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This investigation focuses on the application of computational intelligence to the security of Digital Twins (DTs) graphic data of the Cyber-Physical System (CPS). The intricate and diverse physical space of CPS in the smart city is mapped in virtual space to construct the DTs CPS in the smart city. Besides, Differential Privacy Frequent Subgraph-Big Multigraph (DPFS-BM) is employed to ensure data privacy security. Moreover, the analysis and prediction model for the DTs big graphic data (BGD) in the CPS is built based on Differential Privacy-AlexNet (DP-AlexNet). Alexnet successfully solves the gradient dispersion problem of the Sigmoid function of deep network structures. Finally, the comparative analysis approach is utilized to verify the performance of the model reported here by comparing it with Long Short-Term Memory, Convolutional Neural Network, Recurrent Neural Network, original AlexNet, and Multi-Layer Perceptron in a simulation experiment. Through the comparison in the root mean square error, the mean absolute error, the mean absolute percentage error, training time, and test time, the model proposed here outperforms other models regarding errors, time delay, and time consumption. In the same environment, the system performs better with multi-hop paths, extra relays, and a high fading index; in that case, the outage probability is minimal. Therefore, the DP-AlexNet model is suitable for processing BGD. Moreover, its speed acceleration is more apparent than that of other models, with a higher SpeedUp indicator. The research effectively combines data mining and data security, which is of significant value for optimizing the privacy protection technology of frequent subgraph mining on a single multi-graph. Besides, the constructed DTs of CPS can provide excellent accuracy and a prominent acceleration effect on the premise of low errors. In addition, the model reported here can provide reference for the intelligent and digital development of smart cities.

Computational Intelligence in Security of Digital Twins Big Graphic Data in Cyber-physical Systems of Smart Cities