Mathematical modelling of acoustic leakage channels in cyber-physical systems

Acoustic leakage channels are among the most underestimated threats to cyber-physical systems, since their occurrence is caused by complex wave processes that are difficult to capture using traditional control tools. The aim of the study was to develop and experimentally verify integrated approaches to modelling, identification and neutralisation of acoustic leaks based on a combination of wave models, active compensators and predictive systems. The methodology was based on 40 numerical experiments performed on four groups of models with subsequent repeated runs to ensure statistical reliability of the results. Significant differences were found between the four groups of wave models: the basic configurations (38-46 dB, 4-7% variance) were the simplest; the vibration scenarios formed 3-6 resonances with a variance of up to 18%; and the ultrasonic ones appeared to be the most critical (18-38 kHz, 71-89 dB, up to 11 resonances); the acousto-optic models demonstrated mixed time–frequency profiles with a variance of 16-24%. Among the active neutralisation methods, white noise showed the lowest efficiency (11-14 dB), while narrowband masking provided 19-23 dB, and Adaptive Noise Cancelling (ANC) achieved the best performance (34-39 dB, stability 96-97%, detection time 0.4-0.7 s). Among the predictive models, Long Short-Term Memory (LSTM) showed the best results (latency 0.42-0.55 s, stability 93-96%, reconstruction error 6-8%), while autoencoders were the least accurate (10-14%). The integral safety index reflected a clear stratification of risks: basic models – 0.62; vibration – 0.71; acousto-optic – 0.79; ultrasonic – 0.84. Statistical analysis confirmed the significance of the differences between all groups (p < 0.01) and the formation of two clusters of danger. The practical significance of the study lies in the creation of an integrated method for detecting and suppressing acoustic leaks, which can be directly applied when designing security systems for cyber-physical complexes to reduce the risk of covert attacks and increase resistance to multi-frequency influences