Thin-walled structures have been used in many fields due to their superior mechanical properties.In this paper,two types of hierarchical multi-cell tubes,inspired by the self-similarity of Pinus sylvestris,are propose...Thin-walled structures have been used in many fields due to their superior mechanical properties.In this paper,two types of hierarchical multi-cell tubes,inspired by the self-similarity of Pinus sylvestris,are proposed to enhance structural energy absorption performance.The finite element models of the hierarchical structures are established to validate the crashworthiness performance under axial dynamic load.The theoreticalmodel of themean crushing force is also derived based on the simplified super folded element theory.The finite element results demonstrate that the energy absorption characteristics and deformation mode of the bionic hierarchical thin-walled tubes are further improved with the increase of hierarchical sub-structures.It can be also obtained that the energy absorption performance of corner self-similar tubes is better than edge self-similar tubes.Furthermore,multiobjective optimization of the hierarchical tubes is constructed by employing the response surface method and genetic algorithm,and the corresponding Pareto front diagram is obtained.This research provides a new idea for the crashworthiness design of thin-walled structures.展开更多
In structural simulation and design,an accurate computational model directly determines the effectiveness of performance evaluation.To establish a high-fidelity dynamic model of a complex assembled structure,a Hierarc...In structural simulation and design,an accurate computational model directly determines the effectiveness of performance evaluation.To establish a high-fidelity dynamic model of a complex assembled structure,a Hierarchical Model Updating Strategy(HMUS)is developed for Finite Element(FE)model updating with regard to uncorrelated modes.The principle of HMUS is first elaborated by integrating hierarchical modeling concept,model updating technology with proper uncorrelated mode treatment,and parametric modeling.In the developed strategy,the correct correlated mode pairs amongst the uncorrelated modes are identified by an error minimization procedure.The proposed updating technique is validated by the dynamic FE model updating of a simple fixed–fixed beam.The proposed HMUS is then applied to the FE model updating of an aeroengine stator system(casings)to demonstrate its effectiveness.Our studies reveal that(A)parametric modeling technique is able to build an efficient equivalent model by simplifying complex structure in geometry while ensuring the consistency of mechanical characteristics;(B)the developed model updating technique efficiently processes the uncorrelated modes and precisely identifies correct Correlated Mode Pairs(CMPs)between FE model and experiment;(C)the proposed HMUS is accurate and efficient in the FE model updating of complex assembled structures such as aeroengine casings with large-scale model,complex geometry,high-nonlinearity and numerous parameters;(D)it is appropriate to update a complex structural FE model parameterized.The efforts of this study provide an efficient updating strategy for the dynamic model updating of complex assembled structures with experimental test data,which is promising to promote the precision and feasibility of simulation-based design optimization and performance evaluation of complex structures.展开更多
A class of large-scale hierarchical control systems is considered, the overall objective function is a nonlinear and nonseparable function of multiple quadratic performance indices.The separation strategy of the multi...A class of large-scale hierarchical control systems is considered, the overall objective function is a nonlinear and nonseparable function of multiple quadratic performance indices.The separation strategy of the multiobjective optimization technique and the three-level objective coordination method are applied to the large -sacle systems, and a four-level hierarchical algorithms of optimization control is obtained.展开更多
Based on the observational hourly precipitation data and the European Centre for Medium-Range Weather Forecasts(ECMWF)Reanalysis 5(ERA5)products from 2006 to 2020,22 rainstorm processes in the eastern foot of Helan Mo...Based on the observational hourly precipitation data and the European Centre for Medium-Range Weather Forecasts(ECMWF)Reanalysis 5(ERA5)products from 2006 to 2020,22 rainstorm processes in the eastern foot of Helan Mountain are objectively classified by using the hierarchical clustering method,and the circulation characteristics of different patterns are comparatively analyzed in this study.The results show that the occurrences of rainstorm processes in the eastern foot of Helan Mountain are most closely related to three circulation patterns.PatternsⅠandⅢmainly occur in July and August,with similar zonal circulations in synoptic backgrounds.Specifically,the South Asia high and the western Pacific subtropical high are stronger and more northward than those in normal years.The frontal systems in westerlies are inactive,while the water vapor from the ocean surface in the south is mainly transported to the rainstorm area by the southerly jet stream at 700 h Pa.The dynamic lifting anomalies are relatively weak,the instability of atmospheric stratification is anomalously strong,and thus the localized severe convective rainstorm is more significant.Comparatively,rainstorm processes of patternⅠare accompanied by stronger and deeper ascending motions,and the warm-sector rainstorm is more extreme.PatternⅢshows a stronger and deeper convective instability,accompanied by larger low-level moisture.Rainstorm processes of patternⅡmainly occur in early summer and early autumn,presenting a meridional circulation pattern of high in the east and low in the west in terms of geopotential height.Moreover,the two low-level jets transporting the water vapor northward from the ocean on the east of China encounter with the frontal systems in westerlies,which makes the ascending motion in patternⅡanomalously strong and deep.The relatively weak instability of atmospheric stratification causes weak convection and long-lasting precipitation formed by the confluence of cold air and warm air.This study may help improve rainstorm for展开更多
Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arb...Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.展开更多
基金The authors are grateful to the National Natural Science Foundation of China(Grant No.11902183)the Doctoral Research Foundation of Shandong University of Technology(Grant No.4041/418017).
文摘Thin-walled structures have been used in many fields due to their superior mechanical properties.In this paper,two types of hierarchical multi-cell tubes,inspired by the self-similarity of Pinus sylvestris,are proposed to enhance structural energy absorption performance.The finite element models of the hierarchical structures are established to validate the crashworthiness performance under axial dynamic load.The theoreticalmodel of themean crushing force is also derived based on the simplified super folded element theory.The finite element results demonstrate that the energy absorption characteristics and deformation mode of the bionic hierarchical thin-walled tubes are further improved with the increase of hierarchical sub-structures.It can be also obtained that the energy absorption performance of corner self-similar tubes is better than edge self-similar tubes.Furthermore,multiobjective optimization of the hierarchical tubes is constructed by employing the response surface method and genetic algorithm,and the corresponding Pareto front diagram is obtained.This research provides a new idea for the crashworthiness design of thin-walled structures.
基金co-supported by National Natural Science Foundation of China(No.51975124)Shanghai International Cooperation Project of One Belt and One Road of China(No.20110741700)Major Research Special Project of Aeroengine and Gas Turbine of China(No.J2019-IV-0016)。
文摘In structural simulation and design,an accurate computational model directly determines the effectiveness of performance evaluation.To establish a high-fidelity dynamic model of a complex assembled structure,a Hierarchical Model Updating Strategy(HMUS)is developed for Finite Element(FE)model updating with regard to uncorrelated modes.The principle of HMUS is first elaborated by integrating hierarchical modeling concept,model updating technology with proper uncorrelated mode treatment,and parametric modeling.In the developed strategy,the correct correlated mode pairs amongst the uncorrelated modes are identified by an error minimization procedure.The proposed updating technique is validated by the dynamic FE model updating of a simple fixed–fixed beam.The proposed HMUS is then applied to the FE model updating of an aeroengine stator system(casings)to demonstrate its effectiveness.Our studies reveal that(A)parametric modeling technique is able to build an efficient equivalent model by simplifying complex structure in geometry while ensuring the consistency of mechanical characteristics;(B)the developed model updating technique efficiently processes the uncorrelated modes and precisely identifies correct Correlated Mode Pairs(CMPs)between FE model and experiment;(C)the proposed HMUS is accurate and efficient in the FE model updating of complex assembled structures such as aeroengine casings with large-scale model,complex geometry,high-nonlinearity and numerous parameters;(D)it is appropriate to update a complex structural FE model parameterized.The efforts of this study provide an efficient updating strategy for the dynamic model updating of complex assembled structures with experimental test data,which is promising to promote the precision and feasibility of simulation-based design optimization and performance evaluation of complex structures.
文摘A class of large-scale hierarchical control systems is considered, the overall objective function is a nonlinear and nonseparable function of multiple quadratic performance indices.The separation strategy of the multiobjective optimization technique and the three-level objective coordination method are applied to the large -sacle systems, and a four-level hierarchical algorithms of optimization control is obtained.
基金National Natural Science Foundation of China(41965001)Program of Technology and Innovation for Leading Talents in Ningxia Hui Autonomous Region(2021GKLRLX05)。
文摘Based on the observational hourly precipitation data and the European Centre for Medium-Range Weather Forecasts(ECMWF)Reanalysis 5(ERA5)products from 2006 to 2020,22 rainstorm processes in the eastern foot of Helan Mountain are objectively classified by using the hierarchical clustering method,and the circulation characteristics of different patterns are comparatively analyzed in this study.The results show that the occurrences of rainstorm processes in the eastern foot of Helan Mountain are most closely related to three circulation patterns.PatternsⅠandⅢmainly occur in July and August,with similar zonal circulations in synoptic backgrounds.Specifically,the South Asia high and the western Pacific subtropical high are stronger and more northward than those in normal years.The frontal systems in westerlies are inactive,while the water vapor from the ocean surface in the south is mainly transported to the rainstorm area by the southerly jet stream at 700 h Pa.The dynamic lifting anomalies are relatively weak,the instability of atmospheric stratification is anomalously strong,and thus the localized severe convective rainstorm is more significant.Comparatively,rainstorm processes of patternⅠare accompanied by stronger and deeper ascending motions,and the warm-sector rainstorm is more extreme.PatternⅢshows a stronger and deeper convective instability,accompanied by larger low-level moisture.Rainstorm processes of patternⅡmainly occur in early summer and early autumn,presenting a meridional circulation pattern of high in the east and low in the west in terms of geopotential height.Moreover,the two low-level jets transporting the water vapor northward from the ocean on the east of China encounter with the frontal systems in westerlies,which makes the ascending motion in patternⅡanomalously strong and deep.The relatively weak instability of atmospheric stratification causes weak convection and long-lasting precipitation formed by the confluence of cold air and warm air.This study may help improve rainstorm for
基金The research was supported by the National Natural Science Foundation of China[grant number 11671146].
文摘Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.
