Reliability design of mechanical structures with small samples

Abstract In traditional mechanical structure reliability optimization design, the treatment of uncertain parameters relies on large sample data to obtain the probability density function or statistical characteristics, especially the first four moments. However, in actual engineering applications, the cost of obtaining data samples is high, and the number is limited, leading to the limitation of traditional methods in handling small sample problems, not only making it difficult to accurately represent uncertainty but also potentially leading to unreasonable optimization results and failure risks. Therefore, this paper proposes an improved method based on bootstrapping to expand the original small number of samples to a larger scale, so as to reconstruct the statistical characteristics of uncertain parameters in the case of data scarcity. Specifically, this paper first uses bootstrapping to perform self-sampling expansion of the sample data and calculates the first four central moments of the expanded sample to obtain information of the central moments of the uncertain parameters. On this basis, the probability density function is established using the maximum entropy principle, and the most consistent probability distribution model is generated by maximizing the information entropy, achieving reliability calculation. This method not only expands the applicability of reliability optimization design under small sample data conditions but also improves the accuracy of uncertainty description, providing a new method and idea for engineering structure reliability analysis.