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.     

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.     

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     

Performance analysis of general tracking algorithms

A general family of tracking algorithms for linear regression models is studied. It includes the familiar least mean square gradient approach, recursive least squares, and Kalman filter based estimators. The exact expressions for the quality of the obtained estimates are complicated. Approximate, and easy-to-use, expressions for the covariance matrix of the parameter tracking error are developed. These are applicable over the whole time interval, including the transient, and the approximation error can be explicitly calculated     

An analytical-numerical approach for parameter determination of a five-parameter single-diode model of photovoltaic cells and modules

Parameter extraction of the five-parameter single-diode model of solar cells and modules from experimental data is a challenging problem. These parameters are evaluated from a set of nonlinear equations that cannot be solved analytically. On the other hand, a numerical solution of such equations needs a suitable initial guess to converge to a solution. This paper presents a new set of approximate analytical solutions for the parameters of a five-parameter single-diode model of photovoltaic (PV) cells and modules. The proposed solutions provide a good initial point which guarantees numerical analysis convergence. The proposed technique needs only a few data from the PV current-voltage characteristics, i.e. open circuit voltage V_oc, short circuit current I_sc and maximum power point current and voltage I_m; V_m making it a fast and low cost parameter determination technique. The accuracy of the presented theoretical I–V curves is verified by experimental data.     

Issues in sampling and estimating continuous-time models with stochastic disturbances

The standard continuous time state space model with stochastic disturbances contains the mathematical abstraction of continuous time white noise. To work with well defined, discrete time observations, it is necessary to sample the model with care. The basic issues are well known, and have been discussed in the literature. However, the consequences have not quite penetrated the practice of estimation and identification. One example is that the standard model of an observation, being a snapshot of the current state plus noise independent of the state, cannot be reconciled with this picture. Another is that estimation and identification of time continuous models require a more careful treatment of the sampling formulas. We discuss and illustrate these issues in the current contribution. An application of particular practical importance is the estimation of models based on irregularly sampled observations.     

超高效液相色谱法测定山楂原料、提取物和相关食品中金丝桃苷和异槲皮苷的含量

目的 建立超高效液相色谱法测定山楂原料、提取物和相关食品中金丝桃苷和异槲皮苷的分析方法。方法 采用ACQUITY UPLC BEH C18柱, 以甲酸乙腈-甲酸水为流动相进行梯度洗脱分离金丝桃苷和异槲皮苷, 在紫外检测波长360 nm下进行检测, 外标法定量。结果 金丝桃苷和异槲皮苷的检出限(limit of detections, LODs, S/N=3)均为2 mg/kg, 定量限(limit of quantifications, LOQs, S/N=10)均为5 mg/kg; 在0.5~10.0 mg/L的浓度范围内线性关系良好, 相关系数均为0.999; 在原料、提取物和相关食品中, 金丝桃苷和异槲皮苷的平均回收率分别为83.0%~108.0%和86.2%~105.0%, 相对标准偏差(relative standard deviations, RSDs)分别为1.6%~5.7%和1.1%~3.9%。结论 本方法操作简便、快速、分离度和准确度高, 可用于山楂原料、提取物和相关食品的质量控制。     

The influence of contact zone configuration on the flow structure in a dissolved air flotation pilot plant

The dissolved air flotation process is used in water and wastewater treatment. Among many parameters the fluid dynamics determine the capacity of the process. The contact zone is assumed to be important for the removal function, as it is believed to be the location for the aggregation of bubbles and flocs. This paper presents an experimental study on the flow structure in a contact zone of a DAF pilot tank and the influence of contact zone configuration. The flow structure in the contact zone was examined for different horizontal lengths of the zone and for different heights and inclinations of the shaft wall. The hydraulic surface loading was 11 m/h over the total tank surface area and the recycle rate was constant at 10% of the main flow. The examined hydraulic surface loading over the contact zone ranged from 40 to 98 m/h. Water velocities in the longitudinal, central section of the tank were measured with an acoustical Doppler velocimeter in a grid net for the different contact zone configurations, giving an insight into the flow structure. The result showed that the flow structure in the contact zone was characterised by a turbulent lower region and a plug-flow higher region. The hydraulic surface loading, a function of the length of the contact zone, seemingly determined the extension of the turbulent region. A higher hydraulic surface loading decreased the turbulent region while the lower loading increased it. A hydraulic surface loading of 65 m/h was suggested for design. It was not possible to determine the turbulent intensity quantitatively due to the measurement method. The height and inclination of the shaft wall did not seem to have a significant influence on the turbulent region. However, an increased height of the contact zone enhanced the higher, plug flow region and a recommended height of 0.81 m or higher for the recommended hydraulic surface loading was suggested when both mixing and plug-flow are desired. The separation zone was characterised by a stratified flow structure, mainly influenced by the cross-flow velocity that is a function of the distance between the shaft wall top and the water surface. A cross-flow velocity of 37m/h or higher resulted in a clearly defined stratification, believed to be crucial for an efficient separation of flocs. Finally, the extension of the lower, denser plug-flow region in the separation zone increased when the shaft wall height increased.     

Biosensor assay for determination of haptoglobin in bovine milk

Despite more than 30 years of research into mastitis diagnostics, there are few alternatives to the somatic cell count (SCC) in practical use for identification of cows with subclinical mastitis. Mastitis is not only an animal welfare problem, but also affects the yield, composition and technological properties of milk. Hence, dairy cooperatives give farmers a premium quality payment to encourage low SCC although there is no clear scientific data defining the level of SCC in bulk tank milk that is associated with additional benefits in terms of milk quality. Recent research on alternative markers for inflammatory reactions in the lactating cow, e.g. in mastitis, includes investigations of the acute phase protein, haptoglobin (Hp). So far, the content of Hp in milk has mainly been studied in relation to mastitis diagnostics, with little attention given to its importance for milk composition and technological properties. At present, Hp in milk is measured using ELISA, but this technique is not suitable for routine large-scale analysis. In recent years, optical biosensor technology has been used for automated and rapid quantitative analysis of different components in milk, but so far not for analysis of acute phase proteins. The aim of the present study was to develop a rapid and sensitive biosensor method to determine Hp in milk. An affinity sensor assay based on the interaction between Hp and haemoglobin was developed using surface plasmon resonance (SPR) biosensor technology. The assay was used to analyse Hp in composite milk samples from cows without any clinical signs of mastitis and quarter milk samples with a weak to strong reaction in the California Mastitis Test (CMT). A commercial ELISA for determination of Hp in milk was used for comparison. The limit of detection (LOD) of the biosensor assay was determined as 1.1 mg/l. Within-assay and between-day variations were determined both with bulk tank milk spiked with human Hp and with composite milk samples containing bovine Hp. Coefficients of variation varied between 3.6 and 8.6% at concentrations between 4.0 and 12 mg/l, respectively. Agreement between the results obtained by the biosensor assay and the ELISA was satisfactory; however, the results obtained by the biosensor were generally lower than the results obtained by the ELISA. Possible explanations for this observation are discussed.