Nonlinear coupled asymmetric stochastic resonance for weak signal detection based on intelligent algorithm optimization基于智能算法优化的非线性耦合非对称随机共振弱信号检测
![]()
Ma SJ, Liu Y, Ma XY, Liu YT, 2024. Nonlinear coupled asymmetric stochastic resonance for weak signal detection based on intelligent algorithm optimization. Probabilistic Engineering Mechanics, 78: 103697.DOI: 10.1016/j.probengmech.2024.103697
随机共振在弱信号检测中得到了广泛研究。为提高弱信号诊断能力，本文研究了一类非线性耦合非对称随机共振 (nonlinear coupled asymmetric stochastic resonance, NCASR) 新系统。首先，将非对称双稳系统与单稳系统耦合，建立非线性耦合非对称随机共振系统。进而，基于绝热近似理论推导了该系统的稳态概率密度 (steady-state probability density, SPD) 函数、平均首次超越时间 (mean first passage time, MFPT) 和信噪比 (signal-to-noise ratio, SNR) 的表达式。此外，分析了系统参数对稳态概率密度、平均首次超越时间和信噪比的影响。然后，通过模拟试验，验证了 Lévy 噪声下非线性耦合非对称随机共振系统检测弱信号的有效性。最后，采用自适应加权粒子群优化 (adaptive weighted particle swarm optimization, AWPSO) 算法对非线性耦合非对称随机共振系统进行优化，并应用于轴承故障信号检测。与经典双稳随机共振 (classical bistable stochastic resonance, CBSR) 系统优化相比，非线性耦合非对称随机共振系统在检测轴承故障信号方面的表现更好。关键词: 弱信号检测, 随机共振, 智能优化算法, 非线性耦合非对称系统Stochastic resonance has been extensively studied for detecting weak signals. To improve the diagnostic ability of weak signals, a novel nonlinear coupled asymmetric stochastic resonance (NCASR) system is investigated in this paper. Firstly, the NCASR system is established by coupling the asymmetric bistable system with the monostable system. Next, the expressions for the steady-state probability density (SPD) function, the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) of the proposed system are derived based on the adiabatic approximation theory. Furthermore, the impact of system parameters on the SPD, the MFPT and the SNR is analyzed. Then, by simulation experiments, we verify the effectiveness of detecting weak signals for the NCASR system with Lévy noise. Finally, the NCASR system optimized by Adaptive Weighted Particle Swarm Optimization (AWPSO) algorithm is applied to detect the bearing fault signal. Compared with the optimized classical bistable stochastic resonance (CBSR) system, it is found that the detection performance of the NCASR system is superior to the CBSR system in detecting bearing fault signals.Keywords: Weak signal detection; Stochastic resonance; Intelligent optimization algorithm; Nonlinear coupled asymmetric system.Fig. 1. NCASR system model
图 2: 非线性耦合非对称随机共振系统模型的势函数Fig. 2. Potential function of NCASR system model
Fig. 3. Change of SPD with relevant parameters (a = 2, b = 3, c = 0.4, r = 1, k = 0.1)
Fig. 4. Change of SPD with different parameter a (b = 3, c = 0.4, r = 1, k = 0.1)
Fig. 5. Change of SPD with different parameter b (a = 2, c = 0.4, r = 1, k = 0.1)
Fig. 6. Change of SPD with different parameter c (a = 2, b = 3, r = 1, k = 0.1)
Fig. 7. Change of SPD with different parameter k (a = 2, b = 3, c = 0.4, r = 1)
Fig. 8. Change of SPD with different parameter r (a = 2, b = 3, c = 0.4, k = 0.1)
图 9: 不同参数下非线性耦合非对称随机共振系统的平均首次超越时间Fig. 9. MFPT of the NCASR system with different parameters
图 10: 不同参数下非线性耦合非对称随机共振系统的信噪比Fig. 10. SNR of the NCASR system with different parameters
Fig. 11. Signal detection about NCASR system
Fig. 12. Time domain and frequency spectrum domain of original bearing inner ring fault signal
图 13: 经典双稳随机共振系统的轴承内圈故障检测结果Fig. 13. Test result for bearing inner ring fault of the CBSR system
图 14: 非线性耦合非对称随机共振系统的轴承内圈故障检测结果Fig. 14. Test result for bearing inner ring fault of the NCASR system
Fig. 15. Time domain and frequency spectrum domain of bearing original outer ring fault signal
图 16: 经典双稳随机共振系统的轴承外圈故障检测结果Fig. 16. Test result for bearing outer ring fault of the CBSR system
图 17: 非线性耦合非对称随机共振系统的轴承外圈故障检测结果Fig. 17. Test result for bearing outer ring fault of the NCASR system
作者信息 | Authors
北方民族大学 (North Minzu University) 数学与信息科学学院
Yuan Liu, 通讯作者 (Corresp.)北方民族大学 (North Minzu University) 数学与信息科学学院Email: bfmzly@163.com
北方民族大学 (North Minzu University) 数学与信息科学学院
北方民族大学 (North Minzu University) 数学与信息科学学院
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
