Keywords

19.1 Introduction

Ambient vibration testing of in-service bridges has become an increasingly more common experimental approach for quantitatively characterizing full-scale bridges. The popularity of this experimental approach can be largely traced to its advantages relative to controlled vibration testing in terms of cost and practicality for evaluating bridges while they are in-service. The method has been employed for a broad range of bridge types and sizes, and is generally considered to be a reliable approach by many researchers and practitioners. However, many researchers and practitioners also agree that this testing method is subject to the same potential sources of uncertainty that occur with classical experimental modal testing of such structures, plus some additional uncertainty related to the actual characteristics of the uncontrolled and unmeasured dynamic excitation that is the basis for ambient vibration testing. This dynamic excitation is assumed to have very specific characteristics (e.g. stationary and uncorrelated Gaussian white noise that is spatially well-distributed across the structure), but since the excitation cannot be directly measured and characterized, the effects of variations in these characteristics on the reliability of the identified modal parameters is difficult to predict and quantify. There are limited examples in the literature of studies in which the effects of dynamic excitation characteristic on the modal parameters identified through ambient vibration testing of bridges. Some representative examples include a study that utilized a laboratory model structure [1], and others that attempted to evaluate the influence of the dynamic excitation on the identified modal parameters using different full-scale bridge structures [2–4]. In the latter examples, the evaluation was attempted by analyzing the results obtained from free and forced-vibration responses due to controlled truck loads or by analyzing measurements obtained for different levels of traffic on the structure. These studies do provide some insight to the effects of the dynamic excitation characteristics on the identified modal parameters, but the actual dynamic excitation of the structure is still not controlled or measureable.

The corresponding author recently developed a novel multi-shaker dynamic excitation system that utilizes a network of low-cost tactile transducers that is capable of providing simultaneous and controlled dynamic excitation to short- to medium-span bridges. Tactile transducers are more typically used in home entertainment and amusement park applications for enhancing the users experience through haptic feedback of low frequency audio content. These devices are small and unobtrusive and can produce virtually any type of controlled dynamic excitation signal desired for vibration testing of bridges. The dynamic force, frequency range, and operating characteristics of these devices were systematically evaluated to determine the feasibility of using them for dynamic testing of full-scale bridges [5]. Although their performance and operating characteristics are generally inferior to those of higher quality (and substantially more expensive) linear mass shakers specifically designed for modal testing of structures, this limitation is mitigated to some extent by the capability to deploy large numbers of the devices in a spatially distributed manner on a bridge for the fraction of the cost associated with deploying a single high quality dynamic excitation device. For example, the prototype system developed by the author can provide 16 simultaneous and controlled dynamic inputs to a structure. The total cost for constructing the prototype excitation system was approximately $6,000. A photograph of the multi-shaker system developed specifically and ruggedized for field testing of bridges is shown in Fig. 19.1. It should also be noted that the system has been developed to be able to operate from either AC or DC power sources such as a 12 V car battery. The complete excitation system (with 16 excitation inputs) and the associated data acquisition hardware and computers have also been successfully deployed in the field by the writers using two 3,000 W portable generators to provide power.

Fig. 19.1
figure 1

Muti-shaker excitation system components

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The writers were motivated to utilize the controlled excitation capabilities of this multi-shaker dynamic testing system to investigate the uncertainty related to the dynamic excitation characteristics from a previously untried and impractical approach. This paper presents the results of a study devised and executed for a medium span length truss bridge for this objective. The bridge was evaluated for actual ambient dynamic excitation provided exclusively from the ambient environment and for several controlled excitation cases that simulated the excitation characteristics normally assumed in ambient vibration testing and controlled variations to these characteristics. The measured vibration responses of the bridge from each excitation case are compared in the time domain, and the natural frequencies and damping values identified for the bridge from these excitation cases are compared.

19.2 Experimental Program

The experimental program developed for this research consisted of implementing ambient vibration testing of an in-service truss bridge. The ambient vibration testing was executed for a total of four distinct dynamic excitation cases. The first excitation case consisted of unmeasured and uncontrolled ambient dynamic excitation from the natural environment. The remaining excitation cases consisted of spatially distributed Gaussian white noise with different characteristics that was produced using the multi-shaker dynamic excitation system. Although the characteristics of the dynamic excitation in the latter three cases was known and controlled, the input was treated as though it was unmeasured ambient excitation for the purpose of analysis and for comparisons with the results obtained for real ambient excitation of the structure. The details of the test bridge, the experimental setup and the excitation cases are presented in the following.

19.2.1 Bridge Description

The bridge utilized for this testing program is a Parker pony truss bridge located near Fayetteville, Arkansas that was constructed in 1930. The bridge crossing consists of three identical, 30.5 m-long simply-supported truss spans. The bridge is open to traffic and carries two 3.05 m-wide lanes across the West Fork of the White River. Each truss span has ten panels spaced at 3.05 m. The width of the bridge measured from center-to-center of the trusses is 6.8 m. The height of the trusses varies along the span length and reaches a maximum of height of 4.27 m at the midspan point. The individual truss members consist of rolled and riveted built-up steel sections. The bottom chord sections consist of two channels with intermediate batten plates. The top chord sections consist of two channels, a top cover plate and lacing. The verticals are rolled I-beams, and the diagonals are either rolled I-beams (compression members) or two angles with intermediate batten plates (tension members). The bridge has a 203.2 mm thick reinforced concrete deck that is supported directly on rolled I-beams that span transversely between the two trusses at the bottom panel points. Several photographs of the bridge are shown in Fig. 19.2.

Fig. 19.2
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(a) End view and (b) side view of truss bridge

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This particular bridge was selected for the research program because the number of vehicles using the structure on a daily basis is very low. As a result, the bridge vibrations measured during the execution of the testing program would only be due to ambient environmental sources or the network of shakers installed on the bridge. This also permitted the mass loading effects and dynamic interactions due to vehicles crossing the bridge to be effectively excluded from the measurements. The bridge has also been extensively tested in earlier vibration studies [6, 7] and the modal parameters of the structure are already known with a good degree of confidence. A single end span (west end) of the bridge crossing was tested and evaluated for this research program.

19.2.2 Instrumentation, Data Acquisition and Signal Generation

The structure was instrumented using a total of 18 accelerometers to measure its vibration responses in the vertical direction for each of the dynamic excitation cases. The accelerometers included a mix of Model 393C and Model 393B05 accelerometers from PCB Piezotronics, Inc. The 393C accelerometers have a nominal sensitivity of 1 V/g and a range of ±2.5 g. These accelerometers were located on the bridge were the vibration responses were expected to be largest. The 393B05 accelerometers have a nominal sensitivity of 10 V/g and a range of ±0.5 g. These accelerometers were installed on the bridge at locations where the vibration responses were expected to be smallest. All of the accelerometers were installed on the steel trusses using magnets. The locations of the accelerometers on the bridge are shown in Fig. 19.3.

Fig. 19.3
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Accelerometer and shaker positions on truss bridge

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All measurements were recorded using a PXI mainframe with Model 4472B dynamic signal acquisition modules from National Instruments. The vibration measurements were sampled at a rate of 1 kHz and were later decimated during the data analysis stage. The excitation signals were generated using a laptop computer that was independent of the data acquisition computer connected to the PXI system. A 16 channel analog output module from National Instruments was mounted in a USB chassis and used to generate the electrical excitation signals that were subsequently sent to the shaker amplifiers. A total of 14 shakers were clamped to the bridge members at locations shown in Fig. 19.3.

19.2.3 Excitation Cases

As mentioned previously, the bridge was evaluated for a total of four distinct dynamic excitation cases. The first case evaluated was unmeasured and uncontrolled ambient dynamic excitation from the natural environment. Although it is uncontrolled and un-measureable, this excitation is assumed to have stationary, uncorrelated Gaussian white noise characteristics. Moreover, this dynamic excitation is assumed to be spatially well-distributed across the complete structure. This excitation case is subsequently referred to as the “Pure Ambient” case. The remaining three dynamic excitation cases all utilized inputs that attempted to simulate the assumed characteristics of the unmeasured ambient excitation and slight variations to its assumed nature and were produced using the multi-shaker system. The second excitation case utilized 14 simultaneous and uncorrelated Gaussian white noise inputs that were band pass filtered to produce an effective frequency band for the excitation of 3.5–150 Hz. This case is subsequently referred to as the “Full Band” case since the frequency band of interest for the bridge’s vertical and torsion vibration modes was in the range of 4–40 Hz. The third excitation case was the same as the second case except that the band pass filter limits were set to produce an effective frequency band for the excitation of 3.5–25 Hz. This case is subsequently referred to as the “Low Band” case and was intended to permit the uncertainty of the modes located above this band to be assessed relative to the Pure Ambient and Full Band excitation cases. The final case also used the same type of excitation signals as in the second case, but the limits of the band pass filter were set at 25 and 150 Hz. This case is subsequently referred to as the “High Band” case and was intended to permit the uncertainty of the bridge modes located below this excitation band to be evaluated. A total of 28 min of bridge vibration response data were recorded for each of the excitation cases described above.

19.3 Data Analysis

The measurement data recorded from each of the excitation cases described above were processed using an output-only analysis technique to identify the natural frequencies, mode shapes and percent damping for the bridge’s first seven modes. The measured vibration responses were also evaluated directly in the time domain to assess the global bridge vibration response and its consistency for each of the excitation cases that were implemented. The data analysis methods utilized are further described in the following.

The time domain analysis of the bridge vibrations measured for each excitation case consisted of computing the root-mean-squared (RMS) acceleration amplitudes for each of the accelerometer locations on the bridge. The individual RMS accelerations were subsequently added together to yield a single index, termed the Total RMS acceleration, that characterized the global vibration response level of the bridge for each excitation case from all of the spatially dispersed accelerometer locations. From a theoretical point of view (and assuming there is no noise in the measurements), if the bridge is subject to stationary Gaussian white noise excitation, its vibration response at each of the accelerometer locations should be characterized by the vibration of the bridge in each of its modes. Furthermore, these vibration responses should exhibit a similar level of stationarity (assuming the structure is linear and time invariant) as the dynamic excitation of the structure. The Total RMS acceleration is thus a measure of the stationarity of the excitation. The 28 min measurement records recorded from each excitation case were subdivided into 4 min long segments and the Total RMS acceleration was computed for each segment. The 4 min duration was arbitrarily selected to provide enough time for about 1,000 oscillations of the lowest bridge vibration mode (about 4 Hz) to be present in a given data segment. The mean and standard deviation of the Total RMS acceleration were also computed for the seven segments analyzed from each excitation case for comparison across the different excitation cases.

The modal parameters for the bridge were identified for each excitation case using an output-only analysis approach that was implemented in MATLAB. The basic steps in this analysis included: (1) calculating auto and cross correlations for all of the accelerometer locations to obtain estimates of the impulse response functions [8]; (2) computing FFTs of the correlation functions to obtain a pseudo frequency response function (FRF) matrix; and (3) implementing a CMIF and enhanced FRF identification approach [9, 10] to extract the natural frequencies, mode shapes and percent damping for each mode. The frequency resolution of the measurement data was 0.122 Hz. The modal parameters were identified for the each of the 4 min long data segments extracted from the total measurement record for each excitation case to also evaluate their consistency relative to time.

19.4 Results and Discussion

The Total RMS accelerations computed for each 4 min long data segment in each of the excitation cases are summarized in Table 19.1. One accelerometer malfunctioned during the field testing program and was excluded from data sets, so these results shown in the table are based on the measured responses from a total of 17 accelerometers installed along the upstream and downstream trusses. The Total RMS accelerations provide some clear insight to the dynamic excitation of the bridge for each case. The excitation cases that utilized the multi-shaker excitation system induced significantly larger global vibration of the bridge than did the Pure Ambient case. The mean Total RMS acceleration for the seven time segments from each excitation case was computed and the mean values were normalized relative to the mean Total RMS acceleration from the Pure Ambient excitation case. The normalized mean values indicate that the global vibration response of the bridge for the Full Band excitation case was nearly 15 times larger than what was measured under natural ambient excitation (Pure Ambient). The High Band excitation case produced a bridge vibration response that was 18 times greater than the Pure Ambient case, while the Low Band case produced a global vibration response that was 7 times greater than the Pure Ambient case. These results generally correspond to the level of force produced by the shakers used for the testing program. These devices are stroke limited at lower frequencies [5] and tend to produce larger dynamic forces at high frequencies.

Table 19.1 Total RMS accelerations (g’s) for each excitation case
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The standard deviations of the Total RMS accelerations shown in Table 19.1 for each excitation case indicate that the bridge response over time due to purely ambient dynamic excitation was less consistent than in the cases that utilized the shakers. Of the cases that utilized the shakers, the Full Band case produced the most consistent global vibration response of the bridge, although it was nearly as consistent in the High Band and Low Band cases. The Total RMS acceleration results given in Table 19.1 indicate that the multi-shaker dynamic excitation system used for the testing was capable of exciting this full-scale medium span bridge to a much higher degree and in a more consistent manner than the natural environment.

The natural frequencies and percent damping values identified for the data segments in each excitation case are summarized in Tables 19.2 and 19.3, respectively. The mode shapes computed from the data segments are not shown for brevity, but showed similar trends relative to the excitation as the natural frequencies and percent damping values. A total of seven modes could be identified for the bridge from the measurements obtained for the different excitation cases. The results shown in Table 19.2 indicate that the natural frequencies of the identified modes were generally consistent among the four excitation cases evaluated. The natural frequencies identified from the Full Band excitation case were slightly more consistent over time for the complete set of the modes than in the other excitation cases, as evidenced by the standard deviations for the frequencies shown in the table. It should be noted that Mode 2 (Torsion 1) was only identified in one data segment of the High Band excitation case. In addition, Mode 4 (Bending 3) could not be identified from any of the data segments analyzed from the High Band excitation case. This result appears consistent with the effective frequency band of the white noise excitation used in the High Band excitation case (25–150 Hz) since the natural frequencies for both of these modes are well below the lower frequency limit of the excitation. The Low Band excitation case shows a similar result for Mode 7 of the bridge which is located beyond the upper frequency limit for the excitation used in this case (3.5–25 Hz). The results also appear to indicate that the effective frequency band for the actual ambient excitation of the bridge produced by the environment was less than 20 Hz and is most likely not a broadband input with a flat spectrum as is normally assumed for this excitation.

Table 19.2 Natural frequencies identified from the data segments of each excitation case
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Table 19.3 Percent damping identified from the data segments of each excitation case
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The percent damping results summarized in Table 19.3 show similar trends to those observed for the natural frequencies for the different excitation cases, although their values were more variable than were the frequencies within a given excitation case. It is notable that the damping values identified for the modes were generally larger from the excitation cases that utilized the multi-shaker excitation system. Damping estimates obtained from ambient vibration tests are often associated with a high degree of uncertainty due to the low vibration amplitudes generally measured in such tests. The identified damping values are inconclusive at this point relative to their uncertainty and its relationship to the dynamic excitation characteristics for this bridge. This particular modal parameter should be investigated further and perhaps using other modal parameter identification methods to help clarify the relationship to the ambient excitation characteristics.

19.5 Concluding Remarks

This paper presents the results of a study that was developed to investigate the uncertainty in the dynamic parameters identified in ambient vibration testing of bridges due to the actual characteristics of the dynamic excitation. A basic framework for enabling this potentially significant source of uncertainty was developed using a novel and low-cost multi-shaker dynamic excitation system. This system enabled the authors to provide controlled dynamic excitation of a full-scale bridge structure that was consistent with the assumed nature of the normally uncontrolled and unmeasureable ambient dynamic excitation employed in ambient vibration testing of bridges. The results of this study are promising from the perspective that the multi-shaker excitation system was able to induce larger and more consistent bridge vibration responses than were observed from conventional ambient environmental dynamic excitation. The results also showed that the excitation case that most closely simulated the assumed characteristics of ambient dynamic excitation produced modal parameter results that had the least degree of uncertainty and variation overall. The study presented in this paper represents the first attempt by the authors to evaluate uncertainty in ambient vibration testing of real bridges in the field in a semi-controlled manner. The authors plan to implement the basic framework of this study for other representative short- to medium-span length bridges. They are also presently investigating and evaluating the dynamic characterizations of representative short- to medium-span length bridges using the multi-shaker excitation system to provide measured harmonic, impulsive, and random excitation inputs for MIMO experimental modal analysis.