SCNN and GA Solver for Hybrid Stiffness Matrix with Neural Network Elements

摘要

This paper presents SCNN (structure controllable multi-layer forward neural network) and GA (genetic algorithm) solver for hybrid stiffness matrix in finite element analysis. The hybrid stiffness matrix model [1] which developed from Takeuchi&Kosugi [2] approach is presented to simulate the structural analysis with unknown components. The hybrid stiffness matrix is a global stiffness matrix which combines both conventional finite elements and neural network elements. Because of the neural networks element, the hybrid stiffness matrix is the implicit representation that elements of the matrix are unknown. Conversional direct or iterative methods which concerns matrix decomposition are no longer adoptable. The SCNN approach, which computes with only matrix multiplication, is improved and applied to solve linear equations and eigenvalues of the hybrid stiffness matrix. Another consequence benefit of the SCNN approach is the selection of training set of neural networks. Only n+1 mode should be matched, where n is number of freedoms of the element. The advantages of SCNN solver for hybrid stiffness matrix are summarized as follows: 1) Flexible frame for solving various matrix algebra problems; 2) Performing only matrix multiplication but no decomposition; 3) Input is fixed to base vectors, so the neural network element gives high precision and the solver is stable in all cases; 4) Suitable for parallel computation. In the SCNN approach, a three-layer SCNN is constructed to solve inverse and eigenvalues/ eigenvectors of the hybrid stiffness matrix. Since the input of SCNN is fixed to base vectors, the SCNN solver is stable and gives high precision results compared with previous approaches. Improvement of standard SCNN approach is also presented by adding a smoothing term. Example shows significant increase of convergence rate has been achieved. In the GA approach, an improved and optimized GA is employed to solve linear systems of equations of the hybrid stiffness matrix. A local searching algorithm is presented to overcome the early convergence of standard GA. Additionally, new genetic operations are introduced to increase the convergence rate of standard GA. Example gives a satisfied result.