kCV-B: Bootstrap with Cross-Validation for Deep Learning Model Development, Assessment and Selection

This study investigates the inability of two popular data splitting techniques: train/test split and k-fold cross-validation that are to create training and validation data sets, and to achieve sufficient generality for supervised deep learning (DL) methods. This failure is mainly caused by their limited ability of new data creation. In response, the bootstrap is a computer based statistical resampling method that has been used efficiently for estimating the distribution of a sample estimator and to assess a model without having knowledge about the population. This paper couples cross-validation and bootstrap to have their respective advantages in view of data generation strategy and to achieve better generalization of a DL model. This paper contributes by: (i) developing an algorithm for better selection of training and validation data sets, (ii) exploring the potential of bootstrap for drawing statistical inference on the necessary performance metrics (e.g., mean square error), and (iii) introducing a method that can assess and improve the efficiency of a DL model. The proposed method is applied for semantic segmentation and is demonstrated via a DL based classification algorithm, PointNet, through aerial laser scanning point cloud data

Fatigue crack growth analysis using the bootstrap s-version finite element model

Fatigue is the most common source behind failures of mechanical structures which is expected to contribute in injuries and financial losses in industries. In addition, materials selection, geometry, processing and residual stresses produce uncertainties and possible failure modes in the field of engineering. The problems may remain in computational analysis, which is a complex model, such as a three-dimensional surface crack which may require many degrees of freedom during the analysis. The variations in the fatigue crack growth parameters produce scatter results. Therefore, a reasonable analysis is required to solve the uncertainties. The main objective of this research work is to develop a model for uncertainties in fatigue crack growth analysis. The purpose is to identify a probabilistic distribution of crack growth and stress intensity factors for surface crack problems. The prediction of stress intensity factor (SIF), surface crack growth and fatigue life are evaluated with the empirical calculation and previous experimental results. A finite thickness plate with surface cracks subjected to random constant amplitude loads was considered for the fracture analysis using a Bootstrap S-version Finite Element Model (BootstrapS-FEM). The BootstrapS-FEM is an expansion of the standard finite element model (FEM). The FEM was updated with a refined mesh (h-version), an increased polynomial order (p-version), and the combination of the h-p version which is known as the S-version finite element model. A bootstrap resampling method is utilized for probabilistic analysis, then embedded in the S-version finite element model, and it is called as BootstrapS-FEM in order to obtain an effective sampling strategy. The fatigue crack growth parameters are generated by a resample process from an existing sample data with replacement in normal and lognormal distributions. The SIF is calculated based on the virtual crack closure method (VCCM). The fatigue crack growth is calculated based on Paris’ law and Richard’s criterion. The BootstrapS-FEM is then verified for SIF calculation, surface crack growth, prediction of fatigue life and initial flaw size distribution. The validation process is compared to previous experimental work. The major contribution of this research is for the development of a probabilistic analysis by using bootstrap resampling method for the S-version finite element model. The formulation of uncertainties in this analysis is presented with the ability to model the distribution of the surface crack growth. The forecast of SIFs due to tension loading by using BootstrapS-FEM agreed well with the Newman-Raju solution with percentage errors within range of 0.5% – 10%. The prediction of fatigue life for three-point and four-point bendings by BootstrapS-FEM was well-compared with previous experimental results within range from 5% – 17% of percentage errors. These errors were acceptable for purpose of prediction which are less than 20%. Thus, the predictions by using BootstrapS-FEM shows a better results to compare with the deterministic concept against previous experimental results. The BootstrapS-FEM predicted the surface crack growth for three-point and four-point bendings represented with two beach marks. The predictions were considered acceptable based on its trend and bounds. The interval inspections schedule were represented for lifetime before the catastrophic failure begins by using the design method based on the lognormal initial flaw size distribution. The BootstrapS-FEM was shown to resolve the problem of uncertainties in fatigue analysis where all possible results were considered. The prediction of SIF, fatigue life, surface crack growth were validated and considered as an acceptable range. The BootstrapS-FEM can be further extended for a mixed mode fractures subjected to variable amplitude loadings in an uncertain environment