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Uncertainty quantification of multimodal surface wave inversion using artificial neural networks
(2023)
An inversion of surface waves dispersion curves is a non-unique and ill-conditioned problem. The inversion result has a probabilistic nature, which becomes apparent when simultaneously restoring the shear wave (S-wave) velocity and layer thickness. Therefore, the problem of uncertainty quantification is relevant. Existing methods through deterministic or global optimization approaches of uncertainty quantification via posterior probability density (PPD) of the model parameters are not computationally efficient since they demand multiple solutions of the inverse problem. We present an alternative method based on a multi-layer fully connected artificial neural network (ANN). We improve the current uni-modal approach, which is known from publications, to multi-modal inversion. The learned ANN maps the phase velocity dispersion curves to values of the S-wave velocity and layers thickness. To estimate the uncertainties, we adapt the Monte-Carlo simulation strategy and project onto the resulting velocity model both frequency-dependent data noise and inverse operator errors, which are evaluated by the prediction of the training data set. The proposed combination of surface waves data processing methods, configured with each other, provides a novel surface waves multi-modal dispersion data inversion and uncertainty quantification approach. We first test our approach on synthetic experiments for various velocity models: a positive velocity gradient, a low-velocity layer and a high-velocity layer. This is done considering uni-modal inversion at first and then compared to the multi-modal inversion. Afterwards, we apply our approach to field data and compare resulting models with the body S-wave processing by the generalized reciprocal method (GRM). The experiments show high-potential results using ANN yields the possibility to accurately estimate PPD of restored model parameters without a significant computational effort. The PPD-based comparison demonstrates advantages of a multi-modal inversion over uni-modal inversion. The trained ANN provides reasonable model parameters predictions and related uncertainties in real-time.
The test data for static burst strength and load cycle fatigue strength of pressure vessels can often be well described by Gaussian normal or Weibull distribution functions. There are various approaches which can be used to determine the parameters of the Weibull distribution function; however, the performance of these methods is uncertain. In this study, six methods are evaluated by using the criterion of OSL (observed significance level) from Anderson-Darling (AD) goodness of Fit (GoF), These are: a) the norm-log based method, b) least squares regression, c) weighted least squares regression, d) a linear approach based on good linear unbiased estimators, e) maximum likelihood estimation and f) method of moments estimation. In addition, various approaches of ranking function are considered. The results show that there are no outperforming methods which can be identified clearly, primarily due to the limitation of the small sample size of the test data used for Weibull analysis. This randomness resulting from the sampling is further investigated by using Monte Carlo simulations, concluding that the sample size of the experimental data is more crucial than the exact method used to derive Weibull parameters. Finally, a recommendation is made to consider the uncertainties of the limitations due to the small size for pressure vessel testing and also for general material testing.
The determination of the microscopic dose-damage relationship for DNA in an aqueous environment is of a fundamental interest for dosimetry and applications in radiation therapy and protection. We combine geant4 particle-scattering simulations in water with calculations concerning the movement of biomolecules to obtain the energy deposit in the biologically relevant nanoscopic volume. We juxtaposition these results to the experimentally determined damage to obtain the dose-damage relationship at a molecular level. This approach is tested for an experimentally challenging system concerning the direct irradiation of plasmid DNA (pUC19) in water with electrons as primary particles. Here a microscopic target model for the plasmid DNA based on the relation of lineal energy and radiation quality is used to calculate the effective target volume. It was found that on average fewer than two ionizations within a 7.5-nm radius around the sugar-phosphate backbone are sufficient to cause a single strand break, with a corresponding median lethal energy deposit being E1/2=6±4 eV. The presented method is applicable for ionizing radiation (e.g., γ rays, x rays, and electrons) and a variety of targets, such as DNA, proteins, or cells.
Existing standards for the approval of composite cylinders for the transport of compressed hydrogen are currently based on deterministic (ISO 11119-3) and semi-probabilistic (UN GTR No. 13) criteria. This paper analysis the capabilities of these procedures with respect to the evaluation of burst strength. Their characteristics are compared with the probabilistic approach developed at BAM. Based on Monte-Carlo simulations the available design range (mean value and scatter of burst strength) of all concepts are assessed. In addition, the probability of acceptance for potentially unsafe design types is determined.
The results show large areas of burst properties with a sufficient reliability which cannot be used for the design of composite cylinders, due to current approval criteria. On the other hand, existing standards allow the approval of potentially unsafe designs in case of a very high scatter regarding their burst strength.
It is also shown that existing design types are already designed to the limits of the available design area. A further weight and cost reduction of composite cylinders is therefore closely related to the approval criteria. An example based on UN GTR No. 13 shows how an approval criterion can be optimized by using statistical methods. The example shows that a reduced minimum burst pressure can be combined with a lower probability of acceptance for potentially unsafe design types.
We report on a study in which plasmid DNA in water was irradiated with 30 keV electrons generated by a scanning electron microscope and passed through a 100 nm thick Si3N4 membrane. The corresponding Monte Carlo simulations suggest that the kinetic energy spectrum of the electrons throughout the water is dominated by low energy electrons (<100 eV). The DNA radiation damage, single-strand breaks (SSB) and double-strand breaks (DSB), was determined by electrophoresis. The median lethal dose of D1/2 = 1.7 ± 0.3 Gy was found to be much smaller compared to partially or fully hydrated DNA irradiated under vacuum conditions. The ratio of DSB to SSB was found to be (1:12) as compared to 1:88) found for hydrated DNA. Our method enables quantitative measurements of radiation damage to biomolecules (DNA, proteins) in solutions under varying conditions (pH, salinity, cosolutes) for an electron energy range which is difficult to probe by standard methods.
The improved Monte-Carlo (MC) method for standard-less analysis in laser induced breakdown spectroscopy (LIBS) is presented. Concentrations in MC LIBS are found by fitting model-generated synthetic spectra to experimental spectra. The current version of MC LIBS is based on the graphic processing unit (GPU) computation and reduces the analysis time down to several seconds per spectrum/sample. The previous version of MC LIBS which was based on the central processing unit (CPU) computation requested unacceptably long analysis times of 10's minutes per spectrum/sample. The reduction of the computational time is achieved through the massively parallel computing on the GPU which embeds thousands of co-processors. It is shown that the number of iterations on the GPU exceeds that on the CPU by a factor > 1000 for the 5-dimentional parameter space and yet requires > 10-fold shorter computational time. The improved GPU-MC LIBS outperforms the CPU-MS LIBS in terms of accuracy, precision, and analysis time. The performance is tested on LIBS-spectra obtained from pelletized powders of metal oxides consisting of CaO, Fe2O3, MgO, and TiO2 that simulated by-products of steel industry, steel slags. It is demonstrated that GPU-based MC LIBS is capable of rapid multi-element analysis with relative error between 1 and 10's percent that is sufficient for industrial applications (e.g. steel slag analysis). The results of the improved GPU-based MC LIBS are positively compared to that of the CPU-based MC LIBS as well as to the results of the standard calibration-free (CF) LIBS based on the Boltzmann plot method.
The advent of simultaneous energy dispersive X-ray spectroscopy (EDS) data collection has vastly improved the phase separation capabilities for electron backscatter diffraction (EBSD) mapping. A major problem remains, however, in distinguishing between multiple cubic phases in a specimen, especially when the compositions of the phases are similar or their particle sizes are small because the EDS interaction volume is much larger than that of EBSD, and the EDS spectra collected during spatial mapping are generally noisy due to time limitations and the need to minimize sample drift. The backscatter electron (BSE) signal is very sensitive to the local composition due to its atomic number (Z) dependence. BSE imaging is investigated as a complimentary tool to EDS to assist phase segmentation and identification in EBSD through examination of specimens of meteorite, Cu dross, and steel oxidation layers. The results demonstrate that the simultaneous acquisition of EBSD patterns, EDS spectra, and the BSE signal can provide new potential for advancing multiphase material characterization in the scanning electron microscope.