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

Fast identification of Wiener-Hammerstein systems using discrete optimisation

A fast identification algorithm for Wiener-Hammerstein systems is proposed. The computational cost of separating the front and the back linear time-invariant (LTI) block dynamics is significantly improved by using discrete optimisation. The discrete optimisation is implemented as a genetic algorithm. Numerical results confirm the efficiency and accuracy of the proposed approach

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

Climate reconstruction based on archaeological bivalve shells

Several years of biogeochemical research on bivalve shells yielded in clear proxyrecords carrying potential for reconstruction of paleoseasonal trends in coastal environments. However, the interpretation of the proxy signals is still often problematic. Proxy concentrations can be influenced by several environmental parameters and by physiological processes. With more complex models these problems can be tackled. Two strategies are followed; (1) a statistical black-box model is being developed in parallel with (2) a physiological white-box model.The statistical black-box model can be described as a non-linear multi-proxy model. It is based on chemical measurements in modern bivalve shells and consists of the construction of a curve in a multi-dimensional space. The model describes the variations in the chemical signature of the shell during a full year cycle. The shortest distance from any other data point (e.g. a fossil shell) to the model will give a time point estimation in the annual cycle, which can further be linked to environmental parameters. At present our model approach achieves quite accurate SST reconstructions.A white box model is crucial for understanding the physiological processes and for an unambiguous interpretation of the proxy records. We investigated, in a first phase, in situ the influences of environmental parameters and physiology on the incorporation of proxies in Mytilus edulis at a well documented wave breaker site. In a second phase, in vitro culturing experiments under controlled laboratory conditions were carried out. Experiments were carried out at 8°C and 16°C and at salinities of 18‰ and 28‰. During these experiments mussels were fed under high and low supply regimes. By combining these in situ and in vitro approaches a white box multi-proxy model is generated for the reconstruction of SST and SSS

Non-linear State-space Model Identification from Video Data using Deep Encoders

Identifying systems with high-dimensional inputs and outputs, such as systems measured by video streams, is a challenging problem with numerous applications in robotics, autonomous vehicles and medical imaging. In this paper, we propose a novel non-linear state-space identification method starting from high-dimensional input and output data. Multiple computational and conceptual advances are combined to handle the high-dimensional nature of the data. An encoder function, represented by a neural network, is introduced to learn a reconstructability map to estimate the model states from past inputs and outputs. This encoder function is jointly learned with the dynamics. Furthermore, multiple computational improvements, such as an improved reformulation of multiple shooting and batch optimization, are proposed to keep the computational time under control when dealing with high-dimensional and large datasets. We apply the proposed method to a video stream of a simulated environment of a controllable ball in a unit box. The simulation study shows low simulation error with excellent long term prediction for the obtained model using the proposed method.Comment: Submitted to SYSID 202