Tomas McKelvey

Subspace-based multivariable system identification from frequency response data

Two noniterative subspace-based algorithms which identify linear, time-invariant MIMO (multi-input/multioutput) systems from frequency response data are presented. The algorithms are related to the recent time-domain subspace identification techniques. The first algorithm uses equidistantly, in frequency, spaced data and is strongly consistent under weak noise assumptions. The second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions, promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure.

Subspace identification from closed loop data

The so-called subspace methods for direct identification of linear models in state space form have drawn considerable interest recently. They have been found to work well in many cases but have one drawback — they do not yield consistent estimates for data collected under output feedback. The present paper points to the reasons for this. We stress how the basic idea is to focus on the estimation of the state-variable candidates — the k-step ahead output predictors. By recomputing these from a ‘non-parametric’ (or, rather, high order ARX) one-step ahead predictor model, closed loop data can be handled.

A first-order statistical method for channel estimation

Multipath is a major impairment in a wireless communications environment, and channel estimation algorithms are of interest. We propose a superimposed periodic pilot scheme for finite-impulse response (FIR) channel estimation. A simple first-order statistic is used, and any FIR channel can be estimated. There is no loss of information rate but a controllable increase in transmission power. We derive the variance expression of our linear channel estimate and compare with the Cramer-Rao bound. Numerical examples illustrate the effectiveness of the proposed method.

Microwave-Based Stroke Diagnosis Making Global Prehospital Thrombolytic Treatment Possible

Here, we present two different brain diagnostic devices based on microwave technology and the associated two first proof-of-principle measurements that show that the systems can differentiate hemorrhagic from ischemic stroke in acute stroke patients, as well as differentiate hemorrhagic patients from healthy volunteers. The system was based on microwave scattering measurements with an antenna system worn on the head. Measurement data were analyzed with a machine-learning algorithm that is based on training using data from patients with a known condition. Computer tomography images were used as reference. The detection methodology was evaluated with the leave-one-out validation method combined with a Monte Carlo-based bootstrap step. The clinical motivation for this project is that ischemic stroke patients may receive acute thrombolytic treatment at hospitals, dramatically reducing or abolishing symptoms. A microwave system is suitable for prehospital use, and therefore has the potential to allow significantly earlier diagnosis and treatment than today.

Subspace-based identification of infinite-dimensional multivariable systems from frequency-response data

A new identification algorithm which identifies low complexity models of infinite-dimensional systems from equidistant frequency-response data is presented. The new algorithm is a combination of the Fourier transform technique with the recent subspace techniques. Given noisefree data, finite-dimensional systems are exactly retrieved by the algorithm. When noise is present, it is shown that identified models strongly converge to the balanced truncation of the identified system if the measurement errors are covariance bounded. Several conditions are derived on consistency, illustrating the trade-offs in the selection of certain parameters of the algorithm. Two examples are presented which clearly illustrate the good performance of the algorithm.

Frequency domain identification methods

Methods for estimating linear dynamical models from frequency data are studied, including the properties of frequency domain data generated by the discrete Fourier transform. The stochastic characteristics of the frequency domain data lead to a maximum likelihood (ML) formulation of the frequency domain estimation problem. Both discretetime and continuous time models are discussed. Consistency and variance of the ML estimate are described, and the connection with simpler frequency domain estimation schemes as well as the time domain ML method is pointed out.

Subspace-based system identification for an acoustic enclosure

This paper is aimed at identifying a dynamical model for an acoustic enclosure, a duct with rectangular cross section, closed ends, and side-mounted speaker enclosures. Acoustic enclosures are known to be resonant systems of high order In order to design a high performance feedback controller for an acoustic enclosure, one needs to have an accurate model of the system. Subspace-based system identification techniques have proven to be an efficient means of identifying dynamics of high order highly resonant systems. In this paper a frequency domain subspace-based method together with a second iterative optimization step minimizing a frequency domain least-squares criterion is successfully employed to identify a dynamical model for an acoustic enclosure.

Data driven local coordinates for multivariable linear systems and their application to system identification

In this paper we introduce a new parametrization for state-space systems: data driven local coordinates (DDLC). The parametrization is obtained by restricting the full state-space parametrization, where all matrix entries are considered to be free, to an affine plane containing a given nominal state-space realization. This affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state-space systems at the nominal realization. The application of the parametrization to prediction error identification is exemplified. Simulations indicate that the proposed parametrization has numerical advantages as compared to e.g. the more commonly used observable canonical form.

Frequency Domain Identification

Abstract Techniques to identify parametric transfer functions from noisy frequency domain data are considered. A maximum-likelihood estimation method is presented which in parallel with the system transfer function also estimates a parametric noise transfer function. This leads to a consistent and efficient estimator. It is shown how the discrete Fourier transform can be applied to generate frequency domain data from sampled time domain data. For the finite data case the exact frequency domain expressions are derived relating the transfer function with the discret Fourier transformed data for both continuous and discrete time systems.

Instantaneous Crankshaft Torque Measurements - Modeling and Validation

A simulation model for the dynamic properties of multi-cylinder engines is developed. Specifically, the model is used to describe the relation between the individual cylinder pressures and the resulting torque in the crankshaft. The model is validated against a 5-cylinder SI-engine equipped with a crankshaft integrated torque sensor. The simulation model developed is based on a system of first order nonlinear differential equations where the crankshaft dynamics are expressed as interconnected mass-spring-damper elements. The motivation is to investigate how instantaneous crankshaft torque measurements can be used to deduce information on the combustion process, cylinder by cylinder, for the purpose of engine control. Therefore, a computationally simple simulation method is introduced. For the model validation, an engine testbed has been developed which includes a standard production engine equipped with a crankshaft integrated magneto-elastic based torque sensor and cylinder pressure sensors. The torque sensor provides a crank-angle resolved measurement signal. The model was validated against measurements collected during engine tests at several load cases. The cylinder pressure signals acquired were used as input to the simulation model and the resulting simulated torque was compared with the measured torque signal with promising results.