Nonlinear black-box models in system identification: Mathematical foundations

We discuss several aspects of the mathematical foundations of the nonlinear black-box identification problem. We shall see that the quality of the identification procedure is always a result of a certain trade-off between the expressive power of the model we try to identify (the larger the number of parameters used to describe the model, the more flexible is the approximation), and the stochastic error (which is proportional to the number of parameters). A consequence of this trade-off is the simple fact that a good approximation technique can be the basis of a good identification algorithm. From this point of view, we consider different approximation methods, and pay special attention to spatially adaptive approximants. We introduce wavelet and ‘neuron’ approximations, and show that they are spatially adaptive. Then we apply the acquired approximation experience to estimation problems. Finally, we consider some implications of these theoretical developments for the practically implemented versions of the ‘spatially adaptive’ algorithms.     

4,4‐Dimethyl‐ and Diastereomeric 4‐Hydroxy‐4‐methyl‐ (2S)‐Glutamate Analogues Display Distinct Pharmacological Profiles at Ionotropic Glutamate Receptors and Excitatory Amino Acid Transporters

Subtype‐selective ligands are of great interest to the scientific community, as they provide a tool for investigating the function of one receptor or transporter subtype when functioning in its native environment. Several 4‐substituted (S)‐glutamate (Glu) analogues were synthesized, and altogether this approach has provided important insight into the structure–activity relationships (SAR) for ionotropic and metabotropic glutamate receptors (iGluRs and mGluRs), as well as the excitatory amino acid transporters (EAATs). In this work, three 4,4‐disubstituted Glu analogues 1 – 3 , which are hybrid structures of important 4‐substituted Glu analogues 4 – 8 , were investigated at iGluRs and EAATs. Collectively, their pharmacological profiles add new and valuable information to the SAR for the iGluRs and EAAT1–3.     

Rheological Properties of Concentrated, Nonaqueous Silicon Nitride Suspensions

The rheological properties of nonaqueous silicon nitride powder suspensions have been investigated using steady shear and viscoelastic measurements. The polymeric dispersant, Hypermer KD-3, adsorbed strongly on the powder surfaces, and colloidally stable, fluid suspensions up to a volume fraction of φ= 0.50 could be prepared. The concentrated suspensions all displayed a shear thinning behavior which could be modeled using the high shear form of the Cross equation. The viscoelastic response at high concentrations was dominated by particle interactions, probably due to interpenetration of the adsorbed polymer layers, and a thickness of the adsorbed Hypermer KD-3 layer, Δ∼10 nm, was estimated. The volume fraction dependences of the high shear viscosity of three different silicon nitride powders were compared and the differences, analyzed by using a modified Krieger-Dougherty model, were related to effective volume effects and the physical characteristics of the powders. The significantly lower maximum volume fraction, φ_m= 0.47, of the SN E-10 powder was referred to the narrow particle size distribution and the possibility of an unfavorable particle morphology.     

Evaluation of prestress losses in prestressed concrete specimens subjected to freeze–thaw cycles

Prestressed concrete structures are considered to be reliable and durable. However, their long-term performance when subjected to frost attack is still unclear. In this work, experiments were carried out to evaluate the prestress losses in post-tensioned prestressed concrete specimens subjected to freeze–thaw cycles (FTCs). Two cases were considered: in one case, a series of specimens were prepared and tested in a freeze–thaw chamber; in the second case, the same series of specimens were tested in an indoor environment (outside the chamber). The difference between the prestress losses of the specimens inside the freeze–thaw chamber and those outside the chamber equalled the prestress losses due to FTCs. When using mathematical models to predict the prestress losses due to the FTCs, it was found that they were relatively small when the concrete was slightly damaged. However, they increased rapidly when the FTCs were repeated. The eccentricity of the prestress wires led to larger prestress losses when subjected to FTCs. Moreover, the same cross section and eccentricity resulted in similar prestress losses due to the FTCs, and the relatively high-strength concrete could withstand more FTCs.     

Mobilisation of heavy metals by deicing salts in a roadside environment

The seasonal variations of some selected heavy metals (Cd, Cu, Pb and Zn) and principal anions in soil solutions were monitored as a function of distance from the road at two field sites in Sweden. During the winter, the conductivity, concentrations of dissolved sodium and chloride increased dramatically due to the application of deicing agents (i.e. NaCl). Due to ion exchange, the pH decreased one unit in the soil solutions, whereas the concentrations of total organic carbon decreased due to coagulation and/or sorption to stationary solids. The heavy metal concentrations increased during the winter, but through different mechanisms. Cadmium concentrations in the aqueous phase increased as a response to ion exchange, possibly also enhanced by the formation of chloride complexes. Similarly, the concentrations of zinc increased, due to ion exchange, with calcium and protons. The mechanisms of mobilisation for copper and lead were not that clear probably due to association with coagulated or sorbed organic matter in combination with colloid dispersion.     

Structural classification of Quillaja saponins by electrospray ionization ion trap multiple-stage mass spectrometry in combination with multivariate analysis, proof of concept

MS² and MS³ spectra of thirteen previously identified saponin structures from Quillaja saponaria Molina were obtained by electrospray ionization ion trap multiple-stage mass spectrometry (ESI-ITMSⁿ) in positive ion mode. The spectra were analysed by partial least squares regression-discriminant analysis (PLS-DA) yielding a method that can classify the spectra according to saponin structure. For this method a referencing of the m/z axis was essential to obtain a correlation between peaks in the spectra and common structural elements. The MS² and MS³ spectra could be classified according to the structures of the oligosaccharides at C-3 and C-28 of the corresponding saponins. Terminal residues with the same mass, such as β-d-Apif and β-d-Xylp, could also be distinguished. The PLS-DA method was applied on Quillaja saponins separated from a commercial bark extract by reversed-phase chromatography.The method outlined here is applied on a specific group of Quillaja saponins, but can be used on other types of glycoconjugates. Combination of this technique with chromatography would give a very powerful tool for rapid identification of components in complex mixtures.     

Forces Measured between Zirconia Surfaces in Poly(acrylic acid) Solutions

We have studied the forces between a sphere and a plane surface of yttria-partially-stabilized tetragonal-zirconia immersed in aqueous solutions of low-molecular-weight ( M _w= 10 000) poly(acrylic acid) (PAA) using atomic force microscopy. The measurements are performed at high pH where the adsorbed, highly charged anionic polyelectrolyte extends far into the solution, resulting in a combination of polymeric (steric) and electrostatic interactions. Analysis of the experimental data using scaling theory shows that the polymeric contribution dominates and that the electrostatic contribution is small at relatively high ionic strength (0.01 M NaCl). We find that the measured forces are highly dependent on time and interaction history of the absorbed PAA layer; consecutive compression-decompression cycles result in an increase of the surface coverage and the range of the repulsive polymeric interaction. This buildup of PAA at the interface is strongly related to attractive bridging interactions manifested as strong adhesion during decompression at less than full surface coverage. The force results are compared to rheological observations of zirconia suspensions stabilized by the same dispersant; the poor colloidal stability and high viscosity at low surface coverage of PAA are related to the attractive bridging interactions.     

Molecular mechanisms involved in creep phenomena of paper

The phenomenon of mechanosorptive creep (i.e., the increasing creep occurring in some hygroscopic materials subjected to moisture cycling) was studied for paper from a molecular point of view. Paper was tested in creep at different loading levels in a constant high humidity of 90% relative humidity (RH) and in a cyclic climate between 30 and 90% RH. Throughout the creep tests, spectra from the mid‐ and near‐IR, as well as dynamic mechanical data, were recorded to determine molecular changes occurring with time. In tensile stress scans the instantaneous, dynamic elastic modulus was found to increase. It is suggested that this increase was due to orientation of the cellulose molecules, which was detected as changes in the mid‐IR spectra at 1160 cm⁻¹ assigned to the C₁ O C₄ stretching. During creep in constant and cyclic humidity, the modulus was found to increase with time, more so for the cyclic humidity. Changes in the mid‐IR spectra at 1184 and 1030 cm⁻¹, which is assigned to CH₂, CH, and C O, may indicate sliding between the cellulose chains. The near‐IR measurements mainly showed differences in the moisture content. In stress scans the moisture content increased with increasing tensile load. In creep at constant 90% RH, the moisture content was also found to increase in a manner similar to the stress scan. In the cyclic humidity with a conditioning time of 70 min at 90% RH the moisture content decreased successively with increasing numbers of cycles. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 1590–1595, 2001