Empirical identifications technique

Most work on the development of dynamic process models has been empirical this work is usually referred to as process identification. As mentioned earlier, two classes of empirical identification techniques are available one uses deterministic (step, pulse, etc.) functions, the other stochastic (random) identification functions. With either technique, the process is perturbed and the resulting variations of the response are measured. The relationship between the perturbing variable and the response is expressed as a transfer function. This function is the process model. Empirical identification of process models by the deterministic method has been reported by various workers [55-58]. A drawback of this method is the difficulty in obtaining a measurable response while restricting the process to a linear response (small perturbation). If the perturbation is large, the process response will be nonlinear and the representations of the process with a linear process model will be inaccurate. 

For continuous process systems, empirical models are used most often for control system development and implementation. Model predictive control strategies often make use of linear input-output models, developed through empirical identification steps conducted on the actual plant. Linear input-output models are obtained from a fit to input-output data from this plant. For batch processes such as autoclave curing, however, the time-dependent nature of these processes—and the extreme state variations that occur during them—prevent use of these models. Hence, one must use a nonlinear process model, obtained through a nonlinear regression technique for fitting data from many batch runs. 

Structural analysis from electronic spectra yields little information because of their relative simplicity. In the 1940s, however, before the advent of more powerful identification techniques, UV/VIS visible spectroscopy was used for structural identification. The study of a great number of spectra of various molecules has revealed correlations between structures and the positions of absorption maxima. The most widely known empirical rules, due to Woodward, Fieser and Scott, involve unsaturated carbonyls, dienes and steroids. Using incremental tables based on various factors and structural features, it is possible to predict the position of the n —> n absorption bands in these conjugated systems (Table 11.3). Agreement between the calculated values and the experimentally determined position of absorption bands is usually good, as can been seen by the following four examples ... 

Implementation Issues A critical factor in the successful application of any model-based technique is the availability of a suitaole dynamic model. In typical MPC applications, an empirical model is identified from data acquired during extensive plant tests. The experiments generally consist of a series of bump tests in the manipulated variables. Typically, the manipulated variables are adjusted one at a time and the plant tests require a period of one to three weeks. The step or impulse response coefficients are then calculated using linear-regression techniques such as least-sqiiares methods. However, details concerning the procedures utihzed in the plant tests and subsequent model identification are considered to be proprietary information. The scaling and conditioning of plant data for use in model identification and control calculations can be key factors in the success of the apphcation. 

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

Capillary electrophoresis (CE) either coupled to MS or to laser-induced fluorescence (LIF) is less often used in metabolomics approaches. This method is faster than the others and needs a smaller sample size, thereby making it especially interesting for single cell analysis [215] The most sensitive mass spectrometers are the Orbitrap and Fourier transform ion cyclotron resonance (FT-ICR) MS [213]. These machines determine the mass-to-charge ratio of a metabolite so accurate that its empirical formula can be predicted, making them the techniques of choice for the identification of unknown peaks. 

An ion containing a less abundant combination of isotopes, also included under P.I.D., is not classified separately because identification is usually more simple from the more abundant isotopic combination. The mass number and relative abundance of isotopic ions can be calculated from the accompanying table. It might be argued that classification of these could be useful where the more abundant isotopic combination is obscured by another ion of nominally identical mass. This, however, will be an unusual circumstance and can be overcome by careful use of the table or by the use of exact empirical structure determination through high resolution techniques. 

The IR-spectra of very many — perhaps most — new inorganic coordinate complexes are yearly recorded. Most of these spectra are just fingerprinting and identification purposes or for empirical correlations and predictions. There is a definite need to put most of these empirical correlations — some of the evidence is usually very flimsy, spectroscopically speaking, and the reader is warned not to put too much faith in it - on a firmer footing through normal-coordinate analyses. Only a few solid state compounds were described by such theoretical techniques in the past few years, the most important being listed below. 

It is an empirical finding that the diffraction patterns of many organic explosives display prominent diffraction peaks that lend themselves to material identification [13]. XDI is sensitive to a wide range of explosives, and its low false-alarm rate (FAR) when confronted with the harmless materials that comprise the vast majority of suitcase contents is unsurpassed by alternative bulk detection techniques. 

While luminescence in vapor-deposited matrices accordingly should be a powerful technique for detection and quantitation of subnanogram quantities of PAH in complex samples, it suffers from two major limitations. First, it is obviously limited to the detection of molecules which fluoresce or phosphoresce, and a number of important constituents of liquid fuels (especially nitrogen heterocyclics) luminesce weakly, if at all. Second, the identification of a specific sample constituent by fluorescence (or phosphorescence) spectrometry is strictly an exercise in empirical peak matching of the unknown spectrum against standard fluorescence spectra of pure compounds in a hbrary. It is virtually impossible to assign a structure to an unknown species a priori from its fluorescence spectrum qualitative analysis by fluorometry depends upon the availabihty of a standard spectrum of every possible sample constituent of interest. Inasmuch as this latter condition cannot be satisfied (particularly in view of the paucity of standard samples of many important PAH), it is apparent that fluorescence spectrometry can seldom, if ever, provide a complete characterization of the polycyclic aromatic content of a complex sample. 

Once a range of suitable pH and ionic strength are selected, the effect on protein stability is evaluated for the final selection of an optimal formulation pH. Only when the optimal pH and addition of common salts do not render the desired solubility are other additives considered. This adds to the complexity of the formulation and the challenge of maintaining stability. Recently, an empirical approach to determine protein phase diagrams using various biophysical techniques has been used to facilitate identification of optimal formulation conditions (Fan etal., 1995). 

For biomarker identification, it is also possible to separate out substances of interest from a complex biofluid sample using techniques such as solid phase extraction or HPLC. For metabolite identification, directly coupled chromatography-NMR spectroscopy methods can be used. The most powerful of these hyphenated approaches is HPLC-NMR-MS [24] in which the eluting HPLC peak is split with parallel analysis by directly coupled NMR and MS techniques. This can be operated in on-flow, stopped-flow, and loop-storage modes and thus can provide the full array of NMR and MS-based molecular identification tools. These include MS-MS for identification of fragment ions and FT-MS or TOF-MS for accurate mass measurement and hence derivation of molecular empirical formulae. 

Scanning electron microscopy (SEM) with an x-ray analyzer and transmission electron microscopy (TEM) are the most common techniques in electron microscopy. In the former technique, samples are scanned at 600 X and 2000 X and the metal ratios are quantitated from x-ray data. Element mass ratios, cation/anion ratios, and morphology are compared with empirical data from reference standards to identify the asbestos type. Air, water, and bulk samples may be analyzed by this technique. In blind tests, the correct identifications were made for more than 94% of fibers (Sherman et al. 1989). 

---