Chair for Medical Engineering, Ruhr University Bochum, 44801 Bochum, Germany.
Rev Sci Instrum. 2021 Mar 1;92(3):035103. doi: 10.1063/5.0036696.
When identifying nonlinear systems with input-output measurements, a suitable test signal must be selected. Nonlinear systems are almost always in a cascade with linear systems, i.e., a Wiener-Hammerstein type system cascade. A suitable test signal is preferably less influenced by the linear systems and is therefore sinusoidal, if time-varying signals are required for the measurement principle, e.g., for induction or vibration measurements. Then, a sinusoidal excitation with different DC offsets is a suitable signal to analyze a static nonlinear system in a Wiener-Hammerstein type cascade by measuring the cascade output at higher harmonics of the input frequency in a steady state, e.g., by using sensitive lock-in techniques. To calculate the cascade output given the input signal or to reconstruct the static nonlinear system also given the output signal, the transfer function of the DC offset at the nonlinear system input to the higher harmonics at the nonlinear system output is required. Those transfer functions are calculated here with emphasis on the first harmonic component. The reconstruction of a static nonlinear system is demonstrated in a simple simulation scenario by inverse filtering, i.e., deconvolution, with the derived transfer function. It is pointed out that a commonly made small signal assumption to the test signal is bypassed with the deconvolution method, which can lead to more precise measurements in applications due to a higher signal-to-noise ratio at the cascade output.
在使用输入-输出测量来识别非线性系统时，必须选择合适的测试信号。非线性系统几乎总是与线性系统串联，即威纳-汉默施坦（Wiener-Hammerstein）类型的系统串联。如果测量原理需要时变信号，例如感应或振动测量，则合适的测试信号最好受线性系统的影响较小，因此是正弦信号。然后，对于威纳-汉默施坦类型的级联中的静态非线性系统分析，使用不同直流偏置的正弦激励是一种合适的信号，可以通过在稳态下测量输入频率的较高谐波处的级联输出来实现，例如使用灵敏的锁定技术。为了在给定输入信号的情况下计算级联输出，或者在给定输出信号的情况下重建静态非线性系统，需要计算非线性系统输入处的直流偏置到非线性系统输出处的较高谐波的传递函数。这里重点计算了第一谐波分量的传递函数。通过使用推导的传递函数进行逆滤波（即去卷积），在一个简单的仿真场景中演示了静态非线性系统的重建。指出，去卷积方法绕过了测试信号的常用小信号假设，由于级联输出处的信噪比更高，因此在应用中可以进行更精确的测量。
