Convergence and stability analysis of recurrent neural networks for rapid structural damage assessment under seismic loads

Non-stationary earthquake responses and sensor noise often make RNN-based damage assessment difficult to optimize and unstable at inference. We develop a stability-controlled, lightweight LSTM that: (i) penalizes gradient overshoot to smooth the update trajectory and prevent exploding/vanishing gradients; (ii) uses a temporal attention gate to emphasize damage-critical segments; and (iii) performs multi-scale sliding-window inference to stabilize long-horizon predictions. Casting the LSTM-with-attention into a discrete-time state-space view, we provide sufficient conditions for non-expansive updates and BIBO stability by bounding the Jacobian spectral norm and constraining attention gains.Empirically, under 10 dB noise our method reaches loss < 0.01 in 18 epochs with only 3 gradient-explosion events, and achieves σ(out)=0.032 with max Δ-rate = 0.085 ± 0.009, outperforming standard LSTM/GRU/BiLSTM/RNN baselines in accuracy, stability, and latency. On-device tests (Jetson Nano) confirm < 5 ms end-to-end delay at 100 Hz, supporting real-time deployment.