Because the Duffing equation is very sensitive to weak signals and noise immunity, the modified Duffing detection system is applied to detect the weak nonlinear signal in nonlinear ultrasonic experiment. Firstly, the Duffing equation is improved to construct detection models to detect the nonlinear ultrasonic signal wave mixing in experiment. Then, the maximum Lyapunov exponent of detection model with state change is calculated to evaluate the fatigue damage. When the collected nonlinear receiving signal in wave mixing experiment is substituted into four detection models, if the phase portraits of Duffing equation changes from the chaotic state into periodic state, the difference frequency signal at 3 MHz can be detected and this states the specimen has fatigue damage. In addition, the maximum Lyapunov exponent of detection model with state change is calculated and less than 0. The damage index is induced and it has a good corresponding relation with fatigue damage of metallic specimen, which the correspondence would be used to quantitatively evaluate the fatigue damage of specimen within a certain range. Therefore this research work is beneficial to extract the weak nonlinear signals for fatigue damage evaluation of metallic components.

由于Duffing方程对微弱信号和抗扰度非常敏感，因此在非线性超声实验中，将改进的Duffing检测系统用于检测微弱的非线性信号。首先，对Duffing方程进行了改进，构造了检测模型，用于检测实验中非线性超声信号的混合。然后，计算具有状态变化的检测模型的最大Lyapunov指数，以评估疲劳损伤。将在混波实验中采集到的非线性接收信号代入四个检测模型后，如果Duffing方程的相图从混沌状态变为周期状态，则可以检测到3 MHz的差频信号，表明样品存在疲劳损害。此外，计算出状态变化的检测模型的最大李雅普诺夫指数，其最大值小于0。诱发损伤指数，并与金属试样的疲劳损伤具有良好的对应关系，该对应关系可用于定量评估试样的疲劳损伤在一定范围内。因此，这项研究工作有益于提取微弱的非线性信号，以进行金属部件的疲劳损伤评估。