Structural damage identification by sparse deep belief network using uncertain and limited data

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.