Minimizing Structural Vibrations via Guided Flow Matching Design Optimization

Structural vibrations are a source of unwanted noise in engineering systems like cars, trains or airplanes. Minimizing these vibrations is crucial for improving passenger comfort. This work presents a novel design optimization approach based on guided flow matching for reducing vibrations by placing beadings (indentations) in plate-like structures. Our method integrates a generative flow matching model and a surrogate model trained to predict structural vibrations. During the generation process, the flow matching model pushes towards manufacturability while the surrogate model pushes to low-vibration solutions. The flow matching model and its training data implicitly define the design space, enabling a broader exploration of potential solutions as no optimization of manually-defined design parameters is required. We apply our method to a range of differentiable optimization objectives, including direct optimization of specific eigenfrequencies through careful construction of the objective function. Results demonstrate that our method generates diverse and manufacturable plate designs with reduced structural vibrations compared to designs from random search, a criterion-based design heuristic and genetic optimization. The code and data are available from https://github.com/ecker-lab/Optimizing_Vibrating_Plates.

The impact of AI on engineering design procedures for dynamical systems

Artificial intelligence (AI) is driving transformative changes across numerous fields, revolutionizing conventional processes and creating new opportunities for innovation. The development of mechatronic systems is undergoing a similar transformation. Over the past decade, modeling, simulation, and optimization techniques have become integral to the design process, paving the way for the adoption of AI-based methods. In this paper, we examine the potential for integrating AI into the engineering design process, using the V-model from the VDI guideline 2206, considered the state-of-the-art in product design, as a foundation. We identify and classify AI methods based on their suitability for specific stages within the engineering product design workflow. Furthermore, we present a series of application examples where AI-assisted design has been successfully implemented by the authors. These examples, drawn from research projects within the DFG Priority Program \emph{SPP~2353: Daring More Intelligence - Design Assistants in Mechanics and Dynamics}, showcase a diverse range of applications across mechanics and mechatronics, including areas such as acoustics and robotics.

Vibroacoustic Frequency Response Prediction with Query-based Operator Networks

Understanding vibroacoustic wave propagation in mechanical structures like airplanes, cars and houses is crucial to ensure health and comfort of their users. To analyze such systems, designers and engineers primarily consider the dynamic response in the frequency domain, which is computed through expensive numerical simulations like the finite element method. In contrast, data-driven surrogate models offer the promise of speeding up these simulations, thereby facilitating tasks like design optimization, uncertainty quantification, and design space exploration. We present a structured benchmark for a representative vibroacoustic problem: Predicting the frequency response for vibrating plates with varying forms of beadings. The benchmark features a total of 12,000 plate geometries with an associated numerical solution and introduces evaluation metrics to quantify the prediction quality. To address the frequency response prediction task, we propose a novel frequency query operator model, which is trained to map plate geometries to frequency response functions. By integrating principles from operator learning and implicit models for shape encoding, our approach effectively addresses the prediction of resonance peaks of frequency responses. We evaluate the method on our vibrating-plates benchmark and find that it outperforms DeepONets, Fourier Neural Operators and more traditional neural network architectures. The code and dataset are available from https://eckerlab.org/code/delden2023_plate.