Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Abstract

Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested.

Moment-independent sensitivity analysis of a fold mechanism based on an active learning kriging method

“…Sampling, also known as Design of Experiments (DOE), is a pivotal issue in experiments or simulations. 9,10 Sampling techniques can be classified into one-shot sampling and sequential sampling. Monte Carlo sampling is one of the most widely used one-shot sampling approach.…”

“…Comparing with one-shot sampling, sequential sampling technique needs lower computational budget but better in approximations. 9 Variance-based approaches are a kind of classical sequential sampling approaches. 12 In the whole design space, variance-based approach assumes that regions with large prediction variances contain more errors.…”

“…The surrogate model, also known as the meta-model, is another way to reduce computation. 9 In surrogate model, a cheap-to-run approximation model is constructed to replace the original complex model. Up to now, various surrogate models have been presented.…”

Novel Bayesian Inference-Based Approach for the Uncertainty Characterization of Zhang’s Camera Calibration Method

“…In this sense, one of the challenges in modern metrology is to provide the mathematical tools to quantify the uncertainties of inverse and non- linear problems in scientific modeling [ 19 ]. In fact, this is a research hotspot where the solutions presented to date combine different mathematical algorithms [ 20 ]. Among them, the Bayesian method has proved its worth in the inverse uncertainty inference [ 21 , 22 , 23 ].…”

Editorial Conclusion for the Special Issue “Advances in Computational Mechanics for Symmetrical Engineering Systems”

“…Subsequently, under uncertain circumstances, Sleesongsom et al [2] investigated the multi-objective reliability-based optimization design of an aircraft structure and presented a novel two-step analysis strategy that could greatly reduce the analysis complexity and enhance the efficiency of predicting the possibility safety index. Additionally, as the surrogate-model-assisted practices have obtained ever-increasing attentions in recent decades for uncertainty-related symmetrical engineering systems, Wang et al [3] accomplished a comprehensive review of surrogate modeling methods available for uncertainty quantification and propagation. Besides the popular single and hybrid surrogate models, state-of-art experimental design technologies including one-shot and adaptive sampling strategies were discussed in detail.…”