J191014 システム同定への適用を考慮した悪条件行列の正則化による連立一次方程式の近似解法([J19101]構造・材料の高度化に向けた宇宙工学と材料力学の展開(1))

概要

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A method is proposed for solving a set of simultaneous equations with an ill conditioned coefficient matrix to apply system identification. To find an approximate solution, the coefficient matrix is regularized by adding a small positive value e to its diagonal elements. A regularized matrix is provided in different expressions that depend on the coefficient matrix. This paper regularizes a rectangular coefficient matrix and then a square coefficient matrix. Improvement of solution accuracy is possible by removing the very small singular values. Therefore, rank estimation of the coefficient matrix is a key to obtain an accurate solution. This paper describes a method that estimates the rank by setting an appropriate value of E.
一般社団法人日本機械学会の論文
2011-09-11