Differentiation of Noisy Experimental Data for Interpretation of Nonlinear Stress-Strain Behavior

Interpretation of nonlinear stress-strain behavior of a material may require differentiating the load-displacement curve constructed from experimental data. Pressuremeter and torsional shear tests in geotechnical engineering are two examples that require such an operation. Differentiating experimental data is tricky because (1) it is very sensitive to the noise inevitably existing in the measurements, and (2) the experimental data are usually only available in discrete pairs, conventional finite-difference calculations give only an approximation to the true differentiation. For these reasons, in practice the direct differentiation of experimental data is rarely performed. Instead, the experimental data are usually fitted into a particular form of mathematical function, resulting in a set of parameters representing the material behavior in an optimum sense. This paper presents a markedly different approach. The method is based on the sampling theorem and utilizes a noise-filtered differentiator to simultaneously differentiate the data and filter out the noise. The method performs true differentiation without a preassumed mathematical expression. Examples are given to show the effectiveness and limitation of this reported method.