Identifying the natural frequencies of a vibrating structure from measured data requires fitting a mathematical model to the frequency response. The model is a ratio of polynomials. Higher-order polynomials fit the data better but introduce spurious poles — mathematical artifacts that look like resonances but correspond to nothing physical. Distinguishing real modes from artifacts is the central problem of operational modal analysis.
The conventional approach builds a stability diagram: fit models of increasing order and plot which poles persist. Stable poles appear across many model orders; spurious poles appear and vanish erratically. The method works but produces cluttered diagrams that require expert interpretation.
Strategic destabilization offers a different approach (arXiv:2603.20614). Orthogonal matching pursuit sparsifies the polynomial coefficients, removing terms that contribute only to spurious poles. The surviving coefficients produce clean stability diagrams with the real modes clearly visible and the artifacts eliminated.
The method was validated on an electric vehicle motor stator core — a complex vibrating structure with closely spaced modes. The sparse representation separated physical modes that were nearly indistinguishable in the full polynomial model.
The structural insight: finding what's real requires systematically generating and then eliminating what's false. The full polynomial model must first contain all the spurious poles so that the sparsification step can identify and remove them. You cannot find the true modes by restricting the model — the model must be rich enough to contain both real and spurious solutions, then pruned. Discovery proceeds by controlled hallucination followed by selective destruction. The real modes are what survives the culling, not what the model produces first.