IoT Thrust Seminar | The Consideration of Spatiotemporal Correlation in Bayesian Model Updating and System Identification

In system identification, accurately modeling prediction errors presents a significant challenge, particularly in time-domain analysis. This complexity arises from the need to account for responses across multiple measured degrees of freedom and time steps. Traditionally, this issue is addressed by assuming that prediction errors are independent and identically distributed (i.i.d.) across data points. This simplifying assumption often proves inadequate in practical applications. The i.i.d. condition is frequently violated due to:

• Low signal-to-noise ratios
• Significant variations in noise intensities across measurement channels
• Inter-channel correlations
• System-specific characteristics including damping levels, material nonlinearities, and fine finite-element meshes that induce localized response interactions
• The simultaneous consideration of multiple quantities of interest

This seminar introduces a novel model class that eliminates this assumption, enabling adaptive modeling of spatiotemporal correlations in structural time-history responses (and their prediction errors). The proposed approach requires few parameters while maintaining computational efficiency, particularly for determinant and inverse operations. The proposed adaptive model class enables simultaneous optimization of spatiotemporal correlations alongside other uncertain parameters within a Bayesian system identification framework. Beyond developing this adaptive spatiotemporal model, a key contribution of this work lies in the analytical evaluation of both the posterior probability density function (PDF) and relative entropy. These analyses demonstrate the critical importance of accounting for correlation effects in system identification problems.

To verify the proposed approach, we constructed multiple spatiotemporal correlation model classes using conventional functions and evaluated their performance against both the adaptive model class and an uncorrelated model class through Bayesian model class selection. The verification study included: (1) a simulated cantilever beam example, and (2) a real-world case study of a ballasted railway track system. Results showed that the adaptive model class consistently outperformed conventional correlation models. Furthermore, the analysis revealed that neglecting prediction error correlations leads to significantly misleading model updating outcomes.