Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Singular-spectrum analysis: a toolkit for short, noisy chaotic signals
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
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We apply the methods of the time series analysis for obtaining upper bounds on the number of degrees of freedom significant for description of oscillations of moving on rough roads machines such as cars, trucks or agricultural machines. The upper bounds can justify or reject the application of low-dimensional mathematical models of the dynamics of the observed machine. For the investigated stationary and nonstationary time series an upper bound is given by the statistical dimension calculated on the basis of the singular spectrum analysis of the time series. For stationary time series the bound can be lowered by calculation of the correlation dimension after a noise reduction by use of the largest principal components of the time series. As an illustration we investigate time series from several working regimes of an agricultural tractor. For the case of nonstationary time series we choose time series with included bouncing: large amplitude oscillations than can mask the action of the other significant degrees of freedom. For the case of stationary time series we use time series from tractor with attached subsoiler. In addition to the calculation of the upper bounds we show that by the singular spectrum analysis we can isolate the bouncing in the two largest principal components of the time series. The positive values of the maximum Lyapunov exponents show that the regimes of work of the tractor with subsoiler are chaotic.