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This paper proposes a hybrid neural network employing an attention mechanism (AM) strategy in nonlinear parameter identification for updating structural models based on dynamic response data, which integrates the characteristics of both a convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) to address the nonlinearity and time sequentiality of structural dynamic response data varying with time. First, one-dimensional CNNs are employed to extract spatial features from the time-series data of structural dynamic responses, which are subsequently compressed using max pooling. The data processed by the CNNs are subsequently used as inputs for BiLSTM to extract temporal features. Additionally, the time-series features obtained from the hidden layers of the BiLSTM are supplied to the AM, which employs weighting techniques to mitigate the impact of redundant information on parameter identification by discerning the importance of the response data. Finally, the attention-weighted outputs are fed into a fully connected layer to estimate the parameters of the structural nonlinear model. To evaluate the performance of the hybrid neural network, a numerical simulation based on a nonlinear model of the tower subjected to earthquake excitation is performed. Moreover, a shake table test of a scaled steel-concrete composite bridge tower is further conducted. Both simulation and experimental results demonstrate that the proposed CNN-BiLSTM-AM model effectively addresses the challenge of structural nonlinear model updating, particularly for dynamic response data from earthquake excitations, by improving parameter identification accuracy and enhancing model calibration.