Residual sensitivity function

Section 5.3.1 has shown that parameter sensitivities of ARR residuals may be obtained from an incremental bond graph. The latter bond graph can be systematically developed from an initial bond graph with nominal parameters by replacing elements with parameters to be estimated by their incremental component model. Inputs into the incBG are variations of the parameters to be estimated multiplied by a power variable of the initial BG. Outputs may be parameter variations of ARR residuals. They are a weighted sum of the parameter variations and the weighting factors are just the residual sensitivity functions. 

In the following, first, sensitivity pseudo bond graphs are briefiy reviewed and are then used to obtain residual sensitivity functions needed for the previously presented least squares ARR residuals minimisation. The simple hybrid network in Fig.4.1 is used again for illustration of the approach. 

Deducing Residual Sensitivity Functions from a Sensitivity Pseudo Bond Graph... 

A sensitivity pseudo bond graph from which residual sensitivity functions for parameter estimation can be deduced is constructed by simply replacing those elements in a DBG by their sensitivity component model whose parameters are to be estimated. Equations for parameter sensitivities of ARR residuals can then be deduced from the SPBG in the same way as the equations of a state space model are deduced from a behavioural BG or equations for ARR variations from an incBG. 

In the illustrating example, residual sensitivity functions have been deduced from a single SPBG as partial derivatives of ARR residuals with respect to a non-specific parameter 0. The parameter sensitivities of ARR residuals needed for the parameter estimation procedure are obtained by letting successively 9 be one of the parameters... 

Random mutagenesis studies on TM7 of rat SERT identified six amino acid residues as functionally significant by their sensitivity to nonconservative mutations (26). Four... 

In summary, the presumption from thermal curing data is that heating above 165 °C results in sulfur-sulfur bond rupture and weight loss. Since the degradation is not quantitative, the residual thiosulfate functionality renders the "cured" films somewhat water sensitive, resulting in swelling and weakening of the polymer upon exposure to water. 

Several of the reactions mentioned in this chapter proved to be successful for diastere-omerically pure but racemic substrates 355. No reason is seen why racemization or epimerization should occur and therefore application to optically active substrates is possible without expecting difficulties. Of course, one must take into account sensitive functional groups, eventually being present in the residues R and R. ... 

A variety of analytical techniques [e.g., radiochemical labeling [3-7], UV-VIS [8,9], HNMR [8,9], and CNMR [10-15] have been used to determine the initiator residues incorporated into vinyl polymers during their preparation. In general, these techniques are not sufficiently sensitive to the environment of the initiator derived functionality to allow assignment of its mode of incorporation into the polymer. However, by using labeled initiators, NMR has been successfully utilized to analyze the nature of initiator derived residues and functionalities in polystyrene. 

The mild reaction conditions employed enables the preparation of chlorides without disrupting chiral or other sensitive functionality. The use of hexane has been found particularly suitable for microscale preparation of high purity Mosher s acid chloride as it enables residual DMFCl to be filtered from solution (eq 2). ... 

Multiple parameter fault isolation by means of minimisation of least squares of ARR residuals needs residual parameter sensitivity functions if a gradient search based method is used. If ARRs can be derived in closed symbolic form from a bond graph, their analytical expressions can be used in the formulation of the least squares cost function and can be differentiated with respect to the vector of targeted parameters either numerically or residuals as functions of the targeted parameters can be differentiated symbolically. If ARRs are not available in symbolic form, they can be numerically computed by solving the equations of a DBG. 

Generally the conditions required to carry out the Horner-Wittig reaction are not compatible with sensitive functional groups such as hydroxy-, nitro-, and keto-aldehydes these residues must normally be protected. However, the use of a heterogeneous base such as K CO in either aqueous or organic media allows the condensation of these sensitive substrates with activated phosphorates to take place directly. The synthesis of Royal Jelly acid from 8-... 

NMR methods can be applied to give quantitative determination of initiator-derived and other end groups and provide a wealth of information on the polymerization process. They provide a chemical probe of the detailed initiation mechanism and a greater understanding of polymer properties. The main advantage of NMR methods over alternative techniques for initiator residue detection is that NMR signals (in particular nC NMR) are extremely sensitive to the structural environment of the initiator residue. This means that functionality formed by tail addition, head addition, transfer to initiator or primary radical termination, and various initiator-derived byproducts can be distinguished. 

Its suitable sensitivity to friction and impact (comparable to that of MF), its stability and high flame temp, render it very suitable for percussion-fuze use. An additional asset is that LNP functions in a practically smokeless manner, leaving little residue or slag Refs 1) Mellor 8 (1928), 887 2) E.R. von... 

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