Detection-Performance Tradeoff for Watermarking in Industrial Control Systems

The watermarking method, which adds unique watermarks to data, has been widely used for integrity attack detection in industrial control systems (ICSs). Existing literature generally designs watermarking mechanisms without considering the existence of noises, which cannot be trivially applied to realistic ICS scenarios in the presence of strong noise interference. On one hand, the low-intensity watermarking will be ineffective under the strong noise environment; while on the other hand, the oversized watermarking can possibly degrade the control performance or even destabilize the system. Therefore, the intensity of watermarks plays a fundamental role in balancing the tradeoff between detection effectiveness and control performance, which, to the best of our knowledge, has never been thoroughly analyzed yet. To this end, in this paper, we for the first time propose an optimal watermarking design method for ICSs considering the detection-performance tradeoff. To begin with, we shift the watermark container from data points to segments and update the detection metrics to reduce the noise impact. Then, we formulate an optimization problem to determine the strength of watermarks to balance the detection-performance tradeoff. Meanwhile, the detection effectiveness and control performance metrics are analytically modeled and theoretically analyzed considering the discrepancy between added watermarks and noises, signal quality, detection latency, as well as estimation of detection metrics. Finally, extensive numerical simulations and systematical experiments based on a practical Ethanol Distillation ICS are conducted to validate the theoretical analysis and demonstrate the outperformance of our proposed watermarking method in comparison with related works.