In empirical system identification, it is important to take into account the effect of structural disturbances, such as outliers and trends in the data, which might otherwise deteriorate the identification accuracy. A commonly used approach is to preprocess the data to remove outliers and trends, followed by system identification using the processed data. This approach is not optimal because before a system model is available it may not be possible to separate outliers and trends in the data from excitation by the system inputs. In this study a procedure is presented for simultaneous identification of ARX and ARMAX system models and unknown structural disturbances, consisting of outliers and piece-wise linear offsets or trends. This is achieved by introducing sparse representations of the disturbances, having only a few non-zero values. The system identification problem is formulated as a least-squares problem with a sparsity constraint. The sparse optimization problem is solved using l(1)-regularization with iterative reweighting, which can be solved efficiently as a sequence of convex optimization problems. Simulated examples and experimental data from a pilot-plant distillation column are used to demonstrate that using the proposed method accurate system models can be identified from experimental data containing unknown trends and outliers.
- Sparse optimization
- Trend detection