Lightly damped systems exhibit strong resonances which should be accurately characterised to prevent potential harmful damage in real-world applications. Characterising these resonances using frequency response function measurements is challenging due to long transient behaviour and spectral leakage. Local modelling techniques exist which allow to remedy these difficulties but they introduce a bias or do not use an appropriate model structure. In this paper, we solve these problems by developing two local rational modelling techniques which remove the bias on the frequency response function measurement. The proposed techniques involve the use of the bootstrapped total least squares estimator on the one hand and the incorporation of prior knowledge of the pole locations on the other hand. Furthermore, the performance of both techniques is demonstrated by measuring the flexural vibrations of a steel beam.

A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leakage) errors cause important bias and variance errors in the FRF estimate. To decrease these errors, several local modeling techniques have been proposed in the literature. This paper presents an overview of the existing methods and gives an indepth bias and variance analysis of the FRF and disturbing noise variance estimates. In addition, a new local modeling approach is described that combines the small bias error of the local rational approximation with the low noise sensitivity of the local polynomial approximation. It is based on an automatic local model order selection procedure applied to a specific subclass of rational functions.

The low frequency Forced Oscillation Technique (FOT) has a high diagnostic potential for the detection of respiratory diseases. However, it is not yet widely accepted in clinical practice, partly because the natural breathing frequency usually interferes with the measurement, thus requiring patientunfriendly breathing maneuvers. The presence of a subject's breathing generally results in patient-unfriendly measurement protocols. These are needed to extract the important low frequency information about the subject's respiratory system.This work presents a technique enabling the application of low frequency FOT during spontaneous breathing. This is accomplished by adding an external visual stimulus to encourage the subject to synchronize his/her breathing to the measurement apparatus, in combination with an excitation signal that is adapted to the subject's natural breathing frequency. This way, the contributions of the breathing and the excitation signal can be separated. This paper discusses the implementation, testing and the actual measurement results in a clinical setting using this method.

A Distortion Contribution Analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its sub-circuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the actual source of the distortion. Classically, the DCA uses the Volterra theory to model the circuit and its sub-circuits. This DCA has been proven useful for small circuits or heavily simplified examples. In more complex circuits however, the amount of contributions increases quickly, making the interpretation of the results difficult. In this paper, the Best Linear Approximation (BLA) is used to perform the DCA instead. The BLA represents the behaviour of a sub-circuit as a linear circuit with the unmodelled distortion represented by a noise source. Combining the BLA with a classical noise analysis yields a DCA which is simple to understand, yet capable to handle complex excitation signals and complex strongly non-linear circuits.

Old and recent experiments show that there is a direct response to the heating power of transport observed in modulated ECH experiments both in tokamaks and stellarators. This is most apparent for modulated experiments in the Large Helical Device (LHD) and in Wendelstein 7 advanced stellarator (W7-AS). In this paper we show that: (1) this power dependence can be reproduced by linear models and as such hysteresis (in flux) has no relationship to hysteresis as defined in the literature; (2) observations of ‘hysteresis’ (in flux) and a direct response to power can be perfectly reproduced by introducing an error in the estimated deposition profile as long as the errors redistribute the heat over a large radius; (3) non-local models depending directly on the heating power can also explain the experimentally observed Lissajous curves (hysteresis); (4) how non-locality and deposition errors can be recognized in experiments and how they affect estimates of transport coefficients; (5) from a linear perturbation transport experiment, it is not possible to discern deposition errors from non-local fast transport components (mathematically equivalent). However, when studied over different operating points non-linear-non-local transport models can be derived which should be distinguishable from errors in the deposition profile. To show all this, transport needs to be analyzed by separating the transport in a slow (diffusive) time-scale and a fast (heating/non-local) time-scale, which can only be done in the presence of perturbations.