灵敏度的模态区间分析方法及其在不确定性参数识别中的应用

A sensitivity modal interval analysis method and its application to uncertain parameter identification

由于存在区间过估计及无法获知结构响应表达式的问题,区间灵敏度分析方法难以广泛地应用于实际复杂结构中。为此,提出一种基于响应面的灵敏度模态区间分析方法,该方法在区间响应面模型上分别对每个区间参数进行模态区间扩张得到响应区间,进而计算相对模态区间灵敏度,通过比较相对模态区间灵敏度即可判断结构响应对参数的敏感程度。通过数值算例探讨响应面形式对计算结果的影响,阐述灵敏度区间分析与灵敏度模态区间分析的优缺点。最后以钢板试验及钢筋混凝土拱桥不确定性参数识别算例来验证所提方法在复杂结构分析中的可行性。灵敏度分析结果表明该方法有效地解决区间过估计问题,提高了灵敏度分析的精度。对参数在多个范围内的灵敏度分析,所提方法具有较高的计算效率。参数识别结果表明将逆响应面与模态区间分析结合可避免区间优化过程,在保证精度的前提下,提高了参数识别效率。

Because of the unknown expression of response and the interval overall estimation ,interval sensitivity analysis method is difficult to be used in complex structures .For this reason ,a new sensitivity modal interval analysis method based on response surface model is presented in this paper .The reasonable experiment design and regression analysis method are adopted to build an interval response surface model which reflects the relationship between parameters and responses .Then the modal interval extension is applied to each interval parameter in the model to get the value ranges of structural responses .The influence degree of parameter on structural responses is estimated by comparing the calculated value of relative modal interval sensi ‐ tivity .The effect of the response surface form on the result of modal interval sensitivity analysis is discussed ,and the advantages and disadvantages of classic interval sensitivity analysis and modal interval sensitivity analysis are explored through the nu ‐ merical simulation example .Finally ,the proposed approach is applied to the uncertain parameter identification of steel plates and the reinforced concrete arch bridge ,respectively .The sensitivity analysis results show that the proposed method can solve the problem of interval overall estimation and be available to the sensitivity analysis of a complex structure .The process of interval optimum can be avoided by the combination of the inverse response surface and modal interval analysis method . The computational efficiency is improved without decrease the precision .