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为解决应用传统遗传算法优化的随机共振(Stochastic resonance,SR)方法易出现的计算发散问题,提出一种基于稳定约束的自适应随机共振方法。对求解随机共振的Langevin方程进行了稳定性分析,得到了考虑输入信号的条件下,使系统输出稳定的频率压缩比R的约束公式。将该稳定性条件应用于遗传算法参数的寻优过程,将原来的无约束最优化问题转化为有约束最优化问题。将改进后的自适应随机共振方法应用于转子早期碰摩故障检测,分析结果表明,该方法确保了系统输出的稳定性,寻优过程中的频率压缩比R的取值均在约束值以下,避免了计算发散现象,实现了在强噪声条件下对微弱故障信号的提取。
In order to solve the computational divergence problem which is easily applied to the Stochastic Resonance (SR) method optimized by traditional genetic algorithm, an adaptive stochastic resonance method based on stability constraint is proposed. The stability of the Langevin equation for solving stochastic resonance is analyzed, and the constraint formula of the frequency compression ratio R that makes the system output stable under the condition of input signal is obtained. The stability condition is applied to the optimization of genetic algorithm parameters, and the original unconstrained optimization problem is transformed into a constrained optimization problem. The improved adaptive stochastic resonance method is applied to the detection of rotor early rub impact fault. The analysis results show that this method ensures the stability of the system output. The value of the frequency compression ratio R in the optimization process is below the constraint value, The calculation of divergence is avoided, and the faint fault signal is extracted under the condition of strong noise.