New Method Improves Structural Uncertainty Analysis Using Complex Variables

Uncertainties are an inherent and unavoidable reality in modern engineering, significantly impacting the predicted mechanical responses of complex structures. To accurately model and predict structural behavior, robust uncertainty analysis models are essential. While the traditional Taylor series expansion method offers a simple and efficient approach to uncertainty propagation, its utility is severely limited when dealing with structural responses that exhibit strong nonlinearity or non-monotonic behavior. When structural response intervals contain extreme points and strong nonlinearity, the accuracy of the standard Taylor series expansion degrades significantly, posing a major challenge for engineers designing reliable systems.

Addressing this critical limitation, researchers have proposed an improved interval analysis method based on second-order Taylor series expansion, termed MSTEM. The core innovation of this approach lies in transforming the second-order Taylor series expansion into a parabolic expression. By meticulously determining the locations of approximate stationary points within this parabolic framework, the method effectively eliminates the detrimental influence of non-monotonicity, thereby enhancing the predictive power of the analysis.

To further refine the accuracy of structural response bounds under intensely nonlinear conditions, the MSTEM method incorporates a sophisticated sensitivity modification strategy. This strategy is designed to boost the precision of the predictions. Furthermore, to achieve both enhanced accuracy and greater computational efficiency in sensitivity computation, the research team successfully derived a complex-variable formulation of MSTEM.

The effectiveness and reliability of this newly proposed methodology were rigorously tested through various numerical examples.

Subject of Research: Development of an advanced uncertainty propagation method for structural mechanics.

Article Title: Structural uncertainty propagation analysis by sensitivity-modification based on second order Taylor series expansion with complex variables

Article References: Zhang, Y. (2026). Structural uncertainty propagation analysis by sensitivity-modification based on second order Taylor series expansion with complex variables. Scientific Reports. https://doi.org/10.1038/s41598-026-77376-x

Image Credits: AI Generated

DOI: 10.1038/s41598-026-77376-x

Keywords: Structural Analysis, Uncertainty Propagation, Taylor Series Expansion, Complex Variables, Engineering Mechanics, Nonlinearity, MSTEM, Structural, uncertainty, propagation, analysis, sensitivity-modification