Machine learning knowledge driven investigation for immunity infused fractional industrial virus transmission in SCADA systems

Abstract

Supervisory control and data acquisition (SCADA) environment is a highly sensitive and crucial industrial control system primarily deployed to monitor, control and automate the critically integrated and interconnected complex networks. Due to revolution in communication technology, SCADA systems encounter escalating cybersecurity threats and mandate proactive safeguard mechanisms to prevent cyberattack surfaces that may interrupt critical core services, maleficent equipment, and even threaten the social security in certain circumstances. This work aims to enhance the standard nonlinear industrial virus transmission (NIVT) model with immunity for SCADA systems by incorporating fractional‐order processing and then leveraging machine learning through nonlinear multilayer autoregressive exogenous (NM-ARX) neural networks iteratively trained with Bayesian regularization (BR)—the NM-ARX-BR methodology. The Caputo fractional differentiation operator inspired fractional implicit Adams–Moulton and explicit Adams–Bashforth multistep solvers are used to generate reference simulation dataset for NM-ARX-BR neuroarchitecture in case of fractional kinetic of immunity-based NIVT model with five dynamic states susceptible nodes S, enhanced-susceptible nodes E, latent nodes L, breakout nodes B, and recovered nodes R in the SCADA environment. The rigorous simulation based comprehensive comparative evaluation revealed that the low value of fitness on mean square error (MSE) in the range of 10⁻¹⁴ to 10⁻¹⁶ is achieved by NM-ARX-BR neurocomputational framework for sundry case studies of immunity-based NIVT system and performance is further validated by proximity analysis, cross correlation and autocorrelation analysis, histogram frequency distribution and regression statistics. The presented NM-ARX-BR framework depicts the resilience, accuracy, and consistency in modelling the fractional kinetics of immunity-based nonlinear industrial virus transmission in the SCADA systems by executing single and multiple step-ahead prediction measures during the exhaustive numerical simulations with error ranges of 10⁻¹³ to 10⁻¹⁶. The performance assessment is carried out utilizing three standard error metrics MSE, mean absolute error (MAE), root mean square error (RMSE) and phase space error (PSE). The error values of MSE, MAE, PSE and RMSE are remarkably low 10⁻⁰⁷ to 10⁻⁰⁹, demonstrate the robustness, generalization capability and high fidelity of NM-ARX-BR technique.