Regularization of ill-conditioned problems based on a more sensitive functional and visual analysis of its local cross-sections

Abstract

The article discusses an approach to regularization of ill-conditioned problems using imitation of input signals time shift. One of the sources of such problems is structural difference between models and real objects, which finds expression as interferences in experimental data. While independent errors are readily observable and in many cases could be successfully eliminated, in the case of correlated disturbances even their presence is sometimes difficult to confirm. Proposed transformation changes degree of  correlation between the interference and underlying signal, thus making problem tractable by the standard tools of identification methods. Another advantage of this approach consists in the fact, that it obtains multiple realization by varying the duration of the shift, and increasing the amount of data available for processing. For that reason time shift method could be easily applicable without purposeful changes to the experiments themselves or increase in their number, and is suitable to the application of statistical methods. The article proposes the functional based on standard deviation of model parameters, which appears more sensitive to correlated interferences than standard least square functional and improves the quality of parameter estimations. Since detailed analysis of functional level surfaces is time-consuming and labor-intensive, suggested approach consists in utilization of local cross-sections of lesser dimensions. The article demonstrates effectiveness of the imitation of input signal time shift method for the problem of separate identification of thrust and drag coefficients. This regularization allowed us to significantly reduce errors in estimations of model parameters from 4.5 and 6.5% to 0.7-1.7% and 0.5-1.5%, in cases of constant drag coefficient and thrust respectively for data obtained using aircraft flight simulation.