Investigation of Spatial Variability on Strut Diameters of Additively Manufactured Lattice Structures

2020 ◽  
Author(s):  
Recep M. Gorguluarslan ◽  
O. Utku Gungor
Keyword(s):  
Spatial Variability ◽  
Random Field ◽  
Extrusion Process ◽  
Optical Microscope ◽  
Measured Data ◽  
Good Representation ◽  
Lattice Structures ◽  
Spatial Correlations ◽  
Correlation Lengths ◽  
Geometric Uncertainties

Abstract In this study, the influence of the spatial variability of geometric uncertainties on the strut members of the lattice structures fabricated by additive manufacturing is investigated. Individual struts are fabricated with various printing angles and diameters using a material extrusion process and PLA material. The diameter values of the fabricated samples are measured along the printing and radial directions at each layer under an optical microscope. Spatial correlations are characterized based on the measurements using the experimental autocorrelation function. Candidate autocorrelation functions are fitted to the measured data to identify the best fitted one for each diameter parameter and the corresponding correlation lengths are evaluated for random field. The applicability of the Karhunen-Loeve expansion (KLE) is investigated to reduce the dimensionality of the random field discretization. The results show that the diameters of the strut members at each layer are spatially dependent and the KLE method was found to give a good representation of the random field.

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

2021 ◽  
pp. 1-58
Author(s):  
Recep M. Gorguluarslan ◽  
Gorkem Can Ates ◽  
Olgun Utku Gungor ◽  
Yusuf Yamaner
Keyword(s):  
Extrusion Process ◽  
Training Data ◽  
Training Dataset ◽  
Small Data ◽  
Lattice Structures ◽  
Statistical Parameters ◽  
Data Set ◽  
Random Field Theory ◽  
Geometric Uncertainties ◽  
Upscaling Technique

Abstract 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.

scholarly journals Bayesian updating of subsurface spatial variability for improved prediction of braced excavation response

2019 ◽  
Vol 56 (8) ◽  
pp. 1169-1183 ◽  
Author(s):  
M.K. Lo ◽  
Y.F. Leung
Keyword(s):  
Spatial Variability ◽  
Random Field ◽  
Bayesian Updating ◽  
Field Measurements ◽  
Longitudinal Direction ◽  
Prediction Intervals ◽  
Model Bias ◽  
Efficient Manner ◽  
Actual Performance ◽  
Hypothetical Scenario

This paper introduces an approach that utilizes field measurements to update the parameters characterizing spatial variability of soil properties and model bias, leading to refined predictions for subsequent construction stages. It incorporates random field simulations and a surrogate modeling technique into the Bayesian updating framework, while the spatial and stage-dependent correlations of model bias can also be considered. The approach is illustrated using two cases of multi-stage braced excavations, one being a hypothetical scenario and the other from a case study in Hong Kong. Making use of all the deflection measurements along an inclinometer, the principal components of the random field and model bias factors can be updated efficiently as the instrumentation data become available. These various sources of uncertainty do not only cause discrepancies between prior predictions and actual performance, but can also lead to response mechanisms that cannot be captured by deterministic approaches, such as distortion of the wall along the longitudinal direction of the excavation. The proposed approach addresses these issues in an efficient manner, producing prediction intervals that reasonably encapsulate the response uncertainty as shown in the two cases. The capability to continuously refine the response estimates and prediction intervals can help support the decision-making process as the construction progresses.

Stochastic finite element analysis of rockfill dam considering spatial variability of dam material porosity

2019 ◽  
Vol 36 (9) ◽  
pp. 2929-2959
Author(s):  
Hui Chen ◽  
Donghai Liu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Spatial Variability ◽  
Random Field ◽  
Model Parameters ◽  
Mechanical Parameters ◽  
Stochastic Finite Element ◽  
Content Type ◽  
Rockfill Dam ◽  
Stochastic Fem

Purpose The purpose of this study is to develop a stochastic finite element method (FEM) to solve the calculation precision deficiency caused by spatial variability of dam compaction quality. Design/methodology/approach The Choleski decomposition method was applied to generate constraint random field of porosity. Large-scale laboratory triaxial tests were conducted to determine the quantitative relationship between the dam compaction quality and Duncan–Chang constitutive model parameters. Based on this developed relationship, the constraint random fields of the mechanical parameters were generated. The stochastic FEM could be conducted. Findings When the fully random field was simulated without the restriction effect of experimental data on test pits, the spatial variabilities of both displacement and stress results were all overestimated; however, when the stochastic FEM was performed disregarding the correlation between mechanical parameters, the variabilities of vertical displacement and stress results were underestimated and variation pattern for horizontal displacement also changed. In addition, the method could produce results that are closer to the actual situation. Practical implications Although only concrete-faced rockfill dam was tested in the numerical examples, the proposed method is applicable for arbitrary types of rockfill dams. Originality/value The value of this study is that the proposed method allowed for the spatial variability of constitutive model parameters and that the applicability was confirmed by the actual project.

scholarly journals Self-similarity in glacier surface characteristics

2003 ◽  
Vol 49 (167) ◽  
pp. 547-554 ◽  
Author(s):  
Neil S. Arnold ◽  
W. Gareth Rees
Keyword(s):  
Surface Roughness ◽  
Energy Balance ◽  
Spatial Variability ◽  
Snow Depth ◽  
Surface Albedo ◽  
Small Scale ◽  
Late Winter ◽  
Glacier Surface ◽  
Correlation Lengths ◽  
Aerodynamic Roughness

AbstractCatchment-wide information on glacier snow-cover depth, surface albedo and surface roughness is important input data for distributed models of glacier energy balance. In this study, we investigate the small-scale (mm to 100 m) spatial variability in these properties, with a view to better simulating this variability in such models. Data were collected on midre Lovénbreen, a 6 km2 valley glacier in northwest Svalbard. The spatial variability of all three properties was found to be self-similar over the range of scales under investigation. Snow depth and albedo exhibit a correlation length within which measurements were spatially autocorrelated. Late-winter and summer properties of snow depth differed, with smaller depths in summer due to melt, and shorter correlation lengths. Similar correlation lengths for snow depth and surface albedo may suggest that snow-depth variation is an important control on the small-scale spatial variability of glacier surface albedo. For surface roughness, the data highlight a possible problem in energy-balance studies which use microtopographic surveys to calculate aerodynamic roughness, in that the scale of the measurements made affects the calculated roughness value. This suggests that further investigations of the relationships between surface form and aerodynamic roughness of glacier surfaces are needed.

An Effective Random Field Characterization for Probability Analysis and Design

2008 ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn
Keyword(s):  
Spatial Variability ◽  
Random Field ◽  
Goodness Of Fit ◽  
Random Parameter ◽  
Probability Analysis ◽  
Field Variation ◽  
Random Parameters ◽  
Goodness Of Fit Test ◽  
Analysis And Design ◽  
Engineering Design Problems

So far manufacturing tolerance variability over samples has been widely considered in many engineering design problems. Traditionally the tolerance variability is modeled as a spatially independent random parameter although the variability is a function of spatial variables (x, y, and z) in many engineering applications. Little attention has been paid to spatial variability (or random field) in manufacturing and operational conditions, which may dominantly affect system performances in smaller scale applications. This paper presents an effective approach to characterize a random field for probability analysis and design. The Proper Orthogonal Decomposition (POD) method is employed to extract the important signatures of the random field over product samples. A normalized posteriori error is defined to automatically decide the minimal number of the important signatures while preserving a prescribed accuracy in approximating the random field. The random projected values of the spatial variability over the samples onto each important signature are modeled as a random parameter. The signatures and corresponding random parameters are thus used for modeling the random field. A Chi-Squae goodness-of-fit test is used for determining statistical models of random parameters. This proposed approach can facilitate to characterize the random field for probability analysis and design. By modeling the random field with the most significant random signatures, the Eigenvector Dimension Reduction (EDR) method can be employed for probability analysis because of its relatively high efficiency and accuracy. Two examples (one beam and Micro-Electro-Mechanical Systems (MEMS) bistable mechanism) are used to illustrate the effectiveness of the proposed approach while considering only a geometric random field. Compared to Monte Carlo Simulation (MCS), the proposed random field approach is appeared to be very accurate and efficient. Moreover, the results show that the random field variation cannot be neglected for probability analysis and design practices.

scholarly journals Controls on the temporal and spatial variability of soil moisture in a mountainous landscape: the signatures of snow and complex terrain

2008 ◽  
Vol 5 (4) ◽  
pp. 1927-1966 ◽  
Author(s):  
C. J. Williams ◽  
J. P. McNamara ◽  
D. G. Chandler
Keyword(s):  
Spatial Distribution ◽  
Soil Moisture ◽  
Spatial Variability ◽  
Complex Terrain ◽  
Soil Depth ◽  
Snow Accumulation ◽  
Slope Aspect ◽  
Spatial Correlations ◽  
Static Properties ◽  
Semi Arid

Abstract. The controls on the spatial distribution of soil moisture include static and dynamic variables. The superposition of static and dynamic controls can lead to different soil moisture patterns for a given catchment during wetting, draining, and drying periods. These relationships can be further complicated in snow-dominated mountain regions where soil water input by precipitation is largely dictated by the spatial variability of snow accumulation and melt. In this study, we assess controls on spatial and temporal soil moisture variability in a small (0.02 km2), snow-dominated, semi-arid catchment by evaluating spatial correlations between soil moisture and site characteristics through different hydrologic seasons. We assess the relative importance of snow with respect to other catchment properties on the spatial variability of soil moisture and track the temporal persistence of those controls. Spatial distribution of snow, distance from divide, soil texture, and soil depth exerted significant control on the spatial variability of moisture content throughout most of the hydrologic year. These relationships were strongest during the wettest period and degraded during the dry period. As the catchment cycled through wet and dry periods, the relative spatial variability of soil moisture tended to remain unchanged. We suggest that the static properties in complex terrain (slope, aspect, soils) impose first order controls on the spatial variability of snow and consequent soil moisture, and that the interaction of dynamic (timing of water input) and static properties propagate that relative constant spatial variability through the hydrologic year. The results demonstrate snow exerts significant influence on how water is retained within mid-elevation semi-arid catchments throughout the year and infer that reductions in annual snowpacks associated with changing climate regimes may strongly influence spatial and temporal soil moisture patterns and catchment physical and biological processes.

scholarly journals UMA ALTERNATIVA PARA CARACTERIZAR O VALOR DA CONDUTIVIDADE HIDRÁULICA EM SOLO SATURADO

Irriga ◽  
2018 ◽  
Vol 4 (2) ◽  
pp. 54-60
Author(s):  
Maria Vilma Tavares de Moura ◽  
Paulo Rodolfo Leopoldo ◽  
Sérgio Marques Júnior
Keyword(s):  
Hydraulic Conductivity ◽  
Spatial Variability ◽  
Probability Density ◽  
Data Distribution ◽  
Rio Grande ◽  
Measured Data ◽  
Probability Density Functions ◽  
Density Functions ◽  
E Mail ◽  
Soil Spatial Variability

UMA ALTERNATIVA PARA CARACTERIZAR O VALOR DA CONDUTIVIDADE HIDRÁULICA EM SOLO SATURADO   Maria Vilma Tavares de MouraSecretaria da Agricultura e Abastecimento do Estado do Rio Grande do Norte Br 101 - Km 0 – Lagoa Nova - Fone: (084) 2311212 CEP 57075-050  -   Natal-RNPaulo Rodolfo LeopoldoFCA/UNESP – Depto. Engenharia Rural Fone: (014)8213883; Fax: (014) 8213438 CEP 18603-970 - Botucatu-SPSérgio Marques JúniorDepto. Engenharia Rural - CCA/UFSC Rodovia Admar Gonzaga, Km 03 - Itacorubi CEP 88037-500 - Florianópolis-SC - Fone: (048) 2341013 e-mail: [email protected]   1 RESUMO   O objetivo do presente artigo é apresentar um estudo sobre a variabilidade espacial da condutividade hidráulica do solo estimada em meio saturado, apresentando alternativas para caracterização de seu valor em uma determinada porção do solo. A partir de uma série de dados, verificou-se a existência de não normalidade na distribuição, justificando a utilização de outras funções de densidade de probabilidade para o estudo. Nesta situação, a distribuição dos dados amostrados apresentou bom ajuste às funções de densidade gama incompleta e beta.   UNITERMOS: Condutividade hidráulica, variabilidade espacial do solo, funções de densidade de probabilidade.   MOURA, M.V.T., LEOPOLDO, P.R., MARQUES JÚNIOR, S.M.AN ALTERNATIVE TO CHARACTERIZE THE HYDRAULIC CONDUCTIVITY IN SATURATED SOIL   2 ABSTRACT   The aim of this paper was to study the spatial variability of soil saturated hydraulic conductivity, offering an strategy to characterize its value in a set of soil. It was observed the occurrence of non-normal distribution, justifying the use of probability density functions. In this study, measured data distribution showed good fitting with incomplete gamma and beta distribution.    KEYWORDS: Hydraulic conductivity, soil spatial variability, probability density functions.

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