Extraction method of modulation frequencies of propulsor based on traversal weighted envelope spectrum

doi:10.3785/j.issn.1008-973X.2026.10.020

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (10): 2287-2298 DOI: 10.3785/j.issn.1008-973X.2026.10.020

Extraction method of modulation frequencies of propulsor based on traversal weighted envelope spectrum

Kelin WU1(

),Yuhang SUN1,Jiafeng XU1,Weiqi TONG1,Pan DONG1,2,Dazhuan WU1,*(

)

1. College of Energy Engineering, Zhejiang University, Hangzhou 310027, China
2. SINOPEC International (Ningbo) Co. Ltd, Ningbo 315040, China

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Abstract

Capturing characteristic modulation frequencies of propulsor noise can be challenging, as the actual acoustic signals in the scenario of passive acoustic detection exhibit extremely low signal-to-noise ratios. To tackle this challenge, an enhanced demodulation method, the Traversal Weighted Envelope Spectrum (TWES), was proposed, tailored for extracting the modulation frequencies of blade-type marine propulsor noise. First, the cyclostationary model for blade-type marine propulsor noise was established, and its cyclostationary signature was derived in detail. Then, the indicator Frequency-domain Correlated Kurtosis (FCK) was proposed, and a weighting function relying on prior knowledge of shaft frequency was constructed. Ultimately, the TWES was constructed for situations with prior knowledge of shaft frequency. Simulation results showed that the proposed TWES showed better demodulation performance than other benchmark methods even in the situation of SNR=?16 dB. The demodulation detection capability of TWES under low SNR levels was validated by experimental data from the pump jet and the propeller. The comparison with the classical demodulation methods and state-of-the-art demodulation methods further verified the superiority of the proposed TWES.

Key words： propulsor noise passive acoustic detection cyclostationary analysis narrowband envelope demodulation spectral correlation envelope spectrum

Received: 10 July 2025 Published: 29 July 2026

CLC:

TB 535

Fund: 国家自然科学基金资助项目（52406058，U2341242，U23B20107）.

Corresponding Authors: Dazhuan WU E-mail: wukelin@zju.edu.cn;wudazhuan@zju.edu.cn

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	Dazhuan WU

Cite this article:

Kelin WU,Yuhang SUN,Jiafeng XU,Weiqi TONG,Pan DONG,Dazhuan WU. Extraction method of modulation frequencies of propulsor based on traversal weighted envelope spectrum. Journal of ZheJiang University (Engineering Science), 2026, 60(10): 2287-2298.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.10.020 OR https://www.zjujournals.com/eng/Y2026/V60/I10/2287

基于遍历加权包络谱的推进器调制线谱提取方法

水下目标被动声学探测场景中的实测声信号的信噪比低，推进噪声调制线谱的提取受到阻碍. 为此，提出针对叶片式水下推进器调制线谱提取的增强解调方法——遍历加权包络谱（TWES）. 建立叶片式水下推进器辐射噪声的循环平稳信号模型，推导其循环平稳特征；提出频域相关峭度指标，构造依赖于轴频先验信息的加权函数；构建适用于有轴频先验信息场景下的遍历加权包络谱. 仿真分析结果表明，本研究方法能在信噪比低至?16 dB的情况下提取到调制线谱，且在不同信噪比下的解调性能均优于对比方法；泵喷推进器和螺旋桨的辐射噪声数据分析结果表明，本研究所提方法可在强烈噪声干扰下提取推进器轴叶频调制线谱，对轴叶频的解调检测能力优于传统解调方法和前沿解调方法.

关键词： 推进器, 被动声学探测, 循环平稳分析, 窄带包络解调, 谱相关, 包络谱

Fig.1 Schematic illustration of cyclostationary signature of propulsor noise

Tab.1 Parameters setting of simulation signal

Fig.2 Construction process of adaptive threshold curve

Fig.3 Demodulation band selection results of simulation signal

Fig.4 Demodulation analysis results of simulation signal

Fig.5 Evaluation and comparison of demodulation performance based on Monte Carlo simulations

Tab.2 Design parameters of jet pump

Fig.6 Demodulation analysis results of pump-jet propulsor radiated noise (

$ {f}_{\text{SF}}=1\;260 $

r/min)

Fig.7 Schematic of lake trial experiment for underwater vehicle

Tab.3 Parameters of hydrophone

Tab.4 Parameters of data acquisition instrument

Fig.8 Demodulation analysis results of underwater acoustic signal of propulsor (

$ {f}_{\text{SF}}=768 $

r/min)

Tab.5 Comparison of detection capability of different demodulation methods for shaft frequency, blade passing frequency and their harmonics

Fig.9 Demodulation analysis results of propulsor noise (

$ {f}_{\text{SF}}=1\;150$

r/min)


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