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.

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.