Mathematical programming neural network (MPNN) for mechanism design.

摘要

This dissertation develops Mathematical Programming Neural Network (MPNN) theory and algorithms for solving highly nonlinear optimization problems of mechanical design.; Based upon a comprehensive investigation of the prevalent MPNN models, a MPNN model for unconstrained optimization is proposed first, and then applied to the optimal synthesis of the planar-four bar linkage. After combining with the Augmented Lagrange Multiplier (ALM) methods, the proposed MPNN model is extended to the constrained optimization and applied to the constrained optimization of mechanisms. The applications show that the new MPNN model has a global convergence property.; In the first part of MPNN, the exact Hessian matrices of the objective functions and the constraints are required. In the second part, the 'approach' matrix is developed from the two previous first derivative information and the exact Hessian matrix is not needed any more; therefore, the algorithm not only needs less amount of computation but also is applicable to the problems where exact Hessian matrices are very difficult to get.; The relation between the least square and mini-max norm of the function generating mechanisms is also developed and implemented in the algorithm to avoid the direct minimization of the complex structural error.; The applications considered include the optimal synthesis of planar four-bar mechanism, spatial R-S-S-R mechanism, and a beam with variable cross-section. Results show the attractive properties of robustness and global convergence for the proposed MPNN models.; A brief introduction, basic terminology and an outline of new contributions are given in Chapter I. Chapter II includes literature review for mechanism optimization, prevalent MPNN models and Augmented Lagrange Multiplier methods. The function formulation for generating mechanism and the relation between the least square and mini-max norms are described in Chapter III. The MPNN models using the exact Hessian matrix for both unconstrained and constrained optimization are developed in Chapter IV. Chapter V develops the theory of MPNN without using the exact Hessian matrix for both the unconstrained and constrained optimization. Another application of MPNN in the optimization of a beam design is illustrated in Chapter VI.