基于模态区间分析的结构不确定性损伤评估

针对实际工程结构中难以避免的不确定性因素，如材料非均质、边界条件不清晰、测试误差、模型误差等，提出利用模态区间分析求解包含不确定性参数的梁损伤评估方法。首先建立钢箱梁和钢筋混凝土梁的计算模型，以区间形式定义梁几何、材料参数的不确定性，体现各参数的可能波动范围；然后将结构静力学方程扩展成区间方程，通过模态逻辑对区间方程进行重新释义；最后在梁上施加集中荷载，计算得到梁关键应变点的区间工作状态。分析中通过降低梁单元的弹性模量来模拟损伤，再比较确定性方法、经典区间算法和模态区间分析的计算结果。结果表明:与确定性损伤评估方法不同，区间算法允许结构包含不确定性参数，认为落在区间包络线内的应变值是合理的，而当某荷载下应变值超出包络范围时说明梁发生了损伤；模态区间分析计算得到的区间包络范围要明显小于经典区间算法，能够有效避免计算过程的参数区间扩张，而且可以及时发现梁的损伤和损伤时所对应的外荷载，避免结构损伤进一步的恶化。

Damage Assessment of Structures with Uncertainties Using Modal Interval Analysis

In view of uncertain factors difficult to avoid in real world engineering structures, such as inhomogeneous materials, unclear boundary conditions, testing and modeling errors, a method based on modal interval analysis was developed to solve the damage assessment problems of beams with uncertain parameters. Firstly, the calculation models of a steel box beam and a reinforced concrete beam were established in which the uncertainties of the geometric and material parameters were defined by intervals. The intervals reflected the possible fluctuation ranges of the parameters. Then the beam statics equations were extended to their interval forms, which were further interpreted and expressed by the modal logic. After that, the interval working states of the critical strain points of the beam were calculated under certain concentrated loads. In the analysis the damage was simulated by decreasing elastic modulus of the beam elements. The analysis results given by the deterministic method, the classical interval algorithm and the modal interval analysis were compared to find the difference. The results show that different to the deterministic method, interval analysis allows the involvement of uncertain parameters and the strains within the intervals are regarded as rational values. On the contrary, the strains beyond the interval envelope imply the damage occurrence of the beams under the specific loads. Meanwhile, the interval envelope given by the modal interval analysis is obviously smaller than that given by the classical interval algorithm, which means that the former can effectively avoid the interval expansion during the calculation process. Furthermore, the modal interval analysis can early detect the beam damage, as well as the corresponding external load, which can avoid the further deterioration of the damage.