STRiDe - a Self-Tuning Reduced Intelligent Digital environment

Anshu Sharma, E. Tubaldi, Susmita Naskar, E. Patelli, B. Bhowmik

TL;DR: STRiDe provides a robust, interpretable, and data-efficient foundation for hybrid Digital Twins operating under uncertain, nonlinear, and slowly evolving structural conditions and exemplifies how adaptive operator learning can sustain accuracy, interpretability, and resilience – key attributes for next-generation SHM systems in realistic monitoring environments.

Digital Twin (DT) architectures that combine physics-based modelling with machine learning are redefining structural health monitoring (SHM) as a predictive, self-adaptive discipline. A persistent challenge lies in representing nonlinear and evolving dynamics of real-world systems while maintaining interpretability and computational tractability. This study introduces STRiDe - a Self-Tuning Reduced Intelligent Digital environment - which integrates modal reduction, adaptive operator learning, and kernel-based health inference within a hybrid framework for nonlinear SHM. STRiDe is composed of three layers. The first defines a reduced physics-consistent core constructed from the dominant modal subspace of the structural system. This reduction preserves dynamic fidelity while enabling near-real-time simulation. The second module with adaptive identification and regression implements an energy-consistent adaptive operator that incrementally estimates effective stiffness and damping parameters through residual minimisation between measured and predicted responses. This mechanism allows the digital twin to self-adjust to nonlinearity and parameter drift without offline retraining. The third layer employs Kernel Principal Component Analysis (KPCA) to monitor latent-state deviations, producing Hotelling’s T2and Squared Prediction Error (SPE) indices as uncertainty-aware health indicators. The methodology is evaluated on a four-degree-of-freedom (4-DOF) numerical system incorporating a cubic Duffing nonlinearity at the second DOF. A broadband base excitation (0.1-1.8 Hz) is applied, and acceleration responses are simulated using a fourth-order Runge–Kutta scheme. The recorded data are processed using Singular Spectrum Analysis (SSA) for denoising and feature enhancement prior to twin assimilation. The results presented in Fig.1 confirm that STRiDe accurately reconstructs nonlinear behaviour while retaining computational efficiency. The nonlinear frequency-response (amplitude–phase) analysis reveals a reduction in response amplitude from 0.015 ms⁻² rms at 0.2 Hz to 0.002 ms⁻² rms at nearly 1.46 Hz, accompanied by a phase shift exceeding 1 rad, confirming stiffness-dependent hardening. The phase portrait and Poincaré map exhibit the emergence of an asymmetric limit cycle, characteristic of weakly nonlinear oscillation. The Short-Time Fourier Transform (STFT) contour map highlights persistent modal energy concentration near 0.3 Hz, corroborating the dominance of the first mode throughout the excitation sweep. During this transition, the adaptive STRiDe operator identifies gradual stiffness drift, evidenced by a 35% increase in SPE and a rise in T^2 from 7.4 to 8.1, both remaining within the 95% statistical confidence bounds. These indicators demonstrate reliable state sensitivity without false alarms. STRiDe provides a robust, interpretable, and data-efficient foundation for hybrid Digital Twins operating under uncertain, nonlinear, and slowly evolving structural conditions. The framework exemplifies how adaptive operator learning, when embedded within a physics-informed digital environment, can sustain accuracy, interpretability, and resilience – key attributes for next-generation SHM systems in realistic monitoring environments.