Regularised Volterra series models for modelling of nonlinear self-excited forces on bridge decks

Volterra series models are considered an attractive approach for modelling nonlinear aerodynamic forces for bridge decks since they extend the convolution integral to higher dimensions. Optimal identification of nonlinear systems is a challenging task since there are typically many unknown variables that need to be determined, and it is vital to avoid overfitting. Several methods exist for identifying Volterra kernels from experimental data, but a large class of them put restrictions on the system inputs, making them infeasible for section model tests of bridge decks. A least-squares identification method does not restrict the inputs, but the identified model often struggles with noisy (non-smooth) kernels, which is deemed to be unphysical and a sign of overfitting. In this work, regularised least-squares identification is introduced to improve the performance of model identification using least-squares. Standard Tikhonov regularisation and other penalty techniques that impose decaying kernels are also explored. The performance of the methodology is studied using experimental data from wind tunnel tests of a twin deck section. The regularised Volterra models show equal or better results in terms of modelling the self-excited forces, and the regularisation makes the models less prone to overfitting

Nonlinear modelling of aerodynamic self-excited forces: An experimental study

The bridge aerodynamics research community is currently discussing several nonlinear wind load models for bridge decks, but no definite conclusion on which model is superior to the others is currently available. In this paper, we use experimental data for a double-deck section model tested in an advanced forced vibration rig to study the observed nonlinearities and to gain insight into what characteristics the nonlinear load model should be capable of modelling. Single harmonic horizontal, vertical and pitching motion; combined motion; and stochastic motion are considered. This approach allows the investigation of a more extensive range of nonlinear behaviours than regular wind tunnel testing. The typical nonlinear characteristics observed are mean drift, deviation from superposition and harmonic distortion. Further, we introduce a simple response-surface model for force prediction using polynomial combinations of the inputs and its derivatives. The model helps to gain further insight into the nonlinearity of the problem at hand and to select which refined modelling approach can be used in future work