The accuracy of structural damage identification is affected by the uncertainties in the vibration measurements and the finite element modeling. This paper proposes a novel approach based on sparse deep belief network (DBN) for structural damage identification with uncertain and limited data. Vibration characteristics, that is, natural frequencies and mode shapes, are extracted as the input to the network, while the output are the damage locations and severities of the structure. DBN is chosen to train the generated data sets and identify structural damages. Restricted Boltzmann Machines (RBMs) are used as building blocks to composite a DBN. To further enhance the capacity of the RBMs, an arctan‐based sparse constraint is utilized to enable the hidden units to become sparse. This is achieved by adding an arctan norm constraint on the whole of the hidden units' activation probabilities. Numerical and experimental studies are conducted to verify the accuracy and performance of the proposed method. Undetermined damage identification is conducted, in which the quantity of input modal data is less than that of the system parameters to be identified. The identification results show that the proposed sparse DBN based on arctan can identify the damage effectively, and its accuracy is better than those obtained by other methods, even when the modeling uncertainty and the measurement noise exist and only limited data is available.

中文翻译：

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使用不确定和有限的数据通过稀疏深度置信网络识别结构损伤

结构损伤识别的准确性受振动测量和有限元建模的不确定性影响。本文提出了一种基于稀疏深度信念网络（DBN）的不确定性和有限数据的结构损伤识别的新方法。振动特性（即固有频率和振型）被提取为网络的输入，而输出则是结构的损坏位置和严重程度。选择DBN来训练生成的数据集并识别结构损坏。受限玻尔兹曼机（RBM）用作构建DBN的基础。为了进一步增强RBM的能力，利用基于arctan的稀疏约束使隐藏的单元变得稀疏。这是通过在所有隐藏单元的激活概率上添加反正则约束来实现的。进行了数值和实验研究，以验证所提出方法的准确性和性能。进行不确定的损坏识别，其中输入模态数据的数量少于要识别的系统参数的数量。识别结果表明，所提出的基于arctan的稀疏DBN可以有效地识别损伤，即使存在建模不确定性和测量噪声，且数据有限的情况下，其准确性也优于其他方法。进行不确定的损坏识别，其中输入模态数据的数量少于要识别的系统参数的数量。识别结果表明，所提出的基于arctan的稀疏DBN可以有效地识别出损伤，即使存在建模不确定性和测量噪声且只能得到有限数据的情况，其准确性也优于其他方法。进行不确定的损坏识别，其中输入模态数据的数量少于要识别的系统参数的数量。识别结果表明，所提出的基于arctan的稀疏DBN可以有效地识别损伤，即使存在建模不确定性和测量噪声，且数据有限的情况下，其准确性也优于其他方法。