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Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments 被引量:3
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作者 Ruixian Fang Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2020年第4期559-570,共12页
The (180)<sup>3</sup> third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cros... The (180)<sup>3</sup> third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)<sup>3</sup> third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3<sup>rd</sup>-order sensitivities can surpass the importance of the 1<sup>st</sup>- and 2<sup>nd</sup>-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3<sup>rd</sup>-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3<sup>rd</sup>-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3<sup>rd</sup>-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the <em>mixed</em> 3<sup>rd</sup>-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community. 展开更多
关键词 Polyethylene-Reflected Plutonium Sphere 3rd-Order Sensitivities 1st-Order 2nd-Order and 3rd-Order Uncertainty Analysis Microscopic Total Cross Sections Expected Value Variance and Skewness of response distribution
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Distributed Collaborative Response Surface Method for Mechanical Dynamic Assembly Reliability Design 被引量:25
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作者 BAI Guangchen FEI Chengwei 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2013年第6期1160-1168,共9页
Because of the randomness of many impact factors influencing the dynamic assembly relationship of complex machinery, the reliability analysis of dynamic assembly relationship needs to be accomplished considering the r... Because of the randomness of many impact factors influencing the dynamic assembly relationship of complex machinery, the reliability analysis of dynamic assembly relationship needs to be accomplished considering the randomness from a probabilistic perspective. To improve the accuracy and efficiency of dynamic assembly relationship reliability analysis, the mechanical dynamic assembly reliability(MDAR) theory and a distributed collaborative response surface method(DCRSM) are proposed. The mathematic model of DCRSM is established based on the quadratic response surface function, and verified by the assembly relationship reliability analysis of aeroengine high pressure turbine(HPT) blade-tip radial running clearance(BTRRC). Through the comparison of the DCRSM, traditional response surface method(RSM) and Monte Carlo Method(MCM), the results show that the DCRSM is not able to accomplish the computational task which is impossible for the other methods when the number of simulation is more than 100 000 times, but also the computational precision for the DCRSM is basically consistent with the MCM and improved by 0.40-4.63% to the RSM, furthermore, the computational efficiency of DCRSM is up to about 188 times of the MCM and 55 times of the RSM under 10000 times simulations. The DCRSM is demonstrated to be a feasible and effective approach for markedly improving the computational efficiency and accuracy of MDAR analysis. Thus, the proposed research provides the promising theory and method for the MDAR design and optimization, and opens a novel research direction of probabilistic analysis for developing the high-performance and high-reliability of aeroengine. 展开更多
关键词 machinery dynamic assembly reliability analysis distributed collaborative response surface method blade-tip radial running clearance
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Distributed collaborative extremum response surface method for mechanical dynamic assembly reliability analysis 被引量:7
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作者 费成巍 白广忱 《Journal of Central South University》 SCIE EI CAS 2013年第9期2414-2422,共9页
To make the dynamic assembly reliability analysis more effective for complex machinery of multi-object multi-discipline(MOMD),distributed collaborative extremum response surface method(DCERSM)was proposed based on ext... To make the dynamic assembly reliability analysis more effective for complex machinery of multi-object multi-discipline(MOMD),distributed collaborative extremum response surface method(DCERSM)was proposed based on extremum response surface method(ERSM).Firstly,the basic theories of the ERSM and DCERSM were investigated,and the strengths of DCERSM were proved theoretically.Secondly,the mathematical model of the DCERSM was established based upon extremum response surface function(ERSF).Finally,this model was applied to the reliability analysis of blade-tip radial running clearance(BTRRC)of an aeroengine high pressure turbine(HPT)to verify its advantages.The results show that the DCERSM can not only reshape the possibility of the reliability analysis for the complex turbo machinery,but also greatly improve the computational speed,save the computational time and improve the computational efficiency while keeping the accuracy.Thus,the DCERSM is verified to be feasible and effective in the dynamic assembly reliability(DAR)analysis of complex machinery.Moreover,this method offers an useful insight for designing and optimizing the dynamic reliability of complex machinery. 展开更多
关键词 complex machinery dynamic assembly reliability (DAR) blade-tip radial running clearance (BTRRC) radial deformation reliability analysis distributed collaborative extremum response surface method (DCERSM) multi-object multidiscipline (MOMD)
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Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method 被引量:2
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作者 高海峰 白广忱 +1 位作者 高阳 鲍天未 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第12期4693-4701,共9页
The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to am... The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode. 展开更多
关键词 complicated mechanical structure reliability analysis multiple random variables multi-component and multi-failure mode distributed collaborative response surface method
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Elastic strain response in the modified phase-field-crystal model
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作者 周文权 王锦程 +4 位作者 王志军 黄赟浩 郭灿 李俊杰 郭耀麟 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第9期106-113,共8页
To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modifi... To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal(MPFC) model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value. 展开更多
关键词 elastic response strain distribution shear modulus modified phase-field-crystal model
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Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework 被引量:2
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作者 Dan Gabriel Cacuci Ruixian Fang 《American Journal of Computational Mathematics》 2020年第4期503-528,共26页
This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u... This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)<sup>2</sup> second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)<sup>3</sup> third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3<sup>rd</sup>-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)<sup>3</sup> third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response. 展开更多
关键词 Polyethylene-Reflected Plutonium Sphere 1st-Order 2nd-Order and 3rd-Order Sensitivities 3rd-Order Adjoint Sensitivity Analysis Microscopic Total Cross Sections Expected Value Variance and Skewness of response distribution
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Two Kinds of Analysis in the Issue of Dealing with EDPs
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作者 Qilin Wu Jiazhi Xiu Zeyi Wen 《Macro Management & Public Policies》 2020年第4期3-13,共11页
The settlement of EDPs[1]is one of the most knotty problems created by climate changes.In this paper,our team will give a comprehensive solution to tackle it.We construct two migration models to maximize the outcome o... The settlement of EDPs[1]is one of the most knotty problems created by climate changes.In this paper,our team will give a comprehensive solution to tackle it.We construct two migration models to maximize the outcome of protecting the rights of EDPs and preserving their unique culture.Firstly,we talked about the reasons why we should protect the rights and culture of EDPs.We conclude that it is not only the spirit of UN,the morale responsibilities of every nation but also a good deed for human being which possibly can stop nationalism in each country from rising.I this process,we decide to use“carbon dioxide emission per capita”as standard to distribute responsibilities to different nations because it is more fair and efficient.Secondly,we start to build Migration Models.By using AHP,We quantify the important characteristics which will eventually make a big difference on the outcome of settlement.Then we get final results which indicate the most suitable countries for EDPs.Analyzing the results of Migration Models,we give policy recommendation at global and national level.For the first one,we suggest that UN should decide where EDPs’be;when emergency happens or there are only few migrants,send them to the nearest countries to make sure of their safety and preservation of their cultures;and when it takes a long time to migrate and there are so many migrants,use Migration Model Two to decide because it needs to take the contribution to the world greenhouse effect,countries’finance and preference of EDPs into consideration.Through the mathematic practice,we also find some factors,such as languages,population density and religious beliefs,can seriously affect the ultimate choice of the migration place so we recommend each nation positively take action to ensure EDPs can easily fit in.After that we bring time factors into our model.We use linear regression model to see the time when those island nations will be submerged.It indicates that UN should step in this issue as soon as possible otherwise it can be uncontrollable owing to the sinking islands and rising nationalism.At last,we list and compare three approaches to deciding where the home of EDPs should be.We conclude that only when UN in charge of this,it can make the best interest of both EDPs and different nations. 展开更多
关键词 Climate change REFUGEE Carbon emission distribution of responsibility among countries Settlement of refugee
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