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A novel robust aerodynamic optimization technique coupled with adjoint solvers and polynomial chaos expansion

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Chinese Journal of Aeronautics 2022年第10期35卷 35-55页

作者： Wei ZHANG Qiang WANG Fanzhi ZENG Chao YAN National Key Laboratory of Computational Fluid Dynamics Beihang UniversityBeijing 100083China Aerospace Times Feipeng Company Limited China Academy of Aerospace Electronics TechnologyKunshan 215000China China Academy of Aerospace Aerodynamics Beijing 100074China

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.

关键词： Adjoint technique polynomial chaos expansion Robust design Uncertainty analysis Uncertainty gradient propagation

An Efficient Sampling Method for Regression-Based polynomial chaos expansion

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Communications in Computational Physics 2013年第4期13卷 1173-1188页

作者： Samih Zein Benoit Colson Francois Glineur Samtech H.Q. LMS International8 rue des chasseurs ardennais AngleurBelgium Center for Operations Research and Econometrics&Information and Communication Technologies Electronics and Applied Mathematics InstituteUniversite catholique de LouvainB-1348 Louvain-la-NeuveBelgium

The polynomial chaos expansion(PCE)is an efficient numerical method for performing a reliability analysis.It relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation(the so-called PCE).Numerically,such an approximation can be obtained by using a regression method with a suitable design of experiments.The cost of this approximation depends on the size of the design of experiments.If the design of experiments is large and the system is modeled with a computationally expensive FEA(Finite Element Analysis)model,the PCE approximation becomes unfeasible.The aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user,in order to make the PCE approximation computationally feasible.It is an optimization algorithm that seeks to find the best design of experiments in the D-optimal sense for the PCE.This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm.The efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.

关键词： polynomial chaos expansion regression D-optimal design Fedorov Algorithm genetic algorithms

A polynomial chaos expansion Trust Region Method for Robust Optimization

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Communications in Computational Physics 2013年第7期14卷 412-424页

作者： Samih Zein Samtech H.Q. 8 rue des chasseurs ardennais AngleurBelgium

Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables.It requires at each iteration the evaluation of some robust measures of the objective function and the constraints.In a previous work,the authors have proposed a method which efficiently generates a design of experiments with respect to the design variable uncertainties to compute the robust measures using the polynomial chaos expansion.This paper extends the proposed method to the case of the robust optimization.The generated design of experiments is used to build a surrogate model for the robust measures over a certain trust region.This leads to a trust region optimization method which only requires one evaluation of the design of experiments per iteration(single loop method).Unlike other single loop methods which are only based on a first order approximation of robust measure of the constraints and which does not handle a robust measure for the objective function,the proposed method can handle any approximation order and any choice for the robust measures.Some numerical experiments based on finite element functions are performed to show the efficiency of the method.

关键词： Reliability based design optimization polynomial chaos expansion trust region method

Response prediction using the PC-NARX model for SDOF systems with degradation and parametric uncertainties

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Earthquake Engineering and Engineering Vibration 2022年第2期21卷 325-340页

作者： Gao Xiaoshu Chen Cheng Hou Hetao Jiao Shenghu School of Civil Engineering Shandong UniversityJinan 250100China School of Engineering San Francisco State UniversitySan Francisco 94132-1722USA Shandong Engineering&Technology Research Center for Green Building and Intelligent Construction Jinan 250100China

Building collapses during recent earthquakes have brought up the need for research on factors pertaining to collapse and the safety of structures.This requires response replication of structures that account for uncertainties from ground motions and structural properties.Structural collapse often implies that the structural system is no longer capable of maintaining its gravity load-carrying capacity,which often points to factors involving strength and stiffness degradation.In this study,the polynomial chaos nonlinear autoregressive with exogenous input form(PC-NARX)model is explored for dynamic response replication of a nonlinear single-degree-of-freedom(SDOF)structure.The generalized hysteretic Bouc-Wen model is applied to emulate stiffness and strength degradation for an SDOF structure close to collapse.A stochastic ground motion model is used to represent the uncertainties in seismic excitation.The PC-NARX model is employed and further evaluated for response replication of an SDOF system with inherent uncertain structural properties.A generic algorithm(GA)is used to select the terms for structural dynamics,and polynomial chaos expansion(PCE)is used to incorporate uncertain parameters into NARX model coefficients.It is demonstrated that the PC-NARX model provides good accuracy to account for both ground motion and structural uncertainties into response replication of SDOF structures with significant strength and stiffness degradation.The PC-NARX model thus presents a promising technique for collapse safety analysis of structures.

关键词： polynomial chaos expansion NARX model hysteresis degradation collapse

Over-limit risk assessment method of integrated energy system considering source-load correlation

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Global Energy Interconnection 2023年第6期6卷 661-674页

作者： Ying Wang Xiaojun Wang Yizhi Zhang Yigang Zhang Zekai Xu School of Electrical Engineering Beijing Jiaotong UniversityBeijing 100044P.R.China

In an integrated energy system,source-load multiple uncertainties and correlations lead to an over-limit risk in operating state,including voltage,temperature,and pressure over-limit.Therefore,efficient probabilistic energy flow calculation methods and risk assessment theories applicable to integrated energy systems are crucial.This study proposed a probabilistic energy flow calculation method based on polynomial chaos expansion for an electric-heat-gas integrated energy system.The method accurately and efficiently calculated the over-limit probability of the system state variables,considering the coupling conditions of electricity,heat,and gas,as well as uncertainties and correlations in renewable energy unit outputs and multiple types of loads.To further evaluate and quantify the impact of uncertainty factors on the over-limit risk,a global sensitivity analysis method for the integrated energy system based on the analysis of covariance theory is proposed.This method considered the source-load correlation and aimed to identify the key uncertainty factors that influence stable operation.Simulation results demonstrated that the proposed method achieved accuracy to that of the Monte Carlo method while significantly reducing calculation time.It effectively quantified the over-limit risk under the presence of multiple source-load uncertainties.

关键词： Probabilistic energy flow polynomial chaos expansion Correlation Risk assessment Analysis of covariance

polynomial chaos surrogate and bayesian learning for coupled hydro-mechanical behavior of soil slope

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Rock Mechanics Bulletin 2023年第1期2卷 27-37页

作者： Lulu Zhang Fang Wu Xin Wei Hao-Qing Yang Shixiao Fu Jinsong Huang Liang Gao State Key Laboratory of Ocean Engineering Department of Civil EngineeringShanghai Key Laboratory for Digital Maintenance of Buildings and InfrastructureShanghai Jiao Tong University800 Dongchuan RoadShanghaiChina Department of Civil Engineering Shanghai Jiao Tong University800 Dongchuan RoadShanghaiChina State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University800 Dongchuan RoadShanghaiChina ARC Centre of Excellence for Geotechnical Science and Engineering University of NewcastleCallaghanNSW2308Australia Faculty of Science and Technology University of MacaoE11Avenida da UniversidadeTaipaMacaoChina

As rainfall infiltrates into soil slopes,the hydraulic and mechanical behaviors of soils are interacted.In this study,an efficient probabilistic parameter estimation method for coupled hydro-mechanical behavior in soil slope is proposed.This method integrates the polynomial chaos expansion(PCE)method,the coupled hydro-mechanical modeling,and the Bayesian learning method.A coupled hydro-mechanical numerical model is established for the simulation of behaviors of unsaturated soil slope under rainfall infiltration,following by training a cheap-to-run PCE surrogate to replace it.Probabilistic estimation of soil parameters is conducted based on the Bayesian learning technique with the Markov Chain Monte Carlo(MCMC)simulation.A numerical example of an unsaturated slope under rainfall infiltration is presented to illustrate the proposed method.The effects of measurement durations and response types on parameter estimation are addressed.The result shows that with the increase of measurement duration,the uncertainties of soil parameters are significantly reduced.The uncertainties of hydraulic properties are reduced significantly using the pore water pressure data,while the uncertainties of soil strength parameters are reduced greatly using the measured displacement data.

关键词： Landslide Hydro-mechanical polynomial chaos expansion Bayesian learning Markov chain Monte Carlo

Methods and advances in the study of aeroelasticity with uncertainties

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Chinese Journal of Aeronautics 2014年第3期27卷 461-474页

作者： Dai Yuting Yang Chao School of Aeronautic Science and Engineering Beihang University

Uncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncer- tainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the ~t method. It covers the numerical calculation algo- rithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation.

关键词： polynomial chaos expansion Probabilisticity Robustness Structured singular value Uncertainty

Analysis of actuator delay and its effect on uncertainty quantification for real-time hybrid simulation

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Earthquake Engineering and Engineering Vibration 2017年第4期16卷 713-725页

作者： Cheng Chen Weijie Xu Tong Guo Kai Chen School of Engineering San Francisco State University Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education Southeast University

Uncertainties in structure properties can result in different responses in hybrid simulations. Quantification of the effect of these tmcertainties would enable researchers to estimate the variances of structural responses observed from experiments. This poses challenges for real-time hybrid simulation （RTHS） due to the existence of actuator delay. polynomial chaos expansion （PCE） projects the model outputs on a basis of orthogonal stochastic polynomials to account for influences of model uncertainties. In this paper, PCE is utilized to evaluate effect of actuator delay on the maximum displacement from real-time hybrid simulation of a single degree of freedom （SDOF） structure when accounting for uncertainties in structural properties. The PCE is first applied for RTHS without delay to determine the order of PCE, the number of sample points as well as the method for coefficients calculation. The PCE is then applied to RTHS with actuator delay. The mean, variance and Sobol indices are compared and discussed to evaluate the effects of actuator delay on uncertainty quantification for RTHS. Results show that the mean and the variance of the maximum displacement increase linearly and exponentially with respect to actuator delay, respectively. Sensitivity analysis through Sobol indices also indicates the influence of the single random variable decreases while the coupling effect increases with the increase of actuator delay.

关键词： real-time hybrid simulation actuator delay polynomial chaos expansion delay differential equation uncertainty quantification

An Uncertainty Analysis Method for Artillery Dynamics with Hybrid Stochastic and Interval Parameters

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Computer Modeling in Engineering & Sciences 2021年第2期126卷 479-503页

作者： Liqun Wang Zengtao Chen Guolai Yang School of Mechanical Engineering Nanjing University of Science&TechnologyNanjing210094China Department of Mechanical Engineering University of AlbertaEdmontonT6G 1H9Canada

This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion(PCE).The uncertainty parameters with sufficient information are regarded as stochastic variables,whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge.In this method,the PCE model is constructed through the Galerkin projection method,in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights.Through the sampling in PCE,the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems,without changing their expressions.The yielded PCE model is utilized as a computationally efficient,surrogate model,and the supremum and infimum of the dynamic responses over all time iteration steps can be easily approximated through Monte Carlo simulation and percentile difference.A numerical example and an artillery exterior ballistic dynamics model are used to illustrate the feasibility and efficiency of this approach.The numerical results indicate that the dynamic response bounds obtained by the PCE approach almost match the results of the direct Monte Carlo simulation,but the computational efficiency of the PCE approach is much higher than direct Monte Carlo simulation.Moreover,the proposed method also exhibits fine precision even in high-dimensional uncertainty analysis problems.

关键词： Uncertainty propagation and analysis artillery dynamics hybrid stochastic and interval uncertainty polynomial chaos expansion ordinary differential equations