Abstract
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.
Highlights
A relevant simulation of nonlinear systems requires well-identified computer models.Numerous approaches for nonlinear system identification have been proposed recently: differential equations [1], NARMAX models [2,3], neural networks [4], spline adaptive filters [5], deep state-space models [6], etc
Rigorous theoretical proof of the Proposition 1 meets sufficient difficulties since it involves several unknown parameters such as noise, parameters of motion, type of numerical method used for integration and differentiation, and parameters of numerical noise introduced by the computer
We considered the problem of nonlinear mechanical system identification in the form of piece-wise linear ordinary differential equation (ODE) from accelerometer data using a variant of the iteratively reweighted least squares method
Summary
A relevant simulation of nonlinear systems requires well-identified computer models. Numerous approaches for nonlinear system identification have been proposed recently: differential equations [1], NARMAX models [2,3], neural networks [4], spline adaptive filters [5], deep state-space models [6], etc. The first idea behind our approach is the application of the IRLS method to differentiated equations of motion in velocity and acceleration instead of conventional equations in position and velocity While this approach does not eliminate the need for double integration to obtain the position, it makes it possible to reduce identification errors significantly without a priori knowledge of the noise properties. Mathematics 2021, 9, 2999 amount of phase space variables is not observed This method is especially applicable to the identification problems utilizing the accelerometer data series.
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