# An Adaptive Hybrid Correlation Kriging Approach for Uncertainty Dynamic Optimization of Spherical-Conical Shell Structure

## TL;DR

This paper introduces a new optimization method using an adaptive Kriging model to improve the design of spherical-conical shell structures under uncertainty.

## Contribution

The novelty lies in the adaptive hybrid correlation Kriging model and the improved multi-objective Salp Swarm Algorithm for uncertainty optimization.

## Key findings

- The adaptive Kriging model accurately captures uncertainty in laminated shell structures.
- The improved algorithm effectively optimizes ply angles for vibration performance.
- The methodology shows high computational efficiency and applicability in engineering.

## Abstract

In this paper, an uncertainty optimization method based on the adaptive hybrid correlation Kriging surrogate model is proposed to optimize the ply angles of laminated spherical-conical shells. First, equations of motion of laminated spherical-conical shells are constructed to calculate the vibration characteristics. Then, this paper proposes a Kriging surrogate model with adaptive weight hybrid correlation functions and validates its accuracy. Based on this framework, the weight distribution of the surrogate model for uncertain parameters in laminated spherical-conical shells under different ply angles is analyzed. To address the uncertainty optimization problem in laminated spherical-conical shell structures, an Improved Multi-objective Salp Swarm Algorithm is developed, and its optimization efficacy is systematically validated. Furthermore, an adaptive hybrid correlation Kriging surrogate model is reconstructed, incorporating both uncertainty parameters and design variables as inputs, with the peak vibration displacement and fundamental frequency serving as the output responses. The uncertainty optimization results confirm that the proposed methodology, along with the enhanced Kriging modeling strategy, exhibits both applicability and computational efficiency for such engineering applications.