Method of Bilaterally Bounded Weighted Residuals with Genetic Algorithm and its Applications in Engineering

• Main Authors: Zong-Yi Lee, 李宗乙
• Other Authors: Cha'o-Kuang Chen
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/55911158919637554026

博士 === 國立成功大學 === 機械工程學系 === 89 === This paper presents a double side approximate method, which combines the Method of Weighted Residual, mathematical programming and maximum principle theory, and which may be used to solve differential equations found within engineering problems. The proposed method may be readily extended to solve a wide range of nonlinear engineering problems. As stated above, a double side approximate method combines mathematical programming with the Method of Weighted Residual (MWR). If the solution Z(x) exists in the defining domain, V, of a problem, then it is bound by two limits, represented by the functions and . These functions satisfy the definite condition that if >0> , then in , where R is the residual operator. It is possible to obtain the values of minimum and maximum which satisfy the above inequality by using the Genetic Algorithms (GAs) optimization method. This paper considers the use of a double side approximate method to solve differential equations and monotone problems, using the vector of residuals as given by the Method of Weighted Residuals. The paper considers the application of the proposed method to several nonlinear differential equation problems. In this way the efficiency and simplicity of this method are illustrated, indicating that the proposed method can be easily extended to tackle other nonlinear engineering problems. It is possible to use different Methods of Weighted Residual to solve the bilateral inequality. As has been mentioned previously, by using the GAs optimization method it is possible to determine the values of the minimum and maximum functions which satisfy the inequality. The Laplace transform is well known as a powerful tool in the analysis of time independent problems. In this paper, a method which combines the use of Laplace transformation and double side approach method, has been applied to the solution of transient nonlinear heat conduction problems. A double side approach method is then used to solve the generalized physical engineering problems. The proposed method demonstrates efficiency, accuracy, simplicity, no convergence problems, and requires less computer processing time, and as such, represents a major step forward from the traditional problem solving techniques.