Open research questions in Probabilistic and Robust Engineering Design
137 gap statements mined from Probabilistic and Robust Engineering Design papers in our 4.5M-paper local library, which holds 1,541 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.
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What the literature leaves open
The need for efficient inference methods in the presence of hybrid uncertainties. The lack of a robust framework for calibrating biofilm growth models.
Bayesian Updating of constitutive parameters under hybrid uncertainties with a novel surrogate model applied to biofilms · 2026 · DOIThe need to develop and implement solution algorithms for tracing nonlinear equilibrium paths within the framework of the SSFEM.
A new generalized displacement control for nonlinear spectral stochastic finite element problems · 2026 · DOIThe improved approximate integral method is limited by fixed empirical formulas that fail to fully compensate for projection-induced bias.
The lack of robust and efficient surrogate models for stochastic simulations that can accurately capture the underlying processes while reducing the influence of noise. The limitation of machine learning methods in capturing predictive uncertainty due to the requirement of large datasets. The need for a novel framework that can combine the local accuracy of SK with the global approximation strength of aPCE.
A Gauss-Seidel-based Stochastic Kriging integrated with arbitrary polynomial chaos expansion for stochastic simulators · 2026 · DOIThe lack of systematic analytical frameworks for uncertainty evaluation in high-dimensional systems. The need for efficient methods to estimate output statistics in the presence of numerous uncertainties. The limitation of existing methods in handling complex systems with multiple uncertain parameters.
MPCM-Taguchi: an efficient method for estimating output statistics in high-dimensional uncertain systems · 2026 · DOITraditional CFD-based UQ is computationally expensive. The uncertainty is inherently unknown and typically inferred through analysis of repeated samples. The training of the SK surrogate model primarily involves sample collection, surrogate model fitting, which can be time-consuming.
A Robust Aerodynamic Design Optimization Methodology for UAV Airfoils Based on Stochastic Surrogate Model and PPO-Clip Algorithm · 2025 · DOIFurther research can be done to improve the efficiency of the RADO process. The application of the proposed methodology to other types of UAVs or flight conditions can be explored. The comparison of the proposed methodology with other optimization algorithms can be conducted.
A Robust Aerodynamic Design Optimization Methodology for UAV Airfoils Based on Stochastic Surrogate Model and PPO-Clip Algorithm · 2025 · DOIVariance-based methods are not well-suited for heavy-tailed or multimodal distributions. Entropy-based methods are difficult to estimate. There is a need for a more efficient and effective method for global sensitivity analysis.
The need to reduce the numerical complexity to make the method applicable to harder test problems. The challenge of adapting the method to batch design, to tackle cases where several instances of the simulator can be run in parallel.
The lack of a Bayesian strategy to solve the Quantile Set Inversion problem. The need for a method to efficiently approximate the set of interest in the context of QSI. The limitation of prior work in addressing the specific challenges of QSI problems.
However, its effectiveness may be significantly affected when experimental or monitoring data are sparse.
A Population-Based Model Bias Correction Framework Using Federated Learning for Simulation Models of Nonlinear Dynamic Systems · 2025 · DOIIt is prevalent in multiple engineering fields, but research regarding reliability analysis (RA) under model uncertainty is relatively sparse.
Reliability Analysis Considering Model Uncertainty Based on Adaptive Expectation Maximization-Enhanced Stochastic Polynomial Chaos Expansion · 2025 · DOIWhile sensitivity analysis improves the transparency and reliability of mathematical models, its uptake by modelers is still scarce.
Although the gPC expansion method was initially selected for the reliability analysis of simulation-based RBCCD, its performance against state-of-the-art, the most-probable-point (MPP) method, has not been established yet.
A Comparative Study Between the Generalized Polynomial Chaos Expansion- and First-Order Reliability Method-Based Formulations of Simulation-Based Control Co-Design · 2024 · DOIIn addition to the previous advantages, the DSSM can be used in contexts were input distributions are not fully known (model uncertainty), and one needs to resort to methods such as the principle of maximum entropy to select the input distributions that best fit available information according to some criteria.
Simple and efficient uncertainty propagation within numerical simulations involving low-dimensional random spaces · 2026 · DOIThe computational precision of the SSIS algorithm remains limited, and its coefficient of variation is considerable. The original SS algorithm has several limitations, such as correlated samples and large coefficient of variation.
An enhanced subset simulation algorithm integrating importance sampling for structural reliability analysis · 2026 · DOIIn particular, the stiffness matrix AMC remains sparse and the complexity of assembling AMC grows only linearly with Nh.
Application of randomized quadrature formulas to the finite element method for elliptic equations · 2026 · DOISatisfying constraints of shared states between subsystems under uncertainty leads to conflict issues and has not been properly studied yet.
The need for validation, verification, and calibration studies to quantify desired system-level reliabilities. The lack of studies investigating system-level reliabilities achieved by component-based and system-based design methods.
System Reliability of Structural Steel Frames Designed Using Component- and System-Based Design Methods · 2026 · DOIInvestigation of the method's applicability to other types of biological systems, - Development of more advanced surrogate models to improve the accuracy of the results, - Exploration of the method's potential for real-time monitoring and control of biofilm…
Bayesian Updating of constitutive parameters under hybrid uncertainties with a novel surrogate model applied to biofilms · 2026 · DOIThe single displacement control is limited to the reaction force corresponding to the prescribed displacement, - The load control is restricted to deterministic external loads, - The SSFEM application to geometrically nonlinear finite element problems remains comparatively…
A new generalized displacement control for nonlinear spectral stochastic finite element problems · 2026 · DOIExploring alternative combinations of basis functions for constructing Kriging metamodels; Investigating other techniques for solving timeindependent reliability analysis problems, such as the inverse reliability method (where the reliability level is an input parameter); Addressing time-dependent reliability problems considering the presence of a stochastic contribution; Solving engineering system design problems…
Sequential and Decoupled Reliability Analysis applied to time-dependent engineering systems · 2026 · DOIThe number of available samples is often limited to a few hundred, - The deep learning-based approaches typically require large datasets to achieve reliable generalization, - The conventional PCE methods require prior knowledge of the input…
A Gauss-Seidel-based Stochastic Kriging integrated with arbitrary polynomial chaos expansion for stochastic simulators · 2026 · DOIFurther research is needed to explore the application of the new entropy proxy to different types of distributions, - The relationship between the entropy and the expectation of the partial derivatives could be further investigated, - The use of the new entropy proxy in combination with other sensitivity analysis methods could be…
To further improve the accuracy and efficiency of the proposed algorithm. To apply the algorithm in various fields, such as engineering and mechanics.
An enhanced subset simulation algorithm integrating importance sampling for structural reliability analysis · 2026 · DOI
Most-cited papers in Probabilistic and Robust Engineering Design
- A Note on the Delta Method · The American Statistician · 1992 · 1,642 citations
- Simulating normalizing constants: from importance sampling to bridge sampling to path sampling · Statistical Science · 1998 · 613 citations
- Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability · Risk Analysis · 1994 · 527 citations
- An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models · Risk Analysis · 1988 · 460 citations
- Variants of uncertainty · Cognition · 1982 · 446 citations
- Testing for an unstable root in conditional and structural error correction models · Journal of Econometrics · 1994 · 434 citations
- MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS · Annals of the New York Academy of Sciences · 1960 · 380 citations
- Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems · Risk Analysis · 1998 · 330 citations
- Generalized theory of uncertainty (GTU)—principal concepts and ideas · Computational Statistics & Data Analysis · 2006 · 264 citations
- A Multidimensional Scaling Stress Evaluation Table · Field Methods · 2000 · 262 citations
Most recent work
- Generative data-physics fusion for hierarchical reliability assessment · Reliability Engineering & System Safety · 2026
- Interval theory-embedded data-driven identification framework for uncertain thermo-elastic parameters · Applied Mathematical Modelling · 2026
- Variational Bayesian inference-assisted approach for multi-objective reliability-based design optimization · Applied Mathematical Modelling · 2026
- A novel reliability-oriented concurrent topology optimization framework based on improved sequential decoupling and interval-modeled boundary modification strategies · Composite Structures · 2026
- Non-intrusive smoothed stochastic finite element method with multi-source uncertainties · International Journal of Mechanical Sciences · 2026
- Compliance- and Reliability-Based Bidesign for Space Manipulator Controller With Correlated Uncertainties and Actuator Degradation · IEEE Transactions on Aerospace and Electronic Systems · 2026
- Uncertainty in lifetime data quantified with Bayesian adaptive Hamiltonian methods · Measurement · 2026
- Trajectory optimization under uncertainty: A convex optimization approach with polynomial chaos-based uncertainty quantification · Chinese Journal of Aeronautics · 2026
- Enhancing the efficiency of time-dependent density functional theory calculations of dynamic response properties · npj Computational Materials · 2026
- Multi-fidelity probabilistic failure onset analysis of composite structures under uncertainties · Computer Methods in Applied Mechanics and Engineering · 2026
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