1 Introduction

Classically, forced vibration tests have been used to identify the dynamic properties of structures for numerical modelling (or design) updating and validation [1,2,3,4,5]. The application of an experimental modal analysis by performing forced vibration tests is an effective and rigorous mean of defining the modal properties of a civil engineering structure. This methodology has been successively employed on dams in the past, as well as on bridges [6] and buildings [7]. Nevertheless, this procedure shows a few disadvantages, since for bridges, and for dams crossed by roads, on one hand, traffic must be interrupted to perform the test, and on the other, the dimensions and weight of the equipment that needs to be used to excite these enormous structures may rise conveyance issues [8].

Notwithstanding, the technological progression that occurred in the area of data acquisition during the past few decades contributed significantly to the dissemination of ambient vibration tests as a reliable alternative. These functional tests allow to carefully identify the modal properties of civil engineering structures with no need to disturb their normal service conditions. Besides, the modal properties are extracted from data acquired under normal operation conditions, instead of artificially created excitation. The successful application of operational modal analysis has already been verified in many different examples of civil engineering structures, such as cable-stayed bridges [9], suspension bridges [10], footbridges [11], viaducts [12], stadia roofs [13], towers [14], wind turbines [15], buildings and infill walls [16, 17], or even nuclear power plants [18]. Ambient vibration tests are often performed, prior to rehabilitation activities to study and to better understand the structure, after the construction of essential infrastructures to validate numerical models or even as part of inspection plans to assess the safety of structures already built. Moreover, the information yielded by operational modal analysis can be used in the definition of dynamic monitoring systems [19] for the shaping and tuning of devices directed to the control of vibrations.

Given that when conducting an ambient vibration test, the vibrations registered are not caused by any artificial source specifically prepared for the test, but to the surrounding ambience or to nearby human activity, the vibration levels detected are usually relatively lower than the ones that are typically verified when forced vibrations are used, leading to the necessity of employing superior equipment during the test, namely sensors and data acquisition system. Nonetheless, the testing of more flexible structures such as towers or pedestrian bridges, which are easier to excite, may proportionate good results, even using equipment of lower quality.

For instance, when testing concrete dams, it usually should be expected to measure low vibration levels [20], given the massive nature of these structures and the isolated locations where many of them are positioned, so superior equipment is needed to perform successful experimental campaigns. Nevertheless, the dynamic testing of concrete dams based on the recording of ambient-induced vibrations has been carried out before [21,22,23,24,25] quite often as a supplement to forced vibration campaigns. Recently, the execution of these tests on dams to correct numerical models and to corroborate structural assumptions became more common [26,27,28,29], prompting the implementation of structural health monitoring systems based on the recording of vibrations that rely entirely in environmental excitation and on dependable measuring and acquisition equipment [30, 31].

Nevertheless, top-quality equipment may not always be available, given that it usually represents high costs. Therefore, in certain situations, low-cost options, with not so high potentialities, can emerge as an alternative solution. In this sense, when performing operational modal analysis, it is essential to examine the accuracy of the outcomes reached with accelerometers with a broad range of potentialities [32].

Therefore, the present work addresses the ambient vibration testing of a set of concrete dams with diverse structural profiles, which had the purpose of identifying the issues related to the low intensity of the signals recorded through the execution of ambient vibration tests on dams, and studying the quality of the results that can be attained with these type of application (Fig. 1).

Fig. 1
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Pictures of the tested dams [33]

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In the following sections, details are presented about the tests performed in Alto Lindoso, Bouçã, and Castelo do Bode dams. Estimates are obtained for the modal properties of the tested dams and the uncertainty associated with these properties. A summarized set of results is presented for the tests performed in Caldeirão, Santa Luzia, and Aguieira dams.

Finally, the time-series of accelerations recorded at Alto Lindoso and Bouçã arch dams are numerically adulterated with growing degrees of noise to simulate that different accelerometers were used during the tests, instead of the force-balance accelerometers that were actually used. The results obtained with real experimental data and with simulated data and studied and compared.

2 Experimental procedure and equipment

Unlike forced vibration tests, which require the use of shakers or instrumented hammers, during ambient vibration tests, there is neither the need to excite the structure artificially nor to measure the input action that is causing the structure to vibrate, rendering a relatively simple experimental procedure [Santos, 34]. Therefore, ambient vibration testing roughly consists of recording the vibrations on a structure that is subjected to anything else than ambient noise. For this, a combination of reference sensors and moving sensors can be used, noting that the first remain fixed at their positions, while the latter may be placed at various locations during the test.

When preparing a dynamic test, it is crucial to have in mind that the spatial precision required to determine the mode shapes of the structure correctly plays an essential role in the definition of the number of points to instrument during the test. For this, and to guarantee that reference points are positioned away from nodal points, it is vital to predicting the mode shapes of the structure, prior to the execution of the test, for which the consideration of similar structures and the analysis of numerical models are of good help. Moreover, the distribution of sensors as references or moving sensors rests on the number of sensors accessible to execute the test and on the size of the structure tested. For instance, if the quantity of sensors available is smaller than the number of points to cover, at least one sensor must be used as a reference, though it is advisable to use more than one reference point. When testing smaller structures and the number of sensors available is not a limitation, it is desirable to perform the test using all the points as fixed sensors (references), since this will simplify data processing.

In terms of data acquisition, it is vital that the dimension of the time-series recorded and the sampling rate selected to record them are chosen carefully, since the volume and quality of the data available largely depends on these two factors. In the case of the sampling frequency, the value to adopt can be limited either by the attributes of the equipment used or by the dynamic properties of the structure under study. So that aliasing errors can be effectively avoided [35], the sampling rate should be greater than at least two times the highest frequency captured by the accelerometers or than the cutting frequency of analogue low-pass filters that may exist in the measuring chain. In addition, the total of vibration modes to be determined will be limited by the sampling rate, since it will only be possible to detect frequencies lower than half of this parameter’s value, and so it should be adopted accordingly.

Furthermore, the quality of the modal parameters’ estimation depends on the length of the time-series recorded in each setup, which impacts, in particular, the estimation of damping estimates. To choose the best length for the time-series, a few points should be considered such as the structure’s first frequency, the values of damping, the ratio between signal and noise intensities, and also the method used to perform the identification of modal properties (parametric methods can improve the quality of the results) [36]. For this reason, the optimal time length varies with the structure studied and with the equipment available to perform the experiment. A rule proposing that time-series as long as 1000–2000 times the value of the first frequency’s period should be acquired can be found in [37], though reliable outcomes can be achieved with relatively shorter lengths (more than five times shorter), as presented by [36]. Time-series with extensions between 15 and 60 min have been used in the experimental campaigns presented in this work, corresponding to lengths from 1800 to 7200 times the period of the respective structure’s first frequency.

Systems used to perform measurements and to record data during experimental campaigns are composed of many elements, the most important of which are probably the sensors. Accelerometers are the most common type of sensor used to test civil engineering structures, and force-balance accelerometers are the adequate type of accelerometer to test them. However, another type of sensors measuring, for instance, displacements, velocities, or strains are also common and alternative types of accelerometers, with various working operational basis, such as piezoelectric, MicroElectroMechanical or capacitive, can be used as well. Force-balance accelerometers start measuring at DC, which means that they can detect the lowest frequencies (as an example, in [38] a tower’s fundamental frequency of just 0.35 Hz is detected using force-balance accelerometers). In addition, these sensors are particularly suited to the testing of deficiently excited structures, such as remotely located concrete dams, since they have high sensitivity and low noise.

Generally, sensors produce continuous electrical signals that are then transformed in analogue-to-digital converters to the discrete signals that are saved in computers. The most relevant property of these converters is the number of bits, since the resolution of the measurement roughly corresponds to the division of the measuring range by two to the power of the number of bits. Therefore, it is worth noting that even if the best sensors are used to perform a measurement, the quality of the digital signal (which will be used to process the data) can be compromised if low-quality analogue-to-digital converters are used to transform the signal. Besides the mentioned elements, low-pass filters or signal amplifiers may be included in the acquisition chain as well to enhance the quality of the digital signal. Furthermore, data processing methods can be used to try to improve the quality of the identification reducing the impact of noise [39].

Experimental tests may either resort to centralized schemes, where the signal produced in each sensor is transferred through electrical cables to a single data acquisition system, and all signals are converted to digital form at this point or to autonomous portable recorders where measuring and conversion occur in the same device, and digital signals are then put together in a computer. Examples of both types of acquisition systems are presented in Fig. 2. These portable recorders consist of tri-axial force-balance accelerometers, that may be located in the interior or in the exterior of the recorder, an analogue-to-digital converter with 24 bits, a flashcard enable the direct download of the recorded data to a computer, and a rechargeable battery that provides energy for many hours. Prior to the test, the recorders parameters must be set up according to the test plan and recording characteristics intended. The synchronization between devices is assured through GPS.

Fig. 2
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On the left: centralized acquisition system with cables; on the right: portable recorder with GPS antenna

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Based on the characteristics of each dam, the experimental campaigns addressed in this work were executed resorting to the portable recording devices or the central acquisition system, according to the pros and cons of each system. For instance, the centralized system used has a range limit of about 150 m, while the portable devices can only be used outside, due to the need of having a GPS signal.

3 Data processing and noise simulation

The data recorded during ambient vibration tests should first be pre-processed, which may include the elimination of offsets, filtering, resampling, and storage. After this, output-only identification algorithms [40, 41] can be used to obtain the modal properties of the structure, which can provide accurate results even if the excitation is not a stationary white noise [42]. In the present work, the peak-picking (PP) [43] and the covariance-driven stochastic subspace identification (SSI-Cov) [44] methods are used.

The peak-picking is a basic identification method, with a few drawbacks, but very helpful for an expeditious analysis of the data. In turn, the SSI-Cov is a robust and stable method, though its application is more time-consuming. Therefore, the sequential application of these methods to accelerations time-series recorded in a structure results in a stable procedure that produces reliable results. In addition, to better understand the accuracy achieved with the identification, a variant of the SSI-Cov method is used that was first introduced by [45] and then computationally improved by [46], which provides the possibility of estimating the uncertainty associated with the identified modal properties and allows to enhance the efficiency of automatic operational modal analysis [47]. Stabilization diagrams are used to help distinguish between real and spurious modes [48].

To enrich the study developed around the data recorded during the experimental campaigns that were carried out, an investigation is conducted to determine the feasibility of using accelerometers with other functioning principles than force-balance (FB). For this, the noise floors that may be expected for regular piezoelectric (P) and MicroElectricalMechanical (MEMS) [49] accelerometers were established. Laboratory experiments were performed on two piezoelectric accelerometers (PE1 and PE2), and two MicroElectricalMechanical accelerometers (MEMS 1 and MEMS 2), representing sensors with medium and high quality, respectively. In all the studied cases, noise floors were constant in the frequency range under analysis.

The spectral noise levels of the studied accelerometers were evaluated in a laboratory environment and then simulated through the numerical generation of white noise time-series, which are presented in Fig. 3. It should be noted that considering the logarithmic nature of the vertical scale in Fig. 3, the difference in quality between MEMS and piezoelectric is evident. The two studied piezoelectric accelerometers show a noise floor below 10–11 [g2/Hz], yet for MEMS, these values are approximately 10–9 and 10–10 [g2/Hz].

Fig. 3
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Noise spectra numerically generated

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In addition, Fig. 4 presents accelerations recorded in the central measuring point of each of the tested dams, when the respective power plants were not operating, so that vibration levels can be compared. The exception is Castelo do Bode dam whose turbines operated during the entire test. The levels of vibration verified vary from tens of micro g, either when human works using heavy machines occur in the surroundings or when the dam is crossed by traffic to just a few micro g in calm conditions.

Fig. 4
figure 4

Time-series of accelerations recorder in the six dams tested

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The auto-spectra obtained with the signals displayed in Fig. 4 are presented in Fig. 5, exposing the minimum signal amplitude that allows to adequately characterize the auto-spectra observed in all the dams tested, which is between 10–13 and 10–14 g2/Hz.

Fig. 5
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Auto-spectra resulting from the time-series presented in Fig. 4

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Comparing Fig. 3 with Fig. 5, it becomes clear that when using MicroElectricalMechanical accelerometers to perform ambient vibration tests on dams, it is likely that only noise will be recorded. This is further analysed in the next few sections.

4 Alto Lindoso dam

4.1 Description of the dam and ambient vibration test

Alto Lindoso is an arch dam with double curvature integrated into a tight canyon located in the north of Portugal (see Fig. 6), which started operating in 1992 [33]. This 110-m high concrete dam has a 297-m long crest which embodies a connection over the two margins of Lima River. The respective power plant is less than 100 m afar from the dam and the two vertical Francis turbines operating in the plant (214.3 rpm–3.57 Hz) represent an installed capacity of 630 MW.

Fig. 6
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Frontal picture [33] and a scheme of cross section [50] from Alto Lindoso dam

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An ambient vibration test was performed on Alto Lindoso dam on the 22nd of February 2017, for which ten recorders with tri-axial force-balance accelerometers were used, though only the radial direction was recorded. Given the dam’s substantial scale, a test layout contemplating 21 recording positions was prepared, with one measuring point for each of the 21 concrete blocks of the dam. The defined test grid was covered over four measuring setups during which four accelerometers acted as moving sensors, while other six accelerometers were used as references throughout the entire test. The reference points were marked in Fig. 7 with red dots, whilst blue dots were used to mark the 15 points covered by moving sensors.

Fig. 7
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Alto Lindoso dam: test layout

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The full test took 4 h, divided into four setups of 58 min, separated by 2-min intervals used for sensor repositioning. The data acquisition was realized with a sampling rate of 100 Hz that was then adjusted to half of that through decimation (50 Hz). During the test, a level of water of 322 m was verified.

4.2 Modal properties’ identification

The identification process starts with the employment of the Peak-Picking method which, though not very accurate, allows to achieve rough estimates of the most relevant natural frequencies in an expeditious manner.

Figure 8 presents the averaged and normalized power spectral density function (ANPSD) that was obtained with the application of this method, where the identified vibration modes and respective peaks are highlighted with orange circles. Then, to achieve natural frequency estimates and mode shapes with higher accuracy, the SSI-Cov method was applied, which allows as well to identify damping values. Model orders between 20 and 90 were considered during the application of SSI-Cov to each measured setup.

Fig. 8
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Alto Lindoso dam: averaged normalized power spectral density function

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Figure 9 presents the stabilization diagram obtained from the third setup, where vertical alignments of poles are clearly distinguished, and blue dashed lines point to the alignments determine as being associated with vibration modes of the structure.

Fig. 9
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Alto Lindoso arch dam: stabilization diagram

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In addition, it is relevant to note that the entire set of peaks and alignments observed, respectively, in the power spectral density function and the stabilization diagram were investigated, which included the analysis of the shapes of the modal configurations resulting from all of them. The group of identified vibration modes settled at the end of the analysis corresponds to the ones that were achieved simultaneously through the two identification methods, and that presented reasonable mode shapes, as well.

The first four modes of vibration of the dam were determined, and Table 1 presents values for their modal properties and the description of their modal configurations. Since four setups were needed to perform the test, the values here presented represent the averaging of the results from stable poles in the stabilization diagrams of each setup. It is worth noting that two distinct frequencies are related to the first symmetric vibration mode (designated as modes 2a and 2b), since quite different frequency values were obtained for the different levels of vibration verified during the test.

Table 1 Modal properties of Alto Lindoso
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The standard deviation values related to the estimates of model properties (i.e., natural frequencies and damping ratios) are presented in Table 1 as well, giving extra insight into the accuracy achieved with the identification. For instance, for Alto Lindoso dam, modes one and four (both antisymmetric) present the smaller values for the standard deviation of both frequency and damping estimates, respectively, below 0.01 Hz and 0.2%. On the other hand, the other two modes (both symmetric) present standard deviations’ estimates that, though acceptable, are significantly higher.

Figure 10 presents the well-delimited and coherent modal configurations that were obtained for the four vibration modes determined. While modes one and four present antisymmetric shapes, modes two and three show nearly symmetric ones.

Fig. 10
figure 10

Mode shapes of Alto Lindoso arch dam first four vibration modes

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In 1992, a forced vibration test was realized in Alto Lindoso Dam [51]. During this test, the level of water in the reservoir was 326 m above sea level, which represents operational conditions close to those verified during the performance of the ambient vibration test in 2017, when the water level was about 4 m below. A numerical model was also developed back in 1992 to compare numerical and experimental results [51].

In the numerical model presented the material constituting the dam is assumed to have an elastic behaviour, the rock mass foundation was assumed as elastic isotropic. In turn, for simplification, the foundation was considered to be massless, and the water in the reservoir was modelled through the addition of Westergaard masses [52]. To compare the results obtained, Table 2 presents the natural frequencies achieved through the experimental tests performed in 1992 and 2017, together with the ones obtained with the numerical model built in 1992, and a good agreement is verified between the modal properties obtained from the three mentioned sources.

Table 2 Comparison between the natural frequencies obtained with the experimental and numerical works developed in 1992 and 2017
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4.3 Noise simulation

The spectra resulting from the time-series recorded in Alto Lindoso dam and the spectra of the noises previously simulated and presented in Fig. 3 are compared in this section. Subsequently, the time-series of noises that were numerically simulated are combined with the measured data, and a comparison is made between the results achieved with the studied scenarios (MEMS1, MEMS2, PE1, PE2, and FB).

The mentioned noise floors are analysed together with auto-spectra resulting from experimental data recorded with two sensors that were in separate points, while the field-testing campaign took place. These spectra are presented in subsections (a) and (b) of Fig. 11. Considering the noise floors related to piezoelectric sensors, it should be noted that even if PE1 is permanently under the peaks of the experimental spectra, in turn, PE2 is under many peaks, but sporadically overpassing some peaks. On the other hand, the contrary is verified with MEMS, given that MEMS2 is permanently above the peaks, while MEMS1 either stands through the peaks or above the peaks.

Fig. 11
figure 11

a, b: Auto-spectra from experimental data (blue) and auto-spectra from noise floors numerically generated; c, d: auto-spectra from experimental data adulterated with numerically generated noises

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Finally, data simulating band-limited white noise were mixed with experimental time-series of accelerations recorded on-site, considering constant spectral noise over the frequency range that is being analysed. New time-series were obtained through the addition of the ones containing noise to the experimental measurements, thus simulating the outcomes that would have been recorded in the case that piezoelectric (or MEMS) accelerometers had been used during the experimental campaign.

Subsections (c) and (d) of Fig. 11 show auto-spectra obtained with experimental data that was actually recorded on-site with the force-balance accelerometers (in blue) and with data simulating piezoelectric and MEMS-based recordings. Most of the peaks in the spectra obtained from the experimental data (FB) appear as well in the results from the analysis of the piezoelectric simulations (PE1 and PE2), which is not verified with the results extracted from the MEMS’ simulated data. In this last case, many time-series result in spectra where the peaks are hidden below the noise floor.

Through the application of the SSI-Cov method, automatic modal identification was performed, first using the experimental data obtained during the test (FB) and then the other four sets of time-series which resulted from the combination of experimental data with numerically simulated noises. Modal properties were identified for the entire set of time-series, including each mode’s natural frequency, damping ratio, and the standard deviations of the previous estimates.

Modal properties’ estimates obtained for the five cases under study are presented in Table 3, including average and standard deviation values of vibrations modes number one and two. Analysing either natural frequencies or damping ratios, it is verified that the values of standard deviations related to these parameters rise parallelly to the intensity of the noise added to the experimental data, even if, for the two piezoelectric cases (PE1 and PE2), just minor result variations are observable, comparing these with the original results. On the other hand, significant changes occur with the results determined from data simulating MEMS measurements, with much higher uncertainties being identified. It is worth noticing that the first mode was not even identified when using MEMS2 time-series, which is also verified with higher order modes.

Table 3 Natural frequencies, damping ratios, and corresponding standard deviations for the first two vibration modes of Alto Lindoso dam
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5 Bouçã dam

5.1 Description of the dam and ambient vibration test

The Bouçã dam is a concrete double arch dam located in Pedrogrão Grande, Portugal, whose reservoir is accomplished with water from the Zêzere River. The 63-m-high and 175-m-long dam is operating since 1955 when two Francis turbines operating at 214.3 rpm (3.57 Hz) were installed in the hydroelectric plant that lays downstream from the dam. An aerial picture of the dam is presented in Fig. 12, side-by-side with a scheme of the cross section.

Fig. 12
figure 12

Aerial view [33] and cross section [50] of Bouçã dam

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On the 12th of June 2018, an ambient vibration test was realized on Bouçã dam. To perform the test, nine force-balance accelerometers were positioned on the first visit gallery of the dam, which were fixed in the same position during the entire test. The nine sensors were connected to a central acquisition station through cables, but the farthest one was only 65 m away.

Nine measuring points were used, so that each sensor were positioned in the middle of each of the dam’s nine interior blocks, corresponding to the part of the dam where the spillway is located. The test layout is presented in Fig. 13 using a scheme of the structure and blue dots to point the position of each measuring point.

Fig. 13
figure 13

Test layout of the ambient vibration test performed on Bouçã dam

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The test consisted of five recording setups, each of them with 13 min of duration, and the data acquisition was performed with a sampling rate of 100 Hz (reduced to 50 Hz during pre-processing). The elevation of the water in the reservoir throughout the experimental procedures was constant at 174.7 m.

5.2 Identification of modal properties

The procedure used in the previous section to identify the modal properties of Alto Lindoso dam was repeated, once again using the Peak-Picking method to obtain a first set of natural frequencies expeditiously. In Fig. 14, orange circles were used to highlight the peaks of the ANPSD function that were identified as being associated with vibration modes. The first vibration mode of the dam was identified with a frequency close to 3.30 Hz, but a significant number of other peaks appear between 3 and 12 Hz.

Fig. 14
figure 14

ANPSD function obtained from data recorded during the experimental campaign carried out at Bouçã dam, with orange circles highlighting the identified vibration modes

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The SSI-Cov method was used afterwards to corroborate the preliminary analysis and to achieve a more accurate group of modal properties estimates, for which model orders between 20 and 80 were used. With the application of the SSI-Cov method to the recorded data, similar results were achieved through all the setups. The stabilization diagram that resulted from the application of this method to the experimental data measured during the third setup is presented in Fig. 15, where precise alignments of poles are observable. Blue lines mark the alignments associated with the vibration modes of the dam.

Fig. 15
figure 15

Stabilization diagram obtained from the application of the SSI-Cov method to data recorded during the ambient vibration test performed at Bouçã dam, with blue lines highlighting the identified vibration modes

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Table 4 presents the modal properties of the eight vibration modes that were identified.

Table 4 Modal properties of Bouçã dam
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Regarding the uncertainties associated with modal properties, it can be noted that smallest standard deviation values are related to the first two vibration modes, whereas the third vibration mode, whose identification was not achieved for the whole set of analysed setups, seem to present the less accurate estimates, showing the highest values for the standard deviations of the modal properties.

Figure 16 presents the modal configurations that were obtained for the eight vibration modes determined, being all of them well characterized. The first two vibration modes are, respectively, antisymmetric and symmetric, similar to what was verified with Alto Lindoso dam. Finally, alternate states of symmetry are found in the configurations of modes 3–8.

Fig. 16
figure 16

Mode shapes of Bouçã arch dam first eight vibration modes

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5.3 Noise simulation

The procedure presented in Sect. 4.3 is repeated, now using data recorded at Bouçã dam to compare the auto-spectra resulting from measured data (FB) with the simulated noise floors associated with piezoelectric (PE1 and PE2) and MEMS (MEMS1 and MEMS2) sensors that were previously defined. This comparison is presented in Fig. 17a.

Fig. 17
figure 17

a: auto-spectra from real data (blue) and auto-spectra from noise floors numerically generated; b: auto-spectra from real data added to numerically generated noises

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Unlike what was observed for Alto Lindoso dam, in the case of the test performed in Bouçã dam, no relevant amplitude variations are verified between spectra obtained from data measured in different positions during the same setup, which can be explained by the shorter length of the crown at Bouçã dam and by the fact that the measuring grid is concentrated in the central part of the dam, reasonably distant from the abutments.

In this case, while the noise floors used to simulate piezoelectric sensors (PE1 and PE2) are either above or crossing the peaks of the spectra obtained from real data, the two spectra simulating MEMS are permanently over such peaks. The procedure consisting of adding the original recordings of accelerations to the data simulating band-limited white noises was repeated, assuming a constant spectral noise inside the studied interval of frequencies. Therefore, time-series of accelerations simulating the dynamic testing of Bouçã dam using piezoelectric and MEMS accelerometers were obtained.

The auto-spectra obtained from real data measured in Bouçã dam with force-balance sensors (in blue) and the auto-spectra that resulted from the four scenarios simulating that piezoelectric and MEMS accelerometers were used during the test are presented in Fig. 17b. It is worth noting that only a minor fraction of the peaks in the spectra resulting from the experimental data (FB) are reflected in the spectra resulting from the time-series used to simulate that piezoelectric sensors had been used (PE1 and PE2) during the test. In turn, the ‘MEMS’ derived spectra do not seem to distinctly show any peak at all, which lay unknown below the noise floors (Fig. 18).

Fig. 18
figure 18

Aerial view [33] and cross section [50] of Castelo do Bode dam

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Such as in the case of Alto Lindoso dam, an automatic operational modal analysis was performed resorting to the application of the SSI-Cov method to the time-series of accelerations available for the five scenarios under study (FB, PE1, PE2, MEMS1, and MEMS2).

The modal properties obtained for the first two vibrations modes of the structure through the study of each of the studied scenarios are presented in Table 5, including mean and standard deviations values of natural frequencies and damping ratios. As was expected, the analysis of Table 5 reflects a relationship between the amplitude of uncertainties and the level of noise added to the recorded time-series, being that the first increases with the second. For instance, only the second vibration mode could be identified using MEMS, and the standard deviation values associated with modal properties identified are excessively high.

Table 5 Natural frequencies, damping ratios, and corresponding standard deviations for the first two vibration modes of Buçã dam
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6 Castelo do Bode dam

6.1 Description of the dam and ambient vibration test

Castelo do Bode is a concrete arch-gravity dam located between Tomar and Abrantes, in Portugal, whose reservoir is accomplished with water from the Zêzere River. The 115-m-high and 402-m-long dam is operating since 1951 when three vertical Francis turbines working at 214.3 rpm (3.57 Hz) where installed in the hydroelectric plant that lays at the downstream foot of the dam. Figure 16 presents an aerial picture of the dam, side-by-side with a scheme of the cross section.

On the 17th of July 2018, an ambient vibration test was realized on Castelo do Bode dam. Since the dam’s crown is too large to be covered using sensors connected to a central acquisition system, ten portable recorders (model GSR-24 from Geosig) where used to perform the test, which remained in the same position during the entire experimental campaign, given that enough sensors were available.

Measuring points were selected, so that every two consecutive concrete blocks at least one of them had a sensor recording data, with the exception being the two spillway blocks where two sensors were positioned, to characterize this particular part of the structure better. All accelerometers were positioned in the middle of a concrete block. The test layout is presented in Fig. 19 using a scheme of the structure and red dots to point the position of each measuring point. The test consisted of eight recording setups, each of them with 13 min of duration, and the data acquisition was performed with a sampling rate of 100 Hz (reduced to 50 Hz during pre-processing). The elevation of the water in the reservoir throughout the experimental procedures was constant at 116.6 m.

Fig. 19
figure 19

Castelo do Bode dam: test layout

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6.2 Identification of modal properties

Once again, the identification of modal properties started with the application of the Peak-Picking method. Auto-spectra and averaged normalized power spectral density functions (ANPSD) were obtained and analysed. The latter is presented in Fig. 20.

Fig. 20
figure 20

ANPSD function obtained from data recorded during the experimental campaign carried out at Castelo do Bode dam, with orange circles highlighting the identified vibration modes

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Since the turbines in the power station operated during the entire test, parasite frequencies corresponding to their rotation frequency (214 rpm ~ 3.57 Hz) and their harmonics are observable in the spectra resulting from all the data series recorded in the dam. This is the case of the first observable peak present in Fig. 20, which is very thin. On the other hand, it is hard to distinguish the peak of the first harmonic (7.14 Hz) in the ANPSD function.

Afterwards, the SSI-Cov method was used to confirm and improve the identification of the dam’s modal properties and similar stabilization diagrams resulted from the analysis of the time-series recorded during the entire test. Figure 21 shows the stabilization diagram obtained from data recorded during the third setup, where blue lines were adopted to point the alignments related to the vibration modes determined. Comparing the stabilization diagram in Fig. 21 with those presented in Figs. 9, 15, it can be observed that in the case of Castelo do Bode dam, except for the first and second vibration modes, higher model orders had to be used until clear and stable vertical alignments of poles were formed. Therefore, model orders between 70 and 150 were considered during the application of SSI-Cov method.

Fig. 21
figure 21

Castelo do Bode arch dam stabilization diagram

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Finally, it is relevant to note that the entire set of peaks and alignments observed, respectively, in the power spectral density function and the stabilization diagram were investigated, which included the analysis of the shapes of the modal configurations resulting from all of them. The group of identified vibration modes settled at the end of the analysis corresponds to the ones that were achieved simultaneously through the two identification methods, and that presented reasonable mode shapes as well.

The modal properties of the five vibration modes identified are presented in Table 6. The presented values result from the averaging of the results obtained from the selected stable poles for the recorded setups.

Table 6 Modal properties of Castelo do Bode
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Besides the estimates of the mean values, also standard deviations are presented for natural frequencies and damping ratios in Table 6, which give extra information on the accuracy of the estimates obtained.

It is relevant to note that the 3rd and 4th modes, which needed higher model orders before getting stabilized (see Fig. 21), coincide with the modes presenting higher standard deviations values for natural frequencies, out of the identified vibration modes. Contrarily, the lower standard deviation estimate is associated with the 2nd mode of vibration, which presents a steady arrangement of poles from much lower model orders.

The dam’s asymmetric nature and the additional stiffness granted by the two elements used for water discharge (see the spillways picture and scheme in Figs. 18, 19) create conditions for the occurrence of local vibration modes, which result in mode shapes with very close modal ordinates near the spillway. In contrast, the other half of the mode configuration match the traditional shapes, presenting a count of geometric inflexions that increase between consecutive modes.

Regarding the global modes identified and their shapes, the two traditional configurations, presenting either one or two geometric inflexions, could not be identified. Furthermore, an identical mode shape to that of the 1st mode (3.648 Hz) was found with a frequency of about 8 Hz. This may be related with a mode of higher order presenting a similar shape at the top of the dam, yet distinctly developing at lower regions of the dam. Consequently, it would have been necessary to synchronously record data in the structure’s galleries, so that this mode could be undoubtedly identified and included in the results presented.

Figure 22 presents the modal configurations of the five vibration modes identified. Global modes are associated with vibration modes 1 and 3, while the other three vibration modes are related to the deflection of the left part of the structure.

Fig. 22
figure 22

Castelo do Bode dam: mode shapes of the identified vibration modes

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7 Other tested dams

The procedures followed during the tests presented before, and the subsequent data processing were used as well in the tests and modal properties identification of Caldeirão, Santa Luzia, and Aguieira dams. The results obtained for these three dams are summarized in this section. More information about the tests performed on these dams can be found in [53].

Natural frequencies and damping ratios for the first two vibration modes identified in each test are presented in Table 7. In addition, the values of reservoir level (above sea level) and the values of turbine rotation frequency in the power plants near each dam are presented as well, since they influence modal properties and the modal identification process, respectively.

Table 7 Modal properties of the first two identified modes and test conditions
Full size table

The damping ratios obtained for the first two identified vibration modes generally present values between 1.5 and 2.1% for the three dams (with the exception being the second mode of Caldeirão dam). In the case of natural frequencies, however, quite different values were obtained for Santa Luzia and Aguieira dams when compared with Caldeirão dam, which present natural frequencies above 12 Hz for the first two modes, showing how stiff the structure is.

Finally, mode shapes for the first two identified modes of each dam are presented in Fig. 23. Identical mode shapes were found in the cases of Caldeirão and Santa Luzia dams, while in the case of Aguieira dam, which is composed by three arches, more complex shapes are obtained, since the complete shape results from the sum of each arches’ individual shape.

Fig. 23
figure 23

Mode shapes of the first two identified modes

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8 Conclusions

Experimental campaigns relying solely on excitation from the surrounding environment have been conducted in a set of six Portuguese concrete dams with quite diverse structural characteristics and the data collected used to identify their modal properties, demonstrating that it is appropriate to use operational modal analysis to the study of concrete dams. The tests were performed under diversified operational conditions, occasionally incorporating excitation due to electricity production turbines rotating in nearby hydroelectric developments. The tested structures include four-arch dams with quite contrasting dimensions, one arch-gravity dam, and one multiple arch dam.

Each dam was tested with (at least) one of the two acquisition systems available, which was chosen for each case regarding the geometrical characteristics of the structure. Most of the tests were conducted in the dam’s crowns, commonly of easy access and consisting of road connecting the two margins of a river. The test performed in Bouçã dam was the exception, since the crown of the dam corresponds to its main spillway, which is not accessible, forcing the test to be performed in the first visit gallery.

The excitation to which dams are subjected may vary significantly from one to the next and even on the same structure depending on the hour of the day. In the cases where there is a power plant in the vicinity of the dam, the intensity of the vibrations recorded may increase 100–1000 times due to the operation of the turbines, thus varying from few micro g to few milli g. This effect was recorded in all the tested dams, except for Santa Luzia dam, whose production complex is located afar from the dam.

Finally, a few conclusions can be drawn to sum up the work developed:

  • Six concrete dams with quite distinct characteristics were submitted to dynamic tests, and it was concluded that operational modal analysis is suited for the testing of these types of structures.

  • Generally, relatively low levels of vibration should be expected, though the proximity to an active power plant may significantly alter this outcome and lead to contamination of the data recorded with the turbine’s rotation frequencies and their multiples.

  • Ideally, to guarantee quality results, force-balance accelerometers should be used during the performance of ambient vibration tests, though piezoelectric ones seem to be suited, as well. On the other hand, MEMS accelerometers are not likely to provide good results.