A Time-Aware BiLSTM-PSO-SVR Framework for Predicting the Hysteretic Response of Circular Steel Tube Braces

Steel braces in concentrically braced frames exhibit nonlinear axial force–displacement responses under repeated tension and compression. This study develops a workflow for predicting the hysteretic response of pin-ended circular steel tube braces. A distributed-plasticity OpenSees model was compared graphically with results from one circular-tube brace test, and a numerical database was generated for model training. The database contains 1620 curves from three cyclic loading protocols and 180 curves from a random loading history, yielding 1800 curves in total. Six sequence-model families were evaluated with 4, 8, 16, 32, 64, and 128 hidden units. The best baseline configuration, a bidirectional long short-term memory network with 128 hidden units (BiLSTM-128n), achieved an MAE of 128.72, an MSE of 34,850.94, an RMSE of 186.68, and an R2 of 0.978. Adding an explicit sequence-position index yielded a time-aware configuration (tBiLSTM-128n) with an MAE of 64.69, an MSE of 7898.09, an RMSE of 88.87, and an R2 of 0.995. A radial-basis-function support vector regression model (RBF-SVR), tuned by particle swarm optimization, predicted selected peaks and was combined with the tBiLSTM trend using Savitzky–Golay filtering. The hybrid output is illustrated through comparison with the simulated response.