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

Compressive power spectrum sensing for vibration-based output-only system identification of structural systems in the presence of noise

Motivated by the need to reduce monetary and energy consumption costs of wireless sensor networks in undertaking output-only/operational modal analysis of engineering structures, this paper considers a multi-coset analog-toinformation converter for structural system identification from acceleration response signals of white noise excited linear damped structures sampled at sub-Nyquist rates. The underlying natural frequencies, peak gains in the frequency domain, and critical damping ratios of the vibrating structures are estimated directly from the sub-Nyquist measurements and, therefore, the computationally demanding signal reconstruction step is by-passed. This is accomplished by first employing a power spectrum blind sampling (PSBS) technique for multi-band wide sense stationary stochastic processes in conjunction with deterministic non-uniform multi-coset sampling patterns derived from solving a weighted least square optimization problem. Next, modal properties are derived by the standard frequency domain peak picking algorithm. Special attention is focused on assessing the potential of the adopted PSBS technique, which poses no sparsity requirements to the sensed signals, to derive accurate estimates of modal structural system properties from noisy sub- Nyquist measurements. To this aim, sub-Nyquist sampled acceleration response signals corrupted by various levels of additive white noise pertaining to a benchmark space truss structure with closely spaced natural frequencies are obtained within an efficient Monte Carlo simulation-based framework. Accurate estimates of natural frequencies and reasonable estimates of local peak spectral ordinates and critical damping ratios are derived from measurements sampled at about 70% below the Nyquist rate and for SNR as low as 0db demonstrating that the adopted approach enjoys noise immunity

A Technique for Measuring Rotocraft Dynamic Stability in the 40 by 80 Foot Wind Tunnel

An on-line technique is described for the measurement of tilt rotor aircraft dynamic stability in the Ames 40- by 80-Foot Wind Tunnel. The technique is based on advanced system identification methodology and uses the instrumental variables approach. It is particulary applicable to real time estimation problems with limited amounts of noise-contaminated data. Several simulations are used to evaluate the algorithm. Estimated natural frequencies and damping ratios are compared with simulation values. The algorithm is also applied to wind tunnel data in an off-line mode. The results are used to develop preliminary guidelines for effective use of the algorithm

Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates

Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation

A study on different linear and non-linear filtering techniques of speech and speech recognition

In any signal noise is an undesired quantity, however most of thetime every signal get mixed with noise at different levels of theirprocessing and application, due to which the information containedby the signal gets distorted and makes the whole signal redundant.A speech signal is very prominent with acoustical noises like bubblenoise, car noise, street noise etc. So for removing the noises researchershave developed various techniques which are called filtering. Basicallyall the filtering techniques are not suitable for every application,hence based on the type of application some techniques are betterthan the others. Broadly, the filtering techniques can be classifiedinto two categories i.e. linear filtering and non-linear filtering.In this paper a study is presented on some of the filtering techniqueswhich are based on linear and nonlinear approaches. These techniquesincludes different adaptive filtering based on algorithm like LMS,NLMS and RLS etc., Kalman filter, ARMA and NARMA time series applicationfor filtering, neural networks combine with fuzzy i.e. ANFIS. Thispaper also includes the application of various features i.e. MFCC,LPC, PLP and gamma for filtering and recognition

Time series analysis for minority game simulations of financial markets

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolut ion. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.Comment: LaTeX 2e (elsart), 17 pages, 3 EPS figures and 2 tables, accepted for publication in Physica

Correlation techniques to determine model form in robust nonlinear system realization/identification

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length