In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) a...In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also, two constants of fundamental importance in AD, s and m, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.展开更多
基于中尺度天气研究与预报(Weather Research and Forecasting,WRF)模式和区域多尺度空气质量(Community Multiscale Air Quality,CMAQ)模式及其伴随(ADJOINT)模式(WRF-CMAQ/ADJOINT模式)对2019年9月海南一次持续10日(9月21-30日)的臭氧...基于中尺度天气研究与预报(Weather Research and Forecasting,WRF)模式和区域多尺度空气质量(Community Multiscale Air Quality,CMAQ)模式及其伴随(ADJOINT)模式(WRF-CMAQ/ADJOINT模式)对2019年9月海南一次持续10日(9月21-30日)的臭氧(O_(3))污染事件进行模拟,对O_(3)污染进行来源解析,量化不同区域和物种排放源对O_(3)污染事件的贡献。结果表明:(1)污染事件期间,臭氧日最大8小时(MDA8-O_(3))平均质量浓度为167μg·m^(-3),其中MDA8-O_(3)峰值质量浓度达到186.1μg·m^(-3)。(2)WRF-CMAQ/ADJOINT模式能够较好模拟海南此次污染事件的O_(3)质量浓度变化过程,伴随模式揭示远距离区域传输是此次O_(3)污染的主要来源,其中海南外排放源平均贡献占比85%,本地排放源平均贡献占比15%,海南外排放源的贡献集中在珠三角地区。(3)对挥发性有机物(volatile organic compounds,VOCs)排放物种来源分析结果表明,异戊二烯在VOCs排放源中贡献最高,平均贡献占比为51%。此次O_(3)污染事件期间海南主要处于NO_(x)控制区,仅有海口处于VOCs和NO_(x)的协同控制区。由于远距离区域传输是此次O_(3)污染事件的主要来源,未来海南和珠三角的区域联防联控对于提高海南空气质量具有重要意义。展开更多
Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency.To achieve efficient trade-off designs,an enhanced on-the...Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency.To achieve efficient trade-off designs,an enhanced on-the-fly unsteady adjoint-based aerodynamic and aeroacoustic optimization methodology is developed,which maintains the fidelity of the Navier-Stokes solution for unsteady flow and of the moving-medium Ffowcs Williams-Hawkings(FW-H)formulation for capturing tonal noise.Furthermore,this on-the-fly approach enables a unified architecture for discreteadjoint sensitivity analysis encompassing both aerodynamics and aeroacoustics,facilitating effective multi-objective weighted optimizations.Subsequently,this proposed methodology is applied to perform trade-off optimizations between aerodynamics and aeroacoustics for a propeller by employing varying weighting factors to comprehend their influence on optimal configurations.The results demonstrate a positive correlation between efficiency and noise sensitivities,and thus indicate an inherent synchronicity where pursing noise reduction through purely aeroacoustic optimization inevitably entails sacrificing aerodynamic efficiency.However,by effectively incorporating appropriate weighting factors(recommended to range from 0.25 to 0.5)into the multi-objective function combined with both aerodynamics and aeroacoustics,it becomes feasible to achieve efficiency enhancement and noise reduction simultaneously.Key findings show that reducing blade planform size and equipping“rotated-S”shaped airfoil profiles in the tip region can effectively restrain noise levels while maintaining aerodynamic performance.展开更多
The primary concern in stealth aircraft design is the very large electrical size objects.However,the computational and storage requirements of these objects present significant obstacles for current highfidelity desig...The primary concern in stealth aircraft design is the very large electrical size objects.However,the computational and storage requirements of these objects present significant obstacles for current highfidelity design methods,particularly when addressing high-dimensional complex engineering design problems.To address these challenges,we developed a surface sensitivity technique based on the multilevel fast multipole algorithm(MLFMA).An access and storage of sparse partial derivative tensor was improved to significantly enhanced the computation performance.The far-field interactions of the surface sensitivity equation were realized by differential the multipole expansion.In addition,we proposed a fast far-field multiplication method to accelerate the multiplication process.The surface mesh derivative with respect to the design variables was calculated by analytical and complex variable methods,substantially improving computational efficiency.These advancements enabled the MLFMAbased surface sensitivity method to millions meshes and large-scale gradients,extending gradientbased optimization for very large electrical size problems.Test cases have verified the effectiveness of this method in optimizing very large electrical objects in terms of both accuracy and efficiency.展开更多
The challenge of establishing top-down constraints for regional emissions of fossil fuel CO_(2)(FFCO_(2))arises from the difficulty in distinguishing between atmospheric CO_(2)concentrations released from fossil fuels...The challenge of establishing top-down constraints for regional emissions of fossil fuel CO_(2)(FFCO_(2))arises from the difficulty in distinguishing between atmospheric CO_(2)concentrations released from fossil fuels and background variability,particularly owing to the influence of terrestrial biospheric fluxes.This necessitates the development of a regional inversion methodology based on atmospheric CO_(2)observations to verify bottom-up estimations independently.This study presents a promising approach for estimating China's FFCO_(2)emissions by incorporating the model residual errors(MREs)of the column-averaged dry-air mole fractions of CO_(2)(XCO_(2))from FFCO_(2)emissions(MREff)retained in the analysis of natural flux optimization.China's FFCO_(2)emissions during the COVID-19 lockdown in 2020 are estimated using the GEOS-Chem adjoint model.The relationship between the MREff and FFCO_(2)is determined using the model based on a regional FFCO_(2)anomaly suggested by posterior NOx emissions from air-quality data assimilation.The MREff is typically one-tenth in magnitude,but some positively skewed outliers exceed 1 ppm because the prior emissions lack lockdown impacts,thereby exerting considerable observation forcing given the satellite retrieval uncertainties.We initialize the FFCO_(2)with posterior NOx emissions and optimize the colinear emission ratio.Synthetic data experiments demonstrate that this approach reduces the FFCO_(2)bias to less than 10%.The real-data experiments estimate 19%lower FFCO_(2)with GOSAT XCO_(2)and 26%lower with OCO-2 XCO_(2)than the bottom-up estimations.This study proves the feasibility of our regional FFCO_(2)inversion,highlighting the importance of addressing the outlier behaviors observed in satellite XCO_(2)retrievals.展开更多
The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a ...The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a novel compound numerical method to study the instability of a functionally graded(FG)beam-type NEMS,considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam.The presented method is based on a combination of the Method of Adjoints(MoA)together with the Bézier-based multistep technique.By utilizing the MoA,a boundary value problem(BVP)is turned into an initial value problem(IVP).The resulting IVP is then solved by employing a cost-efficient multi-step process.It is demonstrated that the mentioned method can arrive at a high level of accuracy.Furthermore,it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods,such as Adams-Bashforth,particularly at higher step sizes.Finally,the effects of axially functionally graded(FG)properties on the pull-in phenomenon and the main design parameters of NEMS,including the detachment length,are inspected.It was shown that the main parameter of design is the modulus of elasticity of the material,as Silver(Ag),which had better mechanical properties,showed almost a 6%improvement compared to aluminum(Al).However,by applying the correct amount of material with sturdier surface parameters,such as Aluminum(Al),at certain points,the nanobeams’functionality can be improved even further by around 1.5%.展开更多
In recent years,incidents of simultaneous exceedance of PM_(2.5)and O_(3) concentrations,termed PM_(2.5)and O_(3) co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation anal...In recent years,incidents of simultaneous exceedance of PM_(2.5)and O_(3) concentrations,termed PM_(2.5)and O_(3) co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation analysis on two typical co-pollution events in Beijing,occurring from July 22 to July 28,2019,and from April 25 to May 2,2020.These events were categorized into pre-trough southerly airflow type(Type 1)and post-trough northwest flow type(Type 2).Subsequently,sensitivity analyses using the GRAPES-CUACE adjoint model were performed to quantify the contributions of precursor emissions from Beijing and surrounding areas to PM_(2.5)and O_(3) concentrations in Beijing for two types of co-pollution.The results indicated that the spatiotemporal distribution of sensitive source region varied among different circulation types.Primary PM_(2.5)(PPM_(2.5))emissions from Hebei contributed the most to the 24-hour average PM_(2.5)(24-h PM_(2.5))peak concentration(41.6%-45.4%),followed by Beijing emissions(31%-35.7%).The maximum daily 8-hour average ozone peak concentration was primarily influenced by the emissions from Hebei and Beijing,with contribution ratios respectively of 32.8%-44.8% and 29%-42.1%.Additionally,NO_(x)emissions were the main contributors in Type 1,while both NO_(x)and VOCs emissions contributed similarly in Type 2.The iterative emission reduction experiments for two types of co-pollution indicated that Type 1 required emission reductions in NO_(x)(52.4%-71.8%)and VOCs(14.1%-33.8%)only.In contrast,Type 2 required combined emission reductions in NO_(x)(37.0%-65.1%),VOCs(30.7%-56.2%),and PPM_(2.5)(31%-46.9%).This study provided a reference for controlling co-pollution events and improving air quality in Beijing.展开更多
It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth ...It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.展开更多
In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation laws.Moreover,miscellaneous sol...In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation laws.Moreover,miscellaneous soliton solutions like dark,bright,periodic,rational,Jacobian elliptic function,Weierstrass elliptic function,and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential equations.All these results are displayed graphically by 3D,2D,and contour plots.展开更多
Economic development has caused a lot of environmental problems,in turn,environmental pollution restricts economic development.Considering the influence of wind direction and speed,temperature and humidity on pollutan...Economic development has caused a lot of environmental problems,in turn,environmental pollution restricts economic development.Considering the influence of wind direction and speed,temperature and humidity on pollutants,as well as the influence of epidemic,war and exchange rate on economic development.In this paper,we develop a stochastic economic-environment model with pollution control strategies.Furthermore,sufficient and necessary conditions for the near-optimality are established.Finally,we perform some numerical simulations to demonstrate the correctness of the theoretical results,which shows that some control strategies could decrease the environmental pollution,and therefore,could alleviate economic losses caused by environmental pollution.展开更多
High-performance compressor design is best achieved with a good trade-off between aerodynamic and structural considerations,which requires efficient and accurate multidisciplinary design and optimization tools.As adva...High-performance compressor design is best achieved with a good trade-off between aerodynamic and structural considerations,which requires efficient and accurate multidisciplinary design and optimization tools.As advanced compressors are defined with a large design space,their optimization is most efficiently achieved using a gradient-based approach,where the gradient can be computed using an adjoint method,at a cost nearly independent of the dimension of the design space.While the adjoint method has been widely used for aerodynamic shape optimization,its use for structural shape optimizations of compressor blades has not been as well studied.This paper discussed a discrete adjoint solver for structural sensitivity analysis developed within the opensource Computational Structural Mechanics(CSM)software CalculiX,and proposed an efficient stress sensitivity analysis method based on the Finite Element Method(FEM)using adjoint.The proposed method is applied to compute the stress sensitivity of a wide-chord fan blade in a highbypass-ratio engine.The accuracy of the adjoint-based stress sensitivity is verified against central finite differences.In terms of computational efficiency,the adjoint approach is about 4.5 times more efficient than the conventional approach using finite differences.This works marks an important step towards fluid-structural coupled adjoint optimization of wide-chord fan blades.展开更多
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a...We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.展开更多
The Cauchy stress equations (1823), the Cosserat couple-stress equations (1909), the Clausius virial equation (1870) and the Maxwell/Weyl equations (1873, 1918) are among the most famous partial differential equations...The Cauchy stress equations (1823), the Cosserat couple-stress equations (1909), the Clausius virial equation (1870) and the Maxwell/Weyl equations (1873, 1918) are among the most famous partial differential equations that can be found today in any textbook dealing with elasticity theory, continuum mechanics, thermodynamics or electromagnetism. Over a manifold of dimension n, their respective numbers are n,n(n−1)/2,1,nwith a total of N=(n+1)(n+2)/2, that is 15 when n=4for space-time. This is also just the number of parameters of the Lie group of conformal transformations with n translations, n(n−1)/2rotations, 1 dilatation and n highly non-linear elations introduced by E. Cartan in 1922. The purpose of this paper is to prove that the form of these equations only depends on the structure of the conformal group for an arbitrary n≥1because they are described as a whole by the (formal) adjoint of the first Spencer operator existing in the Spencer differential sequence. Such a group theoretical implication is obtained by applying totally new differential geometric methods in field theory. In particular, when n=4, the main idea is not to shrink the group from 10 down to 4 or 2 parameters by using the Schwarzschild or Kerr metrics instead of the Minkowski metric, but to enlarge the group from 10 up to 11 or 15 parameters by using the Weyl or conformal group instead of the Poincaré group of space-time. Contrary to the Einstein equations, these equations can be all parametrized by the adjoint of the second Spencer operator through Nn(n−1)/2potentials. These results bring the need to revisit the mathematical foundations of both General Relativity and Gauge Theory according to a clever but rarely quoted paper of H. Poincaré (1901). They strengthen the recent comments we already made about the dual confusions made by Einstein (1915) while following Beltrami (1892), both using the same Einstein operator but ignoring it is self-adjoint in the framework of differential double duality.展开更多
This work highlights the unparalleled efficiency of the “n<sup>th</sup>-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-FASAM-N) by con...This work highlights the unparalleled efficiency of the “n<sup>th</sup>-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The n<sup>th</sup>-FASAM-N methodology is compared to the extant “n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-CASAM-N) showing that: (i) the 1<sup>st</sup>-FASAM-N and the 1<sup>st</sup>-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1<sup>st</sup>-LASS);(ii) the 2<sup>nd</sup>-FASAM-N methodology is considerably more efficient than the 2<sup>nd</sup>-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2<sup>nd</sup>-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2<sup>nd</sup>-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3<sup>rd</sup>-FASAM-N methodology is even more efficient than the 3<sup>rd</sup>-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3<sup>rd</sup>-FASAM-N methodology, while the application of the 3<sup>rd</sup>-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.展开更多
This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the...This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the n<sup>th</sup>-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the n<sup>th</sup>-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the n<sup>th</sup>-FASAM-N methodology becomes identical to the extant n<sup>th</sup> CASAM-N (“n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.展开更多
The tighten couplings of game strategies with adjoint methods for multi-criterion aerodynamic design optimization are ad-dressed. Its numerical implementation is also described in details. In cooperative game,adjoint ...The tighten couplings of game strategies with adjoint methods for multi-criterion aerodynamic design optimization are ad-dressed. Its numerical implementation is also described in details. In cooperative game,adjoint methods are coupled in parallel to compute Pareto front collaboratively. Conversely in a Nash game,adjoint methods are coupled in each player s decision making to achieve Nash equilibrium competitively. In Stackelberg game,adjoint methods used by players are nested hierarchically through incomp...展开更多
In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dyna...In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.展开更多
The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each q...The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.展开更多
文摘In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also, two constants of fundamental importance in AD, s and m, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.
文摘基于中尺度天气研究与预报(Weather Research and Forecasting,WRF)模式和区域多尺度空气质量(Community Multiscale Air Quality,CMAQ)模式及其伴随(ADJOINT)模式(WRF-CMAQ/ADJOINT模式)对2019年9月海南一次持续10日(9月21-30日)的臭氧(O_(3))污染事件进行模拟,对O_(3)污染进行来源解析,量化不同区域和物种排放源对O_(3)污染事件的贡献。结果表明:(1)污染事件期间,臭氧日最大8小时(MDA8-O_(3))平均质量浓度为167μg·m^(-3),其中MDA8-O_(3)峰值质量浓度达到186.1μg·m^(-3)。(2)WRF-CMAQ/ADJOINT模式能够较好模拟海南此次污染事件的O_(3)质量浓度变化过程,伴随模式揭示远距离区域传输是此次O_(3)污染的主要来源,其中海南外排放源平均贡献占比85%,本地排放源平均贡献占比15%,海南外排放源的贡献集中在珠三角地区。(3)对挥发性有机物(volatile organic compounds,VOCs)排放物种来源分析结果表明,异戊二烯在VOCs排放源中贡献最高,平均贡献占比为51%。此次O_(3)污染事件期间海南主要处于NO_(x)控制区,仅有海口处于VOCs和NO_(x)的协同控制区。由于远距离区域传输是此次O_(3)污染事件的主要来源,未来海南和珠三角的区域联防联控对于提高海南空气质量具有重要意义。
基金supported by the National Science and Technology Major Project,China(No.Y2019-I-0018-0017)the National Natural Science Foundation of China(No.11602200)+1 种基金Hunan Innovative Province Construction Special Fund,China(No.2021GK1020)the Priority Academic Program Development of Jiangsu Higher Education Institutions,China。
文摘Propeller design is a highly intricate and interdisciplinary task that necessitates careful trade-offs between radiated noise levels and aerodynamic efficiency.To achieve efficient trade-off designs,an enhanced on-the-fly unsteady adjoint-based aerodynamic and aeroacoustic optimization methodology is developed,which maintains the fidelity of the Navier-Stokes solution for unsteady flow and of the moving-medium Ffowcs Williams-Hawkings(FW-H)formulation for capturing tonal noise.Furthermore,this on-the-fly approach enables a unified architecture for discreteadjoint sensitivity analysis encompassing both aerodynamics and aeroacoustics,facilitating effective multi-objective weighted optimizations.Subsequently,this proposed methodology is applied to perform trade-off optimizations between aerodynamics and aeroacoustics for a propeller by employing varying weighting factors to comprehend their influence on optimal configurations.The results demonstrate a positive correlation between efficiency and noise sensitivities,and thus indicate an inherent synchronicity where pursing noise reduction through purely aeroacoustic optimization inevitably entails sacrificing aerodynamic efficiency.However,by effectively incorporating appropriate weighting factors(recommended to range from 0.25 to 0.5)into the multi-objective function combined with both aerodynamics and aeroacoustics,it becomes feasible to achieve efficiency enhancement and noise reduction simultaneously.Key findings show that reducing blade planform size and equipping“rotated-S”shaped airfoil profiles in the tip region can effectively restrain noise levels while maintaining aerodynamic performance.
基金supported by the National Key Research and Development Program of China(Grant No.2023YFB3002800).
文摘The primary concern in stealth aircraft design is the very large electrical size objects.However,the computational and storage requirements of these objects present significant obstacles for current highfidelity design methods,particularly when addressing high-dimensional complex engineering design problems.To address these challenges,we developed a surface sensitivity technique based on the multilevel fast multipole algorithm(MLFMA).An access and storage of sparse partial derivative tensor was improved to significantly enhanced the computation performance.The far-field interactions of the surface sensitivity equation were realized by differential the multipole expansion.In addition,we proposed a fast far-field multiplication method to accelerate the multiplication process.The surface mesh derivative with respect to the design variables was calculated by analytical and complex variable methods,substantially improving computational efficiency.These advancements enabled the MLFMAbased surface sensitivity method to millions meshes and large-scale gradients,extending gradientbased optimization for very large electrical size problems.Test cases have verified the effectiveness of this method in optimizing very large electrical objects in terms of both accuracy and efficiency.
基金jointly supported by the National Key Research and Development Plan(Grant No.2023YFB3907405)the National Natural Science Foundation of China(Grant No.42175132)the Chinese Academy of Sciences Project for Young Scientists in Basic Research(Grant No.YSBR-037)。
文摘The challenge of establishing top-down constraints for regional emissions of fossil fuel CO_(2)(FFCO_(2))arises from the difficulty in distinguishing between atmospheric CO_(2)concentrations released from fossil fuels and background variability,particularly owing to the influence of terrestrial biospheric fluxes.This necessitates the development of a regional inversion methodology based on atmospheric CO_(2)observations to verify bottom-up estimations independently.This study presents a promising approach for estimating China's FFCO_(2)emissions by incorporating the model residual errors(MREs)of the column-averaged dry-air mole fractions of CO_(2)(XCO_(2))from FFCO_(2)emissions(MREff)retained in the analysis of natural flux optimization.China's FFCO_(2)emissions during the COVID-19 lockdown in 2020 are estimated using the GEOS-Chem adjoint model.The relationship between the MREff and FFCO_(2)is determined using the model based on a regional FFCO_(2)anomaly suggested by posterior NOx emissions from air-quality data assimilation.The MREff is typically one-tenth in magnitude,but some positively skewed outliers exceed 1 ppm because the prior emissions lack lockdown impacts,thereby exerting considerable observation forcing given the satellite retrieval uncertainties.We initialize the FFCO_(2)with posterior NOx emissions and optimize the colinear emission ratio.Synthetic data experiments demonstrate that this approach reduces the FFCO_(2)bias to less than 10%.The real-data experiments estimate 19%lower FFCO_(2)with GOSAT XCO_(2)and 26%lower with OCO-2 XCO_(2)than the bottom-up estimations.This study proves the feasibility of our regional FFCO_(2)inversion,highlighting the importance of addressing the outlier behaviors observed in satellite XCO_(2)retrievals.
文摘The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a novel compound numerical method to study the instability of a functionally graded(FG)beam-type NEMS,considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam.The presented method is based on a combination of the Method of Adjoints(MoA)together with the Bézier-based multistep technique.By utilizing the MoA,a boundary value problem(BVP)is turned into an initial value problem(IVP).The resulting IVP is then solved by employing a cost-efficient multi-step process.It is demonstrated that the mentioned method can arrive at a high level of accuracy.Furthermore,it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods,such as Adams-Bashforth,particularly at higher step sizes.Finally,the effects of axially functionally graded(FG)properties on the pull-in phenomenon and the main design parameters of NEMS,including the detachment length,are inspected.It was shown that the main parameter of design is the modulus of elasticity of the material,as Silver(Ag),which had better mechanical properties,showed almost a 6%improvement compared to aluminum(Al).However,by applying the correct amount of material with sturdier surface parameters,such as Aluminum(Al),at certain points,the nanobeams’functionality can be improved even further by around 1.5%.
基金supported by the National Key Research and Development Program of China(No.2022YFC3701205)the National Natural Science Foundation of China(No.41975173)the Science and Technology Development Fund of the Chinese Academy of Meteorological Sciences(No.2021KJ011)。
文摘In recent years,incidents of simultaneous exceedance of PM_(2.5)and O_(3) concentrations,termed PM_(2.5)and O_(3) co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation analysis on two typical co-pollution events in Beijing,occurring from July 22 to July 28,2019,and from April 25 to May 2,2020.These events were categorized into pre-trough southerly airflow type(Type 1)and post-trough northwest flow type(Type 2).Subsequently,sensitivity analyses using the GRAPES-CUACE adjoint model were performed to quantify the contributions of precursor emissions from Beijing and surrounding areas to PM_(2.5)and O_(3) concentrations in Beijing for two types of co-pollution.The results indicated that the spatiotemporal distribution of sensitive source region varied among different circulation types.Primary PM_(2.5)(PPM_(2.5))emissions from Hebei contributed the most to the 24-hour average PM_(2.5)(24-h PM_(2.5))peak concentration(41.6%-45.4%),followed by Beijing emissions(31%-35.7%).The maximum daily 8-hour average ozone peak concentration was primarily influenced by the emissions from Hebei and Beijing,with contribution ratios respectively of 32.8%-44.8% and 29%-42.1%.Additionally,NO_(x)emissions were the main contributors in Type 1,while both NO_(x)and VOCs emissions contributed similarly in Type 2.The iterative emission reduction experiments for two types of co-pollution indicated that Type 1 required emission reductions in NO_(x)(52.4%-71.8%)and VOCs(14.1%-33.8%)only.In contrast,Type 2 required combined emission reductions in NO_(x)(37.0%-65.1%),VOCs(30.7%-56.2%),and PPM_(2.5)(31%-46.9%).This study provided a reference for controlling co-pollution events and improving air quality in Beijing.
文摘It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.
文摘In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation laws.Moreover,miscellaneous soliton solutions like dark,bright,periodic,rational,Jacobian elliptic function,Weierstrass elliptic function,and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential equations.All these results are displayed graphically by 3D,2D,and contour plots.
基金supported by the National Natural Science Foundation of China(12071407,12171193)the Natural Science Foundation of Hubei Province(2024AFB170)。
文摘Economic development has caused a lot of environmental problems,in turn,environmental pollution restricts economic development.Considering the influence of wind direction and speed,temperature and humidity on pollutants,as well as the influence of epidemic,war and exchange rate on economic development.In this paper,we develop a stochastic economic-environment model with pollution control strategies.Furthermore,sufficient and necessary conditions for the near-optimality are established.Finally,we perform some numerical simulations to demonstrate the correctness of the theoretical results,which shows that some control strategies could decrease the environmental pollution,and therefore,could alleviate economic losses caused by environmental pollution.
基金Supported by the Science Center for Gas Turbine Project,China(No.P2022-C-II-001-001).
文摘High-performance compressor design is best achieved with a good trade-off between aerodynamic and structural considerations,which requires efficient and accurate multidisciplinary design and optimization tools.As advanced compressors are defined with a large design space,their optimization is most efficiently achieved using a gradient-based approach,where the gradient can be computed using an adjoint method,at a cost nearly independent of the dimension of the design space.While the adjoint method has been widely used for aerodynamic shape optimization,its use for structural shape optimizations of compressor blades has not been as well studied.This paper discussed a discrete adjoint solver for structural sensitivity analysis developed within the opensource Computational Structural Mechanics(CSM)software CalculiX,and proposed an efficient stress sensitivity analysis method based on the Finite Element Method(FEM)using adjoint.The proposed method is applied to compute the stress sensitivity of a wide-chord fan blade in a highbypass-ratio engine.The accuracy of the adjoint-based stress sensitivity is verified against central finite differences.In terms of computational efficiency,the adjoint approach is about 4.5 times more efficient than the conventional approach using finite differences.This works marks an important step towards fluid-structural coupled adjoint optimization of wide-chord fan blades.
文摘We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.
文摘The Cauchy stress equations (1823), the Cosserat couple-stress equations (1909), the Clausius virial equation (1870) and the Maxwell/Weyl equations (1873, 1918) are among the most famous partial differential equations that can be found today in any textbook dealing with elasticity theory, continuum mechanics, thermodynamics or electromagnetism. Over a manifold of dimension n, their respective numbers are n,n(n−1)/2,1,nwith a total of N=(n+1)(n+2)/2, that is 15 when n=4for space-time. This is also just the number of parameters of the Lie group of conformal transformations with n translations, n(n−1)/2rotations, 1 dilatation and n highly non-linear elations introduced by E. Cartan in 1922. The purpose of this paper is to prove that the form of these equations only depends on the structure of the conformal group for an arbitrary n≥1because they are described as a whole by the (formal) adjoint of the first Spencer operator existing in the Spencer differential sequence. Such a group theoretical implication is obtained by applying totally new differential geometric methods in field theory. In particular, when n=4, the main idea is not to shrink the group from 10 down to 4 or 2 parameters by using the Schwarzschild or Kerr metrics instead of the Minkowski metric, but to enlarge the group from 10 up to 11 or 15 parameters by using the Weyl or conformal group instead of the Poincaré group of space-time. Contrary to the Einstein equations, these equations can be all parametrized by the adjoint of the second Spencer operator through Nn(n−1)/2potentials. These results bring the need to revisit the mathematical foundations of both General Relativity and Gauge Theory according to a clever but rarely quoted paper of H. Poincaré (1901). They strengthen the recent comments we already made about the dual confusions made by Einstein (1915) while following Beltrami (1892), both using the same Einstein operator but ignoring it is self-adjoint in the framework of differential double duality.
文摘This work highlights the unparalleled efficiency of the “n<sup>th</sup>-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The n<sup>th</sup>-FASAM-N methodology is compared to the extant “n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (n<sup>th</sup>-CASAM-N) showing that: (i) the 1<sup>st</sup>-FASAM-N and the 1<sup>st</sup>-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1<sup>st</sup>-LASS);(ii) the 2<sup>nd</sup>-FASAM-N methodology is considerably more efficient than the 2<sup>nd</sup>-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2<sup>nd</sup>-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2<sup>nd</sup>-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3<sup>rd</sup>-FASAM-N methodology is even more efficient than the 3<sup>rd</sup>-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3<sup>rd</sup>-FASAM-N methodology, while the application of the 3<sup>rd</sup>-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.
文摘This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the n<sup>th</sup>-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the n<sup>th</sup>-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the n<sup>th</sup>-FASAM-N methodology becomes identical to the extant n<sup>th</sup> CASAM-N (“n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.
基金National Natural Science Foundation of China (10872093)
文摘The tighten couplings of game strategies with adjoint methods for multi-criterion aerodynamic design optimization are ad-dressed. Its numerical implementation is also described in details. In cooperative game,adjoint methods are coupled in parallel to compute Pareto front collaboratively. Conversely in a Nash game,adjoint methods are coupled in each player s decision making to achieve Nash equilibrium competitively. In Stackelberg game,adjoint methods used by players are nested hierarchically through incomp...
文摘In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.
文摘The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
