Real-Time Visualization of Finite Element Models Using Surrogate Modeling Methods

Abstract

Parametric finite element analysis (FEA) models are commonly used in iterative design processes to obtain an optimum model given a set of loads, constraints, objectives, and design parameters to vary. In some instances, it is desirable for a designer to obtain some intuition about how changes in design parameters can affect the FEA solution of interest, before simply sending the model through the optimization loop. For example, designers who wish to explore the design space and understand how each variable changes the output in a visual way, looking at the whole model and not just numbers or a response surface of a single FEA node. This could be accomplished by running the FEA on the parametric model for a set of part family members, but this can be very time consuming and only gives snapshots of the model's real behavior. This paper presents a method of visualizing the FEA solution of the parametric model as design parameters are changed in real-time by approximating the FEA solution using parametric FEA modeling, surrogate modeling methods, and visualization methods. The implementation develops a parametric FEA mode that includes mesh morphing algorithms that allow the mesh to change parametrically along with the model geometry. This allows the surrogate models assigned to each individual node to use the nodal solution of multiple finite element analyses as regression points to approximate the FEA solution. The surrogate models can then be mapped to their respective geometric locations in real-time. The results of the FEA calculations are updated in real-time as the parameters of the design model change allowing real-time visualization.

Difference modeling for design space exploration and comparison of three-dimensional structural simulation results

“…10,26 In recent years, surrogate models have been used to emulate the stress and displacement response of each node in a finite element mesh. 5,8,9 A variety of designs are created using a design of experiments (DOE) to find a set of designs that adequately fill the design space. For a model with n input parameters, each design is represented by an n -dimensional vector.…”

“…2 Surrogate modeling has recently been applied to this problem and allows designers to quickly emulate and visualize structural FEA results across a design space. 5,8,9 Surrogate models create a relationship between input data and output data. Instead of computationally expensive simulations, these relationships can predict responses very quickly with low cost.…”

Real-time Finite Element Analysis based on surrogate model

“…Real-time FEA represents a computational strategy grounded in surrogate modeling, with the primary aim of enabling FEA in real-time or near-real-time settings. Surrogate modeling, a cost-effective mathematical approximation [2] , can substitute resource-intensive numerical analyses. By scrutinizing FEA data, it can make real-time predictions of critical performance parameters, including stress, temperature, and strain.…”

Simulation driven machine learning methods to optimise design of physical experiments and enhance data analysis for testing of fusion energy heat exchanger components

“…Full field (FF) surrogates, on the other hand, predict entire results fields generated by a simulation, e.g. predicting the temperature at the nodes of a mesh [40], [41]. These offer more flexibility since a variety of different key metrics can be extracted from the results field, however they come at an increased computational cost since the number of outputs can be very large.…”