Distributed estimation cascade second-order tri-stable stochastic resonance method for random noise suppression in continuous-wave mud pulse telemetry

The extraction of high-quality useful signals in downhole environments has perennially posed a technical challenge for continuous wave mud pulse transmission systems. Traditional denoising methods, such as adaptive filtering and wavelet transform, inevitably compromise the integrity of the original signal's useful components while removing noise. Different from the traditional denoising methods, stochastic resonance (SR) is capable of transferring the energy of noise to the signal, thereby accomplishing the objective of noise suppression. In this paper, based on the second-order tri-stable stochastic resonance detection method combined with the estimation of distribution algorithm (EDA), a distributed estimation cascade second-order tri-stable stochastic resonance (EDA- CSTSR) detection method is proposed for the first time. By constructing 5 groups of simulation signals with different signal-to-noise ratios (SNRs), the denoising performance of distributed estimation CSTSR, Langevin SR, and Duffing SR is analyzed in detail. The results show that compared with Langevin SR and Duffing SR, the EDA-CSTSR can increase the SNR of the input simulation signal by at least 17 dB and significantly increase the amplitude of the useful pulse signal. Moreover, the EDA-CSTSR is applied to process actual data obtained from a drilling site, enabling the recognition of weak signals amidst strong background noise, which highlights the method's excellent practical application value and underscores its potential for further enhancement.