Least-Square-Support-Vector-Machine-based approach to obtain displacement from measured acceleration

Vibration data collected by sensors provide useful information about the condition of a structure or a machine component, facilitating identification of any changes in its performance. While acceleration and displacement data provide complementary information, a cost-effective alternative to monitoring both is to estimate displacements from accelerations. This paper presents a kernel regression approach for obtaining displacement time series from acceleration data. Starting from a second-order central difference approximation, the method performs ridge regression in a feature space induced by the linear kernel. The main advantages of the proposed method are (1) It does not require baseline adjustment, other than removing the mean of the acceleration record; (2) The solution obtained is numerically stable, and thus regularization is not necessary; (3) The reconstructed displacement does not exhibit any long period drift. The validity of the proposed method is demonstrated through examples, where structural systems' displacements computed using the proposed approach were compared to the recorded experimental displacements. While the presented examples focus only on monitoring of vibrations responses of structural systems, the proposed method can be used in other settings where a displacement signal is to be estimated from an acceleration signal with appropriate, application-specific modifications.