Achieving complete data of measured mode shapes is costly during the process of structural dynamic test. This results in a challenge for the damage detection. This paper concentrates on structural damage detection problem with incomplete mode shape data. An efficient method to deal with this problem is proposed. The generalized flexibility matrix (GFM) is employed. By introducing a few new variables and partitioning the involved matrices, a nonnegative linear least square model is derived. Most of the variables in the model are the damage extents of structural elements. Our method does not involve mode shape expansion or reduction technique.

Three numerical examples show that the performance of the proposed method is superior to that of the GFM method combining with mode shape expansion, it is almost the same as that of the GFM approach with complete mode shapes data.

在结构动态测试过程中，获得完整的模态振型数据是昂贵的。这给损坏检测带来了挑战。本文主要研究具有不完整振型数据的结构损伤检测问题。提出了一种有效的方法来处理这个问题。采用广义柔度矩阵 (GFM)。通过引入一些新变量并对涉及的矩阵进行划分，推导出非负线性最小二乘模型。模型中的大部分变量是结构元素的损坏程度。我们的方法不涉及模式形状扩展或减少技术。

三个算例表明，该方法的性能优于结合模态振型扩展的GFM方法，与具有完整模态数据的GFM方法几乎相同。