A direct measurement of the sectional area is quite difficult, in particular, when a nonuniform duct with complex geometry and invisible internal shape is dealt with Among the several indirect methods in measuring the sectional area of a nonuniform duct, the method using the acoustic reflection requires the simplest experimental setup and it is relatively easy to perform the actual measurement. In this study, a method using the acoustic reflection has been studied by employing the measured impulse response function(IRF) in a nonuniform duct and the algorithms to reconstruct the sectional area of such a duct from the measured IRF. A new measurement method for IRF is proposed, that uses the random noise source and discrete inverse Fourier transform. In comparison with the conventional method using an impulse source and a time-consuming regularization process, the proposed method needs a short calculation time and is less sensitive to the measurement errors. The algorithm to reconstruct the duct sectional area is adopted from the analogous inverse-scattering problem. By the experiment, it was shown that the method using the acoustic refilection can be applied to the duct which the area changes abruptly as well as smoothly varying area duct. In the curved duct case, it was also possible to reconstruct the internal duct area accurately as long as the velocity profile deviated about 20% from the plane wave profile. The drror analysis is performed by the Taylor series expansion and the approximated random error of firequency response function between mecrophones. In this study, the variance of reconstructed duct area is determined. From the error analysis, the dffects of several factors on the reconstruction error has been analyzed: large area expansion, abrupt expansion, error accumulation propagated from the prior layers and error of the reflection coefficient. The experimental results show good agreements with the calculated results. The method in this study can be applied to the nondestructive test of various duct systems such as the water piping system for detecting blockage and the human airway for diagnosing various pathologies.
