From Input-Output to Output-Only Modal Identification of Civil Engineering Structures

FROM INPUT-OUTPUT TO OUTPUT-ONLY MODAL IDENTIFICATION OF CIVIL ENGINEERING STRUCTURES Álvaro Cunha, Faculty of Engineering, University of Porto (FEUP) Portugal Elsa Caetano, Faculty of Engineering, University of Porto (FEUP) Portugal E-mail: [email protected] Website: www.fe.up.pt/vibest Abstract This paper presents a brief characterization of the evolution of Experimental Modal Analysis in the Civil Engineering field, from Input-Output to Output-Only Modal Identification Techniques, taking particularly into account the experience of the authors at the Laboratory of Vibrations and Monitoring (VIBEST, www.fe.up.pt/vibest) of FEUP. 1 Introduction Some decades ago, the major concern of Structural Engineers was the development and automatic application of new and powerful numerical methods for the analysis (static and dynamic) and design of large Civil Engineering structures. In this context, the fast development of the finite element techniques accompanied by the tremendous technological progress in the field of personal computers allowed the structural designer to use currently excellent structural analysis software packages, which enable to accurately simulate the structural behaviour. However, the design and construction of more and more complex and ambitious civil structures, like dams, large cable-stayed or suspension bridges, or other special structures, made structural engineers feel the necessity to develop also appropriate experimental tools that might enable the accurate identification of the most relevant structural properties (static and dynamic), providing reliable data to support the calibration, updating and validation of the structural analysis numerical models used at the design stage. Beyond that, the continuous ageing and subsequent structural deterioration of a large number of existing structures made structural engineers gradually more interested in the development and application of efficient vibration based damage detection techniques supported by structural health monitoring systems, in which the regular identification of modal properties plays also an important role. Therefore, the first and natural tendency of Civil Engineering researchers was to take some profit from important previous developments made in System Identification and Experimental Modal Analysis in Electrical and Mechanical Engineering, trying to accurately identify the main dynamic properties of civil structures by applying well established input-output modal identification techniques. The difficulty to excite large civil structures in a controlled form, as well as remarkable technological progresses registered in the area of transducers and analogue to digital converters, made however feasible to open a new and very promising road for the modal identification of large structures, exclusively based on the measurement of the structural response to ambient excitations and application of suitable stochastic modal identification methods. Under these circumstances, the main purpose of this paper is to briefly present the perspective of the authors concerning the evolution of Experimental Modal Analysis in the Civil Engineering field, from Input-Output to Output-Only Modal Identification Techniques, which is naturally strongly influenced and conditioned by their own experience as researchers at the Laboratory of Vibrations and Monitoring (VIBEST, www.fe.up.pt/vibest) of FEUP. 2 Input-Output Modal Identification 2.1 Equipment and test procedures The conventional Modal Testing is based on the estimation of a set of Frequency Response Functions (FRFs) relating the applied force and the corresponding response at several pairs of points along the structure, with enough high spatial and frequency resolution. The construction of FRFs requires the use of an instrumentation chain for structural excitation, vibration measurement and data acquisition and signal processing. In small and medium size structures, the excitation can be induced by an impulse hammer (Fig. 1a), similar to those currently used in Mechanical Engineering. This device has the advantage of providing a wide-band input, able to stimulate different modes of vibration. The main drawbacks are the relatively low spectral estimates’ frequency resolution, which can preclude the accurate estimation of modal damping factors, and the lack of energy to excite some relevant modes of vibration. Due to this last factor, some laboratories have built special impulse devices more specifically designed to excite bridges (Fig. 1b). An alternative, also derived from Mechanical Engineering, is the use of large electrodynamic shakers (Fig. 1c), which can apply a large variety of input signals (random, multi-sine, etc.), when duly controlled both in frequency and amplitude using a signal generator and a power amplifier. The shakers have capacity to excite structures in a lower frequency range and higher frequency resolution can be attained. The possibility of application of sinusoidal forces allows for the excitation of the structure in resonance and, consequently, for a direct identification of the mode shape. Figure 1. a) Impulse hammer; b) Impulse exciation device for bridges (K.U.Leuven); c) Electrodynamic shaker over three load cells; d) Eccentric mass vibrator. The controlled excitation of large Civil Engineering structures requires however the use of specific and heavy excitation equipment. One option frequently used in the past in dynamic testing of dams was the eccentric mass vibrator (Fig. 1d), which enables the application of sinusoidal forces with variable frequency and amplitude. The main drawbacks of this technique are low force amplitude induced at low frequencies and some difficulty to measure the applied force and ensure no relative movement of the vibrator with regard to the structure. A better option in terms of providing a wide band-excitation over the most interesting frequency range for large civil structures was the use servo-hydraulic shakers. Figure 2 shows, for instance, two shakers of this type built at EMPA (www.empa.ch) to excite bridges or dams, vertically and laterally, as well as the electro-hydraulic mass reaction shaker Victoria from Arsenal Research (www.arsenal.ac.at). (a) (b) (c) Figure 2. Servo-hydraulic shakers to excite (a) bridges (vertically), (b) dams (laterally) (EMPA); (c) Electro-hydraulic shaker from Arsenal Research. The dynamic response of the structure is usually measured with accelerometers (Figure 3) (piezoelectric, piezoresistive, capacitive or force balance) [1], due to their relatively low cost and high sensitivity. A particular characteristic of piezoelectric accelerometers is that they don’t need specific power supply and operate well over a wide frequency range. However, most of them are not suited to low frequency applications. On the contrary, piezoresistive, capacitive and force balance accelerometers can provide DC or low frequency response capability. (a) (b) (c) (d) Figure 3. Schematic cross-section of (a) piezoelectric, (b) piezoresistive, (c) capacitive and (d) force balance accelerometers The electrical signals captured by these transducers are usually rather low and so must be amplified by conditioning units, that may also provide anti-aliasing low-pass filtering (allowing lower sampling rates) and analogue integration to velocities or displacements. The data acquisition and storage of measurement data involves the use of an analogue-to-digital (A/D) converter inserted in a digital computer. The digital raw data must be preliminary analysed and processed, considering operations of scale conversion, trend-removal and decimation. Afterwards, the acceleration time series can be multiplied by appropriate time windows (Hanning, Cosine-Taper, etc.), in order to reduce leakage effects, and subdivided in different blocks for evaluation of average spectral auto and cross spectra estimates, using the FFT algorithm. At last, estimates of FRFs can be obtained using estimators H1 or H2 [1]. The automatic evaluation of FRFs requires appropriate software for analysis and signal processing, which is already available in commercial Fourier analyzers. These analyzers are sometimes simply materialized through the insertion of a specific PCMCIA card into a laptop, allowing either the acquisition of data through input channels or the control of a shaker through an output channel. 2.2 Input-Output Modal Identification methods There is presently a wide variety of input-output modal identification methods, whose application relies either on estimates of a set of FRFs or on the corresponding Impulse Response Functions (IRFs), which can be obtained through the inverse Fourier Transform. These methods try to perform some fitting between measured and theoretical functions and employ different optimization procedures and different levels of simplification. Accordingly, they are usually classified according to the following criteria: (i) Domain of application (Time or Frequency); (ii) Type of formulation (Indirect or Modal and Direct); (iii) Number of modes analysed (SDOF or MDOF); (iv) Number of inputs and type of estimates (SISO, SIMO, MIMO, MISO). The former methods of identification were developed in the frequency domain. In the simpler SDOF formulations (e.g. Peak Amplitude, Circle-Fit, Inverse methods), a fitting between a measured and a theoretical FRF of a SDOF system in the vicinity of each resonant frequency is developed, neglecting the contribute of resonant modes. In the more sophisticated MDOF methods (e.g. Rational Fraction Polynomial (RFP), Complex Exponential Frequency Domain (CEFD), Polyreference Frequency Domain (PRFD)), the fitting between measured and theoretical FRFs is made globally in a wide range of frequencies. Time domain methods, which tend to provide the best results when a large frequency range or a large number of modes exist in the data, began to be developed as consequence of some limitation in terms of spectral estimates frequency resolution, as well as leakage errors in the estimates. The most widely known methods are either Indirect (e,g. Complex Exponential (CE), Least-Squares Complex Exponential (LSCE), Polyreference Complex Exponential (PRCE), Ibrahim Time Domain (ITD), Eigensystem Realization Algorithm (ERA)) or Direct (e.g. Autoregressive MovingAverage (ARMA)). The gradual development of all these methods, which are extensively described by Maia et al. [1], shows a tendency to completely automated systems of acquisition, analysis, processing and identification, instead of some initial trend to the use of interactive programs. Beyond that, the bestperforming methods have been implemented in robust Modal Analysis software [2]. A special class of modal identification methods, called Tuned-Sinusoidal methods (e.g. Asher, Mau) corresponds to the particular type of tests that are based on the application of a sinusoidal excitation at each natural frequency, as can happen using eccentric mass vibrators. 2.3 Examples of forced vibration tests The performance of classical input-output modal identification tests in Civil Engineering structures can be of interest both on physical models and on prototypes. Figure 4 shows the physical model of Jindo bridge (South Korea), which was extensively tested to analyze the importance of dynamic cable-structure interaction in terms of seismic response analysis [3]. In this context, several forced vibration tests were performed either using an electro-dynamic shaker or two different shaking tables (at Univ. Bristol and ISMES), and considering two alternative configurations for the model. First, additional masses were distributed along the cables, according to the similitude theory, in order to idealize the cables’ mass and consider the lateral cables vibration. In a second phase, no distributed additional mass was introduced along the cables, but equivalent masses have been concentrated at their extremities. This study permitted to identify the existence of different sets of multiple modes, some being pure cable modes, but others coupled modes. Each of these sets present a common shape for the deck and towers and different cables motion, the corresponding natural frequencies being very close, always in the vicinity of a global mode of the primary system (Figure 6). (a) (b) (c) Figure 4. (a) Jindo cable-stayed bridge; (b) Physical model on shaking table (EERC, Univ. Bristol); (c) Physical model on shaking table (ISMES). (a) (b) (c) Figure 5. (a) Application of electro-dynamic shaker; (b) Response measurement with piezoelectric accelerometer; (c) Measurement of cables tensions. 1.00E-02 1.00E-01 1.00E+00 1.00E+01 8 9 10 11 12 Frequência (Hz) Amplitude FRF ((m/s2)/N) Exp. Ajust. Shaker (a) (b) Figure 6. (a) Amplitude of FRF relating vertical acceleration at 1/3 span with the vertical force applied at the opposite 1/3 span; (b) Identified pattern of a set of multiple modes. Several large Civil Engineering structures, like buildings, bridges or dams, have been also submitted to forced vibration tests in the past, using heavy excitation devices only available at important and well equipped laboratories. That was the case of EMPA, where Cantieni and other researchers have tested a significant number of bridges and dams [4-6]. Figures 7-9 show some examples of that remarkable activity, presenting in particular some of the modes of vibration accurately identified at the sweedish Norsjö dam. (a) (b) (c) Figure 7. (a) Dala bridge; (b) Aarburg bridge; (c) Electro-hydraulic vibrator used at Aarburg bridge (a) (b) (c) Figure 8. (a) Norsjö dam; (b,c) View of instrumented point at downstream side reinforced concrete wall Figure 9. Some identified modes of vibration at Norsjö dam (modes 1, 2, 3, 10, 11, 12). 3 Output-Only Modal Identification The main problem associated to the performance of forced vibration tests in bridges, buildings or dams stems from the difficulty to excite, with sufficient energy and in controlled manner, their most significant modes of vibration in a low range of frequencies. In very large and flexible structures like cable-stayed or suspension bridges, in particular, the forced excitation requires extremely heavy and expensive equipment very seldom available in most dynamic labs. Figure 10 shows, for instance, the impressive shakers used to excite the Tatara and the Yeongjong bridges. (a) (b) Figure 10. Forced vibration tests of (a) Tatara cable-stayed bridge (http://www.hsba.go.jp) and (b) Yeongjong suspension bridge (http://www.yeongjongbridge.com) However, the technological developments registered in the fields of transducers and A/D converters during the last years made feasible the very accurate measurement of very low levels of dynamic response induced by ambient excitations, like wind or traffic, strongly stimulating the development of output-only modal identification methods. Therefore, the performance of output-only modal identification tests became an alternative of extraordinary importance in the field of Civil Engineering, allowing the accurate identification of modal properties of large structures at the commissioning stage or during the structure life time, in a much more comfortable way and avoiding any type of interruption of normal traffic in bridges. 3.1 Equipment and test procedures Figure 11. (a) Force balance accelerometers; (b) Multi-channel data acquisition and processing system for ambient vibration tests; (c) Strong motion tri-axial seismograph Modern force balance accelerometers (Fig. 11a), specially conceived for measurements in the range 0-50Hz and virtually insensitive to high frequency vibrations, have contributed very significantly to the success of ambient vibration tests. In such tests, the structural ambient response is captured by one or more reference sensors, at fixed positions, together with a set of roving sensors, placed at different measurement points along the structure, in different setups. The number of points used is conditioned by the spatial resolution needed to characterize appropriately the shape of the most relevant modes of vibration (according to preliminary finite element modeling), while the reference points must be conveniently far from the corresponding nodal points. Force balance accelerometers require appropriate power supply, and their analogue signals (that may be locally amplified) are usually transmitted to a data acquisition system with an A/D conversion card, of at least 16 bit, through relatively long electrical cables. This system can be based on a normal PC, although some data acquisition and processing systems, specifically conceived for the performance of ambient vibration tests are already available (Fig. 11b), playing a role similar to the Fourier analyzers in the context of classical Experimental Modal Analysis. Although most of the output-only modal identification tests in large civil structures have been based worldwide on the use of long electrical cables, the implementation of this type of solution is rather cumbersome and time consuming. Therefore, there is presently a natural tendency to develop wireless architectures or, at least reduce drastically the cables length, by introducing local digitization and single cable signal transmission. A very efficient and comfortable alternative has been intensively used at FEUP[7] and LNEC[8], based on tri-axial strong motion recorders duly synchronized through GPS sensors. 3.2 Output-Only Modal Identification methods The ambient excitation has commonly a multiple input nature and a wide band frequency content, stimulating a significant number of modes of vibration. For simplicity, output-only modal identification methods assume the excitation input as a zero mean Gaussian white noise, which means that the real excitation can be interpreted as the output of a suitable filter excited with that white noise input. Modelling the behaviour of the filter-structure system, one may conclude that some additional computational poles, without structural physical meaning, appear as consequence of the white noise assumption. There are two main groups of output-only modal identification methods: non-parametric methods essentially developed in frequency domain and parametric methods in time domain. The basic frequency domain method (Peak-Picking), though already applied some decades ago to the modal identification of buildings [9,10] and bridges [11,12], was only conveniently systematized by Felber [13] about twelve years ago. This approach, which leads in fact to estimates of operational mode shapes, is based on the construction of average normalized power spectral densities (ANPSDs) and ambient response transfer functions involving all the measurement points, and allowed the development of software for modal identification and visualization used at UBC and EMPA [13]. The frequency domain approach was subsequently improved [14,15] by performing a single value decomposition of the matrix of response spectra, so as to obtain power spectral densities of a set of SDOF systems. This method (Frequency Domain Decomposition (FDD)) was better detailed and systematized by Brincker et al. [16], and subsequently enhanced [17] in order to extract modal damping factors estimates. In this last approach (EFDD) these estimates are obtained through inspection of the decay of auto-correlation functions, evaluated by performing the inverse Fourier transform of the SDOF systems’ power spectral densities. The time domain parametric methods involve the choice of an appropriate mathematical model to idealize the dynamic structural behaviour (usually time discrete state space stochastic models, ARMAV or ARV models) and the identification of the values of the modal parameters so as that model fits as much as possible the experimental data, following some appropriate criterion. These methods can be directly applied to discrete response time series or, alternatively, to response correlation functions. The evaluation of these functions can be made based on their definition, using the FFT algorithm [18] or applying the Random Decrement method (RD) [19]. A peculiar aspect of output-only modal identification based on the fitting of response correlation functions is the possibility to use methods that stem from classical input-output identification methods, based on impulse response functions. Some of these methods are the Ibrahim Time Domain (ITD) [20], the Multiple Reference Ibrahim Time Domain (MRITD) [21], the Least-Squares Complex Exponential (LSCE) [22], the Polyreference Complex Exponential (PRCE) [23] or the CovarianceDriven Stochastic Subspace Identification (SSI-COV) [24]. An alternative method, that allows direct application to the response time series is the Data-Driven Stochastic Subspace Identification (SSI-DATA) [25]. It’s still worth noting that the Random Decrement technique, usually associated to the application of time domain methods like Ibrahim’s, can be also the base for the application of frequency domain methods, like PP, FDD or EFDD, as it leads to free vibration responses, from which power spectral densities can be evaluated using the FFT algorithm [26], reducing noise effect (methods RD-PP, RD-FDD and RD-EFDD). These methods, schematically represented in Figure 6, have been recently systematized, applied and compared by Rodrigues [8]. Figure 6 also indicates the five different types of numerical techniques employed in their development (FFT, SVD, LS, EVD and QR). PP method FDD and EFDD methods SVD RD-PP method RD-FDD and RD-EFDD methods SVD ITD and MRITD methods LS, EVD LSCE and PTD methods LS, EVD SSI-COV method SVD, LS, EVD modal parameters fi ξi φi Numerical techniques used: FFT fast Fourier transform singular value SVD decomposition least squares fittingLS eigenvector decompositionEVD orthogonal decompositionQR estimates of power spectral density functions Sy(f) SSI-DATA method QR, SVD, LS, EVD y R(t) estimates of correlation functions y (t) time series response FFT direct method y D(t) estimates of RD functions FFT FFT based method RD method Welch method FFT Figure 12. Schematic representation of outpout-only modal identification methods. Very recently, the new operational Polymax parameter estimation method was introduced by LMS (www.lms.be) [27]. 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