An optimized hybrid finite element analyses - Artificial neural networks technique for estimating in-plane orthotropic mechanical properties of printed circuit boards

Abstract

Explicitly modeling Printed Circuit Boards (PCBs) in Finite Element Analysis (FEA) is not practical due to the complex multi-component structure of PCBs. To overcome this complication, a PCB can be simplified and modeled as an orthotropic plate with equivalent mechanical properties that result in the same natural frequencies as the actual PCB. This research introduces an optimized hybrid technique combining FEA and Artificial Neural Networks (ANNs) to accurately estimate the equivalent in-plane orthotropic mechanical properties of PCBs. This study presents a systematic approach where natural frequencies obtained from FEA are used to train ANNs for predicting the equivalent representative mechanical properties. The research employs a rigorous optimization procedure involving various ANN configurations (i.e., different learning algorithms, activation functions, and number of hidden neurons) and training dataset sizes. To further ensure the reliability of the results, 10 cross-validation are carried out for each ANN configuration by employing dynamic data-splitting strategy, and all measures used for assessing the accuracy of the ANN predictions are based on averaged results for the 10 cross-validations. The accuracy of the ANN predictions is tested against both simulated and experimental data. The Mean Absolute Percentage Error (MAPE) is found to be about 4 % based on material properties against the simulated data, and about 1.2 % based on natural frequencies against the experimental data point. The results demonstrate superior predictive accuracy and efficiency compared to existing models, highlighting the potential of the proposed approach in advancing the reliability and performance of PCB mechanical property estimations.