A simple and natural method, called the implicit least-square method, is developed to solve the inverse problem, especially for first-kind Fredholm integral equations of acoustic radiation. Unlike most previous methods, there are no artificial constraints or parameters to be specified. This method is proven to be equivalent to the pseudoinverse method and is tested in three examples: (i) inversion of Poisson's formula of harmonic continuation, (ii) inversion of the free-space turbulent flame noise radiation for the heat release rate source, and (iii) inversion of the ducted combustion system noise radiation for the heat release rate source. Comparisons performed using the results of the present prediction, the exact solution, and the experimental data in these examples are satisfactory.
All Science Journal Classification (ASJC) codes
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics