The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are d...The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are determined by model builders according to some simple fundamental flows, and the suggested values may not be applicable to complex flows, especially supersonic jet interaction flow. In this work, the Bayesian method is employed to recalibrate the closure coefficients of Spalart-Allmaras(SA) turbulence model to improve its performance in supersonic jet interaction problem and quantify the uncertainty of wall pressure and separation length. The embedded model error approach is applied to the Bayesian uncertainty analysis. Firstly, the total Sobol index is calculated by non-intrusive polynomial chaos method to represent the sensitivity of wall pressure and separation length to model parameters. Then, the pressure data and the separation length are respectively served as calibration data to get the posterior uncertainty of model parameters and Quantities of Interests(Qo Is). The results show that the relative error of the wall pressure predicted by the SA turbulence model can be reduced from 14.99% to 2.95% through effective Bayesian parameter estimation. Besides, the calibration effects of four likelihood functions are systematically evaluated. The posterior uncertainties of wall pressure and separation length estimated by different likelihood functions are significantly discrepant, and the Maximum a Posteriori(MAP) values of parameters inferred by all functions show better performance than the nominal values. Finally, the closure coefficients are also estimated at different jet total pressures. The similar posterior distributions of model parameters are obtained in different cases, and the MAP values of parameters calibrated in one case are also applicable to other cases.展开更多
This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.Th...This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.展开更多
Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent year...Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent years,crowd movements at carnival events have attracted the attention of researchers. In contrast to pedestrian behavior in other walking facilities, pedestrians whose attention is attracted by carnival displays or activities may slow down and even stop walking. The Lunar New Year Market is a traditional carnival event in Hong Kong held annually one week before the Lunar New Year. During the said event,crowd movements can be easily identified, particularly in Victoria Park, where the largest Lunar New Year Market in Hong Kong is hosted. In this study, we conducted a videobased observational survey to collect pedestrian flow and speed data at the Victoria Park Lunar New Year Market on the eve of the Lunar New Year. Using the collected data, an extant mathematical model was calibrated to capture the relationships between the relevant macroscopic quantities,thereby providing insight into pedestrian behavior at the carnival event. Bayesian inference was employed to calibrate the model by using prior data obtained from a previous controlled experiment. Results obtained enhance our understanding of crowd behavior under different conditions at carnival events, thus facilitating the improvement of the safety and efficiency of similar events in the future.展开更多
Accurately simulating the geographical distribution and temporal variability of global surface ozone has long been one of the principal components of chemistry-climate modelling.However,the simulation outcomes have be...Accurately simulating the geographical distribution and temporal variability of global surface ozone has long been one of the principal components of chemistry-climate modelling.However,the simulation outcomes have been reported to vary significantly as a result of the complex mixture of uncertain factors that control the tropospheric ozone budget.Settling the cross-model discrepancies to achieve higher accuracy predictions of surface ozone is thus a task of priority,and methods that overcome structural biases in models going beyond naïve averaging of model simulations are urgently required.Building on the Coupled Model Intercomparison Project Phase 6(CMIP6),we have transplanted a conventional ensemble learning approach,and also constructed an innovative 2-stage enhanced space-time Bayesian neural network to fuse an ensemble of 57 simulations together with a prescribed ozone dataset,both of which have realised outstanding performances(R2>0.95,RMSE<2.12 ppbv).The conventional ensemble learning approach is computationally cheaper and results in higher overall performance,but at the expense of oceanic ozone being overestimated and the learning process being uninterpretable.The Bayesian approach performs better in spatial generalisation and enables perceivable interpretability,but induces heavier computational burdens.Both of these multi-stage machine learning-based approaches provide frameworks for improving the fidelity of composition-climate model outputs for uses in future impact studies.展开更多
基金supported by the National Numerical Windtunnel Project,China(No.NNW2019ZT1-A03)the National Natural Science Foundation of China(No.11721202)。
文摘The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are determined by model builders according to some simple fundamental flows, and the suggested values may not be applicable to complex flows, especially supersonic jet interaction flow. In this work, the Bayesian method is employed to recalibrate the closure coefficients of Spalart-Allmaras(SA) turbulence model to improve its performance in supersonic jet interaction problem and quantify the uncertainty of wall pressure and separation length. The embedded model error approach is applied to the Bayesian uncertainty analysis. Firstly, the total Sobol index is calculated by non-intrusive polynomial chaos method to represent the sensitivity of wall pressure and separation length to model parameters. Then, the pressure data and the separation length are respectively served as calibration data to get the posterior uncertainty of model parameters and Quantities of Interests(Qo Is). The results show that the relative error of the wall pressure predicted by the SA turbulence model can be reduced from 14.99% to 2.95% through effective Bayesian parameter estimation. Besides, the calibration effects of four likelihood functions are systematically evaluated. The posterior uncertainties of wall pressure and separation length estimated by different likelihood functions are significantly discrepant, and the Maximum a Posteriori(MAP) values of parameters inferred by all functions show better performance than the nominal values. Finally, the closure coefficients are also estimated at different jet total pressures. The similar posterior distributions of model parameters are obtained in different cases, and the MAP values of parameters calibrated in one case are also applicable to other cases.
基金This work has been partially supported by the Ministry of Science and Technology,Taiwan[Grant Numbers MOST 108-2221-E-019-013 and MOST 109-2221-E-019-010].
文摘This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. Poly U 5243/13E)respectively supported by the Postdoctoral Fellow Scheme and Francis S. Y. Bong Professorship in Engineering of The University of Hong Kong
文摘Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent years,crowd movements at carnival events have attracted the attention of researchers. In contrast to pedestrian behavior in other walking facilities, pedestrians whose attention is attracted by carnival displays or activities may slow down and even stop walking. The Lunar New Year Market is a traditional carnival event in Hong Kong held annually one week before the Lunar New Year. During the said event,crowd movements can be easily identified, particularly in Victoria Park, where the largest Lunar New Year Market in Hong Kong is hosted. In this study, we conducted a videobased observational survey to collect pedestrian flow and speed data at the Victoria Park Lunar New Year Market on the eve of the Lunar New Year. Using the collected data, an extant mathematical model was calibrated to capture the relationships between the relevant macroscopic quantities,thereby providing insight into pedestrian behavior at the carnival event. Bayesian inference was employed to calibrate the model by using prior data obtained from a previous controlled experiment. Results obtained enhance our understanding of crowd behavior under different conditions at carnival events, thus facilitating the improvement of the safety and efficiency of similar events in the future.
文摘Accurately simulating the geographical distribution and temporal variability of global surface ozone has long been one of the principal components of chemistry-climate modelling.However,the simulation outcomes have been reported to vary significantly as a result of the complex mixture of uncertain factors that control the tropospheric ozone budget.Settling the cross-model discrepancies to achieve higher accuracy predictions of surface ozone is thus a task of priority,and methods that overcome structural biases in models going beyond naïve averaging of model simulations are urgently required.Building on the Coupled Model Intercomparison Project Phase 6(CMIP6),we have transplanted a conventional ensemble learning approach,and also constructed an innovative 2-stage enhanced space-time Bayesian neural network to fuse an ensemble of 57 simulations together with a prescribed ozone dataset,both of which have realised outstanding performances(R2>0.95,RMSE<2.12 ppbv).The conventional ensemble learning approach is computationally cheaper and results in higher overall performance,but at the expense of oceanic ozone being overestimated and the learning process being uninterpretable.The Bayesian approach performs better in spatial generalisation and enables perceivable interpretability,but induces heavier computational burdens.Both of these multi-stage machine learning-based approaches provide frameworks for improving the fidelity of composition-climate model outputs for uses in future impact studies.
