Data-driven modeling of dynamical systems has drawn much research attention recently, with the goal of approximating the underlying governing rules of a dynamical system with data-driven differential equations. Many real-world dynamical systems can be modeled as coupled oscillators, such as chemical reactors, ecological systems, integrated circuits, and mechanical systems. In those systems, the response can be described by coupled differential equations in which multi-dimensional state variables describe the timeevolution. However, in practice, the full set of state variables is often difficult or expensive to measure. This paper shows an attempt to develop a data-driven model for damped coupled oscillators from a mixed-mode response signal using neural differential equations. The univariate time-series data of the impulse response is first resampled into a multi-variate time-delayed embedding. A singular value decomposition is then applied to find the dominant orthogonal basis (oscillator modes). The decoupled modes are then modeled with parameterized neural differential equations. The unknown parameters can be learned from a segment of historical data. The proposed methodology is validated using impact testing data of an end mill in a machine tool spindle. The results demonstrate that the proposed method can effectively model damped coupled oscillators.
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machine learning, neural differential equation, impulse response, dynamics, coupled oscillator
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