This paper proposes a linear quadratic approximation approach to dynamic nonlinear rationally inattentive control problems with multiple states and multiple controls. An efficient toolbox to implement this approach is provided. Applying this toolbox to five economic examples demonstrates that rational inattention can help explain the comovement puzzle in the macroeconomics literature.

Designing vibrating systems is challenging due to component interaction. One approach to reduce the resulting complexity is top-down design where requirements on components are formulated such that the overall system achieves the design goal. Previous work showed how to derive quantitative and solution-neutral requirements on components of a vibrating system, expressed as permissible ranges of impedance. This work adapts the methodology to a practical use case and provides a concrete technical solution: A hammer drill that can cause white finger syndromes to users is equipped with an appropriate vibration absorber. The hammer drill is represented by a lumped mass model and validated using experimental data of a reference design. Solution-neutral and quantitative component requirements on the overall dynamics of the vibration absorber expressed by impedance are derived. They provide a clear target for the component design. A vibration absorber in form of a Tuned Mass Damper (TMD) is designed accordingly. The final design is validated experimentally and shown to reduce the vibration by 47%.

Fault-tolerant hardware architectures for autonomous vehicles can be implemented through redundancy, diversity, separation, self-diagnosis, and reconfiguration. These approaches can be coupled with majority redundancy through M-out-of-N independent system architectures. The development of fault- tolerant systems is of central importance in the launch of autonomous driving systems from level 4. The increasing complexity of electrical and electronic systems is challenging for the design of safety-critical systems. This work aims to develop a method to manage this complexity in product development and to use it to compare different types of architectures. The basis is a system consisting of sensors and microcontrollers. The reliability of all possible MooN configurations of the system is calculated automatically by numerically solving the master equation of the corresponding Markov chain. Subsequently, a software-based fault tree analysis enables more detailed modeling of the component structure. The results show that four-line architectures can provide suitable results and that the development effort for 2-ECU systems is higher than for 1-ECU systems with respect to the ISO 26262 target values.

Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here.

The present analytical design of shrink fits typically results in an uneven stress condition that can lead to failure in a variety of manners. With increasing loads and the use of brittle materials, the optimization of the stresses in the shrink fit hence becomes increasingly necessary. Currently existing approaches do not solve the problem satisfactorily or increase the manufacturing and design effort. This paper therefore considers the implementation of an AI-based stress optimization using reinforcement learning, which performs stress optimization by geometrically contouring the interstice.

Increasing product complexity and individual customer requirements make the design of optimal product families difficult. Numerical optimization supports optimal design but must deal with the following challenges: many design variables, non-linear or discrete dependencies, and many possibilities of assigning shared components to products. Existing approaches use simplifications to alleviate those challenges. However, for use in industrial practice, they often use irrelevant commonality metrics, do not rely on the actual design variables of the product, or are unable to treat discrete variables. We present a two-level approach: (1) a genetic algorithm (GA) to find the best commonality scheme (i.e., assignment scheme of shared components to products) and (2) a particle swarm optimization (PSO) to optimize the design variables for one specific commonality scheme. It measures total cost, comprising manufacturing costs, economies of scales and complexity costs. The approach was applied to a product family consisting of five water hose boxes, each of them being subject to individual technical requirements. The results are discussed in the context of the product family design process.

One of the fundamental requirements for dual purpose casks, which are used for the transport and interim storage of spent fuel assemblies, is the safe removal of the resulting decay heat. To ensure this the temperature fields are determined using numerical methods. However, their modelling is complex and the computation time-consuming.

In order to accelerate this thermal assessment, we have developed z88ENSI, an independent simulation tool based on finite element analysis. With regard to the modelling, various parameters can be varied quickly with our newly designed mesh manipulation procedure. Concerning the computation time, we developed and implemented an approach for calculating three-dimensional temperature fields, based on an already existing two-dimensional method which lacked precision. We accelerate the calculation by using extended thermal gap constraints, which depict the thermal behaviour of the non-meshed, gas-filled gaps inside the cask. We validate the results of our calculation tool by comparing them with those generated with Ansys. The results of the comparison temperatures differ between −0.8% and 3.7%. The speedup of z88ENSI for the specific validation setting is between 6.9 and 15.0.

Political districts may be drawn to favor one group or political party over another, or gerrymandered. A number of measurements have been suggested as ways to detect and prevent such behavior. These measures give concrete axes along which districts and districting plans can be compared. However, measurement values are affected by both noise and the compounding effects of seemingly innocuous implementation decisions. Such issues will arise for any measure. As a case study demonstrating the effect, we show that commonly used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law. We further show that an adversary could manipulate measurements to affect the assessment of a given plan. This instability complicates using these measurements as legislative or judicial standards to counteract unfair redistricting practices. This paper accompanies the release of packages in C++, Python, and R that correctly, efficiently, and reproducibly calculate a variety of compactness scores.

In the domain of optical engineering, optomechatronic systems are predominantly developed using conventional ray tracing methods such as sequential and non-sequential ray tracing. However, the increasing complexity of these systems in combination with the demand for high efficiency and high image quality leads to the fact that conventional methods to develop these systems reach their limits. In order to be able to develop highly efficient systems with high image quality, this contribution introduces a hybrid ray tracing method using an advanced optimization function.

The observational properties of isolated NSs are shaped by their magnetic field and surface temperature. They evolve in a strongly coupled fashion, and modelling them is key in understanding the emission properties of NSs. Much effort was put in tackling this problem in the past but only recently a suitable 3D numerical framework was developed. We present a set of 3D simulations addressing both the long-term evolution (≈ 104–106 yrs) and short-lived outbursts (≲ 1 yr). Not only a 3D approach allows one to test complex field geometries, but it is absolutely key to model magnetar outbursts, which observations associate to the appearance of small, inherently asymmetric hot regions. Even though the mechanism that triggers these phenomena is not completely understood, following the evolution of a localised heat injection in the crust serves as a model to study the unfolding of the event.

Recently, design researchers have begun to use neuroimaging methods (e.g., functional magnetic resonance imaging, fMRI) to understand a variety of cognitive processes relevant to design. However, common neuroimaging analysis techniques require significant assumptions relating temporal and spatial information during model formulation. In this work, we apply hidden Markov Models (HMM) in order to uncover patterns of brain activation in a design-relevant fMRI dataset. The underlying fMRI data comes from a prior research study in which participants generated solutions for twelve open-ended design problems from the literature. HMMs are generative models that are able to automatically infer the internal state characteristics of a process by observing state emissions. In this work, we demonstrate that distinct states can be extracted from the design ideation fMRI dataset, and that designers are likely to transition between a few key states. Additionally, the likelihood of occupancy within these states is different for high and low performing designers. This work opens up the door for future research to investigate the patterns of neural activation within the discovered states.

Gears are essential machine elements in the drivetrain and transmission technology. The operational behaviour of a gear pairing is influenced by the design of the gear kinematics as well as the component properties. With regard to an improvement of performance and service life, the targeted modification of tooth geometry and component properties offers a promising approach. Thus, the achievable geometric and mechanical component properties are influenced by the manufacturing process, which must be taken into account in the design process. The application of virtual evaluation methods is suitable for this purpose. For the manufacturing of steel gears, cold forging provides the potential of achieving beneficial mechanical properties in a highly productive process. Major challenges for the industrial application are the short service life of the cost- intensive tools and the low geometric accuracy in comparison to machining processes. Within this study the design of the tooth geometry as well as the associated forming tool are investigated. The aim is to derive recommendations regarding an optimization of the resulting component properties and operational behaviour.