Maximum Likelihood Estimation of the Parameters of Linear Systems

A method is presented which estimates the parameters of Linear Systems (LS), modelled by their transfer function, using a very efficient iteration algorithm. The estimator is an error in variables method and takes into account the noise on the input and output measurements. During the estimation process, an approximation of the Cramer-Rao lower bound on the covariance matrix of the estimates is derived and the 'mean' model error is discussed

Nonlinear system-identification of the filling phase of a wet-clutch system

The work presented illustrates how the choice of input perturbation signal and experimental design improves the derived model of a nonlinear system, in particular the dynamics of a wet-clutch system. The relationship between the applied input current signal and resulting output pressure in the filling phase of the clutch is established based on bandlimited periodic signals applied at different current operating points and signals approximating the desired filling current signal. A polynomial nonlinear state space model is estimated and validated over a range of measurements and yields better fits over a linear model, while the performance of either model depends on the perturbation signal used for model estimation

Separate initialization of dynamics and nonlinearities in nonlinear state-space models

This work focuses on the identification of nonlinear dynamic systems. In particular the problem of obtaining good starting values for the identification of nonlinear state-space models is addressed. A fast and efficient initialization algorithm is proposed, combining the use of methods from the statistical learning community to model the nonlinearities and classic system identification tools to capture system dynamics. The performance of the method is evaluated on simulation examples

Spectral analysis of block structured nonlinear systems

It is a challenge to investigate if frequency domain methods can be used for the analysis or even synthesis of nonlinear dynamical systems. However, the effects of nonlinearities in the frequency domain are non-trivial. In this paper analytical tools and results to analyze nonlinear systems in the frequency domain are presented. First, an analytical relationship between the parameters defining the nonlinearity, the LTI dynamics and the output spectrum is derived. These results allow analytic derivation of the corresponding higher order sinusoidal input describing functions (HOSIDF). This in turn allows to develop novel identification algorithms for the HOSIDFs using identification experiments that apply broadband excitation signals, which significantly reduces the experimental burden previously associated with obtaining the HOSIDFs. Finally, two numerical examples are presented. These examples illustrate the use and efficiency of the theoretical results in the analysis of the effects of nonlinearities in the frequency domain and broadband identification of the HOSIDFs

Spectral analysis of block structured nonlinear systems

It is a challenge to investigate if frequency domain methods can be used for the analysis or even synthesis of nonlinear dynamical systems. However, the effects of nonlinearities in the frequency domain are non-trivial. In this paper analytical tools and results to analyze nonlinear systems in the frequency domain are presented. First, an analytical relationship between the parameters defining the nonlinearity, the LTI dynamics and the output spectrum is derived. These results allow analytic derivation of the corresponding higher order sinusoidal input describing functions (HOSIDF). This in turn allows to develop novel identification algorithms for the HOSIDFs using identification experiments that apply broadband excitation signals, which significantly reduces the experimental burden previously associated with obtaining the HOSIDFs. Finally, two numerical examples are presented. These examples illustrate the use and efficiency of the theoretical results in the analysis of the effects of nonlinearities in the frequency domain and broadband identification of the HOSIDFs

Practical synthesis of ternary sequences for system identification

Several issues related to the practical synthesis of ternary sequences with specified spectra are addressed in this paper. Specifically, sequences with harmonic multiples of two and three suppressed are studied, given their relevance to system identification applications. In particular, the effect of non-uniform Digital to Analog Converter (DAC) levels on the spectral properties of the generated signal is analyzed. It is analytically shown that the DAC non-uniform levels result in degraded harmonic suppression performance. Moreover, a new approach is proposed for designing ternary sequences, which is flexible and can be adapted to suit different requirements. The resulting sequences, denoted as randomized constrained sequences, are compared to direct sequences already proposed in the literature. The approach is validated by numerical simulations and experimental results, showing the potential to achieve harmonic suppression performance of approximately 100 dB

Astronomical component estimation (ACE v.1) by time-variant sinusoidal modeling

Accurately deciphering periodic variations in paleoclimate proxy signals is essential for cyclostratigraphy. Classical spectral analysis often relies on methods based on (fast) Fourier transformation. This technique has no unique solution separating variations in amplitude and frequency. This characteristic can make it difficult to correctly interpret a proxy's power spectrum or to accurately evaluate simultaneous changes in amplitude and frequency in evolutionary analyses. This drawback is circumvented by using a polynomial approach to estimate instantaneous amplitude and frequency in orbital components. This approach was proven useful to characterize audio signals (music and speech), which are non-stationary in nature. Paleoclimate proxy signals and audio signals share similar dynamics; the only difference is the frequency relationship between the different components. A harmonic-frequency relationship exists in audio signals, whereas this relation is non-harmonic in paleoclimate signals. However, this difference is irrelevant for the problem of separating simultaneous changes in amplitude and frequency. Using an approach with overlapping analysis frames, the model (Astronomical Component Estimation, version 1: ACE v.1) captures time variations of an orbital component by modulating a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters that determine the model are the mean frequency of the orbital component and the polynomial coefficients. The first parameter depends on geologic interpretations, whereas the latter are estimated by means of linear least-squares. As output, the model provides the orbital component waveform, either in the depth or time domain. Uncertainty analyses of the model estimates are performed using Monte Carlo simulations. Furthermore, it allows for a unique decomposition of the signal into its instantaneous amplitude and frequency. Frequency modulation patterns reconstruct changes in accumulation rate, whereas amplitude modulation identifies eccentricity-modulated precession. The functioning of the time-variant sinusoidal model is illustrated and validated using a synthetic insolation signal. The new modeling approach is tested on two case studies: (1) a Pliocene-Pleistocene benthic delta O-18 record from Ocean Drilling Program (ODP) Site 846 and (2) a Danian magnetic susceptibility record from the Contessa Highway section, Gubbio, Italy