Model Falsification for Predicting Dynamical Responses of Uncertain Structural Systems

TL;DR

The paper tackles uncertainty in structural dynamics when many candidate input–output models exist by introducing a likelihood-bound falsification approach guided by false discovery rate (FDR) control to prune implausible models. Unfalsified models are then weighted in a Bayesian framework to predict responses to new inputs, achieving substantial computational savings relative to full Bayesian model averaging. The method is validated on three challenging structural scenarios: a 4-DOF base-isolated building, a 1623-DOF wind-excited building with tuned mass dampers, and a full-scale base-isolated shake-table experiment, with results showing accurate predictions and dramatic reductions in the number of required simulations. The work demonstrates a practical, scalable strategy for robust response prediction under model-structure uncertainty, particularly for structures with passive control devices and limited data.

Abstract

Accurate prediction of dynamical response of structural system depends on the correct modeling of that system. However, modeling becomes increasingly challenging when there are many candidate models available to describe the system behavior. Furthermore, uncertainties can be present even for the parameters of these model classes. The plausibility of each input-output model class of the structures with uncertain components can be determined by a Bayesian approach from measured dynamic responses to one or more input records; predictions of the structural system response to alternate input records can then be made. However, this approach may require many model simulations, even though most of those model classes are quite implausible. An approach is proposed herein to use a bound, computed from the false discovery rate, on the likelihood of measured data to falsify models considering uncertainties in the passive control devices that do not reproduce the measured data to sufficient accuracy. Response prediction is then performed using the unfalsified models in an approximate Bayesian sense by assigning weights, computed from the likelihoods, only to the unfalsified models approach incurring only a fraction of the computational cost of the standard Bayesian approach. The proposed approach for response prediction is illustrated using three structural examples: an earthquake-excited four--degree-of-freedom building model with a hysteretic isolation layer; a 1623--degree-of-freedom three-dimensional building model, with tuned mass dampers attached to its roof, subjected to wind loads; and a full-scale four-story base-isolated building tested on world's largest shake table in Japan's E-Defense lab. The results exhibit accurate response predictions and significant computational savings, thereby illustrating the potential of the proposed method.

Figures (25)

• Figure 1: Using false discovery rate models with their residual error falling inside the shaded box are unfalsified.
• Figure 2: Likelihood bounds with two measurements. (${\bar{\alpha}}_1=\alpha/2$ determines $\text{\underline{${\text{}}$}}_j$ and $\overline{\text{}}_j$; ${\bar{\alpha}}_2=\alpha$ determines $\text{\underline{${\text{}}$}}_j^{\prime}$ and $\overline{\text{}}_j^{\prime}$. Uncorrelated joint densities are depicted but this need not be assumed.)
• Figure 3: Base-isolated building model
• Figure 4: Several model classes to represent the force-displacement loops.
• Figure 5: True absolute base accelerations of the 4 DOF building subjected to the Kobe earthquake, and those predicted from models likelihood-bound-unfalsified using the El Centro data.