A Fast Grid Deformation Algorithm for Aerodynamic Shape Optimization

2010 ◽  
Author(s):  
Kaveh Mohamed ◽  
Kurt Sermeus ◽  
Eric Laurendeau
Keyword(s):  
Optimization Problems ◽  
Flow Simulation ◽  
Surface Model ◽  
Initial Surface ◽  
Surface Mesh ◽  
B Spline ◽  
Mesh Movement ◽  
Spline Surface ◽  
The Difference ◽  
Volume Mesh

A mesh movement algorithm suitable for aerodynamic design optimization problems is presented. It involves B-spline surface construction, projection and evaluation on B-spline faces for the surface mesh movement, as well as inverse-distance and 2D/3D TFI interpolations for the volume mesh deformation. The algorithm is fast and exhibits an excellent parallel efficiency. It is used to deform the surface and volume mesh of an ONERA-M6 wing undergoing several planform changes. The quality of the deformed mesh is preserved as long as the difference between the initial surface mesh and the B-spline surface model is small. A good agreement reported between the flow simulation results on the deformed mesh and those obtained on initial fixed mesh.

scholarly journals A Reconstruction Algorithm for Blade Surface Based on Less Measured Points

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jia Liu ◽  
Ji Zhao ◽  
Xu Yang ◽  
Jiming Liu ◽  
Xingtian Qu ◽  
...  
Keyword(s):  
Reconstruction Algorithm ◽  
Surface Model ◽  
Machining Accuracy ◽  
Blade Surface ◽  
B Spline ◽  
Design Concepts ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Machining Allowance ◽  
Curvature Continuity

A reconstruction algorithm for blade surface from less measured points of section curves is given based on B-spline surface interpolation. The less measured points are divided into different segments by the key geometric points and throat points which are defined according to design concepts. The segmentations are performed by different fitting algorithms with consideration of curvature continuity as their boundary condition to avoid flow disturbance. Finally, a high-quality reconstruction surface model is obtained by using the B-spline curve meshes constructed by paired points. The advantage of this algorithm is the simplicity and effectivity reconstruction of blade surface to ensure the aerodynamic performance. Moreover, the obtained paired points can be regarded as measured points to measure and reconstruct the blade surface directly. Experimental results show that the reconstruction blade surface is suitable for precisely representing blade, evaluating machining accuracy, and analyzing machining allowance.

scholarly journals Development of Support System for Ship-Hull Plate Forming Using Laser Scanner

2021 ◽  
Vol 15 (3) ◽  
pp. 290-300
Author(s):  
Masahito Takezawa ◽  
◽  
Kohei Matsuo ◽  
Takahiro Ando
Keyword(s):  
Point Cloud ◽  
Laser Scanner ◽  
Target Surface ◽  
Ship Hull ◽  
B Spline ◽  
Spline Surface ◽  
Lines Of Curvature ◽  
Plate Shape ◽  
The Difference ◽  
Ship Hull Plate

In this study, we developed a new system that outputs the additional press work procedures necessary to obtain the desired ship-hull surface. This study is unique in terms of determining the additional press work procedures required according to the current plate shape at any work stage by measuring the plate shape using a laser scanner. In the proposed method, a B-spline surface is constructed from a point cloud measured using a laser scanner, and the current plate shape is analyzed based on differential geometry. Additional press lines are estimated based on the difference in the normal curvature along the lines of curvature between the designed target surface and the current surface. We demonstrated the effectiveness of our proposed method through experiments at a shipyard. The proposed system may be used to enhance the efficiency of press work and is expected to be an effective tool for training beginners in the future.

scholarly journals Fuzzy B-Spline Surface Modeling

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
R. U. Gobithaasan
Keyword(s):  
Final Section ◽  
Uncertain Data ◽  
Surface Modeling ◽  
Surface Model ◽  
Data Sets ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Data Points

This paper discusses the construction of a fuzzy B-spline surface model. The construction of this model is based on fuzzy set theory which is based on fuzzy number and fuzzy relation concepts. The proposed theories and concepts define the uncertainty data sets which represent fuzzy data/control points allowing the uncertainties data points modeling which can be visualized and analyzed. The fuzzification and defuzzification processes were also defined in detail in order to obtain the fuzzy B-spline surface crisp model. Final section shows an application of fuzzy B-spline surface modeling for terrain modeling which shows its usability in handling uncertain data.

Surface Reconstruction via Interpolating Boundary Curves and Cross-Boundary Derivatives Simultaneously Approximating Inner Points

2013 ◽  
Vol 321-324 ◽  
pp. 1821-1826 ◽  
Author(s):  
Guo Wang Mu ◽  
Ting Zang ◽  
Shi Jie Dai
Keyword(s):  
Boundary Control ◽  
Surface Reconstruction ◽  
Main Idea ◽  
Initial Surface ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
The Cross ◽  
Boundary Curves

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given boundary curves and the cross-boundary derivatives meanwhile approximates some given inner points. The main idea of our method is: first, we construct an initial surface which interpolates the four given boundary curves and the cross-boundary derivatives on them with minimizing the energy; then, while keeping the boundary control points of the initial surface unchanged, we reposition the inner control points of the surface such that it approximates the inner points with optimization. Examples show that our algorithm is practicable and effective.

scholarly journals On the uncertainty of height anomaly differences predicted by least-squares collocation

2020 ◽  
Vol 10 (1) ◽  
pp. 53-61
Author(s):  
E. Mysen
Keyword(s):  
Least Squares ◽  
Spatial Separation ◽  
Height Anomaly ◽  
Surface Model ◽  
Least Squares Collocation ◽  
Normal Heights ◽  
Gravimetric Quasigeoid ◽  
The Difference ◽  
Grid Interpolation ◽  
Gps Observations

AbstractA network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

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