Simulation of the White Dwarf -- White Dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes and present the corresponding generalized spectral method needed to characterize such process. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.Comment: 14 pages and 6 figures. Submitted to Classical and Quantum Gravity (Proceedings of GWDAW9

The White Dwarf -- White Dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes, present the corresponding generalized spectral method needed to characterize such process, and make a comparison between our analytic results and those obtained by applying our method to the simulated data. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.Comment: 36 pages, 15 figure

Fast, non-monte-carlo estimation of transient performance variation due to device mismatch

This paper describes an efficient way of simulating the effects of device random mismatch on circuit transient characteristics, such as variations in delay or in frequency. The proposed method models DC random offsets as equivalent AC pseudo-noises and leverages the fast, linear periodically time-varying (LPTV) noise analysis available from RF circuit simulators. Therefore, the method can be considered as an extension to DC match analysis and offers a large speed-up compared to the traditional Monte-Carlo analysis. Although the assumed linear perturbation model is valid only for small variations, it enables easy ways to estimate correlations among variations and identify the most sensitive design parameters to mismatch, all at no additional simulation cost. Three benchmarks measuring the variations in the input offset voltage of a clocked comparator, the delay of a logic path, and the frequency of an oscillator demonstrate the speed improvement of about 100-1000x compared to a 1000-point Monte-Carlo method

Early Detection of Rolling Bearing Faults Using an Auto-correlated Envelope Ensemble Average

Bearings have been inevitably used in broad applications of rotating machines. To increase the efficiency, reliability and safety of machines, condition monitoring of bearings is significant during the operation. However, due to the influence of high background noise and bearing component slippages, incipient faults are difficult to detect. With the continuous research on the bearing system, the modulation effects have been well known and the demodulation based on optimal frequency bands is approved as a promising method in condition monitoring. For the purpose of enhancing the performance of demodulation analysis, a robust method, ensemble average autocorrelation based stochastic subspace identification (SSI), is introduced to determine the optimal frequency bands. Furthermore, considering that both the average and autocorrelation functions can reduce noise, auto-correlated envelope ensemble average (AEEA) is proposed to suppress noise and highlight the localised fault signature. In order to examine the performance of this method, the slippage of bearing signals is modelled as a Markov process in the simulation study. Based on the analysis results of simulated bearing fault signals with white noise and slippage and an experimental signal from a planetary gearbox test bench, the proposed method is robust to determine the optimal frequency bands, suppress noise and extract the fault characteristics

A Channel Ranking And Selection Scheme Based On Channel Occupancy And SNR For Cognitive Radio Systems

Wireless networks and information traffic have grown exponentially over the last decade. Consequently, an increase in demand for radio spectrum frequency bandwidth has resulted. Recent studies have shown that with the current fixed spectrum allocation (FSA), radio frequency band utilization ranges from 15% to 85%. Therefore, there are spectrum holes that are not utilized all the time by the licensed users, and, thus the radio spectrum is inefficiently exploited. To solve the problem of scarcity and inefficient utilization of the spectrum resources, dynamic spectrum access has been proposed as a solution to enable sharing and using available frequency channels. With dynamic spectrum allocation (DSA), unlicensed users can access and use licensed, available channels when primary users are not transmitting. Cognitive Radio technology is one of the next generation technologies that will allow efficient utilization of spectrum resources by enabling DSA. However, dynamic spectrum allocation by a cognitive radio system comes with the challenges of accurately detecting and selecting the best channel based on the channelâs availability and quality of service. Therefore, the spectrum sensing and analysis processes of a cognitive radio system are essential to make accurate decisions. Different spectrum sensing techniques and channel selection schemes have been proposed. However, these techniques only consider the spectrum occupancy rate for selecting the best channel, which can lead to erroneous decisions. Other communication parameters, such as the Signal-to-Noise Ratio (SNR) should also be taken into account. Therefore, the spectrum decision-making process of a cognitive radio system must use techniques that consider spectrum occupancy and channel quality metrics to rank channels and select the best option. This thesis aims to develop a utility function based on spectrum occupancy and SNR measurements to model and rank the sensed channels. An evolutionary algorithm-based SNR estimation technique was developed, which enables adaptively varying key parameters of the existing Eigenvalue-based blind SNR estimation technique. The performance of the improved technique is compared to the existing technique. Results show the evolutionary algorithm-based estimation performing better than the existing technique. The utility-based channel ranking technique was developed by first defining channel utility function that takes into account SNR and spectrum occupancy. Different mathematical functions were investigated to appropriately model the utility of SNR and spectrum occupancy rate. A ranking table is provided with the utility values of the sensed channels and compared with the usual occupancy rate based channel ranking. According to the results, utility-based channel ranking provides a better scope of making an informed decision by considering both channel occupancy rate and SNR. In addition, the efficiency of several noise cancellation techniques was investigated. These techniques can be employed to get rid of the impact of noise on the received or sensed signals during spectrum sensing process of a cognitive radio system. Performance evaluation of these techniques was done using simulations and the results show that the evolutionary algorithm-based noise cancellation techniques, particle swarm optimization and genetic algorithm perform better than the regular gradient descent based technique, which is the least-mean-square algorithm

Characterizing Cyclostationary Features of Digital Modulated Signals with Empirical Measurements Using Spectral Correlation Function

Signal detection is widely used in many applications. Some examples include Cognitive Radio (CR) and military intelligence. CRs use signal detection to sense spectral occupancy. Without guaranteed signal detection, a CR cannot reliably perform its role. Similarly, signal detection is the first step for garnering an opponent\u27s information. Wireless signal detection can be performed using many different techniques. Some of the most popular include matched filters, energy detectors (which use measurements such as the Power Spectral Density (PSD) of the signal), and Cyclostationary Feature Detectors (CFD). Among these techniques, CFD can be viewed as a compromise technique, in that it theoretically has better low Signal-to-Noise Ratio (SNR) detection performance than energy detectors and less strict requirements than matched filters. CFD uses the cyclostationarity of a signal to detect its presence. Signals that have cyclostationarity exhibit correlations between widely separated spectral components. Functions that describe this cyclostationarity include the Spectral Correlation Function (SCF). One advantage of cyclostationary approaches such as these is that Additive White Gaussian Noise (AWGN) is cancelled in these functions. This characteristic makes SCF outperform PSD under low SNR environments. However, whereas PSD has been well investigated through empirical experiments throughout many researches, SCF features under real world noise have not been investigated with empirical experiments. In this effort, firstly, the SCF features of modulated signals under real world channel noise are identified and characterized using the concept of path loss. Secondly, outperformance of SCF under low SNR environment with real world signals is verified with real world signals and noise

Fault Detection in Rotating Machinery: Vibration analysis and numerical modeling

This thesis investigates vibration based machine condition monitoring and consists of two parts: bearing fault diagnosis and planetary gearbox modeling. In the first part, a new rolling element bearing diagnosis technique is introduced. Envelope analysis is one of the most advantageous methods for rolling element bearing diagnostics but finding the suitable frequency band for demodulation has been a substantial challenge for a long time. Introduction of the Spectral Kurtosis (SK) and Kurtogram mostly solved this problem but in situations where signal to noise ratio is very low or in presence of non-Gaussian noise these methods will fail. This major drawback may noticeably decrease their effectiveness and goal of this thesis is to overcome this problem. Vibration signals from rolling element bearings exhibit high levels of 2nd order cyclostationarity, especially in the presence of localized faults. A second-order cyclostationary signal is one whose autocovariance function is a periodic function of time: the proposed method, named Autogram by the authors, takes advantage of this property to enhance the conventional Kurtogram. The method computes the kurtosis of the unbiased autocorrelation (AC) of the squared envelope of the demodulated and undecimated signal, rather than the kurtosis of the filtered time signal. Moreover, to take advantage of unique features of the lower and upper portions of the AC, two modified forms of kurtosis are introduced and the resulting colormaps are called Upper and Lower Autogram. In addition, a new thresholding method is also proposed to enhance the quality of the frequency spectrum analysis. Finally, the proposed method is tested on experimental data and compared with literature results so to assess its performances in rolling element bearing diagnostics. Moreover, a second novel method for diagnosis of rolling element bearings is developed. This approach is a generalized version of the cepstrum pre-whitening (CPW) which is a simple and effective technique for bearing diagnosis. The superior performance of the proposed method has been shown on two real case data. For the first case, the method successfully extracts bearing characteristic frequencies related to two defected bearings from the acquired signal. Moreover, the defect frequency was highlighted in case two, even in presence of strong electromagnetic interference (EMI). The second part presents a newly developed lumped parameter model (LPM) of a planetary gear. Planets bearings of planetary gear sets exhibit high rate of failure; detection of these faults which may result in catastrophic breakdowns have always been challenging. Another objective of this thesis is to investigate the planetary gears vibration properties in healthy and faulty conditions. To seek this goal a previously proposed lumped parameter model (LPM) of planetary gear trains is integrated with a more comprehensive bearing model. This modified LPM includes time varying gear mesh and bearing stiffness and also nonlinear bearing stiffness due to the assumption of Hertzian contact between the rollers/balls and races. The proposed model is completely general and accepts any inner/outer race bearing defect location and profile in addition to its original capacity of modelling cracks and spalls of gears; therefore, various combinations of gears and bearing defects are also applicable. The model is exploited to attain the dynamic response of the system in order to identify and analyze localized faults signatures for inner and outer races as well as rolling elements of planets bearings. Moreover, bearing defect frequencies of inner/outer race and ball/roller and also their sidebands are discussed thoroughly. Finally, frequency response of the system for different sizes of planets bearing faults are compared and statistical diagnostic algorithms are tested to investigate faults presence and growth