68 D. Scheg et al. ties of the structure. A high fidelity finite element model (FEM) of the DUT can be used to capture these dynamics in the coupled model. However, a high fidelity FEM tends to have a large computational expense due to the high number ofDOFs. To reduce the computational cost associated with high fidelity models, various reduced-order models (ROM) may be implemented. There are many methods used for creating a ROM such as dynamic mode decomposition [2] and operator inference using deterministic linear regression [3]. In this paper, Guyan reduction (static condensation) [4] and component mode synthesis in the forms of Craig-Bampton and Craig-Chang [5] were used. All three of the used modeling processes begin with static condensation. Craig-Bampton and Craig-Chang also include generalized coordinates to represent a set of eigenmode amplitudes [4]. While both are accurate for static analysis, Craig-Bampton and Craig-Chang are more accurate at high frequency analysis, depending on the included eigenmodes. ROMs, which retain a fraction of the original DOFs, introduce higher uncertainty, on top of the uncertainty present in the high-fidelity FEM. Specifically, joints have been notoriously difficult to model in the past because the global stiffness of the part is highly influenced by the flexibility of the joints. Past works have investigated the impact of these joints on the dynamics of a system [6–9]. This work proposes a novel methodology to select features, such as the most appropriate ROM or joint stiffness values, of a physically coupled shaker-DUT system, with the goal of determining the voltage needed to run an environmental test. To do so, a shaker model was coupled with a model of the chosen DUT, a box assembly with removable component (BARC). The shaker model was a lumped parameter model [1] and the BARC model was a ROM of a high-fidelity FEM. Given an acceleration specification, such as a benign acceleration spectral density (ASD) that operators are certain the shaker can complete, the voltage required to run the given test of the coupled system was calculated, in the form of voltage spectral density (VSD). The connection between the BARC base and removable component was modeled as sets of springs that were given varied stiffness coefficients. Then, using a Bayesian classifier, the joint stiffness model whose VSD most closely matched the experimental VSD was selected, showing the methodology proposed in this paper can be used to compare modeling techniques for a more accurate representation of a physical system. Analytical Methods As aforementioned, the purpose of this project was to: 1. understand the voltage requirements to run an environmental test using a coupled shaker-BARC model, and 2. select features of this system that best represent a set of physical test data. For this purpose, a high DOF model of the BARC system was previously created in Abaqus, a finite element analysis software. This work then implemented ROMs of the BARC to reduce computational expense. The equations of motion (EOMs) from the reduced BARC model and the shaker model were combined to represent the coupled system. The VSD of this coupled EOM was calculated, which estimates the voltage requirements to excite the BARC to the acceleration needed for an environmental test. In order to select features of this system, a Bayesian classifier was used. To demonstrate this method, the spring joint connections between the BARC base and the removable component were varied by using three stiffness coefficients, k =100, 1000, and10, 000N/m. The Bayesian classifier selected the VSD from the class of stiffness coefficient that was closest to the experimental ground truth VSD. Reduced-order modeling The BARC was chosen the DUT because its dynamics are well known. The BARC was modeled in Abaqus using a fine mesh, consisting of over 100,000 DOFs. Three ROM techniques were implemented through Abaqus: Craig-Bampton, Craig-Chang, and Guyan reduction. These reduction methods require the user to specify which DOFs will be retained and fully calculated after reduction. Using engineering judgment, nine nodes were selected that were believed to capture the eight mode shapes of interest. A Modal Assurance Criterion (MAC) was performed, which concluded that the selected nodes adequately retained the overall dynamics of the structure, with an average MAC score of 0.9 for the eight modes. These retained nodes also reflected the positions on the physical BARC where accelerometers would be placed or where the shaker stinger would be connected (see Section 4.2). The first eight natural frequencies of each ROM were compared to the high-fidelity model, of which Craig-Chang had the lowest error. Consequently, this ROM was used for the demonstration of feature selection (joint stiffness) using Bayesian classification. Joint modeling for classification problem The joint model was chosen as a mechanism to demonstrate the feasibility of the Bayesian classifier to select appropriate features of a DUT. The joint model consisted of connecting the base of the BARC to the removable component using sets of
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