中文摘要：

考虑模型误差和测量误差的影响，用概率的观念给出了静力荷载作用下梁式结构的模型误差和测量误差的定义，在此基础上，建立了关于损伤指数的随机控制方程。结合静力凝聚法和摄动法，给出了关于随机损伤指数的随机方程的求解方法。在获得随机损伤指数的解后，可通过结构损伤的概率定义对梁式结构损伤进行识别。最后利用几个数值算例验证了本文方法的有效性。

英文摘要：

Under the condition of static load, model errors and measurement errors involved in practical structures are clearly defined in the view of probability in current paper. With consideration of the impac- tion of uncertain model errors and measurement errors on damage identification, the random control equations with damage index of beam structures under static load are established. Combining static con- densation method and perturbation technique, the solutions of the random equations are determined. Based on the determined damage index, the probability of structural damage can be achieved according to the damage definition provided in the paper. In the end, the several numerical examples of random beam structures are investigated to illustrate the effectiveness of the suggested method.