Blind source separation using second-order cyclostationary statistics

This paper studies the blind source separation (BSS) problem with the assumption that the source signals are cyclostationary. Identifiability and separability criteria based on second-order cyclostationary statistics (SOCS) alone are derived. The identifiability condition is used to define an appropriate contrast function. An iterative algorithm (ATH2) is derived to minimize this contrast function. This algorithm separates the sources even when they do not have distinct cycle frequencies .

Testing second order cyclostationarity in the squared envelope spectrum of non-white vibration signals

Cyclostationary models for the diagnostic signals measured on faulty rotating machineries have proved to be successful in many laboratory tests and industrial applications. The squared envelope spectrum has been pointed out as the most efficient indicator for the assessment of second order cyclostationary symptoms of damages, which are typical, for instance, of rolling element bearing faults. In an attempt to foster the spread of rotating machinery diagnostics, the current trend in the field is to reach higher levels of automation of the condition monitoring systems. For this purpose, statistical tests for the presence of cyclostationarity have been proposed during the last years. The statistical thresholds proposed in the past for the identification of cyclostationary components have been obtained under the hypothesis of having a white noise signal when the component is healthy. This need, coupled with the non-white nature of the real signals implies the necessity of pre-whitening or filtering the signal in optimal narrow-bands, increasing the complexity of the algorithm and the risk of losing diagnostic information or introducing biases on the result. In this paper, the authors introduce an original analytical derivation of the statistical tests for cyclostationarity in the squared envelope spectrum, dropping the hypothesis of white noise from the beginning. The effect of first order and second order cyclostationary components on the distribution of the squared envelope spectrum will be quantified and the effectiveness of the newly proposed threshold verified, providing a sound theoretical basis and a practical starting point for efficient automated diagnostics of machine components such as rolling element bearings. The analytical results will be verified by means of numerical simulations and by using experimental vibration data of rolling element bearings.

Tuning second order cyclostationarity parameters for the diagnostics of rolling element bearings

Failures on rolling element bearings usually originate from cracks that are detectable even in their early stage of propogation by properly analyzing vibration signals measured in the proximity of the bearing. Due to micro-slipping in the roller-races contact, damage-induced vibration signals belong to the family of quasi-periodic signals with a strong second order cyclostationary component. Cyclic coherence and its integrated form are widely considered as the most suitable tools for bearing fault diagnostics and their theoretical bases have been already consolidated. This paper presents how to correctly set the parameters of the cyclostationary analysis tool to be implemented in an automatable algorithm. In the first part of the paper some general guidelines are provided for the specific application. These considerations are further verified, applying cyclostationary tools to data collected in an experimental campaign on a specific test-rig.

The statistics of the second order response of an FPSO in spreading seas

An expression for the probability density function of the second order response of a general FPSO in spreading seas is derived by using the Kac-Siegert approach. Various approximations of the second order force transfer functions are investigated for a ship-shaped FPSO. It is found that, when expressed in non-dimensional form, the probability density function of the response is not particularly sensitive to wave spreading, although the mean squared response and the resulting dimensional extreme values can be sensitive. The analysis is then applied to a Sevan FPSO, which is a large cylindrical buoy-like structure. The second order force transfer functions are derived by using an efficient semi-analytical hydrodynamic approach, and these are then employed to yield the extreme response. However, a significant effect of wave spreading on the statistics for a Sevan FPSO is found even in non-dimensional form. It implies that the exact statistics of a general ship-shaped FPSO may be sensitive to the wave direction, which needs to be verified in future work. It is also pointed out that the Newman's approximation regarding the frequency dependency of force transfer function is acceptable even for the spreading seas. An improvement on the results may be attained when considering the angular dependency exactly. Copyright © 2009 by ASME.

Second-Order Statistics of κ−µ Shadowed Fading Channels

In this paper, novel closed-form expressions for the level crossing rate and average fade duration of κ − μ shadowed fading channels are derived. The new equations provide the capability of modeling the correlation between the time derivative of the shadowed dominant and multipath components of the κ − μ shadowed fading envelope. Verification of the new equations is performed by reduction to a number of known special cases. It is shown that as the shadowing of the resultant dominant component decreases, the signal crosses lower threshold levels at a reduced rate. Furthermore, the impact of increasing correlation between the slope of the shadowed dominant and multipath components similarly acts to reduce crossings at lower signal levels. The new expressions for the second-order statistics are also compared with field measurements obtained for cellular device-to-device and body-centric communication channels, which are known to be susceptible to shadowed fading.

Second-order statistics for equal gain and maximal ratio diversity-combining reception

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for equal gain combining and maximal ratio combining schemes, assuming an arbitrary number of independent branches in a Rayleigh environment. The analytical results are thoroughly validated by simulation.

Second-order statistics for diversity-combining, techniques in Nakagami-fading channels

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for the M branch pure selection combining (PSC), equal gain combining (EGC), and maximal ratio combining (MRC) techniques, assuming independent branches in a Nakagami environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The model developed here is general and can be easily applied to other fading statistics (e.g., Rice).