Residual generation

In general, residuals can be obtained as functions of the measured output ym and its estimate ji computed via the available mathematical model 

Ideally, residuals should be equal to zero in the absence of faults, while they should become nonzero after the occurrence of faults. Of course, in practice, they are always nonzero due to model uncertainties and disturbances. Since the residual generation is the most important issue of quantitative model-based fault diagnosis, most of the works in this research field have been focused on this problem. A wide variety of techniques are available in the literature (see, e.g., [8, 16] for a complete overview). Since a complete review is outwith the scope of this book, in the following, only the basic concepts of the main approaches are briefly discussed. 

The basic idea of observer-based approaches is to estimate the outputs of the system from available measurements by using suitably defined diagnostic observers. Then, the output estimation errors are used as residuals. For isolation purposes, a bank of observers can be adopted, where each observer computes an estimate of the system state sensitive to all faults but one. 

Approaches based on parameter estimation assume that the faults lead to detectable changes of physical system parameters. Therefore, FD can be pursued by comparing the estimates of the system parameters with the nominal values obtained in healthy conditions. The operative procedure, originally established in [23], requires an accurate model of the process (including a reliable nominal estimate of the model parameters) and the determination of the relationship between model parameters and physical parameters. Then, an online estimation of the process parameters is performed on the basis of available measures. This approach, of course, might reveal ineffective when the parameter estimation technique requires solution to a nonlinear optimization problem. In such cases, reduced-order or simplified mathematical models may be used, at the expense of accuracy and robustness. Moreover, fault isolation could be difficult to achieve, since model parameters cannot always be converted back into corresponding physical parameters, and thus the influence of each physical parameters on the residuals could not be easily determined. 

The basic idea of the parity equation approach [18, 52] is to provide a proper check of the consistency of the measured outputs with the known process inputs. The residuals are usually given by the value of the parity equations, which should be, ideally, zero in healthy conditions. Of course, in real situations, the residuals are nonzero due to measurement and process noise, model inaccuracies, and faults. These methods usually adopt linear or linearized models thus, difficulties can be encountered when dealing with complex and highly nonlinear systems. 

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The standard least-squares approach provides an alternative to the Galerkin method in the development of finite element solution schemes for differential equations. However, it can also be shown to belong to the class of weighted residual techniques (Zienkiewicz and Morgan, 1983). In the least-squares finite element method the sum of the squares of the residuals, generated via the substitution of the unknown functions by finite element approximations, is formed and subsequently minimized to obtain the working equations of the scheme. The procedure can be illustrated by the following example, consider... 

According to EPA (1974), pesticides such as endosulfan should be destroyed at high temperature in an approved incinerator with a hydrochloric acid scrubber, if available. Any sludges or solid residues generated from this process are to be disposed of in a manner approved by all applicable federal, state, and local pollution control requirements. EPA strongly recommends that if incineration of excess pesticides is not possible, organic pesticides should be buried in a designated landfill site. 

More Cl and O were observed by adding 1% O2 in CI2 and the amounts of residues were removed by wet cleaning process. It is expected that the residues generated during etching on the gate stack can be removed by wet cleaning process such as dilute HF. 

Run a set of standards of four or more concentration levels covering the expected range of residues. Generate a calibration curve for each analyte and obtain a linear regression with a correlation coefficient of at least 0.90 for each analyte. Do not use any sample run data if the combined regression for the standards run immediately before, during and after the samples does not meet this criterion. 

Benzene releases in byproduct recovery operations Naphthalene residues generated in the final cooling tower Sulfur and sulfur compounds recovered from coke oven gas Wastewater from cleaning and cooling (contains zinc, ammonia still lime, decanter tank tar, or tar distillation residues)... 

Ross, J., Thongsinthusak, T., Fong, H.R., Margetich, S., and Krieger, R. (1990) Measuring potential dermal transfer of surface pesticide residue generated from indoor fogger use an interim report, Chemosphere, 20 349-360. 

Such a method was first proposed by Wyatt and co-workers.43 7,56 In their so-called recursive residue generation method (RRGM), both eigenvalues and overlaps are obtained using the Lanczos algorithm, without explicit calculation and storage of eigenvectors. In particular, the residue in Eq. [41] can be expressed as a linear combination of two residues ... 

Phys., 104, 7807 (1996). Calculation of Vibrational (J=0) Excitation Energies and Band Intensities of Formaldehyde Using the Recursive Residue Generation Method. 

Quantum Dynamics The Recursive-Residue-Generation Method. 

Willoughby, Eds., North Holland, Amsterdam, 1986, pp. 67-79. Quantum Dynamics with the Recursive Residue Generation Method Improved Algorithm for Chain Propagation. 

The major side reaction associated with the use of mixed anhydrides is aminolysis at the carbonyl of the carbonate moiety (Figure 7.4, path B). The product is a urethane that resembles the desired protected peptide in properties, except that the amino-terminal substituent is not cleaved by the usual deprotecting reagents. Hence, its removal from the target product is not straightforward. The problem is serious when the residues activated are hindered (Val, lie, MeXaa), where the amounts can be as high as 10%. Other residues generate much less, but the reaction cannot be avoided completely, with the possible exception of activated proline (see Section 7.22). This is one reason why mixed anhydrides are not employed for solid-phase synthesis. 

P.M. Frank and X. Ding. Survey of robust residual generation and evaluation methods in observer-based fault detection systems. J. Process Control, 7(6) 403-424, 1997. 

Listed hazardous wastes may be process residuals generated during the manufacture of the pesticide itself... 

There are demethylases which act like amine oxidases that are dependent in their mechanism on their cosubstrate flavine adenine dinucleotide (FAD). So far, lysine-specific demethylase 1 (LSDl) is the only representative of this class [62]. LSDl, as an amine oxidase leads to oxidation of the methylated lysine residue, generating an imine intermediate, while the protein-bound cosubstrate FAD is reduced to FAD H2. In a second step, the imine intermediate is hydrolyzed to produce the demethylated histone lysine residue and formaldehyde. Importantly the reduced cosubstrate is regenerated to its oxidized form by molecular oxygen, producing hydrogen peroxide (Figure 5.7) [62, 63]. 

Killday etal. (1988) also provided evidence for internal autoreduction of ferric nitrosyl heme complexes, as previously proposed by Giddings (1977). Heating of chlorohemin( iron-III) dimethyl ester in dimethyl sulfoxide solution with imidazole and NO produced a product with an infrared spectra identical to that of nitrosyl iron(ll) protoporphyrin dimethyl ester prepared by dithionite reduction. Both spectra clearly showed the characteristic nitrosyl stretch at 1663 and 1665 cm. They thus proposed a mechanism for formation of cured meat pigment which includes internal autoreduction of NOMMb via globin imidazole residues. A second mole of nitrite is proposed to bind to the heat-denatured protein, possibly at a charged histidine residue generated in the previous autoreduction step. 

Manufacturing and processing wastes include all residuals generated from material inputs that leave the plant as product output. Office and packaging wastes associated with this sector are included in the urban waste sector. The majority of these wastes are from pulp and paper manufacturing, primary and secondary wood manufacturing, and the construction industry. 

N. M. Poulin, M. J. Bramley, T. Carrington Jr., H. G. Kjaergaard, and B. R. Henry, J. Chem. Phys., 104, 7807 (1996). Calculation of Vibrational (/ = 0) Excitation Energies and Band Intensities of Formaldehyde Using the Recursive Residue Generation Method. 

Total Production, Residue Generation, and Gross Energy Amounts for Three Major Commodity Crops in the United States"... 

Lignocellulosic agroindustrial byproducts are renewable, widespread, and generally an inexpensive source of biomass. Brewery s spent grain (BSG) is a disposal residue generated throughout the year in large amounts, for... 

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