Iterative Weighted

Iterative Weighted Histogram Analysis Method (WHAM)... 

Guillaume P, Parloo E, De Sitter G (2002) Source identification fiom noisy response measurements using an iterative weighted pseudo-inverse approach. In Proceedings of ISMA2002 international conference on noise and vibration engineering, Leuven, pp 1817-1824... 

While the statistical weighting is elegant and rigorous if the uncertainties are known, its applicability is hmited because the uncertainties are seldom known. Commercial simulator models are yet unable to iterate on the parameter estimates against the unit measurements. And, the focus should be on a limited subset of the complete measurements set. 

Line 1 clears the screen and requests the input of the burst pressure of the vessel. Line 2 sets gamma to 1.4 and the absolute temperature to 300. If your pressure or temperature is different, edit the program Line 3 requests the molecular weight of the gas in the vessel. Lines 5-10 loop to perform the iteration. Line 6 iterates I ... 

The u) parameter determines the weight of the charge on the diagonal elements. Since Ga is calculated from the results (MO coefficients, eq. (3.90)), but enters the Hiickel matrix which produces the results (by diagonalization), such schemes become iterative. Methods where the matrix elements are modified by the calculated charge are often called charge iteration or self-consistent (Hiickel) methods. 

In a standard back-propagation scheme, updating the weights is done iteratively. The weights for each connection are initially randomized when the neural network undergoes training. Then the error between the target output and the network predicted output are back-propa-... 

A useful method of weighting is through the use of an iterative reweighted least squares algorithm. The first step in this process is to fit the data to an unweighted model. Table 11.7 shows a set of responses to a range of concentrations of an agonist in a functional assay. The data is fit to a three-parameter model of the form... 

FIGURE 11.9 Outliers, (a) Dose-response curve fit to all of the data points. The potential outlier value raises the fit maximal asymptote, (b) Iterative least squares algorithm weighting of the data points (Equation 11.25) rejects the outlier and a refit without this point shows a lower-fit maximal asymptote. 

Figure 1 Is a flow sheet showing some significant aspects of the Iterative analysis. The first step In the program Is to Input data for about 50 physical, chemical and kinetic properties of the reactants. Each loop of this analysis Is conducted at a specified solution temperature T K. Some of the variables computed In each loop are the monomer conversion, polymer concentration, monomer and polymer volume fractions, effective polymer molecular weight, cumulative number average molecular weight, cumulative weight average molecular weight, solution viscosity, polymerization rate, ratio of polymerization rates between the current and previous steps, the total pressure and the partial pressures of the monomer, the solvent, and the nitrogen.

The algebraic/iterative and the brute force methods are numerical respectively computational techniques that operate on the chosen mathematical model. Raw residuals r are weighted to reflect the relative reliabilities of the measurements. 

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