Additive Model

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem. The algorithms can be used to improve the performance of various processes with phase changes, such as additive manufacturing. Using the authors' innovative design solutions, readers will also be equipped to apply estimation algorithms for real-world phase change dynamics, from polar ice to lithium-ion batteries.

Fatigue failure of structures used in transportation, industry, medical equipment, and electronic components needs to build a link between cutting-edge experimental characterization and probabilistically grounded numerical and artificially intelligent tools. The physics involved in this process chain is computationally prohibitive to comprehend using traditional computation methods. Using machine learning and Bayesian statistics, a defect-correlated estimate of fatigue strength was developed. Fatigue, which is a random variable, is studied in a Bayesian-based machine learning algorithm. The stress-life model was used based on the compatibility condition of life and load distributions. The defect-correlated assessment of fatigue strength was established using the proposed machine learning and Bayesian statistics algorithms. It enabled the mapping of structural and process-induced fatigue characteristics into a geometry-independent load density chart across a wide range of fatigue regimes.

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