自适应Laplace统计模型下的量子降噪算法

受量子理论启发，提出自适应Laplace统计模型下的量子降噪算法，并将其成功应用于机械故障诊断。建立起带自适应参数的Laplace概率密度函数模型，提高统计模型的适用性；结合贝叶斯估计理论，推导出小波系数收缩函数；利用父-子代小波系数的相关性，提出量子叠加态信号与噪声出现概率，并推导出基于量子叠加态参数估计的方差公式，实现小波系数的非线性收缩。通过仿真试验和轴承故障诊断实例分别对此算法进行分析和验证，结果表明，该算法均具有良好的降噪效果，可以有效地对机械振动信号进行降噪。

Quantum Denoising Method of Mechanical Vibration Signals Based on Adaptive Laplace Statistical Model

Inspired by quantum theory, a quantum denoising method is proposed based on an adaptive Laplace statistical model and successfully applied in mechanical fault diagnosis. To enhance the adaptability of the statistical model, a Laplace probability density function with an adaptive parameter is developed. The wavelet coefficient shrinkage function is derived from Bayesian estimation theory. By integrating the inter-scale dependency of coefficients, the quantum superposition-inspired probability of signal and noise is presented. Then, variance is deduced based on quantum superposition-inspired parameters estimation to implement nonlinear shrinkage for the wavelet coefficients. This algorithm is analyzed by simulation and certificated by the bearing fault diagnosis example. Analysis results show that this algorithm has good noise reduction effects and can efficiently reduce the noise of the mechanical fault signal.