Structures usually suffer from natural or artificial damages that might result in shortening their service life and even triggering their collapse. Therefore, vibrational damage detection methods, as cost-effective and nondestructive techniques, are widely investigated by researchers. In the present paper, the modal-strain energy-based two-stage method is enhanced, and a graph-theoretic hierarchical (GHM) method is proposed, which takes advantage of the modal strain energy-based index (MSEBI) and overcomes its potential drawbacks by identifying all damaged elements. This method assigns orders and allocates the computational resources to elements according to the MSEBI as well as the connections represented by a graph model. The water strider algorithm (WSA) is also utilized as an efficient new optimizer, and its results are compared with those of some other well-known algorithms. Several examples are used to substantiate the results and performance of the new GHM framework, showing that the new method outperforms the general classic method, especially when it is combined with the WSA optimizer.

结构通常会遭受自然或人为破坏，这可能会导致其使用寿命缩短甚至崩溃。因此，振动损伤检测方法作为具有成本效益的无损技术，已被研究人员广泛研究。本文对基于模态应变能的两阶段方法进行了改进，并提出了一种基于图论分层能级的图论分层方法（GHM），克服了它的潜力。通过识别所有损坏的元素的缺点。该方法根据MSEBI以及图模型表示的连接来分配顺序并将计算资源分配给元素。Water Strider算法（WSA）也被用作一种高效的新型优化程序，并将其结果与其他一些知名算法的结果进行比较。使用几个示例来证实新GHM框架的结果和性能，表明该新方法优于常规的传统方法，尤其是与WSA优化器结合使用时。