Delay-Embedded Neural Reconstruction for Indirect Sensing in Electrical and Micromechanical Oscillating Systems

Area of Science:

• Sensor Technology
• Dynamic Systems Analysis
• Machine Learning Applications

Background:

• Indirect sensing relies on dynamic responses, not static outputs, for measurand encoding.
• Existing methods face challenges with vector-valued outputs and nonlinearities.
• Previous work utilized simplified models for indirect sensing reconstruction.

Purpose of the Study:

• To develop a robust method for indirect sensing using dynamic system analysis.
• To extend indirect sensing formulations to vector-valued outputs and nonlinear systems.
• To apply and validate the methodology on a microelectromechanical systems (MEMS) gyroscope.

Main Methods:

• Modeling sensors and excitation as autonomous systems with state representation.
• Utilizing delayed output samples to define an invertible observation map.
• Approximating the inverse observation map with a feedforward neural network trained on synthetic data.
• Augmenting output signals to address observability issues in nonlinear transduction.

Main Results:

• Accurate reconstruction of signed angular rate in a MEMS gyroscope from combined nonlinear capacitive current and AC drive reference.
• Demonstrated effectiveness of the neural network approximation for the inverse observation map.
• Identified a local conditioning indicator based on the Jacobian matrix for assessing reconstruction quality.
• Preliminary robustness assessment under additive output noise.

Conclusions:

• The proposed method enables accurate indirect sensing in complex systems with nonlinearities.
• Neural network approximation of the inverse observation map is a viable approach for measurand reconstruction.
• Augmented outputs are crucial for overcoming observability limitations in specific sensor applications.