Archives of Acoustics, 33, 4(S), pp. 171–176, 2008

Propagation of Soundwaves in Uncertain Environment – New Interval Perturbation Methodology

Silesian University of Technology, Faculty of Civil Engineering

The aim of the paper is to present applications of the new interval algebraic system in acoustic problems. The modified algebraic system operates over specifically strictly determine interval numbers with specially defined addition and multiplication. The introduced perturbation interval numbers are defined as ordered pairs of real numbers. Classical perturbation acoustic problems described by differential equations can be solved in the new interval algebraic system as easy as usual.
A novel 3D interval ray–tracing model of detailed representation of the indoor environment is presented. Interval perturbation ray tracing method is a technique based on geometrical optics with disturbance in parameters. The developed algorithms use the interval perturbation methodology where the perturbed images are applied to produce 3D – field of interval illumination zones. It can be easy considered how interval perturbations (small) of nominal parameters values change solutions of the considered problems.
Keywords: ray tracing, interval geometry, perturbation methods, room acoustic
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