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Curved continuous girder bridges (CCGBs) have been widely adopted in the civil engineering field in recent decades for complex interchanges and city viaducts. Unfortunately, compared to straight bridges, this type of bridge with horizontal curvature is relatively vulnerable to earthquakes characterized by large energy and short duration. Seismic damage can degrade the performance of CCGBs, threatening their normal operation and even resulting in collapse. Detection of seismic damage in CCGBs is thus significantly important but is still not well resolved. To this end, a new method based on wavelet packet singular entropy (WPSE) is proposed to identify seismic damage by analyzing the dynamic responses of CCGBs to seismic excitation. This WPSE-based approach features characterizing damage using synergistic advantage of the wavelet packet transform, singular value decomposition, and information entropy. To testify the algorithm, a finite element model of a typical CCGB with two types of seismic damage is built, in which the seismic damage is individually modeled by stiffness reductions at the bottom of piers and at pier-girder connections. The displacement responses of the model to El Centro seismic excitation is used to identify the damage. The results show that damage indices in the WPSE-based approach can correctly locate the seismic damage in CCGBs. Furthermore, the WPSE-based method is competent to identify damage with higher accuracy in comparison with the wavelet packet energy based method, and has a strong immunity to noise revealed by robustness analysis. An array of responses used in this approach paves the way of developing practical technologies for detecting seismic damage using advanced distributed sensing techniques, typically the optical sensors.
Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model based on deep learning to give full scope to their respective advantages. In classical residual error models, Bayesian inference via Markov chain Monte Carlo (MCMC) is commonly used to provide an estimation of the uncertainty. However, deep neural networks tend to have excessively large numbers of parameters, making MCMC an unsuitable approach. Here, we introduce an alternative to Bayesian MCMC sampling called stochastic variational inference (SVI) which has recently been developed for Bayesian deep learning in Natural Language Processing. We implement SVI in a Long Short‐Term Memory (LSTM) network and construct residual error models in process‐based hydrological models. This approach is examined in the contrasting geographical and climatic characteristics of two catchments from China, the Tangnaihai catchment and the Shiquan catchment. Compared with the Bayesian linear regression model, the Bayesian LSTM provides better uncertainty estimates. Specifically, the proposed method improves the Continuous Ranked Probability Score (CRPS) by over 10% in both two catchments. In the Tangnaihai catchment, it provides more than 10% narrower uncertainty intervals in terms of Sharpness with slightly superior Reliability. In the Shiquan catchment, it provides comparable uncertainty intervals with better Reliability. Further, our study highlights the scalability of SVI to high‐dimensional parameter spaces in hydrological applications (e.g., distributed hydrological models, groundwater models).
Root zone soil moisture plays an important role in water storage in hydrological processes.The recently launched Soil Moisture Active Passive (SMAP) mission has produced a high-resolution assimilation product of global root zone soil moisture that can be applied to improve the performance of hydrological models. In this study, we compare three calibration approaches in the Beimiaoji watershed. The first approach is single-objective calibration, in which only observed streamflow is used as a benchmark for comparison with the other approaches. The second and third approaches use multi-objective calibration based on SMAP root zone soil moisture and observed streamflow. The difference between the second and third approaches is the metric used to characterize the root zone soil moisture. The second approach applies the mean, which was commonly used in previous studies, whereas the third approach applies the hydrologic complexity μ, a dimensionless metric based on information entropy theory. These approaches are implemented to calibrate the distributed hydrological model MIKE SHE. Results show that the root zone soil moisture simulation is clearly improved, whereas streamflow simulation suffers from a slightly negative impact with multi-objective calibration. The hydrologic complexity μ performs better than the mean in capturing the features of root zone soil moisture.
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