(507e) Data Smoothing and Numerical Differentiation by a Regularization Method

While data smoothing by regularization is not new, the method has been little used by scientists and engineers to analyze noisy data. The method is especially useful for determining numerical derivatives of the data trend, where the usual finite-difference methods amplify the noise. Noise amplification by numerical differentiation can be especially severe for oversampled data, which often result from experiments that employ modern electronic data acquisition. The general concepts of the smoothing method and mathematical development necessary for implementation are presented for a variety of data types. The method can easily accommodate unequally spaced and even non-monotonic scattered data. Methods for scaling the regularization parameter and determining its optimal value are also presented. Additionally, it is shown how the smoothing method can be subjected to constraints that are known a priori from the physics or chemistry of the system of study. The utility of the smoothing method is illustrated with a few examples that are relevant to the chemical engineering discipline.