Title: Application of Self-Organization Neural Network Technique (SOM) to Optimize Finite- Element Partial Differential Equation (PDEs) Results in Square-Shaped Structures Analysis.
The finite-element method (FEM) is a computationally method for solving partial differential equations (PDEs) with specific boundary conditions over a domain. When we applying the FEM to a domain, it has to divide to a finite number of elements and nodes. The collections of the elements and nodes form the finite-element mesh, whose quality is an important part in achieving exact numeric result for all finite-element codes.
To achieve a high-quality mesh, we have to decide on:
• The suitable size and topology of the mesh,
• How it should be placed on the area, …show more content…
There are two ways to expound a SOM. Since, the whole weight vectors of a neighborhood nodes move in a same direction, SOM form a map that all close to each other and separating them is impossible. Therefore, we use U-Matrix method to visualize differences in this study.
STEPS SUMMARY:
1. In first step we was modeling and analyzing some square shaped structure with ABAQUS and used results to solve finite-element partial differential equation adaptive to structural analysis. r r t ve a fini l mesh g er ormul n ruc ral analys i to e n sic equ eri lly.
Follo la e s ur lem
̈
( + ) − + − ̈ =
2. In the 2nd step, we start improving our Kohonen algorithm by using Computer
Programming and Math softwares MATLAB and STUDIO-1. During this step, the network must be fed a large number of example vectors that represent the kinds of vectors expected during mapping.
3. In 3rd step, we was applying n-dimensional Toroidal to our algorithm. Toroidal groups play an important part in our research. That is n-dimensional Toroidal have a controlling role to that all elements fit exactly in the assumed …show more content…
Application of neural network technique to structural analysis by implementing an adaptive finite-element mesh generation, M.N Jadid, D.R Fairbairn.
Finite-element mesh generation using self-organization neural networks, L Manevitz, M Yousof, D Givoli
Kohonen, Teuvo, Self-Organized Formation of Topologically Correct Feature Maps Saadatdoost, Robab, Alex Tze Hiang Sim, and Jafarkarimi, Hosein. Application of self- organizing map for knowledge discovery based in higher education data.
A. N. Gorban, A. Y. Zinovyev, Principal Graphs and Manifolds, In: Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques, Olivas E.S. et al Eds. Information Science Reference
Ultsch, Alfred; Siemon, H. Peter (1990). "Kohonen 's Self Organizing Feature Maps for Exploratory Data Analysis". In Widrow, Bernard; Angeniol, Bernard. Proceedings of the International Neural Network Conference.
Tony Phillips, Tony Phillips ' Take on Math in the Media, American Mathematical Society, October 2006
"Methods with high accuracy for finite element probability computing" by Peng Long,
The finite-element method (FEM) is a computationally method for solving partial differential equations (PDEs) with specific boundary conditions over a domain. When we applying the FEM to a domain, it has to divide to a finite number of elements and nodes. The collections of the elements and nodes form the finite-element mesh, whose quality is an important part in achieving exact numeric result for all finite-element codes.
To achieve a high-quality mesh, we have to decide on:
• The suitable size and topology of the mesh,
• How it should be placed on the area, …show more content…
There are two ways to expound a SOM. Since, the whole weight vectors of a neighborhood nodes move in a same direction, SOM form a map that all close to each other and separating them is impossible. Therefore, we use U-Matrix method to visualize differences in this study.
STEPS SUMMARY:
1. In first step we was modeling and analyzing some square shaped structure with ABAQUS and used results to solve finite-element partial differential equation adaptive to structural analysis. r r t ve a fini l mesh g er ormul n ruc ral analys i to e n sic equ eri lly.
Follo la e s ur lem
̈
( + ) − + − ̈ =
2. In the 2nd step, we start improving our Kohonen algorithm by using Computer
Programming and Math softwares MATLAB and STUDIO-1. During this step, the network must be fed a large number of example vectors that represent the kinds of vectors expected during mapping.
3. In 3rd step, we was applying n-dimensional Toroidal to our algorithm. Toroidal groups play an important part in our research. That is n-dimensional Toroidal have a controlling role to that all elements fit exactly in the assumed …show more content…
Application of neural network technique to structural analysis by implementing an adaptive finite-element mesh generation, M.N Jadid, D.R Fairbairn.
Finite-element mesh generation using self-organization neural networks, L Manevitz, M Yousof, D Givoli
Kohonen, Teuvo, Self-Organized Formation of Topologically Correct Feature Maps Saadatdoost, Robab, Alex Tze Hiang Sim, and Jafarkarimi, Hosein. Application of self- organizing map for knowledge discovery based in higher education data.
A. N. Gorban, A. Y. Zinovyev, Principal Graphs and Manifolds, In: Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques, Olivas E.S. et al Eds. Information Science Reference
Ultsch, Alfred; Siemon, H. Peter (1990). "Kohonen 's Self Organizing Feature Maps for Exploratory Data Analysis". In Widrow, Bernard; Angeniol, Bernard. Proceedings of the International Neural Network Conference.
Tony Phillips, Tony Phillips ' Take on Math in the Media, American Mathematical Society, October 2006
"Methods with high accuracy for finite element probability computing" by Peng Long,