corresponding mode shapes. Reviewing the latest developments in the various facets of structural health monitoring (SHM), two main types of methods, vibration-based and wave-propagation-based methods are employed. Seismic interferometry and the related deconvolution methods are used for the extraction of structural wave propagation in civil structures. However, the application of global wave screening to local structural components in buildings is not yet validated. We demonstrate three examples of structural assessment and compare the damage detection methods using the dynamic analysis and the wave propagation analysis. The application of wave propagation is completed by means of the Normalized Input Output Minimization (NIOM) method. For damage localization, transmissibility functions (TFs), which interpret the correlation characteristics between frequency response functions in a local element, are taken into account. The study shows that wave velocities are sensitive to the local stiffness of a structure and the difference of TFs contributes to a damage index (DI). With the measures we tried to establish a standard procedure for damage identifcation. Finally, we expand the concept of wave screening for structural assessment of civil structures in this work. Our research of the promising damage assessment approach is validated by the comparison of velocities from structural waves propagating in civil structures and the proposed DI for damage localization., Die Gebrauchstauglichkeit ist ein wichtiges Thema für seismische Zonen. Tragwerke werden von Erdbeben beschädigt, und die dadurch geschwächte Steifheit führt zu einer Änderung der Eigenfrequenzen. Die Eigenfrequenz ist eine globale dynamische Eigenschaften des Tragwerks, die allein für die Schadensdetektion und -identifkation nicht ausreichen. In den letzten zwanzig Jahren haben sich Bauingenieure mit Hilfe der Modalanalyse um die Strukturüberwachung oder zu Englisch Structural Health Monitoring (SHM) bemüht. Wir haben jedoch Schwierigkeiten, Schäden zu lokalisieren und das Schadensniveau in den Tragwerken zu bewerten. Schwingungsbasierte und wellenausbreitungsbasierte Methoden werden als zwei Haupt-Methoden der neuesten Entwicklungen der Strukturüberwachung verwendet. Die seismische Interferometrie und die Entfaltungsmethoden werden zur Extraktion der Wellenausbreitung in Bauwerke verwendet. Die Anwendung der Abtasttechnik durch globale Wellen auf Bauteile in den Gebäuden ist jedoch noch nicht validiert. Wir zeigen drei Beispiele für die Bewertung der Tragstruktur und vergleichen die Schadensdetektionsmethoden mithilfe der Modalanalyse und der Wellenausbreitungsanalyse. Die Anwendung der Wellenausbreitung wird mithilfe der Methode "Normalized Input Output Minimization (NIOM)" durchgeführt. Bei der Schadenslokalisierung werden Übertragbarkeitsfunktionen oder zu Englisch Transmissibility Functions (TFs) berücksichtigt, die die Korrelation zwischen Frequenzantwortfunktionen im Bauteil interpretieren. Die Studie zeigt, dass Wellengeschwindigkeiten empfindlich auf Strukturänderungen oder Schäden reagieren und die Differenz von TFs zu einem Indikator für die Schadensdetektion beiträgt. Mit den Maßnahmen haben wir versucht, ein Standardverfahren zur Schadenserkennung zu etablieren. Schließlich erweitern wir in dieser Arbeit das Konzept der Wellenausbreitung zur Bewertung der Tragstrukturen. Unsere Forschung zum vielversprechenden Schadensbewertungsansatz wird durch den Vergleich der Geschwindigkeiten von Wellen, die sich in den Tragwerken ausbreiten, und die abzuleitende Indikatoren aus TFs zur Schadenslokalisierung bestätigt.

Mechanical Systems and Signal Processing, 162, ISSN:0888-3270, ISSN:1096-1216

International audience; The dynamic behavior of structures can be studied by the identification of their modal parameters. Classical modal analysis methods are based on the relation between the forces applied to structures (inputs) and their vibration responses (outputs). In real operational conditions it is difficult, or even impossible, to measure the excitation. For this reason, operational modal analysis approaches which consider only output data are proposed. However, most of these output-only techniques are proposed under the assumption of white noise excitation. If additional components, like harmonics for instance, are present in the exciting force, they will not be separated from the natural frequencies. Consequently, this assumption is no longer valid. In this context, an operational modal identification technique is proposed in order to only identify real poles and eliminate spurious ones. It is a method based on transmissibility functions. The objective of the proposed paper is to identify modal parameters in operational conditions in the presence of harmonic excitations. Identification is performed using a method based on transmissibility measurements and then with the classical stochastic subspace identification method, which is based on white noise excitation. These two methods are first applied to numerical examples and then to a laboratory test. Results validate the novel ability of the method based on transmissibility measurements to eliminate harmonics, contrary to the stochastic subspace identification approach.

In recent years, the authors have proposed an innovative approach for Operational Modal Analysis based on transmissibility measurements. A method was proposed based on combining 2 single-reference transmissibility functions that were obtained during 2 different loading conditions. However in practice one in general has access to multiple transmissibility functions and perhaps even multiple loading conditions. In this paper a new method is introduced that combines all the measured single-reference transmissibility functions in a unique matrix formulation in order to identify system poles. It will be shown that each element of the pseudo-inverse of this matrix is a rational function with poles equal to the system poles. The proposed method reduces the risk to miss system poles and to identify extra non-physical poles. Therefore the method increases the usability and reliability of transmissibility based operational modal analysis (TOMA). The method will be demonstrated and validated by means of an experiment on a beam excited at multiple inputs for three different loading conditions.

The modal characterization of automotive lighting systems becomes difficult using sensors due to the light weight of the elements which compose the component as well as the intricate access to allocate them. In experimental modal analysis, high speed 3D digital image correlation (HS 3D-DIC) is attracting the attention since it provides full-field contactless measurements of 3D displacements as main advantage over other techniques. Different methodologies have been published that perform modal identification, i.e., natural frequencies, damping ratios, and mode shapes using the full-field information. In this work, experimental modal analysis has been performed in a multi-component automotive lighting system using HS 3D-DIC. Base motion excitation was applied to simulate operating conditions. A recently validated methodology has been employed for modal identification using transmissibility functions, i.e., the transfer functions from base motion tests. Results make it possible to identify local and global behavior of the different elements of injected polymeric and metallic materials.

Periodical loads, such as waves and rotating machinery, form a problem for operational modal analysis (OMA). In OMA only the vibrations of a structure of interest are measured and little to nothing is known about the loads causing these vibrations. Therefore, it is often assumed that all dynamics in the measured data are linked to the system of interest. Periodical loads defy this assumption as their periodical behavior is often visible within the measured vibrations. As a consequence most OMA techniques falsely associate the dynamics of the periodical load with the system of interest. Without additional information about the load, one is not able to correctly differentiate between structural dynamics and the dynamics of the load. In several applications, e.g. turbines and helicopters, it was observed that because of periodical loads one was unable to correctly identify one or multiple modes. Transmissibility based OMA (TOMA) is a completely different approach to OMA. By using transmissibility functions to estimate the structural dynamics of the system of interest, all influence of the load-spectrum can be eliminated. TOMA therefore allows to identify the modal parameters without being influenced by the presence of periodical loads, such as harmonics. One of the difficulties of TOMA is that the analyst is required to find two independent datasets, each associated with a different loading condition of the system of interest. This poses a dilemma for TOMA; how can an analyst identify two different loading conditions when little is known about the loads on the system? This paper tackles that problem by assuming that the loading conditions vary continuously over time, e.g. the changing wind directions. From this assumption TOMA is developed into a time-varying framework. This development allows TOMA to not only cope with the continuously changing loading conditions. The time-varying framework also enables the identification of the modal parameters from a single dataset. Moreover, the time-varying TOMA approach can be implemented in such a way that the analyst no longer has to identify different loading conditions. For these combined reasons the time-varying TOMA is less dependent on the user and requires less testing time than the earlier TOMA-technique.

International audience; This paper deals with the use of transmissibility functions for damage localization. The first part is dedicated to a critical review of the state-of-the-art highlighting the major difficulties when using transmissibility functions for damage detection and localization. In the second part, an analytical study is presented for non dispersive systems such as chain-like mass-spring systems. The link between the transmissibility function and the mechanical properties of four subsystems defined by the boundary conditions, the position of the excitation and the two measurement locations used for the computation of the transmissibility functions is derived. This result is used to discuss the situations in which damage localization is likely to work. The last section discusses the extension of these results to more general dispersive systems such as beams or plates.

Structural health monitoring aims to provide an accurate diagnosis of the condition of civil infrastructures during their life-span by analyzing data collected by sensors. To this purpose, detection and localization of damages are fundamental tasks. This paper introduces a wireless sensor network for structural damage detection and localization in which the sensor nodes, in order to estimate the energies of specific frequency bands, process the acceleration data locally in real-time using the Goertzel algorithm. The nodes then share their results inside the network and exploit them to compute transmissibility functions, which can be exploited as damage indicators and for correctly localizing damages within the monitored structure. The use of the embedded Goertzel algorithm prevents the nodes from transmitting large volumes of acceleration data to the sink node for off-line analysis, reducing the latency and increasing the life time of the cyber-physical system by 80 % and 52 %, respectively. The tests performed on a truss structure confirm the capability of the distributed approach in correctly detecting and localizing structural damages.

Monitoring the modal parameters of civil and mechanical system received plenty of interest the last decades. Several approaches have been proposed and successfully applied in civil engineering for structural health monitoring of bridges (mainly based on the monitoring of the resonant frequencies and mode shapes). In applications such as the monitoring of offshore wind turbines and flight flutter testing the monitoring of the damping ratios are essential. For offshore wind turbine monitoring the presence of time-varying harmonic components, close to the modes of interest, can complicate the identification process. The difficulty related to flight flutter testing is that, in general, only short data records are available. The aim of this contribution is to introduce system identification methods and monitoring strategies that result in more reliable decisions and that can cope with complex monitoring applications. Basic concepts of system identification will be recapitulated with attention for monitoring aspects. The proposed monitoring methodology is based on the recently introduced Transmissibility-based Operational Modal Analysis (TOMA) approach.

Through Operational Modal Analysis (OMA) the modal parameters of an operational structure can be monitored over its lifetime. In recent years several interesting applications have illustrated this concept and it has been applied successfully at different locations across Europe. However, one of the disadvantages of most OMA techniques is the poor estimation and reliability in the presence of (varying) harmonics, e.g. due the passing blades of a wind turbine. Therefore, it is very hard to monitor the modal parameters of these structures using classic OMA-techniques. TOMA, OMA based on transmissibility functions, is potentially uninfluenced by these harmonics and could therefore resolve this limitation of OMA. This paper will discuss the differences between the automation of classic OMA and automating TOMA. It will suggest a strategy to achieve a fully automated TOMA approach that is uninfluenced by the harmonics present in the measured vibrations.

The concept of using Scalar Transmissibility functions in Operational Modal Analysis was first introduced several years ago. It was immediately clear that using the input-spectrum independent scalar transmissibility functions for modal analysis could yield multiple significant advantages (such as the absence of any white noise assumption typical for OMA). However the use of these functions was limited in situations where multiple uncorrelated forces excite the structure. To resolve this one can use the multivariable transmissibility functions that again become input-spectrum independent even when multiple uncorrelated forces excite an operational structure. However it was not immediately clear how one could obtain the modal parameters from these multivariable transmissibility functions. Our research group recently introduced a technique for obtaining modal parameters from these multivariable transmissibility functions. In this paper we'll discuss and highlight the most recent advances since the introduction of the aforementioned technique and discuss the current state of the art in the use of transmissibility functions for Operational modal analysis.

Periodical loads, such as waves and rotating machinery, are a problem for operational modal analysis (OMA). In OMA only the vibrations of a structure of interest are measured and little to nothing is known about the loads causing these vibrations. Therefore, it is often assumed that all dynamics in the measured data are linked to the system of interest. A novel approach to this problem is the research into time-varying transmissibilities for OMA, recently pub- lished in MSSP. In that contribution it was shown how to use time-varying single-reference transmissibilities to estimate the modal parameters from a single dataset without being influenced by the periodical loads. However, transmissibilities are only independent of the input spectra, and therefor the periodical loads, when the number of references equals the number of uncorrelated loads. This property limits the applicability of a single-reference approach to systems excited by a single distributed load. The solution is to use multi-reference transmissibilities for OMA a.k.a. pTOMA. With pTOMA the estimated modal parameters can again be independent of the input spectra. The main goal of this paper is to expand the estimation of time-varying transmissibilities to multi-reference transmissibilities. And to use these time- varying multi-reference transmissibilities for pTOMA. This paper will recapitulate the time-varying version of single reference TOMA. We will introduce the time-varying version of multi-reference TOMA (pTOMA). The newly introduced algorithm will be demonstrated and discussed trough a lab experiment.

Operational modal parameter estimation (OMA) techniques perform system identification without or with only limited knowledge of the operational inputs acting on the system. However, most of the current operational identification techniques impose multiple conditions on the spectral content of the unknown inputs. As a consequence, modeling errors occur if these assumptions are not met. Therefore, there is a general interest in operational identification techniques that can operate independent of the unknown input spectra. This paper introduces poly-reference Transmissibility based Operational Modal Analysis (pTOMA). pTOMA uses parametrically estimated transmissibility functions associated with different loading conditions to obtain the system eigenvalues and eigenvectors using output-only data. Unlike most OMA techniques no strong assumptions are necessary considering the input spectrum. The method is therefore able to correctly identify the system parameters while the excitation may contain (varying) harmonics or strong coloration. A framework to use pTOMA is formulated, the algorithm is introduced and the claimed properties are illustrated by means of a numerical experiment.

Operational modal analysis (OMA) is the collective term for different techniques that estimate the modal parameters of a linear structure using only the structural responses to unknown excitations. Therefore, OMA is the preferred approach when operational forces are hard to measure, when operational conditions are hard to replicate in a controlled environment or when an experimental modal analysis (EMA) is too time-consuming. However, OMA does not allow us to determine the relative contribution of each mode, i.e. the mode shapes found with OMA are unscaled. This paper introduces a novel approach to estimate the relative contributions of all modes within a given bandwidth and to reconstruct frequency response functions (FRF) that are proportional to the true FRFs of the system. This novel technique requires only response data and a general knowledge of the input locations of the dominant forces acting on the system. It is shown that even when only a limited number of input locations are known the proposed method can still be used by considering multiple loading conditions. Finally, since the technique is based on transmissibility functions, there are no necessary assumptions considering the spectral content of the excitations. Several numerical examples illustrate the claimed properties and are used to quantify the influence of measurement and ambient noise.