Multi-objective Optimization of Tube Hydroforming Using Hybrid Global and Local Search
Bibliographic record
Abstract
An investigation of non-linear multi-objective optimization is conducted in order to define a set of process parameters (i.e. load paths) for defect-free tube hydroforming. A generalized forming severity indicator that combines both the conventional forming limit diagram (FLD) and the forming limit stress diagram (FLSD) was adopted to detect excessive thinning, necking/splitting and wrinkling in the numerical simulation of formed parts. In order to rapidly explore and capture the Pareto frontier for multiple objectives, two optimization strategies were developed: normal boundary intersection (NBI) and multi-objective genetic algorithm (MOGA) based on the concept of "dominated solutions". The NBI method produced a uniformly distributed set of solutions. For the MOGA method, a stochastic Kriging model was used as a surrogate model. Furthermore, the MOGA constraint-handling technique was improved, Kriging model updating was automated and a hybrid global-local search was implemented in order to rapidly explore the Pareto frontier. Both piece-wise linear and pulsating pressure paths were investigated for several case studies, including straight tube, pre-bent tube and industrial tube hydroforming. For straight tube hydroforming, the optimal load path was obtained using the NBI method and it showed a smaller corner radius compared to that predicted by the commercial program LS-OPT4.0. Moreover, the hybrid method coupling global search (MOGA) and local search (sequential quadratic programming: SQP) was applied for straight tube hydroforming, and the results showed a significant improvement in terms of the stress safety margin and reduced local thinning. For a commercial refrigerator door handle, the MOGA method was utilized to inversely analyze the loading path and the calculated path correlated well with the production path. For a hydroformed T-shaped tubular part, the amplitude and frequency of the pulsating pressure were optimized with MOGA. Thinning was reduced by 25% compared with experimental results. A multi-stage (prebent) tube hydroforming simulation was performed and it indicated that the reduction in formability due to bending can be largely compensated by end feeding the tube during hydroforming. The loading path optimized by MOGA showed that the expansion into the corner of the hydroforming die increased by 16.7% compared to the maximum expansion obtained during experimental trials.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".