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Emerging Concepts and Approaches for Efficient and Realistic Uncertainty Quantification
Published in Dan Frangopol, Yiannis Tsompanakis, Maintenance and Safety of Aging Infrastructure, 2014
Michael Beer,, Ioannis A. Kougioumtzoglou, Edoardo Patelli
In reality, acquired environmental excitation and/or structure response data in most cases are either limited or a critical portion of them for reliable signal processing is missing. Missing data can occur for many reasons including sensor failures, data corruption, limited bandwidth/storage capacity, power outages etc. Unfortunately most spectral estimation approaches (including the aforementioned ones) require uniformly sampled data. Nevertheless, there are tools available for spectral analysis which can handle missing data, though many come with restrictions and assumptions about the nature of the original signal. 5.2.3.1 Fourier Transform with Zeros One of the simplest and most intuitive methods for addressing the problem of missing data when conducting a spectral analysis (especially if FFT is utilized) is to fill the gaps of the realizations with zeros. Nevertheless, note that if large amounts of data are missing, this approach can yield false peaks and significantly misleading artifacts in the spectrogram/power spectrum estimate (Muller and MacDonald 2002). 5.2.3.2 Clean Deconvolution A method of spectral analysis of incomplete data that has been shown to perform reasonably well for seismological applications (Baisch and Bokelmann 1999) was developed by Roberts et al. (1987), based on the "CLEAN deconvolution'' algorithm. The CLEAN algorithm provides an iterative method for removing undesired artifacts in the frequency domain that occur as a consequence of performing the DFT with zeros in place of missing data. However, the technique is effective only when there are a limited number of dominant frequencies in the recorded data and is not applicable to non-stationary signals, at least in a straightforward manner. 5.2.3.3 Autoregressive Estimation Further, an approach proposed by (Fahlman and Ulrych 1982) is based on an autoregressive (AR) model representation of the process. The proposed algorithm fills gaps by fitting AR models to available data and uses them to estimate the unknown quantities. A severe restriction of the methodology is that the final order of the autoregressive model must be shorter than the shortest data segment. This means that the method can be potential inapplicable depending on the spacing of the data as short autoregressive models have difficulties in capturing low-mid range frequencies. 5.2.3.4 Least Squares Spectral Analysis Furthermore, (Lomb 1976; Scargle 1982) presented a method of least-squares spectral analysis that can be used to calculate the power spectrum for unevenly spaced data known as the Lomb-Scargle periodogram. In this regard, sine and cosines are matched with the signal via least-squares optimization which negates the requirement for uniformed samples. However, the total power of the signal as determined by the transform may not be equal to the total power of the original signal; also, particular frequencies
A cyclically adjusted spatio-temporal kernel density estimation method for predictive crime hotspot analysis
Published in Annals of GIS, 2023
Ya Han, Yujie Hu, Haojie Zhu, Fahui Wang
The first step in the analysis is to detect the crime period present in the data using the periodogram method in spectral analysis. One advantage of this method is its capacity to deal with missing samples or uneven sampling steps, and therefore it has broad applications (Venturini and Baralis, 2016). The periodogram is also referred to as least-squares spectral analysis, as it fits a least-square of sinusoidal functions over the data. The original daily robbery data are aggregated into a monthly resolution, as shown in Figure 2.