No abstract

Resilience as a concept has found its way into different disciplines to describe the ability of an individual or system to withstand and adapt to changes in its environment. In this paper, we provide an overview of the concept in different communities and extend it to the area of mechanical engineering. Furthermore, we present metrics to measure resilience in technical systems and illustrate them by applying them to load-carrying structures. By giving application examples from the Collaborative Research Centre (CRC) 805, we show how the concept of resilience can be used to control uncertainty during different stages of product life.

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.

No abstract

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.

This chapter describes three general strategies to master uncertainty in technical systems: robustness, flexibility and resilience. It builds on the previous chapters about methods to analyse and identify uncertainty and may rely on the availability of technologies for particular systems, such as active components. Robustness aims for the design of technical systems that are insensitive to anticipated uncertainties. Flexibility increases the ability of a system to work under different situations. Resilience extends this characteristic by requiring a given minimal functional performance, even after disturbances or failure of system components, and it may incorporate recovery. The three strategies are described and discussed in turn. Moreover, they are demonstrated on specific technical systems.

No abstract