Authors: Bach Do, Makoto Ohsaki  

This paper proposes a new method for optimizing planar steel frame structures in the presence of uncertainties in material properties, external loads, and discrete design variables.  The strategy employs the power of Gaussian mixture models (GMMs) to address this complex problem. Based on selected data, the GMM is trained to predict the relationship between the random input variables and their structural response. It does this by determining the joint probability distribution function.  

The foundation of the research involves using a simple regression function to predict the structural response of the variables. With this in place, a multi-objective robust design optimization (RDO) problem is defined, comprising of three important objective functions: total mass of the structure, mean and variance of maximum inter-story drift, and maximum inter-story drift. This optimization issue is solved using a multi-objective genetic algorithm that uses the trained GMM to predict the statistical values of the impact of each variable on the structural performance. The effectiveness of this approach is demonstrated through two design examples. 

Software & Plugins Used

• MATLAB R2018a Statistics and Machine Learning Toolbox for coding and training the Gaussian mixture model (GMM) 

Paper Information

• Paper Title: Gaussian Mixture Model for Robust Design Optimization of Planar Steel Frames 
• Author(s): Bach Do, Makoto Ohsaki  
• Year: 2020 
• Link: https://link.springer.com/article/10.1007/s00158-020-02676-3 
• Type: Journal Paper
• ML Tags: Gaussian Mixtures
• Topic Tags: Structural Design, Multi-Objective Robust Design
  Optimization (RDO), Multi-Objective Genetic Algorithm
  (MOGA)