Kriging Surrogate Modeling for Refined Finite Element Response
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Solution Overview
Problem
The inefficiency and high computational demands of refined finite element models for complex structures, particularly in dynamic response analysis, due to their stringent memory and computing power requirements, hinder effective pre-safety and stability assessments.
Innovation Solution
A method utilizing a Kriging model-driven rough mirror information model to predict the response of refined finite element models, incorporating Latin Hypercube Sampling and probabilistic finite element analysis to construct a surrogate model, reducing dependence on model fineness and computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a refined finite element model is used to characterize structural characteristics, then the accuracy of structural response prediction is improved, but the computational time and resource requirements increase significantly
Solution Approach 1:
The patent creates a surrogate model that copies the essential input-output behavior of the refined finite element model without replicating its complex computational structure. The surrogate model learns the mapping between input parameters and structural responses through training on a subset of data, enabling fast predictions that mimic the refined model's accuracy without its computational burden.
Solution Approach 2:
The patent replaces the expensive and time-consuming refined finite element model with a cheaper surrogate model that can be rapidly evaluated. The surrogate model uses simplified mathematical operations (such as neural network forward propagation) compared to the full finite element analysis, making it computationally inexpensive while maintaining predictive accuracy for engineering purposes.
2Reliability
If a refined finite element model is used for dynamic response analysis, then the reliability of safety and stability assessment is improved, but the memory and computing power requirements become extremely stringent
Solution Approach 1:
The surrogate model captures the essential input-output relationships of the refined finite element model through training, creating a simplified representation that maintains predictive reliability for safety and stability assessments. The model learns the mapping from input parameters to structural responses, enabling reliable predictions without requiring the complex computational resources needed for direct finite element analysis.
Solution Approach 2:
The surrogate model acts as an intermediary between the input parameters and the structural responses. Instead of directly computing responses through the complex refined finite element model, the surrogate model serves as a mediator that translates inputs to outputs using learned relationships, reducing the computational barrier while maintaining assessment reliability.
3Measurement precision
If the fineness of the structural finite element model is increased, then the accuracy of structural characterization is improved, but the calculation efficiency deteriorates
Solution Approach 1:
The surrogate model copies the input-output behavior of the refined model without copying its computational complexity. By training on data from the refined model, the surrogate learns accurate structural characterization relationships and can evaluate them rapidly using simple mathematical operations, achieving both high accuracy and high calculation efficiency.
Solution Approach 2:
The patent performs preliminary training of the surrogate model using a subset of data from the refined finite element model. This preliminary action captures the essential structural characterization relationships in advance, allowing subsequent predictions to be made efficiently without repeatedly executing the complex finite element analysis for each new input scenario.
Data Source
AI summary
The invention provides a prediction method for the response of a refined finite element model of a complex structure. It includes establishing a refined finite element model and a rough mirror information model with different mesh densities; using Latin Hypercube Sampling (LHS) for random sampling to construct input parameter sample sets of sizes m and n; performing probabilistic finite element analysis and extracting output response sample sets; constructing a Kriging model based on the first m sets of data in the output response sample sets, and using validation error to evaluate predictive accuracy; predicting the output response of the refined finite element model corresponding to the remaining n−m sets of data in the response sample sets of the rough mirror information model according to the Kriging model. This method reduces surrogate model's dependence on the forward calculation model's fineness and significantly reduces calculation time for system response of complex structures.