A convolved multi-Gaussian probability distribution for surface topography applications

A convolved, multi-normal probability distribution model has been developed corresponding to the usual case of successively finer-scale Gaussian structure residing atop the worn upper extremities of the coarser texture immediately below—i.e. secondary structure existing on the worn summits and ridges of rougher primary structure, tertiary structure atop the secondary, etc. Quantification, involving nonlinear regression inside an iterative loop, begins with the global data mean and standard deviation as initial estimates, and yields means, standard deviations, and percent area coverage for all statistically significant structural components. The solution train stops automatically whenever one or more of several termination criteria is met. The method is illustrated graphically with examples of several typical engineered surfaces.