In this paper we use Differential Evolution (DE), with best evolved results refined using a Nelder-Mead optimization, to solve complex problems in orbital mechanics relevant to low Earth orbits (LEO). A class of so-called 'Lambert Problems' is examined. We evolve impulsive initial velocity vectors giving rise to intercept trajectories that take a spacecraft from given initial positions to specified target positions. We seek to minimize final positional error subject to time-of-flight and/or energy (fuel) constraints. We first validate that the method can recover known analytical solutions obtainable with the assumption of Keplerian motion. We then apply the method to more complex and realistic non-Keplerian problems incorporating trajectory perturbations arising in LEO due to the Earth's oblateness and rarefied atmospheric drag. The viable trajectories obtained for these difficult problems suggest the robustness of our computational approach for real-world orbital trajectory design in LEO situations where no analytical solution exists.
This paper presents reference equivalent threshold sound pressure levels (RETSPLs) for the Wireless Automated Hearing Test System (WAHTS), a recently commercialized device developed for use as a boothless audiometer. Two initial studies were conducted following the ISO 389-9 standard [ISO 389-9 (2009). “Acoustics—Reference zero for the calibration of audiometric equipment. Part 9: Preferred test conditions for the determinations of reference hearing threshold levels” (International Organization for Standardization, Geneva)]. Although the standard recruitment criteria are intended to yield otologically normal test subjects, the recruited populations appeared to have slightly elevated thresholds [5–10 dB hearing level (HL)]. Comparison of WAHTS thresholds to other clinical audiometric equipment revealed bias errors that were consistent with the elevated thresholds of the RETSPL populations. As the objective of RETSPLs is to ensure consistent thresholds regardless of the equipment, this paper presents the RETSPLs initially obtained following ISO 389-9:2009 and suggested correction to account for the elevated HLs of the originally recruited populations. Two additional independent studies demonstrate the validity of these corrected thresholds.
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