A new method for updating nonlinear finite element model accounting for modeling errors and uncertainties

Structural systems are generally susceptible to various types of failures. Therefore, to enhance the design and operation of these systems, more efficient calibration models are highly desirable. This has attracted significant attention of researchers who have identified nonlinear finite element-based calibration model as a promising solution. This can be attributed to its advantages regarding its simplicity in structural damage identification and optimization of the available modeling techniques.

Pioneered in the mid-twentieth century, finite element models have significantly improved various aspects of modeling and simulation of complex structures when properly calibrated. Alternatively, recent research work has led to the development of several finite element modeling and simulation techniques as well as calibration of mechanics-based nonlinear models. This has led to efficient model calibration and identification of unknown model parameters thus revealing the important aspects of the structural systems under investigation. Unfortunately, uncertainty associated to modeling errors has remained a big challenge especially in updating nonlinear finite element models.

To this note, Professor Rodrigo Astroza and Mr. Andrés Alessandri at University of los Andes–Chile, together with Professor Joel P. Conte at University of California San Diego developed a new method for updating mechanics-based nonlinear finite element models taking into consideration different sources of uncertainties, including modeling errors, model parameter uncertainty, and measurement noise. Fundamentally, the design approach entailed a dual adaptive filter in which Unscented Kalman filter and linear Kalman filter were used to determine the unknown model parameters and diagonal covariance matrix terms of the prediction error, respectively. Their work is currently published in the research journal, Mechanical Systems and Signal Processing.

In brief, the research team initiated their experimentation by cross-examining the sources and effects of modeling uncertainties in nonlinear structural finite element models. Next, due to the varying nature of the modeling uncertainty with time, the simulation error vector was estimated as the time-variant quantity representing modeling errors and, at the same time, an optimal set of model parameter was also identified based on the input and output data recorded on the structure of interest. Eventually, the feasibility of the new method was validated using a three-story steel frame structure comprising of eight unknown parameters. The sources of modeling errors, in this case, were considered to be structural properties regarding damping, geometry, inertia, and gravity loads.

The new approach provided accurate parameter estimates with minimal discrepancies between the actual and FE-predicted responses, for both measured and unmeasured response quantities, thus outperforming the initially used parameter-only estimation technique.

In summary, Professor Astroza and colleagues successfully developed a dual adaptive filtering technique for updating nonlinear finite element models accounting for different sources of uncertainty. To actualize their study, an earthquake-based excitation was used to evaluate the prediction capabilities of the newly developed approach. Altogether, their approach is a promising solution for the design and optimization of structural systems with numerous benefits such as damage detection in structural components.