Equilibrium Mechanism Based Curve Fitting and Data Smoothing Methods for Data With Single and Multiple Failure Mechanisms Available to Purchase

A recently developed equilibrium mechanism based linear curve/surface fitting method is extended for data with nonlinear characteristics. The concept of k-th order equilibrium ‘moment’ is proposed to derive curve fitting formulae for k-th order polynomial functions. An approach based on the equilibrium concept is also proposed for data smoothing with k-th order polynomial functions, and it is found that the formulae derived are exactly the same as the well-known Savitzky-Golay filter algorithm for smoothing and differentiation. Data pattern identification and characterization are emphasized in this paper for accurate linear and nonlinear data processing. Several examples are provided to demonstrate the developed concepts and procedures for test data with single and multiple underlying failure mechanisms or modes: fatigue crack growth rate under mixed-mode loading, stress-corrosion-cracking, corrosion-fatigue life, thermal-fatigue and creep-fatigue data. A curve fit procedure is also introduced for the creep-fatigue data with a specific data pattern.