This thesis focuses on reducing the computational cost of high-fidelity structural analyses using numerical methods such as finite element method (FEM) by using surrogate models techniques of 3D structures for earthquake analysis to alleviate such computational burden of estimating the seismic response for structures. This done by addressing two surrogate models, this first one is analytical approach using Model Order Reduction (MOR), i.e approximate the original full high-order problems to a system of lower dimension. The second approach is using Machine Learning techniques and use the trained models to predict the response the dynamic response of the structure, i.e., the maximum displacement.  

The first part of this thesis studies the application of Proper Orthogonal Decomposition (POD) to reduce the full-order of linear dynamic models of 2D and 3D frames under seismic excitation and investigate its efficiency in constructing Reduced Order Models (ROM) of the dynamic response of the structures. This is done by, first apply Newmark's method to estimate the dynamic response the full-order model and pick a small discrete time (snapshots) from the solution. Then, truncate perform a Singular Value Decomposition to determine a low-dimensional approximation to high-dimensional model in terms of dominant patterns then by getting a reduced rank of equation of motion (EOM), perform the Newmark's analysis. Finally Having the reduced solutions, map back the the full rank system. The performance of POD is assessed by comparing the results of the reduced systems to the original ones using a using MATLAB script that was developed to perform all the analyses of linear systems and the procedure of POD method.  

The second part of this thesis is Machine Learning techniques i.e., Shallow/Deep Neural Network and Support Vector Machines, each algorithm was used to get trained models to predict the dynamic response of the structure. a large dataset of a ground motions (GM) was collected according to the most common recorded earthquakes in the literature and select the Intensity Measures of the GMs i.e, Peak Ground Acceleration and Spectral Acceleration as input features training dataset along with and the predominant period of the structures, to predict the maximum displacement of two separate cases that were addressed. The first case, to predict the response of single structures, and the second case, is to predict the response a group of structures together. The labels of the training dataset were obtained from the dynamic analysis of linear system using Newmarks's method. The selection of the optimum algorithm was based on the error values obtained from training, validation and testing. Also, a comparison between the methods efficiency according to the prediction accuracy and training time was investigated. Finally, addressing the importance of selection the appropriate input features to get the best accurate outcome.  

Sap2000 was used to creates all the FE 3D models that were investigated in this project, and then the mass and stiffness matrices were extracted to a MATLAB scripts for each case. For the POD case, a MATLAB script was developed according to the literature. And for Machine Learning cases, the MATLAB scripts were generated from the built-in toolboxes with modifying parameters to suit each case accordingly.  

Keywords: Surrogate modeling, Meta modeling, Reduced Order Model (ROM), Model Order Reduction (MOR), Proper Orthogonal Decomposition (POD), Singular Value Decomposition (SVD), Machine Learning, Neural Network, Support Vector Machine, Deep Neural Network, Dynamic Analysis, Structural Analysis, Earthquake Engineering.