Kriging, Polynomial Chaos Expansion, and Low-Rank Approximations in Material Science and Big Data Analytics

Area of Science:

• Material Science and Engineering
• Computational Mechanics
• Surrogate Modeling

Background:

• Estimating material properties and failure modes relies on experiments and computationally expensive modeling.
• Brittle materials like concrete exhibit highly nonlinear behavior, complicating optimization.
• Current optimization methods are often computationally prohibitive for complex material behaviors.

Purpose of the Study:

• To investigate the application of surrogate models for predicting mechanical characteristics of concrete.
• To evaluate the accuracy of various surrogate modeling techniques for concrete properties.
• To identify an optimal solution for predicting concrete compressive strength using meta-models.

Main Methods:

• Utilized polynomial chaos expansion, Kriging, and canonical low-rank approximation as surrogate models.
• Applied these meta-models to predict the compressive strength of two distinct concrete types.
• Examined various assumptions within surrogate models and assessed their impact on accuracy.

Main Results:

• Demonstrated the feasibility of using surrogate models for predicting concrete mechanical properties.
• Evaluated and compared the predictive accuracy of different surrogate modeling approaches.
• Successfully identified an optimal surrogate model configuration for the investigated problem.

Conclusions:

• Surrogate models offer a computationally efficient alternative to traditional methods for material property prediction.
• The study provides a framework for applying surrogate modeling in material science and engineering.
• This research paves the way for broader applications of meta-models in predicting complex material behaviors.