Although data integrity attack detections are critical to cyber-physical systems (CPSs), replay attack detection in industrial CPSs, especially data-based detection methods against replay attacks, has not been well-studied. Because it is difficult to distinguish replayed historical measurements and current measurements, replay attacks are hard to detect. In this paper, we propose a permutation entropy based detection scheme according to the complexity characteristics of sensor measurements. As sensor measurements generated during replay attacks present some sort of regularity, the significant decreasing of permutation entropy indicates the occurrence of replay attacks. Support vector data description (SVDD) is used to classify replay attacks according to permutation entropy of sensor measurements. Considering the manipulative attacker who mixes gaussian white noise or gaussian colored noise with measurements to bypass the entropy detection, we use wavelet analysis to denoise the measurements in advance. Finally, we demonstrate the efficiency of the proposed method through its application to a semi-physical simulation testbed. The experiment results show that our method can detect replay attacks accurately.

尽管数据完整性攻击检测对于网络物理系统（CPS）至关重要，但是尚未充分研究工业CPS中的重播攻击检测，尤其是针对重播攻击的基于数据的检测方法。由于很难区分重播的历史测量值和当前测量值，因此很难检测到重播攻击。在本文中，我们根据传感器测量的复杂性特征提出了一种基于置换熵的检测方案。由于重放攻击过程中生成的传感器测量值呈现某种规律性，因此排列熵的显着降低表明重放攻击的发生。支持向量数据描述（SVDD）用于根据传感器测量值的排列熵对重放攻击进行分类。考虑到操纵性攻击者将高斯白噪声或高斯色噪声与测量值混在一起以绕过熵检测，因此我们预先使用小波分析对测量值进行降噪。最后，我们通过将其应用到半物理模拟测试台上证明了该方法的有效性。实验结果表明，该方法可以准确地检测出重播攻击。