A Methodological Framework for Chaos-Aware Evaluation of Self-Organization in Swarm-Based Engineering Systems

In the field of engineered systems, there has been an increasing trend in the utilization of self-organizing and swarm-based methodologies. These methodologies are employed to ensure the maintenance of functionality in the presence of uncertainty. However, prevailing evaluation continues to be dominated by task-level KPIs (e.g., coverage, latency), providing limited insight into organizational quality, specifically stability near critical regimes and recoverability. This paper proposes a methodological framework based on the Chaos-Aware Design Index (CADI), integrated into a Descriptive Study II (DS-II) context. Validation follows a dual-tier strategy: (i) tier I (behavioral), utilizing a behavioral emulator of consensus dynamics; (ii) tier II (urban), employing a macro-scale manifold analysis of 17,692 urban spatial polygons from the nuScenes dataset. Results demonstrate that an ensemble-based surrogate model (Random Forest), trained on a representative manifold curated via Latin Hypercube Sampling (LHS), captures organizational stability with high predictive fidelity (R2 = 0.9136, p < 0.001) under strict scene-independent (GroupKFold) validation. Stability descriptors are grounded in spectral graph theory, leveraging algebraic connectivity (λ2) and morphological proxies (node density, aspect ratio, convexity). The CADI framework serves as an auditable reporting scaffold, proving that swarm coherence is governed by observable geometric manifold dynamics. The findings establish that urban morphology exerts a dominant deterministic influence on collective stability, providing a rigorous foundation for early-stage design decisions in autonomous systems.