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Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with damping

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Acta Mechanica Sinica 2021年第6期37卷 983-996,I0002页

作者： zhiping qiu Haijun Xia Institute of Solid Mechanics School of Aeronautic Science and EngineeringBeihang UniversityBeijing100083China

In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response with damping.Firstly,the linear Hamiltonian system is briefly introduced and its conservation law is proved based on the properties of the exterior products.Then the symplectic perturbation series methodology is proposed to deal with the non-conservative linear Hamiltonian system and its conservation law is further proved.The structural dynamic response problem with eternal load and damping is transformed as the non-conservative linear Hamiltonian system and the symplectic difference schemes for the non-conservative linear Hamiltonian system are established.The applicability and validity of the proposed method are demonstrated by three engineering examples.The results demonstrate that the presented methodology is better than the traditional Runge–Kutta algorithm in the prediction of long-time structural dynamic response under the same time step.

关键词： Symplectic perturbation series methodology Non-conservative Hamiltonian system Structural dynamic response Symplectic difference scheme

A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

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Acta Mechanica Sinica 2016年第5期32卷 941-958页

作者： Zheng Lv zhiping qiu Institute of Solid Mechanics Beihang University

In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process.The proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are made.By solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good agreement.Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.

关键词： Direct probabilistic approach Nonlinear dynamic system Nonstationary random process Response’s moments Multiscale algorithm

Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters

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Science China(Physics,Mechanics & Astronomy) 2018年第6期61卷 62-74页

作者： zhiping qiu PengBo Wang Institute of Solid Mechanics Beihang University Beijing 100191 China

In this article, we propose a parameter vertex method to determine the upper and lower bounds of the dynamic response of structures with interval parameters, which can be regarded as an extension of the matrix vertex method proposed by qiu and Wang. The matrix vertex method requires considerable computation time and encounters the dependency problem in practice,thereby limiting its application in engineering. The proposed parameter vertex method can avoid the dependency problem, and the number of possible vertex combinations in the proposed method is significantly less than that in the matrix vertex method.The parameter vertex method requires that each matrix element in the dynamic differential equation is monotonic with respect to the uncertain parameter, and that the dynamic response reaches its extreme value when the uncertain parameter is at its endpoint.To further reduce the runtime, both vertical and transversal parallel algorithms are introduced and integrated into the parameter vertex method to improve its computational efficiency. Two numerical examples are presented to demonstrate the proposed method combined with both parallel algorithms. The performances of the two parallel algorithms are thoroughly studied. The parameter vertex method combined with parallel algorithm can be used for large-scale computing.

关键词：平行算法动态反应参数结构顶点矩阵元素评估大规模计算计算时间

The need for introduction of non-probabilistic interval conceptions into structural analysis and design

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Science China(Physics,Mechanics & Astronomy) 2016年第11期59卷 90-92页

作者： zhiping qiu Lei Wang Institute of Solid Mechanics Beihang University

With the growing complexity of engineering structures and the severity of their service environments,the uncertainties related to material properties,external loads,boundary conditions,measurement noises,etc.,have increased.Uncertainty greatly influences structural safety,and hence,it is necessary to completely understand all the uncertainties involved when tackling analysis and design issues[1].Traditional approaches to uncertainty analysis and

关键词：设计问题结构分析概率区间不确定性分析工程结构材料性能边界条件测量噪声

Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

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Acta Mechanica Sinica 2015年第6期31卷 845-854页

作者： Qi Li zhiping qiu Xudong Zhang Institute of Solid Mechanics Beihang University (Beijing University of Aeronautics and Astronautics)

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

关键词： Interval parameters · Second-order Taylorseries expansion · Static response of uncertain structures Quadratic programming problems · DCA

Combination of structural reliability and interval analysis

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Acta Mechanica Sinica 2008年第1期24卷 61-67页

作者： zhiping qiu Di Yang Isaac Elishakoff Institute of Solid Mechanics Beihang University Beijing 100083 China Department of Mechanical Engineering Florida Atlantic UniversityBoca Raton FL 33431-0991 USA

In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.

关键词： Non-probabilistic Reliability Interval analysis Parameter estimation

A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications

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Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1535-1557页

作者： zhiping qiu Nan Jiang Institute of Solid Mechanics School of Aeronautic Science and EngineeringBeihang UniversityBeijing 100083China

In this paper,a novel symplectic conservative perturbation series expansion method is proposed to investigate the dynamic response of linear Hamiltonian systems accounting for perturbations,which mainly originate from parameters dispersions and measurement errors.Taking the perturbations into account,the perturbed system is regarded as a modification of the nominal system.By combining the perturbation series expansion method with the deterministic linear Hamiltonian system,the solution to the perturbed system is expressed in the form of asymptotic series by introducing a small parameter and a series of Hamiltonian canonical equations to predict the dynamic response are derived.Eventually,the response of the perturbed system can be obtained successfully by solving these Hamiltonian canonical equations using the symplectic difference schemes.The symplectic conservation of the proposed method is demonstrated mathematically indicating that the proposed method can preserve the characteristic property of the system.The performance of the proposed method is evaluated by three examples compared with the Runge-Kutta algorithm.Numerical examples illustrate the superiority of the proposed method in accuracy and stability,especially symplectic conservation for solving linear Hamiltonian systems with perturbations and the applicability in structural dynamic response estimation.

关键词： Linear Hamiltonian system perturbation series expansion method symplectic structure,symplectic algorithm structural dynamic response

PROBABILISTIC DAMAGE IDENTIFICATION OF STRUCTURES WITH UNCERTAINTY BASED ON DYNAMIC RESPONSES

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Acta Mechanica Solida Sinica 2014年第2期27卷 172-180页

作者： Xiaojun Wang Chen Yang Lei Wang zhiping qiu Institute of Solid Mechanics Beihang University QIAN-Xuesen Laboratory of Space Technology China Accademy of Space Technology

The probabilistic damage identification problem with uncertainty in the FE model parameters, external-excitations and measured acceleration responses is studied. The uncertainty in the system is concerned with normally distributed random variables with zero mean value and given covariance. Based on the theoretical model and the measured acceleration responses, the probabilistic structural models in undamaged and damaged states are obtained by two-stage model updating, and then the Probabilities of Damage Existence （PDE） of each element are calculated as the damage criterion. The influences of the location of sensors on the damage identification results are also discussed, where one of the optimal sensor placement techniques, the effective independence method, is used to choose the nodes for measurement. The damage identification results by different numbers of measured nodes and different damage criterions are compared in the numerical example.

关键词： damage identification model updating uncertainty probabilistic approach dynamic response

Six sigma robust design optimization for thermal protection system of hypersonic vehicles based on successive response surface method

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Chinese Journal of Aeronautics 2019年第9期32卷 2095-2108页

作者： Jingjing ZHU Xiaojun WANG Haiguo ZHANG Yuwen LI Ruixing WANG zhiping qiu Institute of Solid Mechanics School of Aeronautic Science and EngineeringBeihang UniversityBeijing 100083China The 704 Research Institute of CSIC Shanghai 200031China Institute of Mechanics Chinese Academy of ScienceBeijing 100190China

Lightweight design is important for the Thermal Protection System(TPS) of hypersonic vehicles in that it protects the inner structure from severe heating environment. However, due to the existence of uncertainties in material properties and geometry, it is imperative to incorporate uncertainty analysis into the design optimization to obtain reliable results. In this paper, a six sigma robust design optimization based on Successive Response Surface Method(SRSM) is established for the TPS to improve the reliability and robustness with considering the uncertainties. The uncertain parameters related to material properties and thicknesses of insulation layers are considered and characterized by random variables following normal distributions. By employing SRSM, the values of objective function and constraints are approximated by the response surfaces to reduce computational cost. The optimization is an iterative process with response surfaces updating to find the true optimal solution. The optimization of the nose cone of hypersonic vehicle cabin is provided as an example to illustrate the feasibility and effectiveness of the proposed method.

关键词： Hypersonic vehicle Six sigma robust optimization Successive response surface Thermal protection system Uncertainty