This paper presents a data-driven algorithm for identification of locally differentially flat output from system output measurements. No detailed mathematical model of the system is needed. Trial output is written as a linear combination of measured outputs. An optimal linear combination is identified so that the trial output achieves the highest relative degree. When the relative degree is equal to the order of the system, the output is flat. The identification is done in the frequency domain by taking advantage of the asymptotic behaviour of transfer functions of linear systems. We have also developed data handling strategies to obtain the best estimate of the relative degree in the presence of measurement noise, high-frequency dynamics and Nyquist digitisation effect. The proposed algorithm is validated by numerical examples and an experimental study of a rotary crane system.

本文提出了一种数据驱动算法，用于从系统输出测量中识别局部差异平坦的输出。不需要系统的详细数学模型。试验输出写为测量输出的线性组合。确定最佳线性组合，使试验输出达到最高的相对程度。当相对度等于系统的阶数时，输出是平坦的。通过利用线性系统传递函数的渐近行为，在频域中进行识别。我们还开发了数据处理策略，以在存在测量噪声、高频动态和 Nyquist 数字化效应的情况下获得相对程度的最佳估计。