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In this Special Issue on symmetry, we mainly discuss the application of symmetry in various structural health monitoring. For example, considering the health monitoring of a known structure, by obtaining the static or dynamic response of the structure, using different signal processing methods, including some advanced filtering methods, to remove the influence of environmental noise, and extract structural feature parameters to determine the safety of the structure. These damage diagnosis methods can also be effectively applied to various types of infrastructure and mechanical equipment. For this reason, the vibration control of various structures and the knowledge of random structure dynamics should be considered, which will promote the rapid development of the structural health monitoring. Among them, signal extraction and evaluation methods are also worthy of study. The improvement of signal acquisition instruments and acquisition methods improves the accuracy of data. A good evaluation method will help to correctly understand the performance with different types of infrastructure and mechanical equipment.

real-time hybrid simulation --- H∞ control --- time delay --- mixed sensitivity --- structural health monitoring --- deep learning --- data anomaly detection --- convolutional neural network --- time–frequency extraction --- micro inertial measurement unit (MIMU) --- variational mode decomposition (VMD) --- Hilbert–Huang transform (HHT) --- frequency-domain integration approach (FDIA) --- torsion angle calculation --- offshore oil platform --- self-anchored suspension bridge --- cable clamp --- slippage --- force analysis --- high formwork --- ARMA --- BPNN --- stress trend prediction --- crack detection --- improved YOLOv4 --- concrete surface --- substructure shake table testing --- integration algorithm --- finite element method --- damper --- digital twin --- prestressed steel structure --- construction process --- safety assessment --- intelligent construction --- structural health monitoring (SHM) --- vibration --- frequency domain --- time domain --- time-frequency domain --- technical codes --- multiple square loops (MSL)-string --- seismic excitation --- dynamic response --- seismic pulse --- near and far field --- three-dimensional laser scanning --- surface flatness of initial support of tunnel --- curved surface fitting --- flatness calculation datum --- curvedcontinuous girder bridge --- collision response --- seismic mitigation --- pounding mitigation and unseating prevention --- heavy-duty vehicle --- road --- coupling model --- terrestrial laser scanning --- RGB --- genetic algorithm --- artificial neutral network