Interval optimization approach using Progressive Trigonometric Mixed Response Surface Method - Zheng, Guanchao (2022)
For structural designs, uncertainty is ubiquitous, ranging from simple models to complicated systems, especially in the design of the composite submersible hull. To deal with this problem, a method named uncertain interval optimization was introduced in recent decades. However, the existing interval optimization methods, such as the Nonlinear Interval Number Programming (NINP), which is based on the first-order Taylor expansion, are only suitable for small interval uncertainties. A large range of uncertainties will lead to a significant error. The key challenge becomes how to develop another effective type of interval optimization approach with enough efficient and reliable constraints. Therefore, this research performs a novel double-loop interval optimization approach using the Progressive TMRSM, the reliable constraints, and the MATLAB software to limit the constraints effectively. Nevertheless, double-loop optimization means a high computational cost even if a simulation such as the Finite Element Method (FEM) or experiment is used. To solve this difficulty, a surrogate method is introduced to replace the experiment or the FEM. Recently, there have been various surrogate approaches for structural engineering. Scholars always seek to attain more accurate and simpler models with fewer sample points. Determining how to create a better surrogate model with fewer and more reliable sample points and less other information becomes a critical and urgent topic. This research first updates the traditional Response Surface Method (RSM) to a new proposed Trigonometric Mixed Response Surface Method (TMRSM), which can obtain a more accurate surrogate model with fewer and more reliable sample points. However, the decision of the highest order of the TMRSM should be determined in advance by designers for some high-nonlinear complex structural problems. Another deficiency to be concerned about is how to determine the highest order of polynomials for the RSM surrogate model. Thus, a Progressive Trigonometric Mixed Response Surface Method (Progressive TMRSM) is put forward to determine the highest order for the TMRSM. This Progressive TMRSM consists of the t-test criterion, the determination coefficient, and the mean relative error. The accuracy and the fitting performance of the TMRSM and the Progressive TMRSM have been verified by four well-known numerical functions. The results show that the Progressive TMRSM has the best accuracy and perfect fitting performance. Due to the complex pressure environment under the water and the uncertainty of the layup technology, the design process of the submersible is faced with several uncertain factors. But the optimization design considering the uncertain factors has not been studied by any scholars. How to apply interval optimization design in the field of submersible designs becomes another significant research issue. So, this research carries out an uncertain interval optimization design (the buckling properties and the failure criterion) for the composite submersible hull based on the interval optimization approach, the Progressive TMRSM, and the Finite Element Method (FEM) method by ANSYS software. This approach can obtain a better solution with a narrower deviation of the objectives compared with NINP.