Reliability-Based Robust Design Optimization Using Data-Driven Polynomial Chaos Expansion

As the complexity of modern engineering systems continues to increase, traditional reliability analysis methods still face challenges regarding computational efficiency and reliability in scenarios where the distribution information of random variables is incomplete and samples are sparse. Therefore, this study develops a data-driven polynomial chaos expansion (DD-PCE) model for scenarios with limited samples and applies it to reliability-based robust design optimization (RBRDO). The model directly constructs orthogonal polynomial basis functions from input data by matching statistical moments, thereby avoiding the need for original data or complete statistical information as required by traditional PCE methods. To address the statistical moment estimation bias caused by sparse samples, kernel density estimation (KDE) is employed to augment the data derived from limited samples. Furthermore, to enhance computational efficiency, after determining the DD-PCE coefficients, the first four moments of the DD-PCE are obtained analytically, and reliability is computed based on the maximum entropy principle (MEP), thereby eliminating the additional step of solving reliability as required by traditional PCE methods. The proposed approach is validated through a mechanical structure and five mathematical functions, with RBRDO studies conducted on three typical structures and one practical engineering case. The results demonstrate that, while ensuring computational accuracy, this method saves approximately 90% of the time compared to the Monte Carlo simulation (MCS) method, significantly improving computational efficiency.