Application of Mathematical Programming for Experimental Data Analysis
Keywords:
Split Hopkinson (Kolsky) Bar, Mathematical Programming, Digital Signal ProcessingAbstract
Purpose: A common way to study the behavior of materials in the range of deformation speed 102–104 s–1 is using a split Hopkinson
(Kolsky) bar. There are various methods for a through calibration of such experimental stands; however, they do not remove a number
of factors: the variance of the loading pulse forms, inaccuracies in timing the pulses, the noise components in the pulses, etc. All these
factors can influence the methods of finding the characteristics of the materials, such as incubation time. The aim is to use digital signal
processing techniques to filter and analyze the experimental data as an interconnected triad of the loading, reflected and transmitted
pulses, taking into account the physical processes in the material. Results: Efficient algorithms were proposed for combined filtering/
analysis of experimental signals obtained at a Hopkinson’s stand. It was shown that this problem can be formulated as a mathematical
programming problem and reduced to quadratic programming, filtering an interrelated triad of the loading, reflected and transmitted
pulses. The problem can be described as a sequence of quadratic programming problems in the case when the pulses are coherently
filtered and the phase shifts between them are calculated. Practical relevance: The proposed filtering/analysis algorithms helped to
identify the signals components which are due to the influence of the experimental stand and eliminate them from further calculation
of the characteristics. This resulted in a significant (more than twice) reduction in the standard deviation. In contrast to the standard
filtering techniques (Fourier transform, wavelet analysis, correlation analysis), the proposed algorithms have relations which do not
contradict the physics of the material tested. These algorithms can be improved by introducing new models of materials.