Assessment of the Bill Emerson Memorial Bridge - FTP Directory ...

Polyreference Complex Exponential (PRCE) (Vold et al., 1982) or the Covariance-Driven Stochastic Subspace Identification (SSI-COV) (Peeters, 2000). Note that theRandom Decrement technique, typically applied in time domain, can also be a startingpoint for the development of frequency domain methods, as it leads to free vibrationresponses and thus power spectral densities by FFT.The basic method in frequency domain, such as peak picking, was already applied to themodal identification of buildings and bridges several decades ago. Even so, it was notuntil a decade ago that these methods have been systematically presented for practicalapplications (Felber, 1993). Based on the construction of average normalized powerspectral densities and ambient response transfer functions involving all measurementpoints, this approach leads to the estimates of operational mode shapes. It allows thedevelopment of software for modal identification and visualization (Felber, 1993). Thefrequency domain approach was subsequently improved by performing a single valuedecomposition of the matrix of response spectra, so as to obtain power spectral densitiesof a set of single-degree-of-freedom (SDOF) systems. This method (Frequency DomainDecomposition) was better detailed and systematized by Bincker et al. (2001) andsubsequently enhanced in order to estimate modal damping factors (Brincker et al.,2000). In the last approach, these estimates were obtained by inspecting the decay ofauto-correlation functions that are basically inverse Fourier transforms of the powerspectral densities of SDOF systems.Peak picking is the simplest way to identify the modal parameters of a structure. Thismethod is initially based on the fact that a frequency response function (FRF) reaches apeak around each of the natural frequencies. In the context of vibration measurements,the FRF is replaced by an auto-spectral density of the output-only test data. The naturalfrequencies are determined simply by observing those frequencies corresponding to thepeaks of average response spectra. The average response spectra are basically evaluatedby converting the measured acceleration time histories to their Fourier transforms infrequency domain. The coherence function between two simultaneously recorded outputsignals has values close to one at the natural frequencies. This attribute can be used toconfirm which frequencies can be considered as natural frequencies. In the followingsection, the Peak-Picking (PP) method is employed to analyze the measured data from theBill Emerson Memorial Cable-stayed Bridge.3.4.2. Theory of Peak-Picking methodThe raw data collected from an output-only field test are many arrays of accelerationsmeasured at various locations of the cable-stayed bridge. For a specified location, a seriesof acceleration data points (samples) can be denoted as f k(k=0,…, N-1) where Nrepresents a total of sample points. Its Discrete Fourier Transform (DFT) Fncan beevaluated byFnN 1= ∑ −2 ikn / Nf ke πk =0 (n = 0,1...N −1)(3.1)27