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Physics-constrained graph neural networks for solving adjoint equations 认领 引用
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作者 Jinpeng Xiang Shufang Song +2 位作者 Wenbo Cao Kuijun Zuo Weiwei Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第1期178-191,共14页
The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow fie... The adjoint method is widely used in gradient-based optimization with high-dimensional design variables.However,the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field,resulting in expensive computational costs.To improve the efficiency of solving adjoint equations,we propose a physics-constrained graph neural networks for solving adjoint equations,named ADJ-PCGN.ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data,serving as a replacement for the computationally expensive numerical solution of adjoint equations.A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities.Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples,results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method.In addition,ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies,mesh densities,and out-of-distribution conditions.It holds the potential to become a universal model for aerodynamic shape optimization involving states,geometries,and meshes. 展开更多
关键词 Adjoint method Deep learning Graph neural network Physics-constrained Fast aerodynamic analysis
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Trade-off between propeller aerodynamics and aeroacoustics using unsteady adjoint-based design optimization 认领 引用 被引量：1
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作者 Haolin ZHI Shuanghou DENG +2 位作者 Tianhang XIAO Ning QIN Jingliang GUO 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2025年第8期347-366,共20页
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
关键词 Aerodynamic Aeroacoustic Multidisciplinary optimization Propeller Unsteady adjoint method
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Sensitivity analysis of PM2.5and O3 co-pollution in Beijing based on GRAPES-CUACE adjoint model 认领 引用
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作者 Zhe Liu Xingqin An +2 位作者 ChaoWang Jiangtao Li Meng Cui 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2025年第12期461-475,共15页
In recent years,incidents of simultaneous exceedance of PM2.5and O3 concentrations,termed PM2.5and O3 co-pollution events,have frequently occurred in China.This study conducted atmospheric circulation anal... In recent years,incidents of simultaneous exceedance of PM2.5and O3 concentrations,termed PM2.5and O3 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 PM2.5and O3 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 PM2.5(PPM2.5)emissions from Hebei contributed the most to the 24-hour average PM2.5(24-h PM2.5)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,NOxemissions were the main contributors in Type 1,while both NOxand 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 NOx(52.4%-71.8%)and VOCs(14.1%-33.8%)only.In contrast,Type 2 required combined emission reductions in NOx(37.0%-65.1%),VOCs(30.7%-56.2%),and PPM2.5(31%-46.9%).This study provided a reference for controlling co-pollution events and improving air quality in Beijing. 展开更多
关键词 Adjoint modeling PM2.5and O3co-pollution Sensitivity analysis Pollution control Beijing
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Adjoint-based RCS surface sensitivity calculation for very large electrical size object 认领 引用
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作者 Jun Deng Zhenghong Gao +3 位作者 Lin Zhou Ke Zhao Jiangtao Huang Wei Zhang 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2025年第5期164-179,共16页
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
关键词 Surface sensitivity Gradient MLFMA Discrete adjoint Very large electrical size RCS
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Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework 认领 引用 被引量：3
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作者 Dan Gabriel Cacuci 《American Journal of Computational Mathematics》 2020年第3期329-354,共26页
This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters a... This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities. 展开更多
关键词 Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM) First-Level Adjoint Sensitivity System (1st-LASS) Second-Level Adjoint Sensitivity System (2nd-LASS) Operator-Type Response Second-Order Sensitivities to Uncertain Model Boundaries Second-Order Sensitivities to Uncertain Model Parameters
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Machine learning for adjoint vector in aerodynamic shape optimization 认领 引用 被引量：4
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作者 Mengfei Xu Shufang Song +2 位作者 Xuxiang Sun Wengang Chen Weiwei Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2021年第9期1416-1432,I0003,共17页
Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for it to obtain the gradients of all design variables. However, the computational cost of adjoint vector is app... Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for it to obtain the gradients of all design variables. However, the computational cost of adjoint vector is approximately equal to that of flow computation. In order to accelerate the solution of adjoint vector and improve the efficiency of adjoint-based optimization, machine learning for adjoint vector modeling is presented. Deep neural network (DNN) is employed to construct the mapping between the adjoint vector and the local flow variables. DNN can efficiently predict adjoint vector and its generalization is examined by a transonic drag reduction of NACA0012 airfoil. The results indicate that with negligible computational cost of the adjoint vector, the proposed DNN-based adjoint method can achieve the same optimization results as the traditional adjoint method. 展开更多
关键词 Machine learning Deep neural network Adjoint vector modelling Aerodynamic shape optimization Adjoint method
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Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method 认领 引用 被引量：16
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作者 Qian ZHANG Shenren XU +3 位作者 Xianjun YU Jiaxin LIU Dingxi WANG Xiuquan HUANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第2期17-21,共5页
Manufactured blades are inevitably different from their design intent,which leads to a deviation of the performance from the intended value.To quantify the associated performance uncertainty,many approaches have been ... Manufactured blades are inevitably different from their design intent,which leads to a deviation of the performance from the intended value.To quantify the associated performance uncertainty,many approaches have been developed.The traditional Monte Carlo method based on a Computational Fluid Dynamics solver(MC-CFD)for a three-dimensional compressor is prohibitively expensive.Existing alternatives to the MC-CFD,such as surrogate models and secondorder derivatives based on the adjoint method,can greatly reduce the computational cost.Nevertheless,they will encounter’the curse of dimensionality’except for the linear model based on the adjoint gradient(called MC-adj-linear).However,the MC-adj-linear model neglects the nonlinearity of the performance function.In this work,an improved method is proposed to circumvent the lowaccuracy problem of the MC-adj-linear without incurring the high cost of other alternative models.The method is applied to the study of the aerodynamic performance of an annular transonic compressor cascade,subject to prescribed geometric variability with industrial relevance.It is found that the proposed method achieves a significant accuracy improvement over the MC-adj-linear with low computational cost,showing the great potential for fast uncertainty quantification. 展开更多
关键词 Adjoint method Aerodynamics Compressor Manufacturing Monte Carlo method Nonlinearity Uncertainty quantification
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Assimilated Tidal Results of Tide Gauge and TOPEX/POSEIDON Data over the China Seas Using a Variational Adjoint Approach with a Nonlinear Numerical Model 认领 引用 被引量：14
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作者 韩桂军 李威 +2 位作者 何忠杰 刘克修 马继瑞 《Advances in Atmospheric Sciences》 SCIE CAS 2006年第3期449-460,共12页
In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TO... In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TOPEX/POSEIDON （T/P） derived datasets by means of the variational adjoint approach in such a way that unknown internal model parameters, bottom topography, friction coefficients and open boundary conditions, for example, are adjusted during the process. The numerical model is used as a forward model. After the along-track T/P data are processed, two classical methods, i.e. harmonic and response analysis, are implemented to estimate the tide from such datasets with a domain covering the model area extending from 0° to 41°N in latitude and from 99°E to 142°E in longitude. And the results of these two methods are compared and interpreted. The numerical simulation is performed for 16 major constituents. In the data assimilation experiments, three types of unknown parameters （water depth, bottom friction and tidal open boundary conditions in the model equations） are chosen as control variables. Among the various types of data assimilation experiments, the calibration of water depth brings the most promising results. By comparing the results with selected tide gauge data, the average absolute errors are decreased from 7.9 cm to 6.8 cm for amplitude and from 13.0° to 9.0° for phase with respect to the semidiurnal tide M2 constituent, which is the largest tidal constituent in the model area. After the data assimilation experiment is performed, the comparison between model results and tide gauge observation for water levels shows that the RMS errors decrease by 9 cm for a total of 14 stations, mostly selected along the coast of China's Mainland, when a one-month period is considered, and the correlation coefficients improve for most tidal stations among these stations. 展开更多
关键词 tides variational adjoint approach tidal gauges TOPEX/POSEIDON the China Seas
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Integrated passage design based on extended free-form deformation and adjoint optimization 认领 引用 被引量：7
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作者 Xin LI Tongtong MENG +2 位作者 Weiwei Li Ling ZHOU Lucheng JI 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2023年第4期148-164,共17页
Inspired by the three-dimensional design of flow passages in turbomachinery,this study proposes the concept of integrated passage design.The capability of adjoint method for efficient optimization and the flexibility ... Inspired by the three-dimensional design of flow passages in turbomachinery,this study proposes the concept of integrated passage design.The capability of adjoint method for efficient optimization and the flexibility of the parameterization method based on extended free-form defor-mation have been considered to develop a feasible approach to design an integrated passage.This concept was applied to redesign a typical transonic fan,Rotor 67,and the results were analyzed by CFX.It is shown that the passage was adequately adjusted in all three dimensions and reduced the strength of shock wave and wake-induced flow.In particular,the secondary flow was appropriately reorganized and the corner separation was well controlled in the end wall region,leading to signif-icant improvements in adiabatic efficiency and diffusion. 展开更多
关键词 Turbomachinery Aerodynamic Transonic flow Integrated passage design Extended free-form defor-mation Adjoint optimization
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A novel robust aerodynamic optimization technique coupled with adjoint solvers and polynomial chaos expansion 认领 引用 被引量：8
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作者 Wei ZHANG Qiang WANG +1 位作者 Fanzhi ZENG Chao YAN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第10期35-55,共21页
Uncertainty is common in the life cycle of an aircraft, and Robust Aerodynamic Optimization(RAO) that considers uncertainty is important in aircraft design. To avoid the curse of dimensionality in surrogate-based opti... Uncertainty is common in the life cycle of an aircraft, and Robust Aerodynamic Optimization(RAO) that considers uncertainty is important in aircraft design. To avoid the curse of dimensionality in surrogate-based optimization, this study proposes an adjoint RAO technique called “R-Opt”. Polynomial Chaos Expansion(PCE) is coupled with the R-Opt technique to quantify uncertainty in the responses of the target(including its mean and standard deviation). Only one process of PCE model construction is required in each iteration, and the gradients of uncertainty can be inferred via chain rules. The proposed method is more efficient than prevalent methods,and avoids the problem of a disagreement over the best PCE basis from among a number of PCE models(especially in case of sparse PCE). It also supports the application of sparse PCE.Two benchmark tests and two airfoil cases were used to verify R-Opt, and the optimal solutions were deemed to be robust. It improved the mean aerodynamic performance and reduced the standard deviation of the target. 展开更多
关键词 Adjoint technique Polynomial chaos expansion Robust design Uncertainty analysis Uncertainty gradient propagation
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Aerodynamic adjoint optimization of turbomachinery with direct control on blade design parameters 认领 引用 被引量：6
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作者 Xin LI Tongtong MENG +2 位作者 Weiwei LI Ling ZHOU Lucheng JI 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2023年第11期119-134,共16页
Nowadays,the adjoint method has become a popular approach in the optimization of turbomachinery to further improve its aerodynamic performance.However,design variables in these adjoint optimization applications are ge... Nowadays,the adjoint method has become a popular approach in the optimization of turbomachinery to further improve its aerodynamic performance.However,design variables in these adjoint optimization applications are generally not direct design parameters of blade(such as wedge angles or maximum thickness),making the geometric variation by adjoint optimization can hardly be re-extracted as the change of each design parameter.By giving considerations to the G1 continuity constraint of adjoint method on its parameterization method,this manuscript shows how to apply a parameterization method in 3D blade design process into adjoint optimization.Nearly all design parameters can therefore be treated as design variables in the adjoint method and then participate in the sensitivity-based optimization.Finally,a fitted Rotor 67 blade is optimized and the adiabatic efficiency is significantly improved by nearly 0.91%. 展开更多
关键词 Adjoint method Parameterization method Aerodynamic optimization Customized blading method Compressor Turbomachinery
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STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS 认领 引用 被引量：6
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作者 吕咸青 吴自库 +1 位作者 谷艺 田纪伟 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第6期636-646,共11页
It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that... It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention. 展开更多
关键词 data assimilation variational analysis adjoint method tide open boundary condition
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Adjoint-based robust optimization design of laminar flow wing under flight condition uncertainties 认领 引用 被引量：4
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作者 Yifu CHEN Hanyue RAO +3 位作者 Yiju DENG Tihao YANG Yayun SHI Junqiang BAI 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2023年第6期19-34,共16页
It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow contro... It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow control effect,it is necessary to develop an effective optimization design method.Meanwhile,attention must be given to the impact of crossflow(CF)instability brought on by the sweep angle.This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos.Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes(RANS)and simplified eNmethod,which can consider both Tollmien-Schlichting(TS)wave and crossflow vortex instability.We have performed gradient enhancement processing on the general Polynomial Chaos Expansion(PCE),which is advantageous to reduce the computational cost of single uncertainty propagation.This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition.The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations.The framework is applied to the robust design of a 25°swept wing with infinite span in transonic flow.The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy,and qualitatively reveals the factors that dominate in different flow field regions.By the robust optimization design,the mean and standard deviation of the drag coefficient can be reduced by 29%and 45%,respectively,and compared with the deterministic optimization design results,there is less possibility of forming shock waves under flight condition uncertainties.Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction. 展开更多
关键词 Adjoint method Gradient-based optimization Laminar-turbulent transition Robust design Uncertainty propagation
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Couplings in Multi-criterion Aerodynamic Optimization Problems Using Adjoint Methods and Game Strategies 认领 引用 被引量：7
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作者 唐智礼 董军 《Chinese Journal of Aeronautics》 SCIE EI CAS 2009年第1期1-8,共8页
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
关键词 multi-criterion optimization aerodynamics adjoint methods game strategies Nash game Stackelberg game Pareto front
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Adjoint-based Sensitivity Analysis of a Mesoscale Low on the Mei-yu Front and Its Implications for Adaptive Observation 认领 引用 被引量：4
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作者 钟科 董佩明 +2 位作者 赵思雄 蔡其发 兰伟仁 《Advances in Atmospheric Sciences》 SCIE CAS 2007年第3期435-448,共14页
An adjoint sensitivity analysis of one mesoscale low on the mei-yu Front is presented in this paper. The sensitivity gradient of simulation error dry energy with respect to initial analysis is calculated. And after ve... An adjoint sensitivity analysis of one mesoscale low on the mei-yu Front is presented in this paper. The sensitivity gradient of simulation error dry energy with respect to initial analysis is calculated. And after verifying the ability of a tangent linear and adjoint model to describe small perturbations in the nonlinear model, the sensitivity gradient analysis is implemented in detail. The sensitivity gradient with respect to different physical fields are not uniform in intensity, simulation error is most sensitive to the vapor mixed ratio. The localization and consistency are obvious characters of horizontal distribution of the sensitivity gradient, which is useful for the practical implementation of adaptive observation. The sensitivity region tilts to the northwest with height increasing; the singular vector calculation proves that this tilting characterizes a quick-growing structure, which denotes that using the leading singular vectors to decide the adaptive observation region is proper. When connected with simulation of a mesoscale low on the mei-yu Front, the sensitivity gradient has the following physical characters： the obvious sensitive region is mesoscale, concentrated in the middle-upper troposphere, and locates around the key system; and the sensitivity gradient of different physical fields correlates dynamically. 展开更多
关键词 adjoint sensitivity analysis singular vector adaptive observation mei-yu front mesoscale low
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Stress sensitivity analysis for a wide-chord fan blade using an adjoint method 认领 引用 被引量：3
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作者 Han YANG Shoujia GONG +4 位作者 Yi LI Junxing TANG Dingxi WANG Sheng HUANG Shenren XU 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2024年第10期103-117,共15页
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
关键词 Adjoint method Multidisciplinary optimization Stress sensitivity analysis Finite element method Shape optimization
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Aerodynamic optimization design for high pressure turbines based on the adjoint approach 认领 引用 被引量：6
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作者 Chen Lei Chen Jiang 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2015年第3期757-769,共13页
Abstract A first study on the continuous adjoint formulation for aerodynamic optimization design of high pressure turbines based on S2 surface governed by the Euler equations with source terms is presented. The object... Abstract A first study on the continuous adjoint formulation for aerodynamic optimization design of high pressure turbines based on S2 surface governed by the Euler equations with source terms is presented. The objective function is defined as an integral function along the boundaries, and the adjoint equations and the boundary conditions are derived by introducing the adjoint variable vec- tors. The gradient expression of the objective function then includes only the terms related to phys- ical shape variations. The numerical solution of the adjoint equation is conducted by a finite- difference method with the Jameson spatial scheme employing the first and the third order dissipa- tive fluxes. A gradient-based aerodynamic optimization system is established by integrating the blade stagger angles, the stacking lines and the passage perturbation parameterization with the quasi-Newton method of Broyden Fletcher Goldfarb-Shanno （BFGS）. The application of the continuous adjoint method is validated through a single stage high pressure turbine optimization case. The adiabatic efficiency increases from 0.8875 to 0.8931, whilst the mass flow rate and the pressure ratio remain almost unchanged. The optimization design is shown to reduce the passage vortex loss as well as the mixing loss due to the cooling air injection. 展开更多
关键词 Adjoint method Aerodynamic design High pressure turbineOptimization design Objective function
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Estimation of eddy viscosity on the South China Sea shelf with adjoint assimilation method 认领 引用 被引量：4
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作者 ZHANG Yanwei TIAN Jiwei XIE Lingling 《Acta Oceanologica Sinica》 SCIE CAS 2009年第5期9-16,共8页
The eddy viscosity of the ocean is an important parameter indicating the small-scale mixing process in the oceanic interior water column.Ekman wind-driven current model and adjoint assimilation technique are used to c... The eddy viscosity of the ocean is an important parameter indicating the small-scale mixing process in the oceanic interior water column.Ekman wind-driven current model and adjoint assimilation technique are used to calculate the vertical profiles of eddy viscosity by fitting model results to the observation data.The data used in the paper include observed wind data and ADCP data obtained at Wenchang Oil Rig on the SCS(the South China Sea)shelf in August 2002.Different simulations under different wind conditions are analyzed to explore how the eddy viscosity develops with varying wind field.The results show that the eddy viscosity endured gradual variations in the range of 10^-3-10^-2 m^2/s during the periods of wind changes.The mean eddy viscosity undergoing strong wind could rise by about 25%as compared to the value under weak wind. 展开更多
关键词 the SCS eddy viscosity near-inertial Ekman Model adjoint assimilation
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提高基于Adjoint方法翼型优化设计鲁棒性的研究 认领 引用 被引量：4
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作者 樊艳红 宋文萍 韩忠华 《西北工业大学学报》 EI CAS CSCD 北大核心 2013年第4期547-555,共9页
通过引入线搜索方法,提高了基于Adjoint方法翼型优化设计的鲁棒性。针对给定的目标函数,推导了贴体坐标系下相应的Adjoint方程与边界条件的具体表达形式,以及梯度表达式。通过数值求解流动控制方程和Adjoint方程,得到目标函数对设计变... 通过引入线搜索方法,提高了基于Adjoint方法翼型优化设计的鲁棒性。针对给定的目标函数,推导了贴体坐标系下相应的Adjoint方程与边界条件的具体表达形式,以及梯度表达式。通过数值求解流动控制方程和Adjoint方程,得到目标函数对设计变量的梯度,并采用线搜索方法获得最优步长,由此提高了优化算法的鲁棒性。算例表明,线搜索方法可以自动寻找最优的步长,有效解决了传统的取常数步长优化步长选取受到限制,优化结果受步长影响的问题,使得优化方法对步长的依赖性变小,提高了基于Adjoint方法翼型优化设计的鲁棒性。 展开更多
关键词 Adjoint方法 气动优化设计 Navier—Stokes方程
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An Application of the Adjoint Method to a Statistical-Dynamical Tropical-Cyclone Prediction Model (SD-90)Ⅱ:Real Tropical Cyclone Cases 认领 引用 被引量：2
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作者 项杰 廖前锋 +3 位作者 黄思训 兰伟仁 冯强 周凤才 《Advances in Atmospheric Sciences》 SCIE CAS 2006年第1期118-126,共9页
In the first paper in this series, a variational data assimilation of ideal tropical cyclone （TC） tracks was performed for the statistical-dynamical prediction model SD-90 by the adjoint method, and a prediction of ... In the first paper in this series, a variational data assimilation of ideal tropical cyclone （TC） tracks was performed for the statistical-dynamical prediction model SD-90 by the adjoint method, and a prediction of TC tracks was made with good accuracy for tracks containing no sharp turns. In the present paper, the cases of real TC tracks are studied. Due to the complexity of TC motion, attention is paid to the diagnostic research of TC motion. First, five TC tracks are studied. Using the data of each entire TC track, by the adjoint method, five TC tracks are fitted well, and the forces acting on the TCs are retrieved. For a given TC, the distribution of the resultant of the retrieved force and Coriolis force well matches the corresponding TC track, i.e., when a TC turns, the resultant of the retrieved force and Coriolis force acts as a centripetal force, which means that the TC indeed moves like a particle; in particular, for TC 9911, the clockwise looping motion is also fitted well. And the distribution of the resultant appears to be periodic in some cases. Then, the present method is carried out for a portion of the track data for TC 9804, which indicates that when the amount of data for a TC track is sufficient, the algorithm is stable. And finally, the same algorithm is implemented for TCs with a double-eyewall structure, namely Bilis （2000） and Winnie （1997）, and the results prove the applicability of the algorithm to TCs with complicated mesoscale structures if the TC track data are obtained every three hours. 展开更多
关键词 adjoint method TC double eyewalls statistical-dynamical prediction model
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