Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding

Integrate-and-Differentiate Approach to Nonlinear System Identification

In this paper, we consider a problem of parametric identification of a piece-wise linear mechanical system described by ordinary differential equations. We reconstruct the phase space of the investigated system from accelerometer data and perform parameter identification using iteratively reweighted least squares. Two key features of our study are as follows. First, we use a differentiated governing equation containing acceleration and velocity as the main independent variables instead of the conventional governing equation in velocity and position. Second, we modify the iteratively reweighted least squares method by including an auxiliary reclassification step into it. The application of this method allows us to improve the identification accuracy through the elimination of classification errors needed for parameter estimation of piece-wise linear differential equations. Simulation of the Duffing-like chaotic mechanical system and experimental study of an aluminum beam with asymmetric joint show that the proposed approach is more accurate than state-of-the-art solutions.

Identification of Tire Model Parameters with Artificial Neural Networks

Accurate modeling of tire characteristics is one of the most challenging tasks. Many mathematical models can be used to fit measured data. Identification of the parameters of these models usually relies on least squares optimization techniques. Different researchers have shown that the proper selection of an initial set of parameters is key to obtain a successful fitting. Besides, the mathematical process to identify the right parameters is, in some cases, quite time-consuming and not adequate for fast computing. This paper investigates the possibility of using Artificial Neural Networks (ANN) to reliably identify tire model parameters. In this case, the Pacejka’s “Magic Formula” has been chosen for the identification due to its complex mathematical form which, in principle, could result in a more difficult learning than other formulations. The proposed methodology is based on the creation of a sufficiently large training dataset, without errors, by randomly choosing the MF parameters within a range compatible with reality. The results obtained in this paper suggest that the use of ANN to directly identify parameters in tire models for real test data is possible without the need of complicated cost functions, iterative fitting or initial iteration point definition. The errors in the identification are normally very low for every parameter and the fitting problem time is reduced to a few milliseconds for any new given data set, which makes this methodology very appropriate to be used in applications where the computing time needs to be reduced to a minimum.