Strut Diameter Uncertainty Prediction by Deep Neural Network for Additively Manufactured Lattice Structures

Additive manufacturing (AM) introduces geometric uncertainties on the fabricated strut members of lattice structures. These uncertainties result in deviations between the modeled and fabricated geometries of struts. The use of deep neural networks (DNNs) to accurately predict the statistical parameters of the effective strut diameters to account for the AM-introduced geometric uncertainties with a small training dataset for constant process parameters is studied in this research. For the training data, struts with certain angle and diameter values are fabricated by the material extrusion process. The geometric uncertainties are quantified using the random field theory based on the spatial strut radius measurements obtained from the microscope images of the fabricated struts. The uncertainties are propagated to the effective diameters of the struts using a stochastic upscaling technique. The relationship between the modeled strut diameter and the characterized statistical parameters of the effective diameters are used as the training data to establish a DNN model. The validation results show that the DNN model can predict the statistical parameters of the effective diameters of the struts modeled with angle and diameters different from the ones used in the training data with good accuracy even if the training data set is small. Developing such a DNN model with a small data will allow designers to use the fabricated results in the design optimization processes without requiring additional experimentations.

Alternations of interhemispheric functional connectivity in children with strabismus and amblyopia: a resting-state fMRI study

Previous neuroimaging studies demonstrated that patients with strabismus or amblyopia can show significant functional and anatomical changes in the brain, but alterations of interhemispheric functional connectivity (FC) have not been well studied in this population. The current study analyzed whole-brain changes of interhemispheric FC in children with strabismus and amblyopia (CSA) using voxel-mirrored homotopic connectivity (VMHC).A total of 24 CSA (16 males and 8 females) and 24 normal controls (NCs) consisting of 16 and 8 age-, sex, and education-matched males and females, respectively, underwent functional magnetic resonance imaging (fMRI) scans in the resting state. According to Gaussian random field theory, changes in the resting state FC (rsFC) between hemispheres were evaluated using the VMHC method. The relationships between mean VMHC values in multiple brain regions and behavioral performance were evaluated by Pearson correlation analysis. In contrast to NCs, the CSA group showed significantly decreased VMHC values in the bilateral cerebellum, bilateral frontal superior orbital (frontal sup orb), bilateral temporal inferior(temporal inf),and bilateral frontal superior(frontal sup). CSA have abnormal interhemispheric FC in many brain regions, which may reflect dysfunction of eye movements and visual fusion. These findings might provide insight into the underlying pathogenetic mechanisms of CSA.

The expected behaviour of random fields in high dimensions: contradictions in the results of Bansal and Peterson (2018)

Bansal and Peterson (2018) found that in simple stationary Gaussian simulations Random Field Theory incorrectly estimates the number of clusters of a Gaussian field that lie above a threshold. Their results contradict the existing literature and appear to have arisen due to errors in their code. Using reproducible code we demonstrate that in their simulations Random Field Theory correctly predicts the expected number of clusters and therefore that many of their results are invalid.

Reliability of an engineered slope considering the Regression Kriging (RK)-based conditional random field

Many attempts have been made to apply random field theory to the slope reliability analysis in recent decades. However, there are only a few studies that consider real landslide cases by incorporating actual soil data in the probabilistic slope stability analysis with spatially variable soils. In this paper, an engineered slope located in Hong Kong was investigated using the probabilistic approach considering the Regression Kriging (RK)-based conditional random field. The slope had been assessed and considered to be safe by classical deterministic slope stability analyses but failed eventually. In this study, both deterministic slope stability analyses and probabilistic slope stability analyses were conducted, and the comparison was made between the probabilistic approach adopting RK-based conditional random field and that adopting Ordinary Kriging (OK)-based approach. The results show that the deterministic factor of safety (FS) for a slope may not be an adequate indicator of the safety margin. In particular, a slope with a higher deterministic FS may not always represent a lower probability of failure under the framework of probabilistic assessment, where the spatial variability of soil properties is explicitly considered. Besides, the critical portion of the slope could not be found using the OK-based approach that considers a constant trend structure.

Modal Analysis of Beam Structures with Random Field Models at Multiple Scales

Structure material properties are heterogeneous in nature and would be characterized with different statistics at different length scales due to the spatially averaging effects. This work develops a framework for the modal analysis of beam structures with random field models at multiple scales. In this framework, the random field theory is adopted to model heterogeneous material properties, and the cross-correlations between material properties are explicitly considered. The modal parameters of a structure are then evaluated using the finite element (FE) method with the simulated heterogeneous material properties taken as input. With the aid of Monte Carlo simulation, the modal parameters are analyzed in a probabilistic manner. In addition, to accommodate the necessity of different mesh sizes in FE models, an approach of evaluating random field parameters and generating random field material properties at different length scales is developed. The performance of the proposed framework is demonstrated through the modal analysis of a simply supported beam, where the formulation of the multiscale random field approach is validated and the effects of heterogeneous material properties on modal parameters are analyzed. Parametric studies on the random field parameters, including the coefficient of variation and the scale of fluctuation, are also conducted to further investigate the relations between the random field parameters at different scales.

Augmented Gaussian random field: Theory and computation

<p style='text-indent:20px;'>We propose the novel augmented Gaussian random field (AGRF), which is a universal framework incorporating the data of observable and derivatives of any order. Rigorous theory is established. We prove that under certain conditions, the observable and its derivatives of any order are governed by a single Gaussian random field, which is the aforementioned AGRF. As a corollary, the statement "the derivative of a Gaussian process remains a Gaussian process" is validated, since the derivative is represented by a part of the AGRF. Moreover, a computational method corresponding to the universal AGRF framework is constructed. Both noiseless and noisy scenarios are considered. Formulas of the posterior distributions are deduced in a nice closed form. A significant advantage of our computational method is that the universal AGRF framework provides a natural way to incorporate arbitrary order derivatives and deal with missing data. We use four numerical examples to demonstrate the effectiveness of the computational method. The numerical examples are composite function, damped harmonic oscillator, Korteweg-De Vries equation, and Burgers' equation.</p>