Strong noise attenuation method based on the multiuser kurtosis criterion

The strong noise produced by the leakage of electricity from marine seismic streamers is often received with seismic signals during marine seismic exploration. Traditional denoising methods show unsatisfactory effects when eliminating strong noise of this kind. Assuming that the strong noise signals have the same statistical properties, a blind source separation （BSS） algorithm is proposed in this paper that results in a new denoising algorithm based on the constrained multi-user kurtosis （MUK） optimization criterion. This method can separate strong noise that shares the same statistical properties as the seismic data records and then eliminate them. Theoretical and field data processing all show that the denoising algorithm, based on multi-user kurtosis optimization criterion, is valid for eliminating the strong noise which is produced by the leakage of electricity from the marine seismic streamer so as to preserve more effective signals and increase the signal-noise ratio. This method is feasible and widely applicable.

Application of local polynomial estimation in suppressing strong chaotic noise

In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.

Extracting hidden weak sinusoidal signal with short duration from noisy data: Analytical theory and computational realization

Signal detection is both a fundamental topic of data science and a great challenge for practical engineering. One of the canonical tasks widely investigated is detecting a sinusoidal signal of known frequency ω with time duration T：I（t）=Acos ω t＋Γ（t）, embedded within a stationary noisy data. The most direct, and also believed to be the most efficient, method is to compute the Fourier spectral power at ω：B=｜2/T∫0^T I（t）e^iωtdt｜. Whether one can out-perform the linear Fourier approach by any other nonlinear processing has attracted great interests but so far without a consensus. Neither a rigorous analytic theory has been offered. We revisit the problem of weak signal, strong noise, and finite data length T=O（1）, and propose a signal detection method based on resonant filtering. While we show that the linear approach of resonant filters yield a same signal detection efficiency in the limit of T→∞, for finite time length T=O（1）, our method can improve the signal detection due to the highly nonlinear interactions between various characteristics of a resonant filter in finite time with respect to transient evolution. At the optimal match between the input I（t）, the control parameters, and the initial preparation of the filter state, its performance exceeds the above threshold B considerably. Our results are based on a rigorous analysis of Gaussian processes and the conclusions are supported by numerical computations.

Suppression of strong random noise in seismic data by using time-frequency peak filtering

Time-frequency peak filtering (TFPF) is highly efficient in suppressing random noise in seismic data. Although the hypothesis of stationary Gaussian white noise cannot be fulfilled in practical seismic data, TFPF can effectively suppress white and colored random noise with different intensities, as can be theoretically demonstrated by detecting such noise in synthetic seismic data. However, a "zero-drift" effect is observed in the filtered signal and is independent of the average power and variance of the random noise, but related to its mean value. Furthermore, we consider the situation where the local linearization of the seismic data cannot be satisfied absolutely and study the "distortion" characteristics of the filtered signal using TFPF on a triangular wave. We found that over-compensation is possible in the frequency band for the triangular wave. In addition, it is nonsymmetrical and has a relationship to the time-varying curvature of the seismic wavelet. The results also present an improved approach for TFPF.

Applying nonlinear filtering in reverberation time measurement under strong background noise

Nonlinear filtering of impulse response obtained by M-sequence correlation method under strong background noise is presented. The research shows that the new method works very efficiently without the need to cut off impulse response data. Even if the ratio of signal to noise is below -15 dB, the same decay curve ranges can still be obtained as when S/N > 40 dB

Periodic-phase-diagram similarity method for weak signal detection

The periodic-phase-diagram similarity method is proposed to identify the frequency of weak harmonic signals.The key technology is to find a set of optimal coefficients for Duffing system,which leads to the periodic motion under the influence of weak signal and strong noise.Introducing the phase diagram similarity,the influences of strong noise on the similarity of periodic phase diagram are discussed.The principle of highest similarity of periodic phase diagram with the same frequency is detected by discussing the persistence of similarity of periodic motion phase diagram under the strong noise and the periodic-phase-diagram similarity method is constructed.The weak signals of early fault and strong noise are input into Duffing system to obtain the identified system.The stochastic subharmonic Melnikov method is extended to obtain the conditions of the optimal coefficients for the identified system.Based on the results,the constructed frequency conversion harmonic weak signals are considered to form a datum periodic system.With the change of frequency in the datum periodic system,the phase diagram similarity of the two constructed systems can be calculated.Based on the periodic-phase-diagram similarity method,the frequency of weak harmonic signals can be identified by the principle of highest similarity of periodic phase diagram with the same frequency.The results of numerical simulation and the early fault diagnosis results of actual bearings verify the feasibility of the periodic-phase-diagram similarity method.The accuracy of the detection effect is 97%,and the minimum signal-to-noise ratio is−80.71 dB.