Application of Takens's Delay-Embedding to extract indirect measurements from nonlinear oscillating sensors

This paper presents a general procedure for extracting a physical measurand from the output of oscillating or periodically forced sensors, such as mechanical MEMS resonators and electrical or electromagnetic LC/RLC devices. The sensor together with its excitation is modeled as an autonomous dynamical system in which the measurand acts as a slowly varying state, while the excitation is parameterized by a phase variable. Under suitable smoothness and observability assumptions, Takens' delay-embedding theorem guarantees the existence of an injective map from the low-dimensional state space to a higher-dimensional space of delayed output samples, thereby enabling a deadbeat-like reconstruction through an approximate inverse map.Jacobian-based indicators are introduced to verify the necessary condition of local invertibility of this map and to assess the conditioning of the resulting output manifold. The inverse reconstruction map is then approximated through neural-network-based function approximation trained on synthetic data generated from the autonomous model.The proposed methodology is illustrated through a temperature-dependent RLC benchmark under different capacitance-temperature laws. The results highlight the potential of this approach as an indirect sensing strategy for a broad class of oscillating sensors.