A sub-Nyquist co-prime sampling music spectral approach for natural frequency identification of white-noise excited structures

Motivated by practical needs to reduce data transmission payloads in wireless sensors for vibration-based monitoring of civil engineering structures, this paper proposes a novel approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate. The approach adopts the deterministic co-prime sub-Nyquist sampling scheme, originally developed to facilitate telecommunication applications, to estimate the autocorrelation function of response acceleration time-histories of low-amplitude white-noise excited structures treated as realizations of a stationary stochastic process. This is achieved without posing any sparsity conditions to the signals. Next, the standard MUSIC algorithm is applied to the estimated autocorrelation function to derive a denoised super-resolution pseudo-spectrum in which natural frequencies are marked by prominent spikes. The accuracy and applicability of the proposed approach is numerically assessed using computer-generated noise-corrupted acceleration time-history data obtained by a simulation-based framework pertaining to a white-noise excited structural system with two closely-spaced modes of vibration carrying the same amount of energy, and a third isolated weakly excited vibrating mode. All three natural frequencies are accurately identified by sampling at as low as 78% below Nyquist rate for signal to noise ratio as low as 0dB (i.e., energy of additive white noise equal to the signal energy), suggesting that the proposed approach is robust and noise-immune while it can reduce data transmission requirements in acceleration wireless sensors for natural frequency identification of engineering structures

Doppler Spectrum Estimation by Ramanujan Fourier Transforms

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal

New Approaches to Smart Grid Security with SCADA Systems

The use of information technology in electric power grid introduces the vulnerability problem looming the future smart grid. The supervisory control and data acquisition (SCADA)is the first defense, which itself is undermined by potential malicious attacks. This dissertation studies two particular security threats facing the smart grid and SCADA systems: the unobservable attack and the replay attack. The former is well known in fault detection of the power grid and has received renewed interest in the past a few years, while the latter is motivated by the Stuxnet worm allegedly used against the nuclear facilities in Iran. For unobservable attacks, this dissertation adopts the dynamic state estimation approach and treats each bus of the power grid as a dynamic agent. A consensus estimation strategy is proposed to estimate the dynamic states of the power grid, based on which unobservable attacks can be effectively detected. Detection of replay attacks is harder. Two different approaches are proposed in this dissertation. The first is the whitening filter approach that converts the detection of the replay attack into an equivalent white noise detection through whitening a feedback signal. However this approach is less effective, if the replay attack does not change much the whiteness of the filtered feedback signal. Hence a second approach termed as spectrum estimation is proposed. It is shown that the spectrum of the feedback signal in presence of the replay attack can be very different from the case when the replay attack is absent. This approach improves the detection results of the former one. Both are illustrated and examined by the simulation studies