Multi-objective optimization can reveal the complex parameter-objective relationships in the high-dimensional design problems. However, the data-extraction and data-presentation of the high-dimensional complex nonlinear system suffers from the increasing dimensionality. Key features and data-distribution of high-dimensional design spaces:parameter and objective spaces could be obtained by using Self-Organizing Maps (SOM) method, which re-clusters the high-dimensional multi-attribute data existing on the Pareto front into several low-dimensional maps. Correlations among all the design variables can be drawn according the colorized topological structure of the maps. Under the constraints including geometric structure and operating parameters, a low-cost and high accurate Kriging surrogate model was established to optimize a hybrid sliding bearing based on the sequential design method. Correlations between 3 objectives:"friction-to-load" ratio, temperature rise, instability threshold speed and 4 design parameters were extracted by SOM. Optimal feature regions were captured and analyzed. Results show that, within the specific feasible design space, supply pressure, axial bearing land width have important impact on the selected objectives, whereas the other parameters such as deep pocket depth and shallow pocket angle have relatively limited impact. A series of corresponding design decisions and optimization results help to understand the mechanism of the hybrid sliding bearing system in a much more intuitive way.
Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization
