From Reliability Modelling to Cognitive Orchestration: A Paradigm Shift in Aircraft Predictive Maintenance

This study formulates predictive maintenance of complex technical systems as a constrained multi-layer probabilistic optimization problem that unifies four interdependent analytical paradigms. The mathematical framework integrates: (i) Weibull reliability modelling with parametric lifetime estimation; (ii) Bayesian posterior updating for dynamic adaptation under uncertainty; (iii) nonlinear machine-learning inference for data-driven pattern recognition; and (iv) ontology-based semantic reasoning governed by logical axioms and domain-specific constraints. The four layers are synthesized through a formal orchestration operator, defined as a sequential composition, where each sub-operator is governed by explicit mathematical constraints: Weibull cumulative distribution functions, Bayesian likelihood-posterior relationships, gradient-based loss minimization, and description logic entailment. The system operates within a cognitive digital twin architecture, with orchestration convergence formalized through iterative parameter refinement until consistency between numerical predictions and semantic validation is achieved. The framework is validated through a case study on aircraft wheel-hub crack prediction. The mathematical formulation establishes a rigorous analytical foundation for cognitive predictive maintenance systems applicable to safety-critical technical systems including aerospace, energy infrastructure, transportation networks, and industrial machinery.