Global-Local Forward Models within Bayesian Inversion for Large Strain Fracturing in Porous Media

In this work, Bayesian inversion with global-local forwards models is used to identify the parameters based on hydraulic fractures in porous media. It is well-known that using Bayesian inversion to identify material parameters is computationally expensive. Although each sampling may take more than one hour, thousands of samples are required to capture the target density. Thus, instead of using fine-scale high-fidelity simulations, we use a non-intrusive global-local (GL) approach for the forward model. We further extend prior work to a large deformation setting based on the Neo-Hookean strain energy function. The resulting framework is described in detail and substantiated with some numerical tests

Multilevel Global-Local techniques for adaptive ductile phase-field fracture

This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.Comment: 50 pages, 24 Figures, 4 Table

Using layer-wise training for Road Semantic Segmentation in Autonomous Cars

A recently developed application of computer vision is pathfinding in self-driving cars. Semantic scene understanding and semantic segmentation, as subfields of computer vision, are widely used in autonomous driving. Semantic segmentation for pathfinding uses deep learning methods and various large sample datasets to train a proper model. Due to the importance of this task, accurate and robust models should be trained to perform properly in different lighting and weather conditions and in the presence of noisy input data. In this paper, we propose a novel learning method for semantic segmentation called layer-wise training and evaluate it on a light efficient structure called an efficient neural network (ENet). The results of the proposed learning method are compared with the classic learning approaches, including mIoU performance, network robustness to noise, and the possibility of reducing the size of the structure on two RGB image datasets on the road (CamVid) and off-road (Freiburg Forest) paths. Using this method partially eliminates the need for Transfer Learning. It also improves network performance when input is noisy

A Bayesian estimation method for variational phase-field fracture problems

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values. © 2020, The Author(s)

Prediction for traffic accident severity: comparing the artificial neural network, genetic algorithm, combined genetic algorithm and pattern search methods

This paper focuses on predicting the severity of freeway traffic accidents by employing twelve accident-related parameters in a genetic algorithm (GA), pattern search and artificial neural network (ANN) modelling methods. The models were developed using the input parameters of driver's age and gender, the use of a seat belt, the type and safety of a vehicle, weather conditions, road surface, speed ratio, crash time, crash type, collision type and traffic flow. The models were constructed based on 1000 of crashes in total that occurred during 2007 on the Tehran–Ghom Freeway due to the fact that the remaining records were not suitable for this study. The GA evaluated eleven equations to obtain the best one. Then, GA and PS methods were combined using the best GA equation. The neural network used multi-layer perceptron (MLP) architecture that consisted of a multi-layer feed-forward network with hidden sigmoid and linear output neurons that could also fit multi-dimensional mapping problems arbitrarily well. The ANN was applied during training, testing and validation and had 12 inputs, 25 neurons in the hidden layers and 3 neurons in the output layer. The best-fit model was selected according to the R-value, root mean square errors (RMSE), mean absolute errors (MAE) and the sum of square error (SSE). The highest R-value was obtained for the ANN around 0.87, demonstrating that the ANN provided the best prediction. The combination of GA and PS methods allowed for various prediction rankings ranging from linear relationships to complex equations. The advantage of these models is improving themselves adding new data

Bayesian Inversion with Open-Source Codes for Various One-Dimensional Model Problems in Computational Mechanics

The complexity of many problems in computational mechanics calls for reliable programming codes and accurate simulation systems. Typically, simulation responses strongly depend on material and model parameters, where one distinguishes between backward and forward models. Providing reliable information for the material/model parameters, enables us to calibrate the forward model (e.g., a system of PDEs). Markov chain Monte Carlo methods are efficient computational techniques to estimate the posterior density of the parameters. In the present study, we employ Bayesian inversion for several mechanical problems and study its applicability to enhance the model accuracy. Seven different boundary value problems in coupled multi-field (and multi-physics) systems are presented. To provide a comprehensive study, both rate-dependent and rate-independent equations are considered. Moreover, open source codes (https://doi.org/10.5281/zenodo.6451942) are provided, constituting a convenient platform for future developments for, e.g., multi-field coupled problems. The developed package is written in MATLAB and provides useful information about mechanical model problems and the backward Bayesian inversion setting. © 2022, The Author(s)

Bayesian inversion for unified ductile phase-field fracture

The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the R^ - convergence tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples