Using GPS for monitoring tall-building response to wind loading: filtering of abrupt changes and low-frequency noise, variography and spectral analysis of displacements

Abstract

We compare two methods for monitoring the dynamic response of tall buildings to wind loading, using data from a 280-m-high building in Singapore. The first method is based on accelerometer measurements. The second method is based on the Global Positioning System (GPS) technology. The GPS can in principle detect absolute displacements with lower frequencies than the accelerometers, but the GPS positioning signal is usually very noisy. We propose a systematic procedure for modeling the stochastic and systematic components of the GPS displacement time series and for extracting the weak structural response from the dominant noise. The spectrum of the building response obtained from the filtered GPS data exhibits a dominant peak at 0.19 Hz. The frequency of the peak coincides with that obtained from the analysis of the accelerometer data. The proposed analysis of the GPS signal provides a method for cross-validating the GPS and accelerometer measurements, and shows that “educated” filtering of the GPS signal can reveal essential features of the building’s response to wind loading.

Appendix: Semivariogram of random process with periodic trend

Let X(t)  = w(t)  + η(t), where w(t) is a periodic trend and η(t) a correlated random process. The experimental semivariogram of X(t) is defined by means of Eq. (12). In light of the following function:

$$\gamma _{{\eta \zeta}} (p t_{s}) = \frac{1}{{2(N - p)}}{\sum\limits_{i = 1}^{N - p} {{\left[ {\eta (t_{i} + p t_{s}) - \eta (t_{i})} \right]}\;{\left[ {\zeta (t_{i} + p t_{s}) - \zeta (t_{i})} \right]}}}$$

(14)

the semivariogram of X(t) is given by the following:

$$\hat{\gamma}_{X} (p t_{s}) = \gamma _{{ww}} (p t_{s}) + \gamma _{{\eta \eta}} (p t_{s}) + \gamma _{{\eta w}} (p t_{s}),$$

(15)

where γ_ηη (p t _s ) is the noise semivariogram. The cross-term γ_ηw (p t _s ) is zero, since the periodic function w(t) and the random process η(t) are uncorrelated. Finally, for N  − p  >> 1 the term γ _ww (p t _s ) can be approximated as follows:

$$\gamma _{{ww}} (p t_{s}) \approx \frac{1}{{2T}}{\int\limits_0^T {\hbox{d}t}}{\left[ {w(t + p t_{s}) - w(t)} \right]}^{2}$$

(16)

If w(t)  = Acos (ω₀t + ϕ), explicit calculation of the right hand-side of Eq. (16) leads in connection with Eq. (15) to the result of Eq. (13).