Key Engineering Materials Vol. 347 (2007) pp 479-484 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/Sep/15

Automated Operational Modal Analysis as structural health monitoring tool: theoretical and applicative aspects C. Rainieri1,a, G. Fabbrocino2,b and E. Cosenza3,c 1

Department of Structural Analysis and Design, University of Naples “Federico II”, Via Claudio 21, 80125 Naples, Italy

2

Department SAVA, Engineering and Environment Division, University of Molise, Via De Sanctis, 86100 Campobasso, Italy

3

Department of Structural Analysis and Design, University of Naples “Federico II”, Via Claudio 21, 80125 Naples, Italy a

[email protected], [email protected], [email protected]

Keywords: automated system, structural monitoring, operational modal analysis

Abstract. The aim of structural health monitoring for civil structures is not only detection of sudden or progressive damages but also monitoring their performance under operational conditions or under some particular environmental issues such as earthquakes. Seismic protection of buildings at risk can be reached increasing the knowledge of the structural behavior of existing constructions. This circumstance points out the opportunity of monitoring the performance of civil structures over their operational lives. The present paper deals with automated Structural Health Monitoring (SHM) technologies adopted for the School of Engineering Main Building at the University of Naples “Federico II”. In particular, the attention is focused on the development of an automated procedure based on the Operational Modal Analysis (OMA) that must ensure the continuous monitoring and extraction of the modal parameters of the building. Some numerical examples are then discussed in order to point out effectiveness of the algorithm and relevant issues that need to be improved. Introduction Europe (and Italy, in particular) is characterized by a large number of urbanized areas, where a high percentage of constructions has been designed and erected according to obsolete codes of practice. Therefore, structural assessment and rehabilitation are becoming critical issues in urban management and planning. The aim of structural health monitoring for civil structures is not only detection of sudden or progressive damages but also monitoring their performance under operational conditions or under some particular environmental issues such as earthquakes [1]. Web based technologies and advances in communications can facilitate real-time monitoring of structures. Field measures can be processed for long-term assessment and decision making in risk mitigation, too. In the case of earthquake risk analysis, monitoring systems can be used to create a database from measurements taken during the life of the structure, update numerical models and evaluate the ability of the building to withstand seismic events on the base of tremors. In this framework it is evident the relevance of the modal parameters identification of the structures under operational conditions and the techniques for damage detection. The first one, in particular, can be based on the Operational Modal Analysis (OMA), because it is cheaper and faster than traditional Experimental Modal Analysis (EMA) and can be easily applied also to large structures. Among the methods used to perform the analysis, the stochastic subspace methods in the time domain and the Frequency Domain Decomposition procedures in the frequency domain can be mentioned [2]. Recently, the School of Engineering Tower in Naples (Fig. 1), a thirteen stories reinforced concrete building, has been equipped with a monitoring system combining seismological, geotechnical and structural models. It is an open system, since it can be expanded using different and complementary data acquisition and transmission systems [3]. The architecture of the monitoring system has been All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.34-16/04/08,13:28:55)

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designed so that it is able to transmit data also in critical conditions, such as during an earthquake. The data coming from the sensors are stored into a MySQL Database. The instrumented storeys are the third, the seventh and the roof; geotechnical parameters are monitored, too. In the present paper, some aspects related to the development of a software devoted to analyze field measures and extract relevant structural parameters are discussed. In particular, the attention is focused on the ability of OMA procedures to fit the needs of continuous monitoring systems.

Fig. 1: The School of Engineering Tower, Naples Automated identification of the modal parameters State-of-the-Art. During the last few years a large effort in the development of vibration based damage detection techniques is observed [4]. In fact, since the dynamic behavior of a structure is influenced by damage, it is possible to follow the evolution of damage by monitoring the modal parameters and detect occurrence of relevant damage levels [5, 6]. However, changes in environmental and operational conditions can affect the modal parameters estimation [7]. An important aspect for the application of damage detection techniques as a part of monitoring practices is an automated identification and tracking procedure, because traditional modal identification requires extensive interaction from an experienced user [8]. Currently, there are some advancements in this field, with the development of methods based on control theory (both in time and frequency domain) and methods based on conventional signal processing. As regards the first class of methods, during modal analysis the model order is usually over-specified to get all physical modes present in the frequency range of interest. However, physical and mathematical modes have to be distinguished. This practice requires large interaction with an expert user. Moreover, most of the classical model order selection tools used in time domain and in frequency domain identification only allow to verify if the model order used is appropriate but do not separate physical from mathematical modes [9]. Thus, the stabilization diagram is still an important tool in modal analysis to separate physical from mathematical modes. Selection of physical poles is not however a trivial task, since it may be difficult and time-consuming depending on the quality of data, the performance of the estimator (even if there are interesting advancements in this field [10]) and the experience of the user. Extensive interaction between tools and user is basically inappropriate for monitoring purposes. Recently, an interesting proposal for automated modal identification based on Least Square Complex Frequency (LSCF) method has been issued. The method moves from the identification of a model with sufficiently high order using a frequency-domain Maximum Likelihood estimator: a first validation of the poles is performed on the base of both stochastic and deterministic criteria, which allow the identification and removal of a first group of non-physical poles. Two stochastic mode validation criteria are considered, taking into account that the computational modes are characterized by so-called cancelling pole-zero pairs: the first one focuses on the circumstance that a large number of zeroes within an uncertainty circle around the pole pr indicates a computational mode; the radius of the circle is calculated according to:

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R = − 2 log(1 − pb )σ pr

481

(1)

where σpr = std(pr) is the uncertainty on pole pr with r = 1 … Nm, Nm the number of modes and pb the probability of the event that true pole falls inside the circle. In fact, the uncertainty levels of computational poles are often higher (10 to 100 times) than for the physical poles. The second criterion, instead, is based on the computation of the correlation between poles and zeroes, since in the case of mathematical modes they are strongly mutually correlated. Besides the validation approach based on removing pole-zero pairs, validation criteria specifically developed for modal analysis are considered, such as the Modal Phase Collinearity, which is a measure for the degree of complexity of a mode shape (low values of the index indicates computational modes, if the system is lightly damped), and the Mode Overcomplexity, which evaluates the sensitivity of the damped natural frequency for a mass change at each response DOF. After this first validation, the method uses a fuzzy clustering approach or a weighted mode quality index to separate the remaining mathematical modes from the physical ones [8]. Both criteria are based on a set of variables (such as standard deviation of the estimated pole, the inverse of the modal phase collinearity, and so on). In the first case the output is a membership function for the two classes of physical and computational modes: a value greater than 0.5 indicates that the object belongs to that class. The second approach is based on the calculation of the Mode Quality Index, which is a measure of the physical behavior of a mode and can be defined as a weighted sum such as: MQI r = α 1 (1 − X 1r ) + α 2 (1 − X 2 r ) + ... + α k X kr with

∑α

i

(2)

= 1 . A high MQI (greater than 0.7) indicates a physical mode.

As regards the methods based on conventional signal analysis, Guan et al. [11] have proposed the so-called Time Domain Filtering method, which is based on the application of a band-pass filter to the system response with the aim of isolating the single modes in the spectrum. However, the frequency limits of the filter are user-specified based on the Power Spectral Density (PSD) plots of the response signals and, if excitation is unknown, it is sometimes difficult to identify the regions where certain modes may be located according only to power spectrum plots. An automated procedure based on Enhanced Frequency Domain Decomposition (EFDD). An alternative approach to the automated identification of the modal parameters of the structure is herein proposed. It is based on the Enhanced Frequency Domain Decomposition procedure for the modal identification in operational conditions. This method is based on the Singular Value Decomposition (SVD) of the Power Spectral Density (PSD) matrix known at discrete frequencies ω=ωi: ∧

G yy ( jω i ) = U i S iU iH

(3)

where the matrix Ui is a unitary matrix holding the singular vectors uij and Si is a diagonal matrix holding the scalar Singular Values (SV) sij. Near a peak corresponding to the kth mode in the spectrum, only the kth mode is dominant, and the PSD matrix approximates to a matrix with a rank equal to one: ∧

G yy ( jω i ) = si u i1u iH1 ω i → ω k

(4)

where the first singular vector is an estimate of the mode shape. The next step is the identification of the auto power spectral density function of the corresponding Single Degree Of

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Freedom (SDOF) system by comparing the mode shape estimate with the singular vectors at the frequency lines around the peak after defining a Modal Assurance Criterion (MAC) rejection level. The Inverse Fourier Transform (IFT) of the identified spectrum (SDOF Bell function) for the corresponding SDOF system allows the computation of the damping ratio by the logarithmic decrement technique. The described procedure can be automated if the mode shapes (experimental or numerical) of the monitored structure are known according to the procedure shown in Fig. 2. As in the time domain the output of a linear dynamic system can be expressed in terms of its mode shapes and generalized coordinates, performing the SVD of the PSD matrix it is decomposed into a set of auto-spectral density functions, each corresponding to a SDOF system. Since the peaks of the SV plot indicate a mode (when spurious harmonic modes do not exist) and the singular vector associated to the peak frequency is an approximation of the true mode shape, one can identify the peak corresponding to the kth mode from the plot of MAC vs. frequency: in fact, the plot of MAC vs. frequency will show an absolute maximum at the frequency of the mode itself, where the singular vector obtained from the SVD of the PSD matrix approximates the effective mode shape of the structure. After the identification of the peak frequency, the mode characterization is performed according to the standard EFDD procedure. 1. Computation of PSD matrix 2. SVD of PSD matrix Analytical or experimental modes

3. MAC vs. Frequency Plots 4. Identification of peak frequency

Singular value plots

5. Identification of SDOF Bell function 6. Extraction of modal parameters

Fig. 2: The algorithm for automated modal identification In some cases, excitation of the structure could not fit white noise properties and in particular, could be affected by harmonic components. In these conditions, it is worth noting that the role of harmonic excitations can be different depending on the relative distance between structural frequencies of interest and harmonic excitation. Whenever the latter is far away from a structural mode, the operating deflection shape results as a combination of several excited modes and the forces acting on the structure and give low MAC values. Conversely, if the harmonic component is close to a structural mode, MAC values point out a high correlation and the estimated modal parameters can be biased. In particular, the natural frequency could be replaced by the frequency of the harmonic component and an underestimation of the damping ratio could occur. A structural and functional assessment of the monitored buildings is always needed in order to identify presence of harmonic excitations. In such cases, specific algorithms able to identify and remove harmonic components [12], resulting in increased computational efforts and hardware requirements, should be used. Another relevant aspect is related to the role of damping, especially when higher modes are taken into consideration. Biased estimation of damping, in fact, can results from partial identification of SDOF Bell functions. Nevertheless, a large number of civil structures are characterized by moderate irregularities. In such cases, first modes are affected by a large amount of participating mass, so that play a primary role in the dynamic response to earthquakes. Therefore, the number of measures and the cost of monitoring systems can be optimized, without loss of reliability, on the first mode damping properties estimation. Conversely, specific attention has to be paid when strongly irregular structures are considered and the role of higher modes cannot be easily neglected. Preliminary assessments and measures taken on the School of Engineering Main Building show that relevant harmonic excitations are not present, due to the very urbanized surroundings. A large number of similar applications can be forecast in very urbanized areas, so the procedure in the present form allows a continuous identification of the modal parameters of the structure without the need of user intervention. An effective tracking of the modal parameters of the

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structure can be therefore carried out. In particular, changes in the dynamic characteristics of the structure can be monitored to detect the presence of damage and apply an appropriate algorithm of damage detection. Predefined ranges for the various parameters could be used as control conditions to detect anomalies requiring more detailed analyses. Examples. The automated procedure has been tested using two types of dynamic data. The first ones are data obtained by numerical experiments, the second ones are field measures taken on the monitored structure. Numerical experiments have been carried out on a shear-type 15-stories 1-bay r.c. frame; analyses have been carried out using the SAP2000 computer program. A Gaussian white noise has been generated and then used as base excitation. Errors due to measures have been intentionally excluded. Six referenced nodes have been used to assess dynamic properties of the simulated building via the EFDD technique and then via the proposed automated procedure using the mode shapes and the simulated records obtained from the FE model. The results of these calculations are reported in Table 1 and show a very good matching between estimated and calculated values.

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6

FE model [Hz] 1.07 3.21 5.30 7.33 9.27 11.09

EFDD [Hz] 1.08 3.15 5.29 7.27 9.29 11.07

FE vs. EFDD scatter [%] 0.62 1.77 0.20 0.81 0.23 0.22

Automated FDD [Hz] 1.07 3.2 5.27 7.27 9.27 11.07

FE vs. AFDD scatter [%] 0.31 0.21 0.58 0.81 0.02 0,22

Table 1: Comparisons (simulated data)

Fig. 3: Identification through EFDD procedure, SV plots Measures taken from twelve sensors placed, in pairs, at two opposite corners of three different floors of the monitored building (Fig. 1) have been used to check the automated procedure. In particular, time histories about one hour long have been employed. Different preliminary procedures have been used to identify the first three modes (Fig. 3) of the structure and apply the automated procedure. More in detail, experimental mode shapes obtained from an environmental vibration test using EFDD have been used to identify the modal frequencies on a number of different datasets. Table 2 summarizes comparative results and point out the capability of the automated procedure to give very good estimations of the modal parameters of interest. At the present stage, the role of the number of sensors is under investigation. Preliminary results confirm that only six sensors among the twelve placed on the School of Engineering Tower are able to give a robust identification of the modes if observability is ensured. In fact, tests show that the absolute maximum of MAC vs. frequency is always achieved, but further work is needed on the subject.

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Mode 1 Mode 2 Mode 3

EFDD [Hz] 0.92 0.99 1.29

Automated FDD [Hz] 0.91 0.98 1.30

Scatter [%] 0.44 0.51 0.23

Table 2: Comparisons (recorded data) Conclusions Structural Identification for monitoring of critical structures requires automated procedures able to evaluate under service conditions and unknown excitations dynamic relevant modal parameters. In the present paper, a procedure aimed at such an objective has been presented. It is based on a wellknown Operational Modal Analysis procedures such as the Enhanced Frequency Domain Decomposition, from which it takes advantages and limitations. However, the algorithm is very easy to manage and requires only the knowledge (experimental or analytic) of basic mode shapes. A specific computer program implemented in LabView 8 environment has been developed and is interfaced with the Database of the SHM system of the Main Building of the School of Engineering in Naples. Preliminary tests of the procedure have been discussed pointing out promising results. References [1]

A. Mufti: Guidelines for Structural Health Monitoring, University of Manitoba, ISIS, Canada, 2001.

[2]

L. Zhang, R. Brincker and P. Andersen, in: Proc. 1st International Operational Modal Analysis Conference, Copenhagen, Denmark, 2005.

[3]

C. Rainieri, G. Fabbrocino, G. Manfredi and E. Cosenza, in: Proc. 9th CanSmart Meeting International Workshop on Smart Materials and Structures, Toronto, Canada, 2006.

[4]

S. W. Doebling, C. R. Farrar, M. B. Prime, and D. W. Shevitz: Damage identifcation and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review, Tech. Report LA-13070-MS, Los Alamos Nat. Lab, 1996.

[5]

L. Hermans, H. Van der Auweraer, and L. Mevel, in: Proceedings of 17th International Modal Analysis Conference, pages 42-48, Kissimmee, FL, USA, 1999.

[6]

A. S. J. Swamidas and Y. Chen, in: Journal of Sound and Vibration, 186(2):325-343, 1995.

[7]

B. Peeters: System identification and damage detection in civil engineering, PhD thesis, dept. of Civil Engineering, KULeuven, Leuven, Belgium, december 2000.

[8]

P. Verboven, E. Parloo, P. Guillaume and M. Van Overmeire, in: Proc. of Int. Conf. on Structural System Identification, Kassel, Germany, pages 637-646, 2001.

[9]

T. Soderstrom, in: Automatica, 11:537-541, 1975.

[10] J. Lanslots, B. Rodiers and B. Peeters, in: Proc. of the ISAM 2004, , Leuven, Belgium, 2004. [11] H. Guan, V. M. Karbhari and C. S. Sikorsky, in: Proc. 1st IOMAC, Denmark, 2005. [12] N. J. Jacobsen, P. Andersen and R. Brincker, in: Proc. of ISMA 2006, Leuven, Belgium, 2006.