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Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.
A hybrid-electric propulsion system combines the advantages of fuel-based systems and battery powered systems and offers new design freedom. To take full advantage of this technology, aircraft designers must be aware of its key differences, compared to conventional, carbon-fuel based, propulsion systems. This paper gives an overview of the challenges and potential benefits associated with the design of aircraft that use hybrid-electric propulsion systems. It offers an introduction of the most popular hybrid-electric propulsion architectures and critically assess them against the conventional and fully electric propulsion configurations. The effects on operational aspects and design aspects are covered. Special consideration is given to the application of hybrid-electric propulsion technology to both unmanned and vertical take-off and landing aircraft. The authors conclude that electric propulsion technology has the potential to revolutionize aircraft design. However, new and innovative methods must be researched, to realize the full benefit of the technology.
The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.
Laser-based Additive Manufacturing (AM) processes for the use of metals out of the powder bed have been investigated profusely and are prevalent in industry. Although there is a broad field of application, Laser Powder Bed Fusion (LPBF), also known as Selective Laser Melting (SLM) of glass is not fully developed yet. The material properties of glass are significantly different from the investigated metallic material for LPBF so far. As such, the process cannot be transferred, and the parameter limits and the process sequence must be redefined for glass. Starting with the characterization of glass powders, a parameter field is initially confined to investigate the process parameter of different glass powder using LPBFprocess. A feasibility study is carried out to process borosilicate glass powder. The effects of process parameters on the dimensional accuracy of fabricated parts out of borosilicate and hints for the post-processing are analysed and presented in this paper.
Optical Instruments require an extremely stable thermal surrounding to prevent loss of data quality by misalignments of the instrument components resulting from material deformation due to temperature f luctuations (e.g. from solar intrusion). Phase Change Material (PCM) can be applied as a thermal damper to achieve a more uniform temperature distribution. The challenge of this method is, among others, the integration of PCM into affected areas. If correctly designed, incoming heat is latently absorbed during phase change of the PCM, i.e. the temperature of a structure remains almost constant. In a cold phase, the heat during phase change is released again latently until the PCM returns to its original state of aggregation. Thus, the structure is thermally stabilized. At FH Aachen– University of Applied Sciences research is conducted to apply PCM directly into the structures of affected components (baffles, optical benches, electronic boxes, etc.). Through the application of Additive Manufacturing, the necessary voids are directly printed into these structures and filled later with PCM. Additive Manufacturing enables complex structures that would not have been possible with conservative manufacturing methods. A corresponding Breadboard was developed and manufactured by Selective Laser Melting (SLM). The current state of research includes the handling and analysis of the Breadboard, tests and a correlation of the thermal model. The results have shown analytically and practically that it is possible to use PCM as an integral part of the structure as a thermal damper. The results serve as a basis for the further development of the technology, which should maximize performance and enable the integration of PCM into much more complex structures.