Statistical Characterization of Stress Concentrations along Butt Joint Weld Seams Using Deep Neural Networks
Abstract
:1. Introduction
2. State of the Art on Characterization of Weld Geometries and Stress Concentrations
2.1. Characterization of Weld Geometries
2.2. Characterization of Stress Concentrations along Weld Seams
3. Finite Element Modeling and Parametrization
3.1. Geometry of the Butt Joint
3.2. Discretization
3.3. Load Cases and Solution
3.4. Sampling Strategy
4. Generation of the Deep Neural Network
4.1. Restrictions of the FEM Data
- In 36 cases, finite element models could not be generated due to irrational combinations of geometry parameters.
- A further 19 calculated samples were excluded due to extreme parameter combinations. The parameter combinations lead to SCF > 6 and resulted, for example, from the combination of a high plate thickness t, a high weld toe angle β, a small weld toe radius r, and a high ratio of weld seam width to plate thickness w/t.
4.2. Preprocessing of the FEM
4.3. Architecture of the DNN
4.4. Training of the DNN
4.5. Performance of the DNN
5. Statistical Characterization of Weld Geometries and Stress Concentrations along Butt Joint Weld Seams
- The measured sample skewness and kurtosis of the weld toe radii is close to the line representing the lognormal, the gamma, and the inverse gamma distribution. Interestingly, the weld toe radii also show, on average, the smallest scatter of kurtosis.
- The majority of plates have weld toe angles with distributions that are only slightly skewed. This is an indication for a symmetrical distribution such as a normal distribution; nevertheless, the partially high kurtosis indicates that the tails of the distributions are wider than typical for a normal distribution.
- The distributions of undercuts are the most skewed; 70% of the skewness–kurtosis combinations are outside the range plotted in Figure 10. The reason is that very small shape parameters α are required to fit distributions as presented in Figure 9, which increases the skewness and kurtosis; nevertheless, the data are close to the dashed line in and outside the presented range, which represents parameter combinations of a gamma distribution.
- The data for the weld reinforcement heights are clustered around the normal distribution and the region where lognormal, gamma, and inverse gamma distribution are close to each other.
- Except for the weld toe angles and weld reinforcement heights, the majority of datasets have sample kurtosis k ≫ 3 and square of skewness s2 ≫ 0, which suggests that a normal distribution is not suited to describe the data. Similarly, the exponential distribution does not seem to be suitable for any of the assessed parameters and datasets.
- The distributions of weld widths and SCFs show a large scatter. This makes it difficult to relate them to a typical distribution function. Interestingly, the majority of the data on weld width in Figure 10 and thereby in the range of typical less-skewed distribution functions are for plates made by FCAW, which were manually welded. A large fraction of the other joints, which were automatically welded, are outside the range presented in Figure 10.
6. Discussion
6.1. Discussion of the Skewness–Kurtosis Comparison
6.2. Discussion of the Applicability Readiness of the Presented Methodology
7. Summary and Conclusions
- Establishing a DNN for a recurring task such as the determination of SCFs at weld transition significantly decreases the required time to determine the severity of notches along weld seams by combining the mutual influence of stress-raising effects from local weld geometry factors such as weld toe radii, angles, and undercuts.
- The comparison of skewness and kurtosis of the measured samples with theoretical distributions showed that it is difficult to determine suitable distribution functions for the investigated weld geometry parameters and SCFs. This might be related to non-stationary processes that result in variations along weld seams (e.g., due to inhomogeneous temperature fields) but also measurement inaccuracies. Modelling inaccuracies are mitigated by using highly refined FE meshes to calculate the input data for the DNN.
- The majority of weld toe angle sample distributions are only slightly skewed. This is an indication for a symmetrical distribution like a normal distribution; nevertheless, the partially high kurtosis indicates that the tails of the distributions are wider (more outlier-prone) than typical for a normal distribution.
- The distributions of undercuts are the most skewed. The reason is that very small shape parameters α are required to fit distributions as presented in Figure 9, which increases the skewness and kurtosis; nevertheless, the data is close to a gamma distribution. A gamma distribution might be better suited to describe undercut depths (for which the maximum of data is equal to zero) as a lognormal distribution.
- The data for the weld reinforcement heights are clustered around the normal distribution and the region where lognormal, gamma, and inverse gamma distribution are close to each other.
- The distributions of weld widths and SCFs show a large scatter. This makes it difficult to relate them to a typical distribution function. The reason for the scatter of the sample parameters of the SCFs might be related to the fact that the SCF calculation is based on the input of a number of geometrical features. Thus, the variability and any possible inaccuracy in the input parameters and numerical modelling is transferred to the SCFs. In addition, the combination of various parameters could be the reason typical two-parameter distribution functions are not suitable to describe a complex parameter such as a SCF.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Parameter | Symbol | [Lower Bound/Upper Bound] | Unit |
---|---|---|---|
Plate thickness | t | [1/100] | [mm] |
Weld toe angle | β | [5/80] | [°] |
Weld toe radius | r | [0.05/5] | [mm] |
Weld seam width to plate thickness ratio | [0.2/4] | [−] | |
Undercut depth | u | [0/1] | [mm] |
Distribution | Skewness | Kurtosis |
---|---|---|
Normal | 0 | 3 |
Exponential | 2 | 9 |
Lognormal | ||
Gamma | ||
Inverse gamma | for α > 3 | for α > 3 |
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Braun, M.; Neuhäusler, J.; Denk, M.; Renken, F.; Kellner, L.; Schubnell, J.; Jung, M.; Rother, K.; Ehlers, S. Statistical Characterization of Stress Concentrations along Butt Joint Weld Seams Using Deep Neural Networks. Appl. Sci. 2022, 12, 6089. https://doi.org/10.3390/app12126089
Braun M, Neuhäusler J, Denk M, Renken F, Kellner L, Schubnell J, Jung M, Rother K, Ehlers S. Statistical Characterization of Stress Concentrations along Butt Joint Weld Seams Using Deep Neural Networks. Applied Sciences. 2022; 12(12):6089. https://doi.org/10.3390/app12126089
Chicago/Turabian StyleBraun, Moritz, Josef Neuhäusler, Martin Denk, Finn Renken, Leon Kellner, Jan Schubnell, Matthias Jung, Klemens Rother, and Sören Ehlers. 2022. "Statistical Characterization of Stress Concentrations along Butt Joint Weld Seams Using Deep Neural Networks" Applied Sciences 12, no. 12: 6089. https://doi.org/10.3390/app12126089