Abstract
To facilitate the establishment of the probabilistic model for quantifying the vulnerability of coastal bridges to natural hazards and support the associated risk assessment and mitigation activities, it is imperative to develop an accurate and efficient method for wave forces prediction. With the fast development of computer science, surrogate modeling techniques have been commonly used as an effective alternative to computational fluid dynamics for the establishment of a predictive model in coastal engineering. In this paper, a hybrid surrogate model is proposed for the efficient and accurate prediction of the solitary wave forces acting on coastal bridge decks. The underlying idea of the proposed method is to enhance the prediction capability of the constructed model by introducing an additional surrogate to correct the errors made by the main predictor. Specifically, the regression-type polynomial chaos expansion (PCE) is employed as the main predictor to capture the global feature of the computational model, whereas the interpolation-type Kriging is adopted to learn the local variations of the prediction error from the PCE. An engineering case is employed to validate the effectiveness of the hybrid model, and it is observed that the prediction performance (in terms of residual mean square error and correlation coefficient) of the hybrid model is superior to the optimal PCE and artificial neural network (ANN) for both horizontal and vertical wave forces, albeit the maximum PCE degrees used in the hybrid model are lower than the optimal degrees identified in the pure PCE model. Moreover, the proposed hybrid model also enables the extraction of explicit predictive equations for the parameters of interest. It is expected that the hybrid model could be extended to more complex wave conditions and structural shapes to facilitate the life-cycle structural design and analysis of coastal bridges.
Highlights
The predicted wave forces using polynomial chaos expansion (PCE) with degrees varying from 2 to 6 and the true ones in the test data set are compared in Figures 2 and 3, and the variations of R and root mean square error (RMSE) with the PCE degrees for horizontal and vertical wave forces prediction are listed in Tables 2 and 3, respectively
To facilitate the establishment of the probabilistic model for quantifying the vulnerability of coastal bridges to natural hazards and support the associated risk assessment and mitigation activities, a hybrid surrogate model is proposed for efficient and accurate prediction of the solitary wave forces acting on coastal bridge decks and the corresponding predictive equations are obtained from the trained model
The regression-type polynomial chaos expansion (PCE) is employed as the main predictor to capture the global feature of the computational model, whereas the interpolation-type Kriging is adopted to capture the local variations of the prediction error from the PCE
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Various simulation models and analysis methods are available for the investigation of the wave forces exerted on the bridge deck, it would be time-consuming or cumbersome to obtain the prediction due to the intrinsic complicity of the bridge deck-wave interaction. Based on a wind-wave-bridge system, the effects of non-stationary winds and waves on the stochastic response of cable-stayed bridge girders were investigated using ANN [38] It is noted, that the above-mentioned approaches require fine-tuning of the parameters involved in the neural network, which is a cumbersome task involving trial and error. A hybrid surrogate model based on the polynomial chaos expansions (PCE) and Kriging is proposed to establish the predictive model for the solitary wave forces acting on coastal bridge decks. With the availability of the predictive model, the establishment of the probabilistic models for quantifying the vulnerability of the coastal bridges under natural hazards and the associated risk assessment can proceed and efficiently
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