Hybrid Wavelet and Principal Component Analyses Approach for Extracting Dynamic Motion Characteristics from Displacement Series Derived from Multipath-Affected High-Rate GNSS Observations

Abstract

Nowadays, the high rate GNSS (Global Navigation Satellite Systems) positioning methods are widely used as a complementary tool to other geotechnical sensors, such as accelerometers, seismometers, and inertial measurement units (IMU), to evaluate dynamic displacement responses of engineering structures. However, the most common problem in structural health monitoring (SHM) using GNSS is the presence of surrounding structures that cause multipath errors in GNSS observations. Skyscrapers and high-rise buildings in metropolitan cities are generally close to each other, and long-span bridges have towers, main cable, and suspender cables. Therefore, multipath error in GNSS observations, which is typically added to the measurement noise, is inevitable while monitoring such flexible engineering structures. Unlike other errors like atmospheric errors, which are mostly reduced or modeled out, multipath errors are the largest remaining unmanaged error sources. The high noise levels of high-rate GNSS solutions limit their structural monitoring application for detecting load-induced semi-static and dynamic displacements. This study investigates the estimation of accurate dynamic characteristics (frequency and amplitude) of structural or seismic motions derived from multipath-affected high-rate GNSS observations. To this end, a novel hybrid model using both wavelet-based multiscale principal component analysis (MSPCA) and wavelet transform (MSPCAW) is designed to extract the amplitude and frequency of both GNSS relative- and PPP- (Precise Point Positioning) derived displacement motions. To evaluate the method, a shaking table with a GNSS receiver attached to it, collecting 10 Hz data, was set up close to a building. The table was used to generate various amplitudes and frequencies of harmonic motions. In addition, 50-Hz linear variable differential transformer (LVDT) observations were collected to verify the MSMPCAW model by comparing their results. The results showed that the MSPCAW could be efficiently used to extract the dynamic characteristics of noisy dynamic movements under seismic loads. Furthermore, the dynamic behavior of seismic motions can be extracted accurately using GNSS-PPP, and its dominant frequency equals that extracted by LVDT and relative GNSS positioning method. Its accuracy in determining the amplitude approaches 91.5% relative to the LVDT observations.

Evaluation of multi-GNSS high-rate relative positioning for monitoring dynamic structural movements in the urban environment

“…The longerterm multipath effects have relatively long periods (several minutes and more) and low frequency with respect to the frequency band of structure movements. This implies that multipath effect can be effectively mitigated with a high-pass, band-pass or band stop filtering to obtain high-accuracy displacements (Paziewski et al 2019, Kaloop et al 2019. In this study, an 11-order Chebyshev band-pass filter with appropriate parameters for each event was implemented.…”

“…The relative GNSS monitoring system is regularly employed to precisely extract dynamic behaviours of structures. The precise point positioning (PPP) method has been investigated and improved for dynamic analyses of structures (Yigit 2016;Kaloop et al 2018Kaloop et al , 2019Paziewski et al 2019Paziewski et al , 2020Yigit et al 2020). The methods that used GNSS positioning for dynamic analysis of structures can be found in Larocca et al (2005), Moschas and Stiros (2014), Kaloop et al (2017), Yu et al (2018), Shen et al (2019), Yu et al (2020).…”

“…The monitoring of the W tower movements in Guangzhou, China, via GNSS, was carried out and the accuracy of the positions was at the millimetre-level (Zhang et al 2018). More studies on using GNSS for monitoring structure movements can be found in Shen et al (2019), Kaloop et al (2017Kaloop et al ( , 2019, Yu et al (2020), Yigit and Gurlek (2017). However, some errors affect the GNSS accuracy for structure monitoring; multipath error, in particular, is still the primary source of error (Shariati et al 2019;Yu et al 2018).…”

Using GNSS Phase Observation Residuals and Wavelet Analysis to Detect Earthquakes

“…Although the high-rate GNSS allows for deriving high-accuracy results, it suffers from the noise that must be reduced to achieve reliable waveforms. Hence, various methods for denoising are applied to the high-rate GNSS, such as sidereal filtering (Atkins and Ziebart 2016;Wang et al 2018), Butterworth filtering (Kudlacik et al 2019;Kudłacik et al 2021), or wavelets denoising (Kaloop, Cemal O. Yigit, et al 2020;Li, Xu, and Yi 2017). The Butterworth filter (Butterworth 1930) is one of the most popular anti-aliasing filters (Smith 2021) mainly due to a flat frequency response that does not distort the time series (Kudlacik et al 2019).…”

Combining GNSS and accelerometer measurements for evaluation of dynamic and semi-static characteristics of bridge structures

“…Tang et al proved that PPP can extract centimeter-level movements after reducing the influence of tropospheric delays, and it is thus viewed as an efficient alternative to RTK in some extreme conditions and complementary to other sensors [14,15]. Kaloop et al designed a hybrid MSPCA and wavelet transform method to denoise both GNSS relative and PPP-derived displacements, which can be used to extract and estimate the dynamic characteristics of engineering structures or seismic ground motions in the horizontal directions [16]. In addition, the moving average (MA) method has been proven to be suitable in extracting long-period components from the monitored signal [17][18][19].…”