Noise Reduction for Improvement of Ultrasonic Monitoring Using Coda Wave Interferometry on a Real Bridge

The condition of civil infrastructures is mainly influenced by two main factors: temperature variation and load effect. Wave velocity is strongly related to the elastic properties of the propagation medium. The linear relationship between wave propagation velocity and elastic strain when a limited load is acting on the non-linear elastic material (mainly concrete) object has been confirmed in [3, 43, 48]. When the strain variation exceeds a certain level, and damage such as microcracking appeared, the linear relationship is broken. A temperature variation may lead to a geometry and/or elastic properties change of the structure being monitored. Plenty of studies have shown the influence of temperature on the elastic modulus and strength of concrete material [13, 26, 29]. In other words, the temperature variation can indirectly create internal strain changes, leading to a velocity variation. Depending on different situations, the temperature effect could be an unwanted factor or a valuable source. In most cases, the temperature effect needs to be eliminated, and a thermal bias control technique is presented in [49]. On the other hand, temperature-induced strain data could also be used for damage assessment [46]. Grêt et al. used thermally-induced velocity variation to detect microcracking in [15]. The damage level of a concrete specimen was also identified by Sun and Zhu in [41] using the relation between wave propagation velocity and temperature. In this paper, temperature variation is the most crucial variable, and the wave propagation velocity variation is mainly thermally induced.

CWI method is a promising technique to monitor weak wave velocity variations in a heterogeneous medium. When US measurement is carried out in a frequency range exceeding 50 kHz, multiple scattering is caused by the heterogeneity of the concrete [35]. Waves travel along much longer paths through a wider region compared to the direct wave. The impacts of the weak changes in the medium are accumulated, which ensures the high sensitivity of the CWI method in detecting subtle changes. CWI has been successfully applied in laboratory environments to detect stress variation [40, 48], temperature fluctuations [34, 39] and cracks at a very early stage [3, 43] in small-scale specimens. Furthermore, detection of stress-induced velocity change at a large-scale specimen under field conditions [44] and at a real bridge [40] was also achieved.

Figure 1 shows two US signals recorded before and after a weak change in the propagation medium. As one can see, the first arrivals of the two signals are identical; however, a slight perturbation can be found in the later arrivals. The fundamental of the CWI method is to extract two useful features, relative velocity change (dV/V) and correlation coefficient (CC), from two US signals measured in different states. The CC measures the similarity between two signals. It can be used for imaging purpose [24, 47, 50], or to monitor stress change [18, 33]. Various CWI processing approaches have been developed, such as the Doublet techniques [39], Taylor series expansion method [28], and the stretching method [32]. In this paper, the stretching method is chosen for CWI analysis as it provides the most accurate results among these three approaches [49]. The time shift is considered as a time dilation or compression by a factor \(\alpha \), indicating a velocity decrease or increase. \(u_{u}(t)\) and \(u_{p}(t)\) represent the signals recorded in two different states. The \(\alpha \), which maximizes the cross-correlation (Eq. 1) of the two signals within the time window [− T, T], is chosen as the relative velocity change. Window selection for this experiment is presented in Sect. 4.1.

The Gm1-2W bridge is a post-tensioned reinforced concrete bridge constructed in 2014 as an extension of Highway 902, connecting Katowice city and Gliwice city in Poland. The bridge’s total length is 552 m, and it consists of ten interior 48 m long spans and two external 36 m long spans. It is supported by piers, piles, and two girders 8 m apart, as shown in Fig. 2. The monitored part of this bridge was one of the 36 m long, 15.1 m wide external spans located at the south-east end of the Gm1-2W bridge. As the middle part of the span undergoes the most substantial stress changes, the centre part of the girder on the west side was selected for the investigation (Fig. 3). Ultrasonic transducers, thermistors, and vibration wire strain gauges were integrated into this area during its construction before the casting in 2014. The experiment presented in this paper was the first formal analysis on this bridge girder using the combination of all these sensors. The bridge girder was monitored continuously for 5 days to study the changes or damage due to traffic and environmental influences. It was a first step to validate the methodology for long term monitoring.

Figure 9 shows a raw US signal recorded by transducer combination S06E08 at midnight on October 27th 2018 as an example. One hundred samples (0.1 ms) were recorded before the signal transmission (’pre-trigger’) to determine the noise level and offset. Due to electromagnetic interference, crosstalk was recorded at 0.1 ms when the excitation signal was sent. A pre-processing procedure is required to remove offset and crosstalk and to reduce the noise. In a laboratory environment, noise can be filtered in most cases by applying a simple band-pass filter (e.g., passband [10 kHz, 150 kHz]). Details of this procedure are presented in [32]. The evaluation can be limited to the part of the signal containing significant US information. Thus, a suitable window should be selected to improve the efficiency of data processing. In this study, window [600, 1600] ([0.5 ms, 1.5 ms]) is chosen for data analysis and signal-to-noise ratio (SNR) level estimation. Assuming that the same noise (the first 100 samples) runs through the entire signal, SNR could be calculated by Eq. (2), where s(i) represents the amplitude of the signal.

The SNR level of all signals recorded by transducer combination S01E02 for 5 days is shown in Fig. 10 as an example. A significant difference is observed. During the day (from 8 a.m. to 6 p.m.), the average SNR level was around 51.18 dB while it decreased to 42.84 at night. The noise level increased a lot at night. This phenomenon also appears in the measurements by the other transducer combinations. The authors assume that the power supply for the street lights on the bridge caused this difference and created additional electromagnetic noise as soon as the lights were turned on. Hence, the main noise in the measurement on this bridge came from the high voltage electric power supply passing through the lamp cables. This effect had never been observed in the laboratory environment. The average SNR level of all transducer combinations is presented in Fig. 11. This result proves that the noise level became higher during the night. Unfortunately, the SNR levels of transducer combinations S04E07, S05E08, and S05E07 are unexpectedly low. For example, the SNR level of S05E07 is 8 dB, which means the signal’s power was only 6.3 times stronger than that of the noise. The weak signals affects the CWI evaluation. By examining the signals recorded by all the transducer combinations, the noises are almost identical over the whole monitoring area; however, the signal energy was enormously depending on the deviation angle between two US transducers and the coupling condition between the transducers and the concrete. The most intuitive way to study the noise is to analyze it in both time and frequency domain directly. As shown in Fig. 9, the last 1 ms (1000 samples) of the raw data is basically noise. Sixteen signals (eight taken during the day and eight during the night) recorded by transducer combination S05E07 on 28th of October are chosen to take a fingerprint of the noise. The last 1 ms of all sixteen noisy signals and their corresponding amplitude spectrum (fast Fourier transform) are shown in Fig. 12. The amplitudes of the noises recorded during the day fluctuated in the range \(\pm 20\), while they went up to \(\pm 150\) at night. All the frequency components of the noises recorded during the day were kept at a low level (less than 1.75). The main frequencies were distributed around 62 kHz, which is the primary frequency of the SO807 transducer. According to the amplitude spectrum of the noises at night, the noises contained two main frequency components: 40 kHz (FFT amplitude can exceed 10) and 67 kHz (FFT amplitude can exceed 40). Another way to estimate the noise components is to compare the noisy signal recorded at night with a reference signal recorded during the day. The amplitude spectrum differences between forty signals recorded at night and one reference signal recorded during the day by transducer combination S05E07 are shown in Fig. 13. The frequency changed significantly around 40 kHz and 67 kHz, which is in accordance with the previous result.

Three different filters are presented in this section. The basic necessary filter applied to the signal is a normal band-pass filter. It can filter the common low-frequency noises, which are the main reason for the signal ‘trend’ problem (e.g., raw data in Fig. 15). In this study, [30 kHz, 100 kHz] was chosen as the normal frequency band. The Butterworth filter, which provides a flat frequency response, was used to design the band-pass filter. Butterworth filter has a slow roll-off; thus, the order of the filter was chosen to six, indicating a response decrease of − 36 dB per octave. As mentioned in Sect. 3.2.1, the central frequency of the SO807 transducer is around 62 kHz. A Butterworth narrow band-pass filter with a frequency band [50 kHz, 65 kHz] was designed to focus on this frequency. The order of this filter was also fixed to six. Another idea was to eliminate the noise by its specific frequencies. Thus, a double-notch filter was proposed. This filter was a convolution of the normal band-pass filter and two IIR band-reject filters. The band-reject filter was provided by Python SciPy library. As one of the main frequencies of the noise (67 kHz) was close to the central frequency of the SO807 transducer (62 kHz), the bandwidth of the filter should be as narrow as possible. Thus, sixty was chosen as the quality factor, which characterizes the notch filter − 3 dB bandwidth. This filter passed most of the frequencies but attenuated the components of 40 kHz and 67 kHz to a very low level. Frequency responses in dB of these filters are presented in Fig. 14. Twenty signals recorded by transducer combination S05E07 on the 27th of October at midnight are chosen as examples. All the signals were recorded within ten minutes. Thus, the temperature variation was negligible. Theoretically, all the signals should be almost identical. Signals filtered by these different types of filters are shown in Fig. 15 along with the raw data. The normal band-pass filter successfully removed the signal trend, which was mainly caused by low-frequency noise. However, the differences between these signals are still evident that there exists a tiny irregular amplitude variation and time shift. This will affect the calculation of CC and dV/V. The narrow band-pass filter filtered the noise effectively. All the processed signals are approximately identical. As this filter focuses on the central frequency of SO807 transducer, most of the other frequency components are eliminated. The filtered signals became smoother. However, they contained less information. The similarity of the later arrives was high; in some cases, the stretching method might have difficulties identifying the direction of the waveform shift. The double-notch filter retained most of the original signal’s information along with an excellent noise reduction effect. All these three filters were tested for CWI analysis in Sect. 4.4.

As shown in Fig. 16, the internal temperatures of the monitored area changed less and lag behind compared to the outside temperature. The vibration wire SG determines the strain by measuring the frequency, which can then be converted to strain by a specific gauge factor. The SG was not temperature compensated. The trend of the strain variation was between outside and inside temperature changes. The outside temperature and stain increased significantly after 29th of October.

CC and dV/V measured by transducer combination S01E02 are presented in Fig. 17. As the signals recorded by transducer combination S01E02 had the highest SNR level, the normal band-pass filter’s effect is good enough. The double-notch filter reduced the fluctuation of CC and dV/V slightly. The narrow band-pass filter increased the similarity between all the signals (Fig. 17 blue curve in CC); however, it changed the turning points of both CC and dV/V curves unexpectedly. The authors assume that some parts of the filtered signals have some similarities due to information loss caused by the narrow band-pass filter. For instance, the signals filtered by the narrow band-pass filter in Fig. 15 shows a similar quasi-periodic signal after 0.6 ms. In this case, the stretching method does incorrect estimations of the time dilation factor. CC and dV/V measured by transducer combination S05E07 are presented in Fig. 18. Signals measured by transducer combination S05E07 have the lowest SNR level. The noises have a noticeable influence on CC and dV/V estimation. Narrow band-pass filter and double-notch filter did improve the CC results; however, the impact of the noise on CC values still exists. This is because of the uncertain and random strong noises which interfere with the similarity between signals. All noises have similar frequency components and energy, but their phases are random. Nevertheless, the behaviour of the double-notch filter is acceptable for processing the dV/V calculation. This is one of the advantages of the CWI stretching method that velocity variation could be estimated even under noisy adverse conditions. By comparing the results using different filters, the double-notch filter was considered as the most suitable filter in this study for the conditions around the bridge. A Savitzky–Golay filter (window 200 and order 3) was applied to the CC and dV/V curves to ensure the smoothing of the results without distorting its tendency. The filter is also provided by the python Scipy library. It is based on the local polynomial least-squares fitting in the time domain. Details of the filter are presented in [38]. CC and dV/V curves of transducer combination S02E06 filtered by Savitzky–Golay filter are illustrated in Fig. 19 as an example. The result of the filter was remarkable to smooth the result.

Thermistor T1, T2, and T3 captured the internal temperature at three different positions along the same line with US transducer numbers 5 and 6 (Fig. 6). As shown in Fig. 16, these three temperatures have a similar global trend with minor different local variations. An average temperature value \(T_{average}\) of these three measurements was calculated to present the temperature change in transducer combination S05E06 measured area. CC and dV/V values of all transducer combinations are shown in Fig. 20 along with the average temperature. CC curves measured by the first six transducer combinations (from S01E02 to S06E08) whose SNR levels at night were higher than 21 dB had a better continuity compared to the other six. The dV/V curves measured by all the transducer combinations have similar trends and vary slightly in the range [− 0.09%, 0.049%] with a high resolution of 10\(^{-4}\%\). They are in coherence with the average temperature.

As one can see in Fig. 20, the relative velocity variation is mainly thermally induced. The temperature–velocity (T–V) curves of transducer combination S05E06 and S02E05 is displayed in Fig. 21. The T–V curves are divided into two parts for analysis. The first part is the interval from the beginning of the measurement to October 29th. The second part is the interval from 29th of October to the end of the measurement. In this interval, during when the strain and external temperature changed significantly. The slopes of all T–V cures are shown in Fig. 22. There is a slight difference between the slopes of the two parts, which is in accordance with the result in [37]. The slope of the first part of the T–V curve recorded by transducer combination S05E06 is about − 0.019, and the slope of the second part is around − 0.020. However, the slopes of two parts of the T–V curve recorded by transducer combination S02E05 have a more significant difference.

The authors assume two main reasons for the slope difference and curve hysteresis: the \(T_{average}\) is considered the internal temperature variation in the area, covered by transducer combination S05E06. Although the internal temperatures in other areas should be similar to \(T_{average}\), they might still be different. The transducer combination S05E06 measured mainly in the direction perpendicular to the girder’s main axis while S02E05 measured in the parallel direction. In general, the strain variation in the direction parallel to the main axis is higher compared to that of the perpendicular direction. When the tensile stress increased faster after the 29th of October, the wave velocity should be reduced more significantly. Consequently, the slope of the second part of T–V curve decreased, as shown in Fig. 22.

Signals measured by transducer combination S01E02 have the highest SNR level, meaning that the noise’s influence is the lowest. Thus, the dV/V curve of S01E02 is chosen for illustration (Fig. 23) to study the influence of the traffic passing the bridge. The weak fluctuation is considered as the influence of real traffic. The largest range of dV/V during this one hour is 0.0028%, which is extremely small. The influence of real traffic has relatively little effect on overall structural response [8]. The global dV/V change caused by the traffic is negligible, and it can be reduced or eliminated by the Savitzky–Golay filter.