تشخیص سیگنال های سینوسی ضعیف جاسازی شده در یک باند پهن پر سر و صدای تصادفی غیر ثابت ،یک مطالعه شبیه سازی

In the present study, a simple numerical function is proposed for use together with the time–frequency analysis in the detection of very weak sinusoidal signals embedded in a non-stationary random broadband background noise. Its performance is studied through the use of two numerical examples. It is found that the present method enables good recovery of the sinusoidal signals and the instants of their initiations even when the signal-to-noise ratio is down to −17 dB.

Signal detection technique has wide applications in both physics and engineering (for instance, Refs. [1] and [2]). For a modernized heavily serviced building, the early detection of fault signals from rotary machineries, such as the chillers, pumps, motors, etc., is crucial to its smooth operation [3]. Similar situation appears in electricity power plants. The magnitudes of the fault signals are usually very small when the faults are in their initial stages. Though the faults will usually result in abnormal spectral peaks in the machine vibration signals [4], their detection is not straightforward in the initial stage because of the presence of much stronger background signals or noises, which can be stationary or non-stationary. Owing to the importance of signal detection in the machine health monitoring/diagnosis process, many analysis approaches have been introduced in the past few decades. The short-time Fourier transform (STFT) [5] appears to be a very obvious choice. The use of the Wigner distribution and wavelet transforms for analyzing non-stationary signals has also been studied [6] and [7]. Tang [8] investigated the performance of STFT and the harmonic wavelets [9] in retrieving parameters of exponential decaying pulses. Besides, the use of time series techniques for signal analysis has been examined. For example, Zhan and Jardine [10] analyzed gear faults using the auto-regression, while Chan et al. [11] investigated decaying sinusoidal pulses using the stochastic volatility approach. However, though there has been much effort made in improving signal detection and analysis, many of the proposed approaches fail to give satisfactory results when the signal-to-noise ratio (S/N) is close to 0 dB or goes negative, which is the case in the early development of a fault in the building services equipment. Li and Qu [12] investigated the use of the chaotic oscillator for weak signal detection, but their method requires knowledge on the characteristics of the signals to be detected. The focus of the present study is on enhancing the detection of weak signals embedded in a stronger non-stationary signal/noise. A numerical treatment to the original signal made up of the weak sinusoidal signal and the non-stationary noise, which can facilitate a better retrieval of the weak signal after the time–frequency procedure, is proposed. Its performance is examined through two illustrative examples.

A novel but simple method for the detection of weak signals embedded in a non-stationary strong broadband background noise is derived in the present study. A function, which tends to transform sinusoidal wave into a regular pulse train, is proposed to be used together with the Fourier transformation. Its performance is illustrated using two artificial numerical examples. The first one is a very weak but steady sinusoidal signal, while the other an exponentially growing sinusoidal wave generated abruptly within the background noise. For the latter, the recovery of the instant of wave initiation is the focus. The performance of repeated transformations on the signals is also investigated. For the steady sinusoidal wave, the proposed transformation function enables its unambiguous detection even when the S/N drops to −19 dB after the fourth transformation. Further transformation is found to make thing worse and is not recommended. The recovery of the instant of the exponentially growing wave initiation is also enhanced after the application of the transformation function. The associated error is found to be within 300 time steps even for an initial S/N of −17 dB when 200 data are used in the spectral calculation. The recovery of the instant of the wave initiation is improved remarkably by increasing the number of data involved in the calculation. The recovery error becomes negligible when more than 4000 data are used to produce the moving spectral averages.