physics informed neural networks for the analysis and optmization of structures doctor of philosophy major architectural engineering

Physics-informed neural networks for the analysis and optimization of structures MAI TIEN HAU February 2023 Department of Architectural Engineering The Graduate School Sejong University Physics-informed neural networks for the analysis and optimization of structures MAI TIEN HAU A dissertation submitted to Faculty of Sejong University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Architectural Engineering February 2023 Approved by Professor Jaehong Major Advisor Lee Physics-informed neural networks for the analysis and optimization of structures by MAI TIEN HAU Approved - -Professor Kihak Lee, Chair of the committee Approved - -Professor Dongkyu Lee, Member of dissertation committee Approved - -Professor Seunghye Lee, Member of dissertation committee Approved - -Professor JongJae Lee, Member of dissertation committee Approved - -Professor Jaehong Lee, Advisor ABSTRACT This thesis is concerned with nonlinear, stability analyses, and size optimization of truss structures based on physics-informed neural networks (PINNs) For nonlinear analysis one, a robust and simple unsupervised neural network framework is proposed to perform the geometrically nonlinear analysis of inelastic truss structures To guide the training process, the loss function built via the total potential energy principle under boundary conditions (BCs) is minimized in the suggested NN model whose weights and biases are considered as design variables And the training data only contain the spatial coordinates of joints In each training iteration, feedforward, physical laws, and back-propagation are applied for adjusting the parameters of the network to minimize the loss function Once the network is properly trained, the mechanical responses of inelastic structures can be easily obtained without using any structural analysis as well as incremental-iterative algorithms Several benchmark examples regarding geometrical and material nonlinear analysis of truss structures are examined to demonstrate the effectiveness and reliability of the proposed paradigm Subsequently, the proposed first to analyze the stability of truss structures work, neural network (NN) Different from most model is existing is designed to directly locate the critical point by minimizing the loss function involving the residual load and property of the stiff- ness matrix which they are established based on the outputs, loads, and BCs It is also significant because the first critical point will be located at the training end corresponding to the minimum iterative methods loss function without utilizing any incremental- Additionally, this dissertation also develops a Bayesian deep neural network-based parameterization framework to directly solve the optimum design for geometrically nonlinear trusses for the first time In this approach, the parameters of the network are regarded as decision variables of the structural optimization problem, instead of the member’s cross-sectional areas Therein, the loss function is constructed with the aim of minimizing the total structure weight so that all constraints of the optimization problem obtained by supporting fi- nite element analysis (FEA) are satisfied Furthermore, and are-length method Bayesian optimization (BO) is applied to automatically tune the hyperparameters of the network The effectiveness of this model is demonstrated through a series of numerical examples for geometrically nonlinear space trusses And the obtained results demonstrate that our framework can overcome the drawbacks of applications of machine learning in computational mechanics Finally, a physicsinformed neural energy-force network to directly solve the optimum sis is completely removed (PINEFN) framework is first constructed design of truss structures that structural analy- from the implementation of the global optimization in this thesis Herein, the loss function is designed based on the output values and physics laws to guide the training Now only NN is used in our scheme to minimize the loss function wherein weights and biases of the network are con- sidered as design variables In this model, spatial coordinates of truss members are examined as input data, while corresponding cross-sectional areas and re- dundant forces unknown to the network are taken account of output Obtained outcomes indicated that it not only reduces the computational cost dramatically ii but also yields higher accuracy and faster convergence speed compared with recent literature With the above outstanding features, it is promising to offer a unified solver-free numerical simulation for solving complex issues in structural optimization Keywords: Physics-informed, Geometric nonlinear, Structural stabil- ity, Hyperparameter optimization, Force method, Critical points, Complementary energy, Bayesian optimization, iii Truss optimization CONTENTS ABSTRACT 20 ce LIST OF TABLES: LIST OR FIGURES: ee 2.3: i cee eees 6c se csi ciinue ee INTRODUCTION ed ewe we 6 ecto ee eee ee ewe vii ee otis xi ew ee ee ee ee Structural nonlinear analysis 1.2 Sizexoptintization: ot oF BRE om Om we 1.3 Physics-informed neural networks lợi (QJQCHDVỀ OOS 1.5 Organization ee « « «sss wewin eek EER © EMMONS soe Rw SELER eH EEE OF 2.2 NEURAL NETWORK TRUSS STRUCTURES 21 Anoverview 2.2 PINN for nonlinear analysis 2.3 oo EEE HE ERO PHYSICS-INFORMED ANALYSIS i 1.1 LINEAR ee FOR NON- ee 11 ee 11 20.20 00 eee eee 12 2.2.1 Problem siatemenL 13 2.2.2 Unsupervised learning-based approach amework 14 PINN for structural stability analysis 17 2.3.1 Problem statemeniL 17 2.3.2 Direct instability-informed neural network framework 20 iv 2.4 2.6 Numerical examples 0.0000 2.4.1 Material and geometrical nonlinearlles 2.4.2 Geometrical nonlinearity 2.4.3 Material nonlinearity 2.4.4 Structural stability Comebusiovis BAYESIAN vv DEEP ETERIZATION oe eww NEUARL 2.2 waras FOR 2.2.02 00000004 ee ee 8 ee ee Be PARAM- OPTIMUM DESIGN STRUCTURES Imroduelon 3.2 Statement of structural optimization problem 3.3 BDNN-based parameterization framework 3.5 000000004 2.0.2 0.0.00 0004 3.1 3.4 eee NETWORK-BASED FRAMEWORK OEFNONLINEAR we eee ch hy vẻ ky 3.3.1 DNN-based parameterization model 3.3.2 Hyperparameter tuning .00 Numericalexamples 0000 pee ee eee 34,1 25-bar space truss «sees 3.42 52-bardometruss 2.0.0.0 0.0000 3.4.3 56-bar space truss 344 [20-bar dome truss Conclusions FOR ơn «oe a aE EER EE EH 0.0 ee ee eee ee EMM ee OBS eee ee PHYSICS-INFORMED WORK a0 oe ee NEURAL STRUCTURAL ENERGY FORCE OPTIMIZATION NET- ỘỚIẶẶÁa 4.2 Structural optimization based on energy-foree methods 4.3 Physics-informed neural energy-force network 4.4 Numericalexamples 20.200 00: eee eee eee 4.5 AA fRendbar truest 4.4.2 200-bar planar truss 4.4.3 25-barsDpacelTUSS 444 72-bar space truss 44.5 em opm oO we Me ee 106 120 120-bardometruss 000 126 ec ce AND