TY - GEN

T1 - Modelling Periodic Measurement Data Having a Piecewise Polynomial Trend Using the Method of Variable Projection

AU - Handler, Johannes

AU - Ninevski, Dimitar

AU - O'Leary, Paul

PY - 2023/10

Y1 - 2023/10

N2 - This paper presents a new method for modelling periodic signals having an aperiodic trend, using the method of variable projection. It extends the commonly used four parameter sine wave model by permitting the background to be time varying; additionally, any number of harmonics of the periodic portion can be modelled. This paper focuses on using B-Splines to implement a piecewise polynomial model for the aperiodic portion of the signal. A thorough algebraic derivation of the method is presented, as well as a comparison to using global polynomial approximation. It is proven that B-Splines work better for modelling a more complicated aperiodic portion when compared to higher order polynomials. Furthermore, the piecewise polynomial model is capable of modelling the local signal variations produced by the interaction of a control system with a process in industrial applications. An added benefit of using the method of variable projection is the possibility to calculate the covariances of the linear coefficients of the model, enabling the calculation of confidence and prediction intervals. The method is tested on both real measurement data acquired in industrial processes, as well as synthetic data. The method shows promising results for the precise characterization of periodic signals embedded in highly complex aperiodic backgrounds. Finally, snippets of the m-code are provided, together with a toolbox for B-Splines, which permit the implementation of the complete computation.

AB - This paper presents a new method for modelling periodic signals having an aperiodic trend, using the method of variable projection. It extends the commonly used four parameter sine wave model by permitting the background to be time varying; additionally, any number of harmonics of the periodic portion can be modelled. This paper focuses on using B-Splines to implement a piecewise polynomial model for the aperiodic portion of the signal. A thorough algebraic derivation of the method is presented, as well as a comparison to using global polynomial approximation. It is proven that B-Splines work better for modelling a more complicated aperiodic portion when compared to higher order polynomials. Furthermore, the piecewise polynomial model is capable of modelling the local signal variations produced by the interaction of a control system with a process in industrial applications. An added benefit of using the method of variable projection is the possibility to calculate the covariances of the linear coefficients of the model, enabling the calculation of confidence and prediction intervals. The method is tested on both real measurement data acquired in industrial processes, as well as synthetic data. The method shows promising results for the precise characterization of periodic signals embedded in highly complex aperiodic backgrounds. Finally, snippets of the m-code are provided, together with a toolbox for B-Splines, which permit the implementation of the complete computation.

U2 - 10.1109/IECON51785.2023.10312537

DO - 10.1109/IECON51785.2023.10312537

M3 - Conference contribution

SN - 979-8-3503-3183-7

BT - IECON 2023- 49th Annual Conference of the IEEE Industrial Electronics Society

PB - Institute of Electrical and Electronics Engineers

T2 - 49th Annual Conference of the IEEE Industrial Electronics Society - IECON 2023

Y2 - 16 October 2023 through 19 October 2023

ER -