Experimental Modal Analysis Testing - a Powerful Tool for Identifying the In-Service Condition of Bridge Structures

Experimental Modal Analysis testing - a powerful tool for identifying the in-service condition of bridge structures

N. Haritos Department of Civil & Environmental Engineering, The University of Melbourne, Grattan St, Parkville, Victoria 3052, Australia Email: n.haritos @ engineering, unimelb. edu. au

Abstract

The Experimental Modal Analysis (EMA) testing technique provides a great deal more information about the in-service condition of a bridge under test than is possible from the more traditional forms of static testing through identification of the modal properties (natural frequencies, mode shapes and damping levels) of the bridge concerned. This information is of immense value to the "tuning" of Finite Element Method (FEM) based models which can then be used with confidence for assessing bridge load carrying capacity and response to seismic and other dynamic load inputs. This paper outlines some of the key features of the technique highlighting results obtained from its application to the field testing of several bridges by the University of Melbourne structural engineering research team.

1 Introduction

A common method of predicting the behaviour of real systems in many areas of science and engineering is to use relevant mathematical models. One of the fundamental problems faced by scientists and engineers is the verification of such models using data from experimental measurements. In particular, specific parameters of the mathematical model describing the system have to be found that provide the best possible match between the predicted behaviour from the model and actual experimental observations.

A team of researchers at the University of Melbourne has been collaboratively involved over the past few years with the Principal Bridge Engineer's department of VicRoads, the State of Victoria, Australia, road and bridge authority, in the field testing of a number of ageing Reinforced Concrete (RC) bridge superstructures as part of the VicRoads corporate sponsored R&D project: "Load Capacity of In-service Bridges",' ^^.

214 Computer Methods and Experimental Measurements

This testing has featured particular implementations of the Experimental Modal Analysis (EMA) dynamic testing technique* in which the bridge superstructures concerned were dynamically excited using forcing from a Linear Hydraulic Shaker (LHS). Basic parameters (such as the value of Young's modulus of aged RC; the flexibility of pier supports; support conditions at the abutments, etc), in numerical models of these structures based upon the Finite Element Method (FEM) modelling technique were able to be "tuned" so as to obtain as good a fit as conveniently possible between the predicted modal properties from these models and those obtained from the EMA testing. This paper highlights some of the experience gained and the benefits realised from application of the EMA testing technique to a number of bridge structures in the State of Victoria, Australia, by our research team.

2 Description of the EMA testing technique

2.1 Principles of EMA testing

EMA is essentially the process by which the natural modes (mode shapes, frequencies and damping) of a structure under test are identified from performance of a Modal Experiment. Time domain traces of response measurements over a grid of points captured simultaneously with excitation force at a single point, "k", are transformed in the frequency domain to obtain estimates of the Frequency Response Functions (FRFs), A#(co) , via:

£M (l)

where X. fcoj and F*(co) are the Fourier Transforms of the displacement response at point "j", given by Xj(t), and this excitation force, respectively, whereas the theoretical form of the FRF, hjk(co), is given by:

(2)

in which %„ and 9^ represent the j* and k* elements of the complex eigenvector for the n* mode of vibration, and X% is the complex eigenvalue for this mode, with the "*" representing the process of conjugation.

The complex eigenvalue X% in eqn. (2) is related to %„ and coj, the damped and undamped circular frequencies for the n* mode respectively, and £n, the ratio to critical damping for that mode, via:

Aw = -GnWfz + fadn (3)

Through "ensemble averaging" of several realisations of fr/*(a>)obtaine d from repeat test records, the "quality" of the FRF can be improved for subsequent processing by suitable EMA algorithms that attempt to fit modal parameters (%, In and hence co^n and £„)» to the theoretical model of eqn. (2). The DSMA algorithm^, developed for performing EMA by the University of

Melbourne team, achieves "best" estimation of the complex eigenvectors % (mode shapes) and eigenvalues Xn (natural frequencies and damping ratios) by minimising on the square of the difference between all of the "ensemble- averaged" forms of FRFs and their corresponding theoretical counterparts via a non-linear least squares fitting procedure. In practice, only a small number of transducers (say 10 to 15 accelerometers) would be available for measuring the response, so these would need be re-located a sufficient number of times to "cover" the required measurement grid. The excitation would then be repeated as necessary to produce the "ensemble averaged" realisations of A#(oo) for all points "j" on the grid.

2.2 The University of Melbourne EMA testing package

The University of Melbourne system for performing EMA testing comprises the following major components: (i) A Linear Hydraulic Shaker(LHS)/actuator rated at lOOkN for a 20

MPa line operating in the frequency range: 0 - 50 Hz. (ii) A 120 litre/min hydraulic power supply to the actuator. (iii) A three phase electrical power unit normally hired for field use. (iv) A remote console for controlling the actuator in displacement/force mode of controlled excitation via "TSPECTRA"* software. (v) "TSPECTRA" - Real time data acquisition/experimental control

software/hardware system that captures up to 16 simultaneous channels with programmable anti-aliasing filters, gain and offset. (vi) "DSMA"* - a fully non-linear least squares package for EMA. (vii) A set of vibration measurement transducers - choice of 4 servo- based Sundstrand accelerometers (sensitivities of ~5V/g), 6 PCB accelerometers (sensitivities of ~10mV/g) and, more recently, 15

Dytran piezo-electric accelerometers (sensitivities of ~0.5V/g).

2.3 Practical implementation of EMA testing to bridge superstructures

Three major stages necessary to the design and successful performance of EMA testing in field applications have been identified, viz: (i) Selection of the actual grid to be used for response measurement. (ii) Selection of the location(s) for positioning the exciter and (iii) details of the performance of the dynamic testing itself:

characteristics of the excitation; time length and frequency of data sampling; number of repeat tests for ensemble averaging, etc. An "initial" FEM model of the structure to be tested in order to gain some some preliminary understanding of its dynamic characteristics is necessary to algorithms that attempt to optimally perform the first two of these tasks/°. (This model is termed "initial" in the sense that it contains parameters which we initially would be specifying using design estimates but which we would later be revising based upon actual field results obtained from EMA testing). A record length of 2048 data points per data channel at a simultaneous channel sampling rate of 128 Hz corresponding to a time length of record of 16 seconds has been chosen as the basic data capture condition for implementing the EMA testing technique on short span bridges using our EMA testing system. This choice permits identification of the most important

276 Computer Methods and Experimental Measurements

dynamic modes of bridge structures in the ~0 to 50 Hz frequency band. Up to 16 repeat test records of Swept Sine Wave (SSW) forcing (frequency linearly "swept" from 0 to 50 Hz in the 16 second recording period) from the LHS are taken for the purpose of ensemble averaging of the FRFs using "TSPECTRA" which are suitably identified and stored at the end of data collection. A typical experiment, involving the fixing of the exciter, the setting up of steel plates over the measurement grid on which to locate the accelerometers (say a 7 x 7 grid), and the performance of the testing itself assuming that one half of the bridge will be open to clear traffic at periodic intervals between record capture, can all be performed on the one day.

3 EMA testing: application to several bridge superstructures

3.1 Objectives of EMA testing

The principal objective of the earlier EMA testing by the University of Melbourne was to determine the viability of the technique as a method for establishing analytical models of bridge superstructures that could then be reliably used to perform assessments of the Load-carrying Capacity of these structures. The relative performance of this testing technique compared to the more traditional static testing methods for establishing such analytical models, was ascertained on a number of these occasions as the bridge superstructures concerned were often statically tested by VicRoads immediately or soon after completion of EMA testing depending upon static test vehicle availability. A second major objective was to gauge whether the EMA testing method exhibited potential as a "condition monitoring" technique by gaining a "feel" for the level of accuracy to which descriptive parameters of the structural features of the bridge superstructure could be established using such testing. The descriptive parameters for distinctive structural features of a particular bridge superstructure that naturally emerge when using EMA testing are the natural frequencies, mode shapes and associated damping levels that are determined from the DSMA algorithm. The complex mode shapes (amplitudes and respective phases) determined at the discrete positions chosen for the measurement grid can be animated via an option in the DSMA software package to better be able to visualise their properties. Simple inspection of these mode shapes during animation permits the appreciation of some basic features of the bridge superstructure to be realised such as: the condition of restraint at the abutments and over supports (degree of compliancy) and any "anomalous" features that may be present (such as the effects of local degradation, deck delamination, or non-linear structural characteristics).

3.2 "Tuning" FEM model parameters The "initial" FEM model of the bridge superstructure is normally based on a finer mesh of grid points than can be used for the EMA testing (usually an integral factor of two or three times the density in mutually orthogonal directions for a regular bridge superstructure), and assumed values for boundary conditions at the supports and for the effective Young's modulus E^ for an "uncracked" concrete deck cross-section, amongst others, which have been chosen using design assumptions. This FEM model can also be used to

Computer Methods and Experimental Measurements 217 predict the modal properties ("real" mode shapes and associated frequencies) that are dependent upon the structural parameters used in the FEM description. "Tuning" of structural parameters of the FEM model so as to produce as good a fit as conveniently possible to the observed (determined from EMA testing) modal properties of the bridge superstructure concerned leads to a much more reliable model than the "initial" form as it would better reflect the in-service behaviour and characteristics of the bridge superstructure tested. The so-called "Modal Index" (MI) value, is an indication of the "goodness of fit" between any two mode shape vectors ^ and ^ and is given by:

(4)

When ^ and <^ represent the mode shape prediction from the FEM model and from the EMA testing respectively, ideally one would attempt to "tune" structural parameters in the FEM model to achieve a value of MI^ as close to unity as possible for all modes in the frequency range of interest whilst matching the modal frequency corresponding to each. (It should be noted that for "real" structures, the orthogonality principle suggests that for (^ and (^ representing any two distinct modes, MI^ = 0). Experience has shown that a simple "trial and error" sensitivity approach of the predicted modal properties to the structural parameters adopted in the FEM model is normally adequate for performing this "tuning" procedure, especially for short span bridges with simple support conditions,

4 Results of EMA testing of some selected bridges

4.1 First EMA test - adjacent test spans of the La Trobe River Bridge

Figure 1 depicts a sample set of traces for two of the ten accelerometers and the corresponding excitation force from the LHS (3 tonne mass suspended from beneath the bridge deck at the excitation point) for the case of span#l of the La Trobe River bridge, the first bridge tested using our EMA testing system. Figure 2 depicts the form of the FRF (amplitude and phase) taken for the excitation point as an example of such a plot. (The "dots" in Fig. 2 represent the experimental values of the "ensemble averaged" FRF and the

"solid" line, the variation corresponding to eqn. (2) optimally fitted to these observations by program "DSMA"). In the case of the La Trobe River Bridge, comparisons of results for data sets obtained from: "shaker" (actuator vibrates a 3 tonne mass "seismically") and "force" (actuator reacts directly against the ground) modes of vibration on one simply supported span of the bridge (15.2m long x 7.7m wide) and from force mode of vibration of an adjacent nominally identical span were possible.

Figure 3 compares results for the "tuned" STRAND6.1" FEM model mode shapes to those obtained experimentally from the three separate realisations on the adjacent test spans for the first two vibration modes: a simple flexural mode and a torsional mode respectively, by way of example. Only 28 points were used for the measurement grid so that missing points on the outside edges of the span are depicted in "dotted" form for the EMA

Computer Methods and Experimental Measurements

results in this figure. (Grid points were principally positioned along the centrelines of each of the three longitudinal stiffening beams and midway along the slab in between these beams at l/6th span increments). The influence of the shaker mass of 3 tonne in these tests was observed to consistently produce slightly lower natural frequencies than for force mode of operation in all modes with only a "mild" influence on the mode shape, (see examples in Fig. 3). Ml values between modes were found to be better than 90% for most cases whether performed between separate corresponding EMA estimates or between corresponding EMA and FEM mode shape predictions. The "tuned" FEM model obtained from the EMA testing was used to predict deflections at measurement points for a number of static load cases performed independently by VicRoads. The agreement was found to be excellent.

15.00

Time (s)

Figure 1 Sample traces for accelerometers SSI and SS2 and SSW excitation

10.00 20.00 30.00 40.00 180.0 90.00 0.0000 -90.00 -180.0 10.00 20.00 30.00 40.00 Frequency (Hz)

Figure 2 Frequency Response Function for location of SSI in Fig. 1

Computer Methods and Experimental Measurements 279

fo = 8.03 Hz

FEM Mode #1 EMA Mode # 1 (First Span tested Shaker and Force Modes; Second Span Force Mode)

fo = 10.5 Hz

FEM Mode#2 EMA Mode # 2 (First Span tested Shaker and Force Modes; Second Span Force Mode)

Figure 3 Sample modal results for La Trobe River Bridge test spans

This "first off experience in EMA testing using the University of Melbourne EMA testing system in early 1993, was encouraging and prompted the continued support of the collaborative EMA test program between the University of Melbourne and VicRoads on an annual basis.

4.2 Results for other bridges with separate simply supported spans

Several other short span (< 20m) simply supported bridges were tested using the University of Melbourne EMA testing system. These included: (i) The Yarriambiack Creek Bridge - a bridge with a 32" skew and RC deck cast integrally with 5 longitudinal stiffening beams for which

independent data sets were obtained from two separate locations of the LHS on the test span*. (ii) The Campaspe River Bridge - of composite RC beam on steel beam construction (5 beams) where a single span over the floodplains was tested (iii) McCoy's Bridge over the Goulburn River - also of composite RC beam on steel beam construction where two spans were tested: one

15.2m long over the floodplains (3 steel beams) and another -17m long over the river itself (4 steel beams) In the case of the Yarriambiack Creek Bridge, all response measurements were performed using accelerometers mounted on the underside of the bridge deck with the LHS operating from the top of the bridge. In all of the remaining bridges tested, all of the response measurements as well as the excitation from the LHS were performed on the top of the bridge deck. Figures 4 and 5 presents the first mode match from the "tuned" FEM model prediction and the EMA test results for the two separate data sets for Yarriambiack Creek Bridge (LHS located at position "A" then "B") and for the remaining simply supported bridge spans listed above, respectively. In all cases MI values very close to unity were able to be achieved for the first mode after "tuning" parameters in the FEM model whilst exactly "matching" the observed first mode natural frequency.

EMA (LHS at A) EMA (LHS at Br fo= 13.37 Hz fo= 13.45 Hz £ = 5.37%

Figure 4 First mode results for Yarriambiack Creek Bridge (separate data sets)

Campaspe River Bridge McCoy's Bridge - 3 beam McCoy's Bridge - 4 beam

Figure 5 First mode results for Campaspe River and McCoy's Bridge spans

The level of agreement achieved with higher modes (mode shape and natural frequency value), was in most cases very good to excellent (MI better than -0.9 and -0.95 and frequencies within -20% and -10%, respectively). Figure 6 presents a comparison of results for an additional three modes of the Campaspe River Bridge by way of example.

4.3 Results for continuous multi-span bridges

The EMA testing of Fuge's and Concongella Creek Bridge, provided an opportunity to apply the EMA testing system to continuous multi-span (3- span) bridge configurations. In the case of Fuge's Bridge an 80 point grid was used whereas for the Concongella Creek Bridge, a total of 118 points, inclusive of the 8 horizontal acceleration measurement points at mid-height on

Figure 6 Additional modal results for the Campaspe River Bridge

the two pairs of 4 column supporting piers, was adopted for the EMA testing. Figures 7 and 8 provide sample plots of the "tuned" FEM model and EMA mode shapes obtained for these two bridges. Simple inspection of the

EMA mode shapes for both bridges suggests the support conditions at the abutments to be much closer to "pinned" than "en-castre" as assumed in the original design. In addition, local "perturbations" in the animated mode shapes at points "A" and "B" in Fig. 8 were able to be attributed to a discontinuity in the crash-barrier of the Concongella Bridge and to delamination of its bituminous overlay, respectively.

That such "anomalous" conditions can be simply evidenced from the DSMA fitted mode shapes is another powerful attribute of the EMA testing technique demonstrating that the method has the potential to act as a "condition monitoring" tool.

Figure 7 Sample modal results for Fuge's Bridge

FEM 6= 12.6Hz

LHS

Figure 8 Sample modal results for Concongella Creek Bridge

5 Concluding Remarks

The experience gained from the testing of a number of bridge superstructures in the State of Victoria, Australia, using the University of Melbourne EMA testing system has demonstrated that the technique is capable of: • producing "tuned" FEM models of the bridges that accurately

describe their in-service performance/behaviour • identifying major (and even minor) structural features such as the conditions of support at the abutments; delamination of the bituminous overlay from the deck; local discontinuity in the crash barrier at the edge of the bridge, etc The value of the testing system to bridge engineers concerned with maintaining an ageing bridge stock has been obviated.

222 Computer Methods and Experimental Measurements

Acknowledgment

The author would like to acknowledge the active participation of a number of members of the research team in the work reported in this paper, that include: Mr. Hussein Khalaf, Dr Tom Chalko, Dr Vladimir Gershkovich, Mr Marcus Aberle, Mr Emad Gad. Financial support and assistance in kind received from VicRoads Principal Bridge Engineer's Department and the regional offices of VicRoads relevant to the bridge testing is also gratefully acknowledged.

References

1. Haritos, N., Khalaf, H. & Chalko, T. Modal testing of bridge structures using a linear hydraulic shaker, Proc. 13th Australasian Conf. on the Mechs. ofStructs. and Mats., Wollongong, July 1993, pp 349-356. 2. Khalaf, H. & Haritos, N. Dynamic testing of the Latrobe River Bridges, Proc. AUSTROADS'94 Conf., Melbourne, Feb., 1994, pp 17.1-17.10. 3. Haritos, N., Khalaf H. & Chalko, T. Modal testing of a skew reinforced

concrete bridge, Proc. International Modal Analysis Conference IMAC- XIII, Nashville, Feb, 1995, pp 703-709. 4. Haritos, N. & Khalaf, H. Dynamic testing of the Rutherglen Bridges, UNIMELB Report, The University of Melbourne, June, 1995. 5. Haritos, N. & Chalko, T. Dynamic testing of three bridges, UNIMELB Report, The University of Melbourne, May, 1996. 6. Ewins, D. J. Modal Testing: Theory and Practice, John Wiley, New

York, 1985. 7. Chalko, T., Gershkovich, V. & Haritos, N. Direct Simultaneous Modal Approximation Method, Proc International Modal Analysis Conference IMAC-XIV, Dearbourn, February, 1996, pp 1130-1136. 8. TSPECTRA - 16 Channel Spectrum Analyser, User Manual, Scientific Engineering Research P/L, Melbourne, 1992. 9. DSMA - Modal Analysis Program, User Manual, Scientific Engineering

Research P/L, Melbourne, 1996. 10. Chalko, T., Gershkovich, V. & Haritos, N. Optimal design of modal experiments for bridge structures, Proc. IXIHth International Modal Analysis Conference, Nashville, February, 1995 , pp 571-577. 11. Haritos, N., Giufre, A. & Wells, J. Static and dynamic testing of two RC bridges, Proc. Roads'96 Conf, Christchurch, NZ, Sept. 1996, Vol. 3, pp 259-274.

12. STRAND 6.1 - Finite Element Analysis Package. Ref. Guide, G+D Computing P/L., Ultimo NSW, Australia, 1992.