PARAMETRIC STUDY OF PROJECTION-BASED REDUCED ORDER MODEL BY USING PROPER ORTHOGONAL DECOMPOSITION FOR FAST ENGINEERING PREDICTIONS - Bagusjalu Narutama, Priangga
Adapting from a novel ML-based method, this research utilizes the low-dimensional derivation of a system using classical proper orthogonal decomposition (POD) to create a learning map between the computational model’s input to a specific measured quantity. Existing finite element methods from MATLAB’s Partial Differential Equation solver were deployed to the Von Mises stress for problems of stress concentration of plate with circular hole, and jet turbine under combined thermal and pressure stresses. From those solution, multiple snapshots – each utilizing a variation of LHS-generated values of the same parameters – were generated to become the training samples of the learning model. A variation of machine learning models were deployed to find the least prediction error and absolute error. Those models range from simple least-squared regression, localized-based regression to neural network models. The core stage of the process is divided into three stages in Python: decomposition using POD, model training and prediction, and prediction by reconstruction of solutions using POD. Lastly, visualizations were made to evaluate performance and results using MATLAB. Evaluation of the learning models and modal analysis of the implemented cases explored some key insights. To reach a selected cumulative energy threshold, a variation of snapshot numbers of the same case would all require a similar number of modes. To improve the accuracy of the learning map by measuring the decrease of prediction error, it is generally best to increase the utilized cumulative energy threshold and increase samples in the training set. Prediction is found to be the quickest part of the process which varies just by a small amount with an increase of data elements and methods variation, this is when compared to high dependence for POD processing time to data size processed. While the cases explored in this study may have been trivial with the relatively similar solving speed to existing methods, this reduced model approach can expect to accelerate an approximation of more complex experimental systems. These complex systems have yet to be tested due to the lack of datasets available to train on.