利用板殼振動理論搭配機器學習與遺傳演算法反算積層製造結構之正交性彈性常數

Abstract

本研究首先透過熱熔堆疊(FDM)的3D列印機列印出不同堆疊方向的試片，進行共振頻率的量測，藉由歐拉-伯努力梁理論(Euler-Bernoulli Beam Theory)，反算3個方向的材料常數。接著利用3D列印容易改變尺寸的特性，改變試片的寬厚比、長厚比與長寬比，比對實驗與理論以及模擬與理論之間的誤差，探討原理論尺寸比例的適用範圍。 在長厚梁的情況下導入鐵木辛柯梁理論(Timoshenko-Ehrenfest Beam Theory)，並利用有限元素軟體比較模擬與理論之間共振頻率的對應性，選用梁理論中的切變係數(Shear Coefficient, )，由於此梁理論不易直接反算求得材料參數，因此導入基因遺傳演算法(Genetic Algorithm, GA)搭配梁理論，以共振頻率的實驗反算6個方向試片的材料常數。而在薄板的結構則利用疊加法(Superposition Method)的方式求得正交性平板的共振頻率，將其結合於基因遺傳演算法中，實驗上除了量測共振頻率之外，亦透過黏貼壓電纖維於試片的方式量測模態形狀，反算3個方向的材料常數，並比對模態的一致性。 最後透過機器學習(Machine Learning, ML)與深度學習(Deep Learning, DL)方法，以有限元素軟體生成隨機材料常數的共振頻率，先進行特徵選擇(Feature Selection)篩選出特定方向可以進行反算的材料參數，接著利用集群演算法自分群並標注模態類別，將模態資訊與共振頻率輸入至遞迴神經網路(Recurrent Neural Networks, RNN)，建立高度擬合之正交性材料常數反算模型，以利用共振頻率預測材料參數。最後透過卷積神經網路(Convolutional Neural Networks, CNN)，結合有限元素軟體生成的模態圖與集群演算法所標注之類別，建立以模態影像進行模態分類的模型。

This study fabricated specimens with different stacking orientations using a 3D printer through fused deposition modeling (FDM), measured the resonance frequency, and calculated the material constants in orthogonal directions using the Euler-Bernoulli beam theory. Taking advantage of the easy dimensional variation characteristic of 3D printing, the aspect ratios of the specimens, including width-thickness ratio, length-thickness ratio, and length-width ratio, are modified to compare discrepancies between the experimental and theoretical values, and to explore the suitable range for size ratios in theory. For the cases of length-thickness beams, the Timoshenko-Ehrenfest Beam theory is introduced, and a shear coefficient in beam theory is considered. The correspondence of resonant frequency in the theoretical analysis is compared through the finite element method. Since the beam theory is hard to calculate inversely material constants, a genetic algorithm (GA) is proposed, in conjunction with beam theory, to obtain the material constants of test pieces in 6 directions by using an experimental resonant frequency. For the orthotropic structure of thin plates, the resonant frequency is calculated using the superposition method and integrated into the genetic algorithm. In addition to measuring resonant frequency, the mode shape is excited by mounting piezoelectric fibers to the specimen. The experimental results are also verified in the consistency of the results in the numerical calculation, which used material constants in orthogonal directions by inverse calculation. In the final part, machine learning (ML) and deep learning (DL) methods are developed to generate the orthotropic material constants once time. That finite element method inputs optional material constants calculate the resonant frequency. Feature selection is initially performed to filter out the material constants that can be inversely calculated in a specific direction. Then, a clustering algorithm is used to self-cluster and label types by mode shape. The mode shape and resonant frequency are input into a Recurrent Neural Network (RNN) to establish a highly fitting inverse calculation model of orthotropic material constants. Finally, a Convolutional Neural Network (CNN) is used, combining images from the mode shape generated by the finite element method and categories labeled by the clustering algorithm to establish a model for mode types classification.