Estimating dynamic cutting forces of machine tools from measured vibrations using sparse regression with nonlinear function basis

Estimating relationships between system inputs and outputs can provide insight to system characteristics. Furthermore, with an established input-output relationship and measured output, one can estimate the corresponding input to the system. Traditionally, the relationship between input and output can be represented with transfer functions or frequency response functions. However, those functions need to be built on physical parameters, which are hard to obtain in practical systems. Also, the reverse problem of solving for the input with a known/measured output is often more difficult to solve than the forward problem. This paper aims to explore the data-driven input-output relationship between system inputs and outputs for system diagnostics, prognostics, performance prediction, and control. A data-driven relationship can provide a new way for system input estimation or output prediction. In this paper, a sparse linear regression model with nonlinear function basis is proposed for input estimation with measured outputs. The proposed method explicitly creates a nonlinear function basis for the regression relationship. A threshold-based sparse linear regression is designed to ensure sparsity. The method is tested with experimental data from a spindle testbed that simulates cutting forces within machine tools. The results show that the proposed approach can predict the input force based on the measured vibration response with high accuracy. The current model is also compared with neural networks, which is another nonlinear regression method.