CAJ | 학술논문

提出了用幂基多项式拟合频响函数的几点技巧。运用幂基多项式和最小二乘法对频响函数拟合的计算公式进行了推导，得到了用于问题求解的线性代数方程组。为改善该方程组系数矩阵的条件数，对频率变量和系数矩阵进行了规范化处理；频率变量被规范化到0～1的无量纲正实数区域，两个相关矩阵的每列模长被规范为1。然后用奇异值分解的方法求解该方程组，得到拟合频响函数所用的幂基多项式的系数。最后，根据幂基多项式的系数，求出系统的极点和留数，从而识别出系统的模态参数。文中给出了一个悬臂梁模拟算例，结果表明本文算法具有较好的计算精度。
제출료용멱기다항식의합빈향함수적궤점기교。운용멱기다항식화최소이승법대빈향함수의합적계산공식진행료추도，득도료용우문제구해적선성대수방정조。위개선해방정조계수구진적조건수，대빈솔변량화계수구진진행료규범화처리；빈솔변량피규범화도0～1적무량강정실수구역，량개상관구진적매렬모장피규범위1。연후용기이치분해적방법구해해방정조，득도의합빈향함수소용적멱기다항식적계수。최후，근거멱기다항식적계수，구출계통적겁점화류수，종이식별출계통적모태삼수。문중급출료일개현비량모의산례，결과표명본문산법구유교호적계산정도。
Several techniques are set forth in the paper for the frequency response functions （FRFs）fitting by ordinary power polynomials．The formulas for the FRFs fitting by power polynomials are derived using the least square method and the linear equations for the solution are achieved．In order to improve the condition in the coefficient matrix of the equations，the variables of the frequency domain and the coefficient matrix is normalized．The fitting variables are normalized from original ones to a 0～1 domain and the norm of each column of two correlative matrices are normalized to 1．The linear equations are solved by singular value decomposition method to obtain the coefficients of the power polynomials．A simulating example of a cantilever beam is presented and the results show that the accuracy of the algorithm is satisfied．