An Autocorrelation Term Method for Curve Fitting

Abstract

The least-squares method is the most popular method for fitting a polynomial curve to data. It is based on minimizing the total squared error between a polynomial model and the data. In this paper we develop a different approach that exploits the autocorrelation function. In particular, we use the nonzero lag autocorrelation terms to produce a system of quadratic equations that can be solved together with a linear equation derived from summing the data. There is a maximum of solutions when the polynomial is of degree . For the linear case, there are generally two solutions. Each solution is consistent with a total error of zero. Either visual examination or measurement of the total squared error is required to determine which solution fits the data. A comparison between the comparable autocorrelation term solution and linear least squares shows negligible difference.

Prediction of hot ductility of steels from elemental composition and thermal history by deep neural networks

“…For this reason, the model is not accurate when predicting the ductility trough in high-carbon and high-alloy steels in which the distribution of the trough does not have a U or V shape, so another model for high-carbon and high-alloy steels should be developed. Also, a model that uses DNN should be developed to predict actual RA values at each temperature [51,52].…”