242 R. Locke et al. procedures [1]. However, a fundamental divide exists between physical systems and numerical solutions to mathematical models from the uncertainty introduced from the design stage, manufacturing processes, and material variability; this uncertainty is classified as aleatory or irreducible uncertainty [2, 3]. This theoretical chasm is further worsened from uncertainty introduced by the surrounding environment (experimental uncertainty), inaccurate solutions to differential equations (numerical uncertainty), the unknown value and variability of parameters (parameter uncertainty), and poor engineering judgment (bias error) [3]. If this uncertainty is left unaccounted, the accuracy of predicted results can drastically decrease and lead to ill-informed decision making. Verification and validation (V&V) studies, therefore, must be performed to evaluate the uncertainty in these predictive models. This paper will investigate a structural system composed of a coupled modular active spring-damper system and space truss (German acronym MAFDS). The MAFDS was developed in the collaborative research center SFB 805 “Control of Uncertainty in Load-Carrying Structures in Mechanical Engineering” at the Technische Universitaet Darmstadt, its general functionality is comparable to the front landing gear of an aircraft. The main goal of the MAFDS is to study uncertainty in dynamic stability, vibration behavior, and load distribution, and, eventually, to find ways to control or compensate uncertainty with different measures (e.g. active vibration control technology). The test rig of the MAFDS, as shown in Fig. 28.1, is subjected to a variety of loading and boundary conditions to monitor the impact they have on the uncertainty from stability, strength and vibrational behavior [4]. In this contribution, the MAFDS has been evaluated during the process of model selection and validation to quantify uncertainty in the dynamic outputs from Fig. 28.2 for different sets of inputs. An idealized two-degree-of-freedom (2DOF) model, as shown in Fig. 28.4, was implemented to characterize the mechanics and physics of the spring-damper system only, neglecting single truss properties (e.g. truss geometry and member material properties). The 2DOF model was then solved for the dynamic outputs in Fig. 28.2 using the average acceleration Newmark-β method with numerical integration techniques that minimize numerical uncertainty from a conditionally stable step size and, hence, improved the numerical solutions [5]. Experimental uncertainty was also reduced significantly by correctly calibrating the sensors prior to performing tests under controlled environmental conditions. The primary focus of this research is to investigate parameter uncertainty and bias error, commonly referred to as modelform uncertainty, introduced by assumptions about model complexity [6, 7]. As model complexity increases, the functional relationship between input parameters (e.g. linear or nonlinear) varies and the number of parameters required to represent a physical system increases. Increasing model complexity reduces the uncertainty associated with output response features due to the modeling form, but also increases response uncertainty due to a lack of knowledge of the input parameters [8]. The inherent difficulty in this problem is identifying what levels of model-form and parameter uncertainty can be included within a model while still capturing the fundamental physics and providing reliable results. Minimizing model-form and parameter uncertainty of multiple models requires addressing under what conditions and circumstances a simple model will reproduce outputs from the MAFDS compared to a more complex model [4]. Thus, the difficulty in predictive modeling is constructing Fig. 28.1 The structural design in(a) displays components of the MAFDS, and(b) demonstrates how the load path will be distributed after a free fall drop test
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