Research advances in Uncertainty Quantification and Design Optimization for Flight Vehicles

ZHANG Hairui; WANG Yao; HONG Dongpao

doi:10.6052/1000-0992-25-032

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Zhang H R, Wang Y, Hong D P. Research advances in Uncertainty Quantification and Design Optimization for Flight Vehicles. Advances in Mechanics, in press doi: 10.6052/1000-0992-25-032

Citation:

Zhang H R, Wang Y, Hong D P. Research advances in Uncertainty Quantification and Design Optimization for Flight Vehicles. Advances in Mechanics, in press doi: 10.6052/1000-0992-25-032

Zhang H R, Wang Y, Hong D P. Research advances in Uncertainty Quantification and Design Optimization for Flight Vehicles. Advances in Mechanics, in press doi: 10.6052/1000-0992-25-032

Citation:

Zhang H R, Wang Y, Hong D P. Research advances in Uncertainty Quantification and Design Optimization for Flight Vehicles. Advances in Mechanics, in press doi: 10.6052/1000-0992-25-032

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Research advances in Uncertainty Quantification and Design Optimization for Flight Vehicles

doi: 10.6052/1000-0992-25-032 cstr: 32046.14.1000-0992-25-032

China Academy of Launch Vehicle Technology, Beijing 100076, China

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Corresponding author: hloving@163.com
Received Date: 2026-01-02
Accepted Date: 2026-03-04

Available Online: 2026-05-06

Abstract

Abstract

Uncertainty Quantification (UQ) and Uncertainty-Based Design Optimization (UBDO), as an emerging design paradigm for flight vehicles, provides a systematic methodological framework for addressing the precise characterization, propagation, and design optimization of uncertainties. This paper reviews the core concepts and key technologies in this field. It summarizes the uncertainty challenges associated with critical systems and significant environmental conditions of flight vehicles. Based on the latest research progress, five key research directions are identified: (1) High-dimensional uncertainty quantification and efficient propagation: Constructing an adaptive high-dimensional UQ framework by integrating techniques such as dimensionality reduction, compressed sensing, and low-rank tensor decomposition to effectively address the "curse of dimensionality." (2) Hybrid uncertainty quantification and efficient propagation: A unified framework is established to accommodate various types of uncertainties—including probabilistic, interval, fuzzy, and evidence theory. The computational efficiency for complex, multi-source uncertainty problems is further enhanced by incorporating surrogate modeling and active learning strategies. (3) Multi-level and multi-fidelity UQ framework: Achieving dynamic and optimal allocation of computational resources across models of varying fidelities by integrating techniques like generalized approximate control variates and adaptive multi-index stochastic collocation. (4) Uncertainty-based design optimization algorithms and frameworks: Unifying probabilistic constraints and robustness metrics within a multi-objective optimization and decision-making framework under uncertainty, enabling trade-off optimization among performance, reliability, and robustness through single-loop and decoupled optimization strategies. (5) Uncertainty design and analysis based on artificial intelligence techniques: Centered on physics-informed neural networks, this direction incorporates physical knowledge and multi-source data to establish intelligent frameworks for uncertainty quantification and optimization.

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