System identification from noisy measurements by using instrumental variables and subspace fitting

This paper considers the estimation of the parameters of a linear discrete-time system from noise-perturbed input and output measurements. The conditions imposed on the system are fairly general. In particular, the input and output noises are allowed to be auto-correlated and they may be cross-correlated as well. The proposed method makes use of an instrumental variable (IV)-vector to produce a covariance matrix that is pre- and postmultiplied by some prechosen weights. The singular vectors of the so-obtained matrix possess complete information on the system parameters. A weighted subspace fitting (WSF) method is then applied to the aforementioned singular vectors to consistently estimate the parameters of the system. The IV-WSF technique suggested herein is noniterative and easy to implement, and has a small computational burden. The asymptotic distribution of its estimation errors is derived and the result is used to motivate the choice of the weighting matrix in the WSF step and also to predict the estimation accuracy. Numerical examples are included to illustrate the performance achievable by the method.This work has been supported by the Swedish Research Council of Engineering Sciences under contract 93-669 and by the Göran Gustafsson Foundation.     

An organometallic RhIII complex with a distorted octahedral structure: (acetonitrile‐κN)dimethyl(1,4,7‐trimethyl‐1,4,7‐triazacyclononane‐κ3N,N′,N′′)rhodium(III) tetraphenylborate

In the title compound, [Rh(CH₃)₂(C₂H₃N)(C₉H₂₁N₃)](C₂₄H₂₀B), the geometry around the Rh^III centre is distorted octahedral, with elongated Rh—N bonds trans to the metal‐bonded methyl groups. The metal‐containing cations are located in channels formed by an anionic supramolecular mesh, in which aromatic π–π interactions between anionic [B(Ph)₄]^? units play a major role.     

Dynamics of the periodic type-K competitive Kolmogorov systems

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related.     

MODE-type algorithm for estimating damped, undamped, or explosive modes

We propose a new algorithm for estimating the parameters of damped, undamped, or explosive sinusoidal signals. The algorithm resembles the MODE algorithm, which is commonly used for direction of arrival estimation in the array signal processing field. It is derived as a natural approximation to an asymptotically (high-SNR) optimal parameter estimator and has excellent statistical accuracy. Nevertheless, it is computationally simple and easy to implement. Numerical examples are included to illustrate the performance of the proposed method.This work has been supported by the Swedish Research Council for Engineering Sciences (TFR).     

Crystal structure and magnetic properties of two new cobalt selenite halides: Co5(SeO3)4X2 (X=Cl, Br)

Two new isostructural cobalt selenite halides Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂ have been synthesized. They crystallize in the triclinic system space group P−1 with the following lattice parameters for Co₅(SeO₃)₄Cl₂: a=6.4935(8) Å, b=7.7288(8) Å, c=7.7443(10) Å, α=66.051(11)°, β=73.610(11)°, γ=81.268(9)°, and Z=1. The crystal structures were solved from single-crystal X-ray data, R1=3.73 and 4.03 for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively. The new compounds are isostructural to Ni₅(SeO₃)₄Br₂.Magnetic susceptibility measurements on oriented single-crystalline samples show anisotropic response in a broad temperature range. The anisotropic susceptibility is quantitatively interpreted within the zero-field splitting schemes for Co²⁺ and Ni²⁺ ions. Sharp low-temperature susceptibility features, at T_N=18 and 20 K for Co₅(SeO₃)₄Cl₂ and Co₅(SeO₃)₄Br₂, respectively, are ascribed to antiferromagnetic ordering in a minority magnetic subsystem. In isostructural Ni₅(SeO₃)₄Br₂ magnetically ordered subsystem represents a majority fraction (T_N=46 K). Nevertheless, anisotropic susceptibility of Ni₅(SeO₃)₄Br₂ is dominated at low temperatures by a minority fraction, subject to single-ion anisotropy effects and increasing population of S_z=0 (singlet) ground state of octahedrally coordinated Ni²⁺.     

Design and evaluation of an active electromechanical wheel suspension system

This paper presents an electromechanical wheel suspension, where the upper arm of the suspension has been provided with an electric levelling and a damper actuator, both are allowed to work in a fully active mode. A control structure for the proposed suspension is described. The complex design task involving the control of the electric damper and its machine parameters is tackled by genetic optimisation. During this process, these parameters are optimised to keep the power dissipation of the electric damper as low as possible, while maintaining acceptable comfort and road-holding capabilities. The results of the evaluations carried out demonstrate that the proposed suspension can easily adopt its control parameters to obtain a better compromise of performance than that offered by passive suspensions. If the vehicle is to maintain acceptable performance during severe driving conditions, the damper has to be unrealistically large. However, if the electric damper is combined with a hydraulic damper, the size of the electric damper is significantly reduced. In addition, the design of the electric damper with the suggested control structure, including how it regenerates energy, is discussed.     

Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

Pyrolysis—field ionization mass spetrometric investigation of polymeric heterocycles: I. polyquinolines and polyquinoxalines

Pyrolysis—field ionization mass spectrometry was used for the investigation of the mechanism of the thermal degradation of polymeric heterocycles. Heat-resistant polymers containing aromatic and heterocyclic units such as polyquinolines and polyquinoxalines have a strong tendency to form large condensed systems during pyrolysis, and finally will carbonize. In the course of this process, side-groups (phenyl) and small fragments (NH₃, HCN, acetonitrile, acrylonitrile, etc.) are split off. In addition, large heteroatom-containing fragments such as nitriles can be identified. These, together with some fragments that contain the complete heterocyclic ring, are characteristic of the chain building units (“key fragments”). Furthermore, compounds generated by recombination reactions and intramolecular cyclization are constituents of the pyrolysate.     

Crosslinked polystyrene with improved mechanical properties

The synthesis of some divinyl monomers—bis(vinylphenyl)ethane ( 2 ), bis(vinylbenzyloxy)hexane ( 3a ), and bis(vinylbenzyloxy)dodecane ( 3b ) is reported. Copolymers of the new monomers and styrene were evaluated as an alternative to divinylbenzene-crosslinked polymers for use as matrices and absorbents. The mechanical properties and the amount of residual double bonds in the copolymers were compared. It was found that the new copolymers, unlike the divinylbenzene-crosslinked polymers, retained their mechanical strength even at high crosslinking degrees. Stress at break values of 79, 68, and 18 N/mm² were found for the polymers crosslinked with 20 mol % of 3a, 2 , and divinylbenzene; 5, 25 and 45% of the divinyl units in these polymers were left as pendant double bonds. Porous styrene– 2 copolymers were synthesized and shown to have lower surface areas than the corresponding divinylbenzene-crosslinked polymers. The pore size distribution showed that this was due to the absence of the smallest pores which are found in the divinylbenzene-crosslinked polymers in between heavily crosslinked nodules. © 1993 John Wiley & Sons, Inc.     

Independent component analysis yields chemically interpretable latent variables in multivariate regression

This work shows that independent component analysis (ICA) can be used to obtain statistically independent and, therefore, chemically interpretable latent variables (LVs) in multivariate regression. Two novel algorithms based on ICA are introduced and compared with two classical methods on simulated data: principal component regression and partial least-squares regression. All methods compared yield accurate predictions, but only those based on ICA yield LVs that are chemically interpretable. Practical limitations of ICA-based regression with respect to the underlying assumptions, sample size, and measurement noise are discussed and illustrated by means of simulations.