[Paper Review] Back analysis of microplane model parameters using soft computing methods

Anna Kučerová, M. Lepš+1 more|ArXiv.org|Feb 10, 2009

Composite Material Mechanics5 citations

TL;DR

This paper proposes a soft computing framework using Latin Hypercube Sampling, stochastic sensitivity analysis, and genetic algorithm-trained neural networks to identify microplane model M4 parameters for concrete. The method reduces computational cost by replacing direct finite element simulations with trained artificial neural networks, achieving high accuracy in predicting key parameters like $k_2$ and $c_{20}$, though $c_3$ remains undetermined due to minimal influence on stress-strain response.

ABSTRACT

A new procedure based on layered feed-forward neural networks for the microplane material model parameters identification is proposed in the present paper. Novelties are usage of the Latin Hypercube Sampling method for the generation of training sets, a systematic employment of stochastic sensitivity analysis and a genetic algorithm-based training of a neural network by an evolutionary algorithm. Advantages and disadvantages of this approach together with possible extensions are thoroughly discussed and analyzed.

Motivation & Objective

• To address the high computational cost and lack of reliable calibration procedures for the microplane M4 concrete model, which requires numerous phenomenological parameters.
• To develop an efficient, automated parameter identification method that avoids time-consuming trial-and-error calibration.
• To leverage artificial neural networks trained via evolutionary algorithms to predict material parameters from simulated or experimental stress-strain responses.
• To validate the method using both synthetic simulations and real uniaxial compression test data, demonstrating feasibility and accuracy.
• To identify which parameters are most influential and which can be neglected, such as $c_3$, based on sensitivity analysis.

Proposed method

• Employ Latin Hypercube Sampling to efficiently generate diverse input parameter sets for training, reducing the number of required simulations.
• Perform stochastic sensitivity analysis via Monte Carlo simulation to quantify the influence of each parameter on the model response.
• Train layered feed-forward artificial neural networks using the GRADE genetic algorithm to optimize network weights and topology.
• Use the simulated data from sensitivity analysis as the training set for the neural networks, with validation on independent test data.
• Apply the trained neural networks to predict material parameters from experimental stress-strain curves, including real uniaxial compression data.
• Validate predictions by comparing simulated stress-strain curves from predicted parameters with original experimental or simulated data.

Experimental results

Research questions

• RQ1 Can a neural network trained on simulated microplane model responses accurately predict the input parameters of the M4 model?
• RQ2 How does the combination of Latin Hypercube Sampling and stochastic sensitivity analysis improve the efficiency and reliability of parameter identification?
• RQ3 What is the impact of individual parameters on the stress-strain response, and which parameters are negligible (e.g., $c_3$)?
• RQ4 Can the proposed method reduce the computational burden of parameter calibration compared to direct finite element analysis?
• RQ5 To what extent can the trained neural network generalize to real experimental data, such as uniaxial compression tests?

Key findings

• The proposed method successfully identified all microplane model M4 parameters except $c_3$, which showed negligible influence on the stress-strain response.
• The neural network predicted $k_2 = 767.777$ for a target value of $748.857$, demonstrating near-perfect precision in triaxial loading simulations.
• For real uniaxial compression data, the method predicted $c_{20} = 5.27065$, which was outside the training interval but consistent with observed data deviations.
• The training process showed minimal overfitting, with error evolution indicating stable convergence during backpropagation.
• The method reduced the number of required simulations through Latin Hypercube Sampling, though the total computational cost remained high—approximately 25 days on a single PC for 30 uniaxial tests.
• Parallel execution on 7 computers reduced the total time to under 4 days for uniaxial tests and under one day for hydrostatic and triaxial tests.