Is Gps Good Enough for Monitoring the Dynamics of High-rise Buildings?

In structural diagnosis, one of the standard approaches is to first define the “vibrational signature” or “frequency response” of a structure under normal behaviour, and if a sensor during routine operation detects a deviation from this “vibrational signature” that is greater than some limit, it may be concluded that the structure may be damaged and remedial action must be taken. Up to the present, accelerometers have almost exclusively been used to monitor the vibration signals of tall buildings, bridges, towers, and the like. It is tempting to consider whether the GPS technology has a role to play, either as an alternative sensor to the accelerometer, or in addition to such a sensor. The notable advantage of using GPS is that it can detect if the structure has drifted (a few cm) relative to some reference or baseline while accelerometers cannot detect, directly, the absolute or relative displacement of the structure. This paper presents some results of a study on the suitability of using GPS for detecting the displacement and the frequency of vibration of tall buildings. The technique under study is based on high precision, carrier-phase-based, RTK ('real-time kinematic') GPS. A discussion is presented on the feasibility of applying interdisciplinary and GPS-based methods for the monitoring and modelling of the dynamic properties of high-rise buildings. KEY TERMS : High-Rise Building, Continuous GPS (CGPS), Deformational Signature, FFT Signature, Baseline Signature ,Time-Frequency Analysis, Thresholding INTRODUCTION Structural monitoring using time series of GPS data has been motivated through discussions with many researchers at several workshops and conferences, and a study of the published works of Ashkenazi et al. (1997), Guo & Ge (1997), Celebi et al. (1998), Rizos (1998) and Ge (1999), among others. It has been shown that time history analysis is capable of extracting a fast deformational signature from high data-rate carrier-phasebased RTK GPS positioning. The question of whether the GPS field measurements are good enough for extracting both the low and high frequency response for civil structures such as high-rise buildings, however, still remains to be explored. In time series analysis, frequency-domain signature is obtained by converting timedomain data into its unique frequency components using a Fast Fourier Transform (FFT). Through the study of frequency-domain vibration signatures, the natural frequencies of structures can be detected and isolated to form the basic data for seismic and wind response analyses. Such data are valuable as more and more important highrise buildings are analysed through structural performance and seismic loading for improved structural design (Brownjohn et al., 2000). Although the versatility of GPS receiver technology has dramatically improved, GPS results still suffers from noise due to the effects of multipath, residual atmospheric biases, receiver noise and other sources. Therefore, to derive deformation signals from continuous GPS data, time-varying filtering (commonly known as 'adaptive filtering') 2 Trans Tasman Surveyors Congress, Queenstown, New Zealand, 20-26 August, 2000 forms an integral component of any continuous GPS data processing and analysis procedure. The design of Finite Impulse Response (FIR) filters commonly used for mitigating multipath in GPS results requires careful interpretation of the nature of signals through time and spectrum analysis, as suggested in, for example, Han and Rizos (1997). The number of contributions to the work on 'adaptive filtering' has increased dramatically in the last few years. In Embree (1995), for example, Least-Mean-Square (LMS)-based adaptive filtering methods are extensively discussed for various real-time applications in the field of Digital Signal Processing. Haykin (1991) and Cohen (1995) describe techniques of signal decomposition through filtering on the basis of timefrequency analysis. Most recently, the use of adaptive filtering technique based on the LMS algorithm, for the purpose of mitigating multipath as the main noise contributor in Continuous GPS (CGPS) time series, has been stimulated by the work of Ge (1999, 2000). As an alternative method of filtering time series of CGPS data, this paper introduces a new concept of structural deformation signature analysis by considering the problem from the point of view of signal identification and extraction based on time-frequency analysis. According to this approach, a visual comparison of the relative change of the vibration signature and its discrete frequency components over a period of time is carried out. The method permits two or more signatures to be shown on a single display (also referred to as 'waterfall' or multi-spectra analysis), enabling a direct comparison of each frequency component within the signatures. Any significant change in the behaviour of the building can then be identified by comparing the discrete FFT signature to: (i) a baseline or reference signature, or (ii) previous signatures. This can be achieved through multiple plots, ratio analysis or difference analysis. Baseline data sets must be representative of the behaviour of the structure under the normal operating conditions, as they are necessary for the comparison of trends, time series and FFT signatures that are collected over time. The majority of tall buildings are flexible steel framed structures for which the “baseline” or fundamental period can be estimated through the use of the empirical formula : T = 0.1Ns, where Ns is the number of stories of the building (this value vary between [0.05-0.15]Ns depending on the flexibility of the building) (Celebi et al, 1998). Ideally, in the time-frequency analysis, it is preferable to represent the structural signature for each of the three directional components Northings, Eastings and Height in such a way that it: (a) indicates which frequencies existed for a duration, (b) shows how the frequencies change with time and (c) shows the time-based waveform. In the following section the proposed technique is discussed in the light of these three requirements. TIME-FREQUENCY DOMAIN ANALYSIS OF THE BUILDING SIGNATURE Background Time series of CGPS RTK position solutions obtained on top of tall buildings under wind or sesimic loading may be classified under “time-varying” or “nonstationary” 2 Trans Tasman Surveyors Congress, Queenstown, New Zealand, 20-26 August, 2000 signals whose spectral characteristics vary with time. A simple mathematical model that accurately represents such a time-based signal may be (Haykin, 1991) where n(t) is a random noise process and sk(t) are the time-varying signal components described by the amplitude envelope, ak(t) and the instantaneous frequency, fi (t), such that