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 solut ions. One of the main drawbacks involved is that as the number of over lapping peaks increases, the problem becomes progressively more ill-co nditioned. Consequently, small errors in the data (e.g., noise or base line 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 le ad to ambiguous fitting results. Ambiguous fitting is a general proble m in curve fitting and is not limited to the steepest hill-climbing me thods only. In this article we present a method for peak detection usi ng artificial neutral networks and a global search technique for curve fitting based on evolutionary search strategies which does not need a ccurate estimates and is less sensitive to local optima than steepest descent procedures. These statements are corroborated in our comparati ve 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.