Data-Driven and Physics-Aware Machine Learning Methods for Mechanical System Analysis

Abstract

Modeling of complex dynamical systems is necessary to facilitate identification, prediction, and control of those system. Which in turn allows for safe, efficient, well-informed operation of those systems. Specifically, unexpected downtime of manufacturing equipment, Computer Numeric Controlled (CNC) machines for example, costs US manufacturers approximately $50 billion a year [5]. In order to reduce the unplanned downtime of such equipment, dynamic modeling of the operation of those machines should occur. Two methods of modeling the dynamic response of a CNC machining spindle are evaluated in this thesis. Firstly, a method to learn a data-driven model for damped coupled oscillators from a mixed-mode response signal using neural differential equations is proposed. The univariate time-series data of the impulse response is first resampled into a multi-variate time-delayed embedding. A singular value decomposition (SVD) 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. Secondly, a general method to learn a data-driven frequency response function (FRF) is developed. The FRF provides an input-output model that describes the system dynamics. Learning the FRF of a mechanical system can facilitate system identification, adaptive control, and condition-based health monitoring. In this thesis, learning FRFs from operational data with a nonlinear regression approach is investigated. A multiple input, multiple output (MIMO) regression model with a learned nonlinear basis is proposed for FRF learning for run-time systems under dynamic steady state. The proposed method is tested and validated for dynamic cutting force estimation of machining spindles under various operating conditions. It is shown that the proposed method can predict dynamic cutting forces with high accuracy by using measured vibration signals. It is also demonstrated that the learned data-driven FRF can be easily applied with a few-shot learning scheme to machine tool spindles with different frequency responses when limited training samples are available.