Interval model calibration with response-consistent supervised learning network

This manuscript proposes a “response-consistent” supervised interval identification method leveraging an enhanced Multi-layer Perceptron (MLP) neural network for rapid calibration of structural parameter intervals. Unlike traditional calibration methods, which rely on time-consuming optimisation or random sampling, the proposed approach achieves interval calibration in a single forward inference pass. The key innovation, response-consistent supervision, directly supervises MLP training through comparison between the predicted response intervals (propagated from parameter intervals) and experimentally measured response intervals. This ensures that the calibrated parameter intervals inherently yield response intervals consistent with observed experimental data, addressing the limitations of conventional training approaches that focus solely on parameter-space losses. Additionally, a reparameterization-based Monte Carlo (MC) technique is implemented to maintain differentiability of the loss function throughout the interval uncertainty propagation process. To further refine training accuracy, an interval similarity loss function based on a relative position operator is introduced to effectively capture correlations between the upper and lower bounds of response intervals. The effectiveness and efficiency of the proposed method are demonstrated through its application to one numerical case involving a mass-spring system, and two experimental cases, an airplane toy model and a steel plate structure, highlighting its potential for accurate and efficient interval model calibration.