28 Applying Uncertainty Quantification to Structural Systems: Parameter Reduction for Evaluating Model Complexity 243 Fig. 28.2 Dynamic outputs of interest from the MAFDS. Left: The top image shows the average relative displacement zr over time; the middle image shows the force Fsd measured at the upper force sensor over time; and the bottom image shows the force Fef measured at the elastic foot over time. Right: Outputs associated with IDs in Left images a simple mathematical representation that can reduce computational time of more complex models while capturing the governing physics and mechanics of the system. In this study, there are three unique cases for modeling suspension stiffness and two unique cases for modeling the damping force for a total of six 2DOF cases (refer to Table 28.5). These cases have been developed to reproduce the static and dynamic outputs of the MAFDS with varying levels of complexity, similar to [4]. The quantify uncertainty from their simulated outputs, evaluate model-form uncertainty, and, the main goal, to determine which input parameters need to be calibrated in order to capture the data’s variability for each 2DOF case. In this paper, a sensitivity analysis study was performed to determine which input variables contributed the least to the variability of output responses and could be removed of the calibration space, or, in other words, which inputs could be held constant during inversion of the 2DOF MAFDS mathematical model. A statistical screening method that utilized The Analysis of Variation (ANOVA) and the Coefficient of DeterminationR 2 was employed to evaluate each set of input variables from the six 2DOF cases for their contribution to the variability in the output response features. The weighted R 2 value for each set of parameters were compared against each other, and inputs with a R 2 less than 0.02 were identified as having low sensitivity. This form of parameter reduction is expected to improve parameter estimation for the six 2DOF cases, reduce model-form uncertainty, and ameliorate computational efforts. 28.2 Modular Active Spring-Damper System Description The MAFDS, as seen in Fig. 28.1, is a large-scale suspension strut system, analogous to an aircraft landing gear, that consists of: an upper space truss structure and added payload; a suspension system with both stiffness and damping components; a lower space truss structure; guidance links that enable kinematic motion between the lower and upper space trusses; an elastic foot with both stiffness and damping components; and a user-specified drop height hf. The purpose of the MAFDS is not to serve as an aircraft landing gear, but rather as an academic devise to study, in a general sense, the uncertainty in a suspension strut’s dynamic outputs [4]. In this paper, there are a total of eight outputs of interest, these are identified by Fig. 28.2. These outputs are calculated using data from the displacement and force sensors shown in Fig. 28.3. The displacement sensors operate under the linear displacement variable transformer (LVDT) principle, while the elastic foot and suspension forces are recorded using a three axial strain gauge and a single axial strain gauge, respectively. In this study, the MAFDS is represented numerically by an equivalent 2DOF model, Fig. 28.4 indicates the MAFDS components and the free body force diagram for this model. In the 2DOF system, the upper and lower space trusses are idealized as two lumped masses with an upper mass mu and a lower mass ml. The mass values for the 2DOF system were determined to be 180 kg and 40 kg, respectively. The suspension system is represented by a spring with stiffness ks and a dash-pot with viscous damping bs. The elastic foot is also represented by a spring with stiffness kef and a dash-pot with damping bef. Additionally, as indicated in Fig. 28.4, the upper and lower masses have a degree-of-freedom associated with local translational displacements, zu and zl, respectively. The six 2DOF cases represent the stiffness and damping forces of the 2DOF mathematical model with varying functional relationships and number of parameters, or, in other words,
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