94 M. Behling et al. next assembly motion one axis at a time to the base of the component. The authors proposed a method that seeks to improve on this, which is called the Transmission Simulator IMMAT Framework (TS-IMMAT). This method uses multiple shakers to cause the base of the component to exhibit the same motion that it did during flight. If the base of the component is rigid then this entails using at least six shakers to control to six degrees of freedom, although additional shakers can be used if the base is flexible. While this can improve environment reconstruction relative to a traditional single-axis test, past experience has shown that these tests do not generally reproduce the environment on the component as accurately as an IMMAT test [9]. Hence, if one could use the response on the next assembly to estimate the response on the DUT, then one could perform an IMMAT test rather than a TS-IMMAT test, and reproduce the response on the DUT more faithfully, reducing the costs associated with failed parts due to over-test or in field failures due to under-test. Additionally, some tests require component level data, e.g., the intrinsic connection excitation (ICE) framework [10] and fixture neutralization (FINE) methods [11]. In general, controlling component level data compensates for boundary condition mismatches between the flight and lab setups and is useful [12]. The goal of this study is to see if accurate DUT response reconstruction is possible given next assembly measurements only. Specifically, we hope to answer: 1) How much of the next assembly should be included in the expansion model to accurately reconstruct the response on the DUT? 2) How accurate can one expect the reconstructed DUT responses to be if only next assembly measurements are available? 3) If next assembly measurements are insufficient, what is the minimum number of accelerometers that can be placed on the DUT to improve response estimation at unknown locations? These questions are studied by analyzing the Finite Element Model (FEM) case study shown in Figure 1, where the DUT is a stool intended to represent a structure on which a circuit board might rest, and the next assembly is a wedding cake-like structure. In this study, it is assumed that the next assembly geometry does not change from when the environment is measured (or simulated, in this case), i.e., the same system that data was measured on is the current system of interest. In practice, data may only be available from a previous flight, so the next assembly geometry may change. In this case, the methods presented in [13] might be applied to estimate the environment on the new next assembly, and the methods presented in this paper could then be applied to estimate the DUT environment. Fig. 1 Flight Setup Case Study Environment Estimation Methods The first efforts to accurately estimate flight environments in the absence of measured data seem to have been at NASA in the 60’s. One study presented two methods, one for components directly excited by acoustic or aerodynamic pressures, and another for those primarily excited by transmission through other parts of the structure. These methods involved scaling previously measured responses using ratios of forcing function magnitude and the relative masses of the original and new component [14]. Another study divided environment estimation methods into two categories: gross prediction techniques, in which broad correlations between forcing function and response magnitude are derived from previous flights, and custom prediction techniques, which involve more detailed modeling of the forcing function and structure of interest [15]. Statistical energy methods were also proposed as a way to predict environments at higher frequencies [16]. In short, early methods generally modified previous flight data to estimate new environments, though they were hindered by a lack of computational power and the inability to create accurate models of system hardware. These methods might accurately estimate response
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