بررسی فرایند به‌روزرسانی مدل اجزای محدود با استفاده از شکل مودهای POD و معیار انعطاف‌پذیری

Finite element model updating (FEMU) plays a crucial role in structural health monitoring by improving the accuracy of numerical models in representing real structures. Traditional model updating methods typically rely on experimental modal analysis (EMA), where natural frequencies and ordinary mode shapes are extracted and compared with numerical predictions. However, recent advancements in modal identification techniques have introduced alternative approaches, such as the Proper Orthogonal Decomposition (POD), which has shown promise in reducing data dimensionality and extracting dominant modal characteristics. Despite its advantages, the effectiveness of POD mode shapes in finite element model updating has not been extensively evaluated, particularly in terms of their impact on convergence speed, accuracy, and robustness against noise.
This study investigates the efficiency of POD mode shapes in FEMU compared to conventional mode shapes by considering three different damage scenarios in a steel bridge with a concrete deck. The bridge model was developed in SAP2000, where both undamaged and damaged states were simulated. Damage scenarios included (1) a 20% reduction in the height of a main girder, (2) a 20% reduction in the flange and web thickness of the same girder, and (3) a 20% reduction in the elastic modulus of the main girders. The dynamic response of the bridge was obtained through numerical simulations, and both ordinary mode shapes (OMS) and POD mode shapes were extracted. The optimization process was conducted using the Particle Swarm Optimization (PSO) algorithm, with two different objective functions: the flexibility-based objective function and the Modal Assurance Criterion (MAC)-based objective function.
The results demonstrated that the use of POD mode shapes significantly improved the convergence rate of the optimization process. Specifically, in all three damage scenarios, the number of iterations required for convergence was considerably lower when using POD mode shapes compared to conventional mode shapes. Additionally, the accuracy of the estimated parameters was enhanced, particularly when using flexibility as the objective function. It was also observed that the first two POD modes provided results comparable to the first five ordinary modes, indicating that fewer mode shapes were required for achieving the same level of accuracy.
Furthermore, the influence of measurement noise was examined to assess the robustness of POD mode shapes in FEMU. Different levels of Gaussian white noise (1%, 5%, and 10%) were introduced to the acceleration responses before extracting the POD mode shapes. The analysis revealed that the first two natural frequencies remained stable under low noise levels (1% and 5%) , whereas higher mode frequencies exhibited increased variations as noise intensity increased. However, even under 10% noise, the first two modes retained their reliability, demonstrating the resilience of POD mode shapes against noise effects. The impact of noise on the optimization process was also evaluated, and while higher noise levels led to an increased number of iterations for convergence, the final updated parameters remained close to the actual values.
Overall, this study highlights the advantages of employing POD mode shapes in FEMU, particularly in reducing computational costs and improving model accuracy. The results suggest that incorporating POD-based modal information into FEMU frameworks can enhance the reliability and efficiency of structural model updating. Moreover, the flexibility-based objective function, when combined with POD mode shapes, proved to be a more effective criterion for damage detection compared to the MAC-based objective function. These findings contribute to the growing body of research advocating for the adoption of advanced modal identification techniques in structural health monitoring and numerical model updating.