DIFFERENTIATION OF NOISY EXPERIMENTAL-DATA FOR INTERPRETATION OF NONLINEAR STRESS-STRAIN BEHAVIOR

Interpretation of nonlinear stress-strain behavior of a material may r equire differentiating the load-displacement curve constructed from ex perimental data. Pressuremeter and torsional shear tests in geotechnic al engineering are two examples that require such an operation. Differ entiating experimental data is tricky because (1) it is very sensitive to the noise inevitably existing in the measurements, and (2) the exp erimental data are usually only available in discrete pairs, conventio nal finite-difference calculations give only an approximation to the t rue differentiation. For these reasons, in practice the direct differe ntiation of experimental data is rarely performed. Instead, the experi mental data are usually fitted into a particular form of mathematical function, resulting in a set of parameters representing the material b ehavior in an optimum sense. This paper presents a markedly different approach. The method is based on the sampling theorem and utilizes a n oise-filtered differentiator to simultaneously differentiate the data and filter out the noise. The method performs true differentiation wit hout a preassumed mathematical expression. Examples are given to show the effectiveness and limitation of this reported method.