基于变尺度杜芬阵列的超声非线性输出信号检测

针对超声非线性输出信号中二次谐波信号比较弱、且是经过复杂传播的非线性时间序列，利用变尺度杜芬阵列对超声非线性输出信号进行检测评估材料的疲劳损伤。首先对杜芬振子进行频率变换、分析初始相位对检测结果的影响，构建检测实际工程信号的杜芬阵列模型，并对超声非线性输出信号进行变尺度变换，使杜芬阵列与超声非线性输出信号相匹配。当处理信号输入杜芬阵列模型时，第二个杜芬振子相轨迹由混沌状态过渡至大尺度周期状态，微弱二次谐波信号可以被有效的检测出来。根据杜芬振子总驱动力幅值和响应信号幅值之间的对应关系对二次谐波信号幅值进行有效估算。最后，探究随机噪声对检测模型的影响，当待测信号含有噪声时，杜芬振子相图仍变为大尺度周期状态，随着信噪比降低，相轨迹越来越粗糙，且稳定性变差。以上分析表明，利用构建的杜芬阵列模型能够有效检测超声非线性输出信号的二次谐波，对材料的疲劳损伤状态进行有效评估。

Detection the ultrasonic nonlinear output signal based on the variable scale Duffing array

In the nonlinear ultrasonic experiment, the second harmonic signal of output signal is weak and nonlinear time series through complex propagation, the duffing oscillator is proposed to detect the signal to evaluate the fatigue damage of metallic material. Firstly, the frequency transformation is carried out and the influence of initial phase on detection result is analyzed, the Duffing array model is built. In order to detect the weak second harmonic signal, the duffing array is matched with the ultrasonic nonlinear output signal by variable scale transformation. Then the processed signal is input into the Duffing array, the phase trajectory of the second Duffing oscillator converts from chaotic state to large-scale periodic state, and the weak second harmonic signal can be detected. According to the correspondence between the amplitude of the total driving force and response signal, the amplitude of the second harmonic signal is estimated. Finally, the influence of random noise on the Duffing array is explored. When the detected signal contains noise, the duffing oscillator phase diagram still changes to a large-scale periodic state. With the reduction of signal-to-noise ratio, the trajectory of phase diagram becomes more and more rough and the stability becomes worse. The above analysis shows that the constructed Duffing array model can effectively detect the weak second harmonic in the ultrasonic nonlinear output signal to evaluate the fatigue damage state of the material.