Multi-fidelity (FE+ CSA S304) Uncertainty Quantification for Masonry Structures

In civil engineering, uncertainty quantification (UQ) is essential for ensuring the safety and reliability of structures, which lay down in the contemporary limit-state design and next-generation performance- and resilience-based designs. The inherent variability in material properties, environmental factors, and loading conditions means that predictions must account for these uncertainties to minimize risks and make informed decisions. Effective uncertainty quantification allows engineers to better understand and manage the potential variations in their models, leading to more robust designs and construction practices.

To complement this, data-driven surrogate models play a vital role in efficiently simulating complex engineering systems. These models, built on large datasets, provide a faster and more accessible way to approximate the behavior of intricate systems without the need for computationally expensive simulations. By leveraging data-driven approaches, these surrogate models can rapidly produce reliable predictions, making them invaluable tools in the design, analysis, and optimization of engineering projects, all while keeping uncertainty in check.

(1) Multi-fidelity statistics (e.g., mean, variance) estimation for the load resistance of masonry walls

Estimating the mean and variance of load resistance is critical, as explicitly required by the performance-based design guideline ASCE 41-23. This research introduces an efficient and accurate multi-fidelity method that leverages information from multiple sources with varying levels of accuracy. By integrating high-fidelity data with more accessible low-fidelity data, the approach provides a balanced solution that maintains computational efficiency without sacrificing precision. This method enhances the decision-making process in civil engineering by effectively managing uncertainties while ensuring accurate estimates of key statistics.

Highlights:

• Information fusion using high-fidelity (HF) finite element models and low-fidelity (LF) design-code models (CSA S304-14) for masonry walls

• Construction of unbiased statistical estimators, offering superior accuracy compared to biased surrogate model-based estimators

• Significant variance reduction achieved

(2) Multi-fidelity reliability analysis algorithm development

Reliability analysis is a critical component of uncertainty quantification (UQ), providing a quantitative means to evaluate the probability of failure by accounting for the inherent randomness in load and resistance. Reliability analysis is essential for determining load and resistance factors in modern limit-state design. However, traditional reliability analysis methods often require a large sample size within the Monte Carlo simulation framework, leading to significant computational demands. To overcome this challenge, this study presents an efficient algorithm that integrates information fusion and filtering techniques. The algorithm is grounded in the control variate method, a classical variance reduction technique in statistics, plus the adaptive importance sampling.

Highlights:

• Development of a novel reliability analysis algorithm tailored for computationally intensive engineering problems.

• Adaptive importance sampling informed by cross-entropy-based techniques to focus on the most 'important' samples.

• Use of the control variate method to construct unbiased estimators.

• Cross-entropy-based importance sampling to inform the 'important' sampling adaptively

• Validation of the algorithm through multiple case studies.

(3) In-plane and out-of-plane resistance prediction of URM walls assisted by multi-fidelity models

While probabilistic analysis is crucial, accurate deterministic prediction of in-plane and out-of-plane resistance is equally important. Relying solely on design-code models or computationally expensive finite element models can be limiting. This study introduces a multi-fidelity Gaussian process regression model that combines a limited number of finite element model evaluations with a large number of efficient simplified analytical model evaluations, providing a more reliable resistance prediction for masonry walls.

Highlights:

• Surrogate model constructed by the multi-fidelity Gaussian Process

• Enhanced deterministic and probabilistic resistance predictions for URM walls

(4) Surrogate model based global sensitivity analysis for masonry walls under eccentric axial loading

This study focuses on evaluating the importance of various parameters affecting the load resistance of masonry walls under eccentric axial loading, with a particular emphasis on accounting for model error. By compiling an experimental database, the modeling uncertainty is quantified and used to refine the finite element model. With this corrected model, a global sensitivity analysis is conducted to determine the influence of each parameter. To enhance computational efficiency, a surrogate model is also developed.

Highlights:

• Quantification of model error for the finite element model using an experimental database.

• Construction of a polynomial chaos expansion surrogate model.

• Execution of variance-based global sensitivity analysis to assess parameter influence.