This work introduces a canonical structural evaluation framework for the assessment of complex technical systems based on discrete system states rather than dynamic models. A scalar quantity, the structural length, is defined as a state-dependent measure of recoverability relative to a fixed reference configuration. The construction is coordinate-free, scale-invariant, and does not rely on simulation, optimization, or predictive assumptions. The framework separates formal stability from structural operability by quantifying how structural constraints and diminishing system flexibility affect the cost of returning to a reference state. As a result, systems may remain stable in the classical sense while becoming structurally exhausted, a condition that is not detectable by threshold-based indicators alone. The approach is illustrated using publicly available frequency and volatility data associated with the ENTSO-E reported Iberian power system disturbance (Spain–Portugal, April 2025). A pointwise, discrete evaluation of system states reveals a monotonic increase in structural length prior to the critical event, despite nominal frequency behavior. This demonstrates that loss of structural admissibility can be detected earlier than classical stability violations. The proposed framework is intended as a structural evaluation and early classification tool, not as a control or prediction mechanism. It is applicable to a wide range of systems where stability is enforced by design but operational margins may degrade unnoticed. The results suggest that structural exhaustion constitutes a distinct and measurable failure mode complementary to established stability concepts.
Jeanette Leue (Thu,) studied this question.