Machine learning in predicting mechanical behavior of 3d printed beams with triply periodic minimal surface (tpms) sandwich cores

VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH UNIVERSITY OF TECHNOLOGY TRAN QUOC KIM MACHINE LEARNING IN PREDICTING MECHANICAL BEHAVIOR OF 3D PRINTED BEAMS WITH TRIPLY PERIODIC MINIMAL SURFACE (TPMS) SANDWICH CORES Major: Civil Engineering Major ID: 8580201 MASTER THESIS HO CHI MINH CITY, JANUARY 2023 VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY HO CHI MINH UNIVERSITY OF TECHNOLOGY TRAN QUOC KIM MACHINE LEARNING IN PREDICTING MECHANICAL BEHAVIOR OF 3D PRINTED BEAMS WITH TRIPLY PERIODIC MINIMAL SURFACE (TPMS) SANDWICH CORES MƠ HÌNH MÁY HỌC TRONG DỰ ĐOÁN ỨNG XỬ CƠ HỌC CỦA DẦM IN 3D GIA CƯỜNG LÕI SANDWICH BỀ MẶT CỰC TIỂU TAM TUẦN HOÀN Major: Civil Engineering Major ID: 8580201 MASTER THESIS HO CHI MINH CITY, January 2023 THIS THESIS IS ACCOMPLISHED AT HO CHI MINH UNIVERSITY OF TECHNOLOGY – VNU HCMC Supervisors: Dr Nguyen Thi Bich Lieu Signature: Assoc Prof Luong Van Hai Signature: Examiner 1: Dr Thai Son Signature: Examiner 2: Dr Nguyen Phu Cuong Signature: The master thesis is defended at Ho Chi Minh University of Technology – VNU HCMC on 13th January 2023 The thesis defense grading committee consists of: Chairman: Assoc Prof Do Nguyen Van Vuong Secretary: Dr Nguyen Thai Binh Reviewer: Dr Thai Son Reviewer: Dr Nguyen Phu Cuong Council Member: Assoc Prof Luong Van Hai Confirmations of the Chairman of thesis defense grading committee and the Dean of faculty of thesis major after the thesis has been corrected (if any) CHARIMAN OF DEAN OF FACULTY THESIS COMMITTEE FACULTY OF CIVIL ENGINEERING Assoc Prof Do Nguyen Van Vuong i VIETNAM NATIONAL UNIVERSITY HCMC HO CHI MINH UNIVERSITY OF TECHNOLOGY SOCIALIST REPUBLIC OF VIETNAM Independence - Freedom - Happiness MASTER THESIS ASSIGNMENTS Full name: Tran Quoc Kim Date of birth: 30/07/1999 Major: Civil Engineering Student ID: 2170979 Place of birth: Can Tho Major ID: 8580201 I THESIS TITLE: Machine learning in predicting mechanical behavior of 3D printed beams with triply periodic minimal surface (TPMS) sandwich cores Mơ hình máy học dự đốn ứng xử học dầm in 3D gia cường lõi sandwich bề mặt cực tiểu tam tuần hoàn II THESIS ASSIGNMENTS AND CONTENTS: Modeling the triply periodic minimal surface (TPMS) core reinforced beam, and comparing with experimental results; Collecting beam’s behavior data based on simulations while changing beam’s geometric properties; Creating a machine learning model to predict mechanical behavior of the beams III DATE OF DELIVERING: 05/09/2022 IV DATE OF COMPLETION: 27/12/2022 V SUPERVISORS: Dr Nguyen Thi Bich Lieu Assoc Prof Luong Van Hai Ho Chi Minh City, 6th March 2023 SUPERVISORS Dr Nguyen Thi Bich Lieu HEAD OF DEPARTMENT Assoc Prof Luong Van Hai DEAN OF FACULTY FACULTY OF CIVIL ENGINEERING ii ACKNOWLEDGEMENT Having had the opportunity to study a master's program at the Vietnam National University Ho Chi Minh City – Bach Khoa University, I would like to express my sincere appreciation to the school administrators and departments for creating favorable conditions for me to complete the study program I also would like to express my gratitude to the lecturers of the Faculty of Civil Engineering who have always been dedicated to teaching and imparting useful knowledge In addition, I would like to express my deep acknowledgements to Professor Nguyen Xuan Hung and the CIRTech Institute of Technology for giving me the opportunity to work with the excellent lecturers and colleagues at here I would not be able to complete this thesis without the guidance of my supervisors Doctor Nguyen Thi Bich Lieu and Associate Professor Luong Van Hai I would like to express my sincere gratitude to them Their orientations and suggestions are both the motivation and the objective to help me steady to complete the thesis I am truly grateful to Vingroup Innovation Fund (VinIF) for the financial support during my research and implementation of the thesis under project code VINIF.2019.DA04 Moreover, I would like to thank my family and friends for always supporting and encouraging me throughout the study and research process Finally, I would like to wish my teachers, colleagues, family and friends good health, successfulness and happiness This thesis may have several shortcomings, so I would like to receive valuable comments from committee members and other students My sincere thanks Ho Chi Minh City, 6th March 2023 GRADUATE STUDENT TRAN QUOC KIM iii ABSTRACT (Presented in English) Bioinspired porous structures are highly porous structures with an outstanding strength-to-weight ratio Their application has been applied in various fields such as aerospace and biomedical engineering, transportation, etc Recent research has indicated that 3D-printed plastic triply periodic minimal surfaces (TPMS) structure has tremendous impacts on cement beams, reducing maximum deflection, improving peak load, and enhancing ductility This study proposes a machine learning (ML) surrogate model to predict beam behaviors subjected to a static bending load To reinforce the considering beams, different combinations of core layer numbers and plastic volume fractions are adopted Their influences are investigated using the Finite Element Method (FEM) Consequently, the gathered data are used to develop the ML model through a three-phase assessment to achieve the most appropriate model for the present problem This assessment consists of model hyperparameter tuning, first performance assessment, and overfitting handling with Deep Learning (DL) techniques The results indicate a proportional relationship between the volume fraction and the beam peak load as well as the maximum deflection while increasing the number of TPMS layers enhances these properties nonlinearly Additionally, from the model predictions, there might be a limit value that each trait cannot achieve at a specific volume fraction with any number of layers The final model developed in this study is verified by the maximum deviations between FEM and predictions for peak loads and maximum deflections, that are 2.5% and 3.5%, respectively A new early stopping condition can maximize the final model performances on both train and test data, therefore verifying the model's reliability in handling noisy data from FEM iv TÓM TẮT LUẬN VĂN (Trình bày tiếng Việt) Cấu trúc xốp lấy cảm hứng từ sinh học cấu trúc có độ xốp cao tỉ lệ cường độ trọng lượng lớn Chúng ứng dụng nhiều lĩnh vực hàng không vũ trụ, kỹ thuật sinh học, giao thông vận tải, vv Nghiên cứu gần cấu trúc bề mặt cực tiểu tam tuần hồn (TPMS) nhựa in 3D có tác động to lớn đến dầm xi măng, giảm độ võng cực đại, cải thiện tải trọng giới hạn, tăng cường độ dẻo dai Nghiên cứu đề xuất mơ hình thay máy học (ML) để dự đoán hành vi dầm chịu tải uốn tĩnh Để gia cố dầm, nhiều kết hợp khác số lớp lõi tỉ lệ thể tích nhựa áp dụng Ảnh hưởng chúng khảo sát phương pháp phần tử hữu hạn (FEM) Từ đó, liệu thu thập sử dụng để phát triển mơ hình ML thơng qua phương pháp đánh giá ba bước để tìm mơ hình phù hợp cho vấn đề Đánh giá bao gồm điều chỉnh siêu tham số mơ hình, đánh giá hiệu mơ hình đầu xử lý q khớp kỹ thuật học sâu (DL) Kết cho thấy mối quan hệ tỉ lệ thuận tỉ lệ thể tích tải trọng giới hạn dầm độ lệch tối đa tăng số lớp TPMS cải thiện tính chất cách phi tuyến Ngồi ra, dự đốn mơ hình chứng minh tồn giá trị giới hạn mà đặc điểm đạt tỉ lệ thể tích cụ thể với số lớp Mơ hình cuối phát triển nghiên cứu kiểm chứng sai số tối đa FEM dự đoán cho tải cực đại độ lệch tối đa, 2,5% 3,5% Một điều kiện dừng sớm tối đa hóa hiệu mơ hình hai tập liệu huấn luyên kiểm thử, qua chứng minh độ tin cậy mơ hình liệu phức tạp từ FEM v COMMITMENT I hereby declare that this thesis entitled "Machine learning in predicting mechanical behavior of 3D printed beams with triply periodic minimal surface (TPMS) sandwich cores” is my research work All sources referenced are properly and fully cited The research data and results in this thesis are guaranteed to be honest and have never been used to defend any other theses I will take full responsibility for this statement Ho Chi Minh City, 6th March 2023 GRADUATE STUDENT TRAN QUOC KIM vi TABLE OF CONTENTS MASTER THESIS ASSIGNMENTS i ACKNOWLEDGEMENT ii ABSTRACT iii COMMITMENT .v TABLE OF CONTENTS vi LIST OF ABBREVIATIONS viii LIST OF TABLES AND CHARTS ix LIST OF FIGURES x CHAPTER INTRODUCTION 1.1 Research topic 1.2 Research objective and contents 1.3 Research object and scope 1.4 Thesis structure CHAPTER LITERATURE REVIEW 2.1 International research 2.2 Domestic research 2.3 Summary .8 CHAPTER THEORETICAL BACKGROUND 3.1 Triply periodic minimal surface structures 3.1.1 Minimal surface 3.1.2 Triply periodic minimal surface .10 3.1.3 Applications of TPMS .13 3.2 TPMS-reinforced beam .14 3.2.1 Additive manufacturing 14 3.2.2 Cement beam with 3D printed TPMS core 15 3.2.3 Effectiveness of TPMS core 16 3.3 Simulation model 18 3.3.1 Beam geometry .18 vii 3.3.2 Materials .21 3.3.3 Finite element analysis simulation 23 3.4 Machine learning model 27 3.4.1 Introduction to machine learning 27 3.4.2 Artificial neural networks .28 3.4.3 Deep Learning 36 3.5 Thesis tasks 37 CHAPTER RESULTS AND DISCUSSIONS 40 4.1 Finite element method process 40 4.1.1 Mesh convergence study 40 4.1.2 Impact of TPMS-core properties 41 4.2 Machine learning process 46 4.2.1 Model hyperparameter tuning 46 4.2.2 Model assessment 51 4.2.3 Handling overfitting .52 4.2.4 Best model predictions 57 CHAPTER CONCLUSION AND RESEARCH DEVELOPMENT DIRECTION 63 5.1 Conclusion 63 5.2 Research development direction 64 LIST OF PUBLICATIONS 65 REFERENCES 66 BIOGRAPHICAL SKETCH 70 56 contrast, the early stopping model achieved 79% of the maximum train loss performance value (𝐴 ) which is a 94% ratio of the best-test-loss models Figure 4.8 shows that several epochs have comparable loss for both train and test data, but the previous model cannot stop training at those epochs This section’s results suggest that the stop condition of loss correlation can prevent the model from overfitting effectively Therefore, the modified early stopping model with a stop patience of 300 epochs is the most efficient model for this problem Figure 4.13 The convergence history of the final model [1] The convergence history of the model is shown in Figure 4.13 with the minimum loss values for both the train and test data occurring at epoch 99 Although a smaller train loss could be obtained during training, the test loss may be slightly higher The performance metrics of the model are presented in Table 4.7 showing a 10.3 times reduction in correlation index and a significant decrease (three times smaller) in test loss compared to the previous model The high stop patience also results in longer training time, but the model can generate good approximations for the response of beam PC9, which is not included in train data A low average absolute error of 0.1kN and root mean square error of 0.15kN can be found in the test metrics 57 Table 4.7 The assessment values of the final model [1] 𝑀𝑆𝐸 𝑀𝑆𝐸 𝑀𝑆𝐸 (kN ) 𝑀𝑆𝐸 (kN ) 1− 0.0151 0.0222 0.4698 𝑅𝑀𝑆𝐸 (kN) 𝑀𝐴𝐸 (kN) Training time (s) 0.1491 0.0953 89.1 4.2.4 Best model predictions The well-trained model concluded in the previous subsection is used to generate force-displacement curves for nine beams in Figure 4.14 While the calculation time of FEA simulations for each beam varied from 266s to 7600s, 0.806s is the total computational time for all beams with this surrogate model Besides, the ML model provides an excellent approximation for this study problem and can be used as fit curves for the beams' responses, particularly for the three-layer beam data, which is described as noisy data The smoothness of the fit curves is due to the 'SoftPlus' activation function at the output layer In addition, the trained model can predict the behavior of different beams reinforced with TPMS The ML model can make predictions for various TPMSreinforced beams that were not investigated by simulations Using their peak loads and maximum midpoint displacements, the feature surfaces, considering both volume fraction and number of TPMS layers, are illustrated in Figure 4.15 and Figure 4.16 The black dots on these surfaces represent FEA results, while the peak load and deflection of the non-reinforced beam are obtained from a previous study [19], which were 2.88kN and 1.35mm, respectively 58 a) b) c) Figure 4.14 The force-displacement curves of the a) 10%, b) 15% and c) 20% volume fraction reinforced beams from the ML model and the FEA simulations [1] 59 The peak loads obtained from both FEA and the ML model are in good agreement with a maximum deviation of 2.5% The effect of volume fraction on peak load is linear for each number of reinforcement layers, but the lines for different numbers of layers may be parallel with different distances between them For instance, the increase in peak load between one and two layers is about 1.5kN, while between two and three layers it is about 1kN and decreases with increasing volume fraction This increase is greatly reduced to 0.5kN between three and four layers with a 20% volume fraction The relationship between the peak load and the number of layers with a certain volume fraction are nonlinear, and as the volume fraction increases, the curve tends to reach its maximum value with a smaller number of TPMS layers However, for a 5% volume fraction beam, the peak load has a relatively linear relationship with the number of TPMS layers Generally, increasing the number of layers leads to a specific peak load value, which can be achieved with at least four layers of Primitive TPMS in the case of a 20% volume fraction, which is similar to the plastic TPMS beam in the previous research [41] The agreement between FEA and the ML model in terms of maximum deflection is also confirmed, with the largest deviation being 3.5% for beam PC9 The trends in the influence of TPMS reinforcement on deflection are similar to those observed for peak load However, the linear relationships between volume fraction and deflection are not parallel for different TPMS beams For example, the increase in maximum displacement from one-layer to two-layer beams is greater at lower volume fractions This increase from two to three-layer beams and from three to fourlayer beams may remain constant regardless of the volume fraction Additionally, the relationship curves between the considering beam response and the number of TPMS layers are nonlinear 60 a) b) c) Figure 4.15 The final surrogate model’s predictions for the beam peak load with a) the 3D view, the side view of b) the peak load – volume fraction plane and c) the peak load - number of core layers plane [1] The tiny deviations between the maximum displacements of two-layer and three-layer beams may result in reduced accuracy prediction of the surrogate model for this feature However, both FEA and ML approaches show the same tendency for the impact of the number of layers on the deflections, which is similar to that on the peak load It appears that there may be a maximum displacement value that can be achieved for a specific volume fraction despite any number of core layers In another word, as the number of TPMS layers increases, the ceiling value of the maximum displacement is produced 61 a) b) c) Figure 4.16 The final surrogate model’s predictions for the beam maximum deflection with a) the 3D view, the side view of b) the maximum deflection – volume fraction plane and c) the maximum deflection - number of core layers plane [1] In sum, increasing the number of TPMS layers can enhance load-bearing responses in beam structures for both peak load and maximum deflection, but the difficulties in fabrication should be considered The core-shell thickness of 𝑛-layer beams is 𝑛-times thinner than that of single-layer beams as provided in Eq (3.10) Furthermore, one-layer beams can achieve comparable peak loads at higher volume fractions, though they may produce larger deflections than multiple-layer beams at the same load (please see Figure 4.14 ) An example is the small deviations between the force-displacement curves of two and three-layer beams The complexity of the TPMS geometry can be indicated as the main reason for this behavior In fact, by 62 increasing the volume fraction, a greater confinement effect appears On the other hand, as the number of layers increases, the confined cement volume is widened Therefore, with low volume fractions, increasing the number of layers may be more effective as the strength of the cement is greater due to the confinement This relationship is straightforward and can be found in both Figure 4.15c and Figure 4.16c 63 CHAPTER CONCLUSION AND RESEARCH DEVELOPMENT DIRECTION 5.1 Conclusion In this thesis, the plastic reinforced cement beam with the Primitive TPMS type has been studied by FEA simulations These beams’ behaviors have been adopted to conduct a surrogate model based on ML algorithms Some key conclusions can be denoted as follows:  A novel meshing strategy for the complicated geometry of TPMS structures is introduced The reliability of this number-of-element-based mesh has been verified by the experimental results of the reference study;  Nine TPMS reinforced beam scenarios including 10%, 15%, and 20% volume fractions along with one, two, and three core layers are investigated  The relationships between the beam’s peak load and its volume fraction could be denoted as straight lines Similar relations could also be indicated with the impact of this volume fraction on the maximum midpoint displacement However, these linear relations have different inclination angles for each number of layers;  The influences of the number of layers on both maximum deflection and maximum load are nonlinear curves By increasing the number of layers, the beam's mechanical properties tend to attain ceiling values;  The beam strength might mainly depend on the strength of the cement core The most important contribution of the TPMS core may be confinement creation;  The heaviest proposed architecture, which is the three 150-node layers, along with the ‘ReLU’ activation function and ‘Adam’ optimization algorithm can produce good predictions on the training dataset despite the noisy FEA data;  Different deep learning techniques, namely kfolds cross-validation, dropout, and modified early stopping conditions are adopted to alleviate the overfitting in this work; 64  The model which used a new stopping condition of loss correlation could be denoted as the most appropriate model for this thesis problem;  The final model concluded from the proposed three-phase process can produce excellent predictions for various reinforcement cases without inefficient FEA simulations;  Two key mechanical properties, that are the peak load and the maximum displacement, are illustrated as surfaces to indicate the influence of both volume fraction and the number of layers In brief, the surrogate model has been achieved based on a well-trained ANN model with an effective DL technique This result can expand the potential of using the TPMS-reinforced beam in numerous practical applications 5.2 Research development direction Based on the product of this thesis and its limitation, some potential research areas should be noted as follows:  Employing different TPMS types as reinforcement strategies;  Studying other behaviors of the reinforced structures including crack pattern, dynamic response, responses under various boundary conditions, etc.;  Investigating the theoretical solution of this beam type;  Using the TPMS to reinforce other types of concrete structures such as slabs, columns, etc.;  Creating an overall surrogate model that can predict the beam behavior with any configuration  Enhancing the surrogate model with different ML algorithms such as support vector machine (SVM), random forest regression, extreme gradient boosting (XGBoost), and unsupervised or reinforce learning algorithms;  Applying the latest physics-informed neural networks (PINN) to deal with the present problem without FEA simulations 65 LIST OF PUBLICATIONS National conference K Tran-Quoc, V Nguyen-Van, L B Nguyen, V H Luong, and H Nguyen-Xuan, “Influence of plastic triply periodic minimal surface based core layers on cement beams: Finite element method and artificial neural networks approaches,” proceeding of NACOME XI: 11th National Conference on Mechanics, Hanoi, pp 494-503, 02-03/12/2022 National journal K Tran-Quoc, L B Nguyen, V H Luong, and H Nguyen-Xuan, “Machine learning for predicting mechanical behavior of concrete beams with 3D printed TPMS,” Vietnam Journal of Mechanics vol 44, no 4, pp 538-584, 12/31 2022 International journal H Nguyen-Xuan, K Q Tran, C H Thai, and J Lee, “Modelling of functionally graded triply periodic minimal surface (FG-TPMS) plates,” Composites Structures, under peer-review 66 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] K Tran-Quoc, L B Nguyen, V H Luong, and H Nguyen-Xuan, "Machine learning for predicting mechanical 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Very good b Master degree 2021 – 2023: Ho Chi Minh University of Technology - Vietnam National University Ho Chi Minh City Major: Civil engineering Mode of study: Courses + Master thesis WORK EXPERIENCE 09/2021 – 02/2022: Structural engineer, Golden Based Joint Stock Company (GBJSC) 03/2022 – now: Researcher assistant, CIRTech institute, Ho Chi Minh University of Technology (HUTECH), Ho Chi Minh city