In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controller’s performance. In this paper we propose an approach to identify model uncertainty using parameter identification, optimal design of experiments and hypothesis testing. The experimental setup is characterized by optimal sensor positions such that specific model parameters can be determined with minimal variance. This allows for the computation of confidence regions in which the real parameters or the parameter estimates from different test sets have to lie. We claim that inconsistencies in the estimated parameter values, considering their approximated confidence ellipsoids as well, cannot be explained by data uncertainty but are indicators of model uncertainty. The proposed method is demonstrated using a component of the 3D Servo Press, a multi-technology forming machine that combines spindles with eccentric servo drives.
Buckling of slender bars subject to axial compressive loads represents a critical design constraint for light-weight truss structures. Active buckling control by actuators provides a possibility to increase the maximum bearable axial load of individual bars and, thus, to stabilize the truss structure.For reasons of cost, it is in general not economically viable to use such actuators in each bar of the truss structure. Hence, it is an important practical question where to place these active bars. Optimized structures, especially when coupled with active elements to further decrease the number of necessary bars, however, lead to designs, which, while cost-efficient, are especially prone to bardamages, caused, e.g., by material failures. Therefore, this paper presents a mathematical optimization approach to optimally place active bars for buckling control in a way that secures both buckling and general stability constraints even after failure of any combination of a certain number of bars. This allows us to increase the resilience of the system and guarantee stable behavior even in case of failures.
In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.
Load carrying mechanical structures like trusses face uncertainty in loading along with uncertainty in their strength due to uncertainty in the development, production and usage. The uncertainty in production of function integrated rods is investigated, which allows monitoring of load and condition variations that are present in the product in every phase of its lifetime. Due to fluctuations of the semi-finished parts, uncertainty in governing geometrical, mechanical and electrical properties such as Young's moduli, lengths and piezoelectric charge constants has to be evaluated. The authors compare the different direct methodical approaches Monte-Carlo simulation, fuzzy and interval arithmetic to describe and to evaluate this uncertainty in the development phase of a simplified, linear mathematical model of a sensory rod in a consistent way. The criterion to compare the methodical approaches for uncertainty analysis is the uncertain mechanical-electrical transmission behavior of the sensory rod, which defines the sensitivity of the sensory compound.
Each collection presents early findings from experimental and computational investigations on an important area within structural dynamics. Model Validation and Uncertainty Quantification (MVUQ) is one of these areas.Modeling and simulation are routinely implemented to predict the behavior of complex dynamical systems. These tools powerfully unite theoretical foundations, numerical models, and experimental data which include associated uncertainties and errors. The field of MVUQ research entails the development of methods and metrics to test model prediction accuracy and robustness while considering all relevant sources of uncertainties and errors through systematic comparisons against experimental observations. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track.
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