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This research has developed a mathematical model for characterizing nonlinear systems utilizing the earlier methods of Vito Volterra (1860-1940)1 and later by Norbert Wiener (1894-1964)2. More recently, Albert Nuttall, working with coauthors, has made significant improvements over the earlier methods. These enhancements include kernel estimation using a least-square approach for obtaining a best fit to the measured system response. These techniques, among others, include: maximally-sparse sampling of the kernels (for first-, second- and third-order), combatting ill-conditioning on its own terms, realizing an exponential decrease of the growth of the number of kernel coefficients, capturing frequency content beyond input excitation (transmit) band, and estimating the effects of noise on the kernel responses. Extensions of this theory are relevant to problems in acoustics.

Traditionally, solving structural-acoustics problems has posed significant computational challenges at very high wavenumbers because of the mesh refinement required. As such, instead of resolving each wavelength, the fundamental goal in Energy Finite Element Analysis (EFEA) is to average the energy over many wavelengths. The envelope of average energy behaves as a slowly varying exponential, which is much easier to solve numerically. EFEA thus computes the average energy over a region which can be used to determine undersea vehicle self- and radiated noise in much the same way as conventional FEA modeling but the size of the mesh does not suffer the same restrictions. In this talk, self-noise model predictions for a representative undersea vehicle are discussed to demonstrate the effectiveness of EFEA. This model includes an explicitly modeled acoustic domain to allow radiated energy to propagate in the acoustic medium and possibly reenter the vehicle structure. Results are validated with dense FEA models and the post-processing algorithms used for this purpose are discussed.