Erscheinungsjahr 2023

Evaluating robustness is an important goal in simulation-based analysis. Robustness is achieved when the controllable factors of a system are adjusted in such a way that any possible variance in uncontrollable factors (noise) has minimal impact on the variance of the desired output. The optimization of system robustness using simulation is a dedicated and well-established research direction. However, once a simulation model is available, there is a lot of potential to learn more about the inherent relationships in the system, especially regarding its robustness. Data farming offers the possibility to explore large design spaces using smart experiment design, high performance computing, automated analysis, and interactive visualization. Sophisticated machine learning methods excel at recognizing and modelling the relation between large amounts of simulation input and output data. However, investigating and analyzing this modelled relationship can be very difficult, since most modern machine learning methods like neural networks or random forests are opaque black boxes. Explainable Artificial Intelligence (XAI) can help to peak into this black box, helping us to explore and learn about relations between simulation input and output. In this paper, we introduce a concept for using Data Farming, machine learning and XAI to investigate and understand system robustness of a given simulation model.

Application problems can often not be solved adequately by numerical algorithms as several difficulties might arise at the same time. When developing and improving algorithms which hopefully allow to handle those difficulties in the future, good test instances are required. These can then be used to detect the strengths and weaknesses of different algorithmic approaches. In this paper we present a generator for test instances to evaluate solvers for multiobjective mixed-integer linear and nonlinear optimization problems. Based on test instances for purely continuous and purely integer problems with known efficient solutions and known nondominated points, suitable multiobjective mixed-integer test instances can be generated. The special structure allows to construct instances scalable in the number of variables and objective functions. Moreover, it allows to control the resulting efficient and nondominated sets as well as the number of efficient integer assignments.

The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states that are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the short transition paths between these subsequent macroscopic system states by a data-driven learning algorithm that extracts the low-dimensional transition manifold and the related new coordinates, which we term collective variables, in the state space of the complex turbulent flow. We therefore transfer and extend concepts for conformation transitions in stochastic microscopic systems, such as in the dynamics of macromolecules, to a deterministic macroscopic flow. Our analysis is based on long-term direct numerical simulation trajectories of turbulent convection in a closed cubic cell at a Prandtl number Pr=0.7 and Rayleigh numbers Ra=10^6 and 10^7 for a time lag of 10^5 convective free-fall time units. The simulations resolve vortices and plumes of all physically relevant scales, resulting in a state space spanned by more than 3.5 million degrees of freedom. The transition dynamics between the large-scale circulation states can be captured by the transition manifold analysis with only two collective variables, which implies a reduction of the data dimension by a factor of more than a million. Our method demonstrates that cessations and subsequent reversals of the large-scale flow are unlikely in the present setup, and thus it paves the way for the development of efficient reduced-order models of the macroscopic complex nonlinear dynamical system.

The block-term decompositions (BTD) represent tensors as a linear combination of low multilinear rank terms and can be explicitly related to the Canonical Polyadic decomposition (CPD). In this paper, we introduce the SECSI-BTD framework, which exploits the connection between two decompositions to estimate the block-terms of the rank-(Lr, Lr, 1) BTD. The proposed SECSI-BTD algorithm includes the initial calculation of the factor estimates using the SEmi-algebraic framework for approximate Canonical polyadic decompositions via SImultaneous Matrix Diagonalizations (SECSI), followed by clustering and refinement procedures that return the appropriate rank-(Lr, Lr, 1) BTD terms. Moreover, we introduce a new approach to estimate the multilinear rank structure of the tensor based on the HOSVD and $k$-means clustering. Since the proposed SECSI-BTD algorithm does not require a known rank structure but can still take advantage of the known ranks when available, it is more flexible than the existing techniques in the literature. Additionally, our algorithm does not require multiple initializations, and the simulation results show that it provides more accurate results and a better convergence behavior for an extensive range of SNRs.

Aliphatic polyketone is a new-age eco-friendly, high-performance engineering thermoplastic. However, its potential for replacing other polymers depends on its ability to be processed. Considering that the first aliphatic polyketone suitable for processing was developed relatively recently (2015), the material gained new research potential. In this paper screw extrusion-based process was developed for additive manufacturing of aliphatic polyketone. A detailed characterisation of the process and printed samples was done. It was shown that the extruder-base process can produce stable additive-manufactured parts depending on printing speed (process parameters). The interpass temperature has a significant influence on printing properties and it depends on printing speed (travel speed of building platform and extruder rotational speed). With the increase in the printing speed, the interpass temperature increases as well. If it is low causes insufficient heat for diffusion to occur causing delamination and if it is too high causes geometrical deviation of workpieces which leads to defects causing a reduction in inter-road strength. The tensile strength of specimens with raster angle 0˚ was 62.7 ± 1.4 MPa, which is slightly higher than the tensile strength of base material guaranteed by the supplier (60 MPa) while the elongation up to the first crack was 32.8 ± 4.6%. Iinter-road strength in specimens with a raster angle of 90˚ was 37.2 ± 0.8 MPa which is 62% of the base material while interpass temperature was 189 ± 3.3 ˚C.