CURVE-FITTING USING NATURAL COMPUTATION

In curve fitting the most commonly used technique is an iterative hill-climbing procedure that makes use of partial derivatives to calculate the steepest path to an optimum in solution space. However, reliable and accurate initial estimates of the number of peaks, individual peak positions, heights, and widths are necessary to find acceptable solutions. One of the main drawbacks involved is that as the number of overlapping peaks increases, the problem becomes progressively more ill-conditioned. Consequently, small errors in the data (e.g., noise or baseline distortions), errors in the mathematical model, or errors in the estimates can be magnified, leading to large errors in the parameters of the final model. In addition to this, more overlapping peaks can lead to ambiguous fitting results. Ambiguous fitting is a general problem in curve fitting and is not limited to the steepest hill-climbing methods only. In this article we present a method for peak detection using artificial neutral networks and a global search technique for curve fitting based on evolutionary search strategies which does not need accurate estimates and is less sensitive to local optima than steepest descent procedures. These statements are corroborated in our comparative case study, which involves the fitting of a series of spectra with strongly overlapping peaks: X-ray equator diffractometer scans of poly(ethylene naphthalate) yarns.