A novel design of time delay fractional nonlinear SIHQR worm transmission model for industrial IoT networks: Machine learning knowledge driven neuroarchitecture analysis

Industrial Internet of Things (IoT) is a revolutionary paradigm that bridges legacy industrial infrastructure and advanced digital innovation to enhance operational proficiency, data-driven decision making, and intelligent automation. Programable Logic Controller (PLC) serves as a key pillar of industrial automation, vulnerable to becoming a target vector for cybercriminals to infiltrate industrial systems through malware dissemination in industrial network ecosystem. This study explores the fractional-order nonlinear industrial worm spread time delay (Fr-NIWS-TD) model in PLC-enabled industrial control networks by leveraging nonlinear multilayer autoregressive exogenous network (NM-ARXN) aided with Levenberg-Marquardt (LM) backpropagation, i.e., NM-ARXN-LM neuroarchitecture. The Adams–Bashforth–Moulton predictor–corrector scheme with Caputo fractional operator is efficaciously employed to simulate the system scenarios that act as a synthetic data for NM-ARXN-LM framework to address the Fr-NIWS-TD model with distinct dynamic state variables of Susceptible S, Infected I, Halted H, Quarantine Q, and Recovered R, (SIHQR) nodes for worm transmission in industrial IoT infrastructure. The methodically structured simulation analysis conducted on sundry Fr-NIWS-TD case-studies such as varying (i) the rate of quarantine node converting to recovered node along with the likelihood that its operational device program blocks are rewritten by updated programs, (ii) the rate of a recovered node losing its immunity R to S node, (iii) shutdown (halting) rate of an infected node induced by worm I to H node, (iv) quarantine rate I to Q node, (v) the rate of intrusion detection system (IDS) effectively interrupting worm spread during a unit time interval. The Fr-NIWS-TD simulation datasets, to be modeled by the intelligent computing paradigm, are stratified into training, validation and testing subsets. The proposed NM-ARXN-LM technique's proficiency is endorsed through comprehensive performance evaluations on mean squared error (MSE) convergence trends, error distribution histograms, correlation evaluation, regression analysis, and time-series fitting patterns, while the structural integrity and convergence stability of neuroarchitecture are further substantiated through numerical comparative analysis with absolute error distribution plots. Extensive evaluations on single-step and multi-step ahead horizons with MSE of order 10−11 to 10−14, empirically underscores robustness, resilience and high-fidelity approximation competence of the NM-ARXN-LM methodology in capturing the complex worm propagation dynamics in Industrial IoT networks.