Formal Integration of ISO/IEC Digital Twin Standards: A Layered Compliance Model with Uncertainty Quantification

Digital Twin (DT) implementations in electrical and industrial systems are governed by fragmented ISO/IEC and IEC standards spanning terminology, architecture, interoperability, lifecycle management, and cybersecurity. This paper proposes a mathematical framework that integrates these standards into a unified compliance model. A layered DT architecture is defined as a finite set of functional abstractions, and standards are linked to layers through a multivalued mapping and an incidence matrix. Traceability, interoperability, fidelity, and security/governance indicators are normalized and aggregated through a bounded weighted functional to obtain a deterministic compliance score. The model is then extended by treating selected indicators as random variables, which enables probabilistic maturity classification and Monte Carlo-based robustness analysis. The resulting functional is bounded, monotone, and stable under bounded perturbations. Numerical experiments on a synthetic portfolio illustrate deterministic scoring and uncertainty effects. The framework provides a proof-of-concept basis for structured DT compliance assessment across heterogeneous electrical systems; however, broader empirical validation is still required before operational deployment.