Differentiable structure of a representative function for experimental data and treatment of errors due to noise.

Abstract

Although it is possible and effective to obtain numerical solutions to differential equations which dominate observed phenomena in experiments, indiscriminate use of the conventional formulas in numerical differentiation leads to poor accuracy in analysis. The authors propose new theories and algorithms not only for analysis of the differentiable structure of a representative function for experimental data but also for treatment of errors due to noise. The numerical differentiation formulas are derived from the concept of differentiation of smoothing polynomials. Namely, the least squares approximation in terms of the central difference is adopted using local quadratic functions with a single variable. Taking two dimensional photoelastic data, that is, isochromatics and iso-clinics, as examples, several differential equations are examined. The results show that the new approach is applicable for quantitative evaluation of stress with good accuracy.