A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

Liu, ZhuangZhuang; Li, Junfeng

doi:10.1007/s11433-014-5641-8

Cited by 11 publications

(5 citation statements)

References 27 publications

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“…Although the approximation accuracy of the higher order polynomial-based Fourier polynomial model is suitable for strong non-linear problems compared to the traditional regression polynomial models (TRP) [30]- [32], especially for periodic problems, it is inappropriate for linear responses. To illustrate this point, consider a one-dimensional function g (x) = 2 + arctan x with the variable x ∈ [−1, 1] as an example, and the Fourier series-based polynomial approximation shown in Fig.…”

Section: B Augmented Fourier Series-based Polynomial Surrogate Modelmentioning

confidence: 99%

Novel Interval Parameter Identification Method Using Augmented Fourier Series-Based Polynomial Surrogate Model

Wang

Zhao

2019

IEEE Access

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Traditional probabilistic-based parameter identification methods cannot operate in practical engineering systems without sufficient available measurements. To overcome this drawback, a novel augmented Fourier polynomial-based interval parameter identification method is proposed in this paper. First, a novel augmented Fourier series-based polynomial surrogate model is established to precisely describe the mathematical relationship between the identified parameters and system responses. Subsequently, to improve the efficiency of the identification procedure, an improved interval-based multi-objective optimization strategy is designed to seek the nominal and fluctuation value of the parameter interval simultaneously. Eventually, the numerical and experimental examples are provided to verify the feasibility of the proposed method. The proposed method can achieve competitive results on various examples, the mass-spring system, and steel plate structure, compared with the previous methods. Moreover, satisfactory results are also obtained when applied to a space truss structure. The identification results demonstrate the feasibility and reliability of the proposed interval parameter identification method. INDEX TERMS Interval theory, parameter identification, augmented Fourier series-based surrogate model, multi-objective optimization strategy.

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Section: B Augmented Fourier Series-based Polynomial Surrogate Modelmentioning

confidence: 99%

Novel Interval Parameter Identification Method Using Augmented Fourier Series-Based Polynomial Surrogate Model

Wang

Zhao

2019

IEEE Access

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“…From Equation (19), the corresponding coefficient vector can be calculated numerically using the Gauss elimination method. Though the approximation accuracy of the higher order polynomial-based Fourier polynomial model is more suitable for strong non-linear problems than the traditional regression polynomial models (TRP) [14,21], especially for periodic problems, it is inappropriate for linear responses. Therefore, in order to make the Fourier series-based polynomial model suitable for linear response problems, the model should be augmented with a linear polynomial, given as [22]:…”

Section: Augmented Fourier Series-based Polynomial Surrogate Modelmentioning

confidence: 99%

A General Integrated Method for Design Analysis and Optimization of Missile Structure

Wang

Yang²,

Guo

et al. 2019

Algorithms

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In the demonstration phase of a missile scheme, to obtain the optimum proposal, designers need to modify the parameters of the overall structure frequently and significantly, and perform the structural analysis repeatedly. In order to reduce the manual workload and improve the efficiency of research and development, a general integrated method of missile structure modeling, analysis and optimization was proposed. First, CST (Class and Shape transformation functions) parametric method was used to describe the general structure of the missile. The corresponding software geometric modeling and FEM (Finite Element Method) analyzing of the missile were developed in C/C++ language on the basis of the CST parametric method and UG (Unigraphics) secondary development technology. Subsequently, a novel surrogate model-based optimation strategy was proposed to obtain a relatively light mass missile structure under existing shape size. Eventually, different missile models were used to verify the validity of the method. After executing the structure modeling, analysis and optimization modules, satisfactory results can be obtained that demonstrated the stability and adaptability of the proposed method. The method presented saves plenty of time comparing to the traditional manual modeling and analysis method, which provides a valuable technique to improve the efficiency of research and development.3D modeling program based on the UG secondary development technology, which has improved the modeling efficiency. Wang et al. [4] used the technology of UG/KF secondary development for the automatic modeling of the wind turbine blades, and the aerodynamic characteristics of the impeller were analyzed by the Fluent software. Moreover, He et al. [5] implemented the parametric modeling of the blended-wing-body underwater glider structure by using UG secondary development technology and studied its structural performance with ANSYS. Therefore, UG is considered as an excellent tool that can realize the integration of modeling and simulation.Meanwhile, airfoils have been parameterized in a wide variety of ways. Among them, CST is considered to be a more effective method, which can represent the different types of geometries in a generic way with fewer parameters. Kulfan and Bussoletti [6] proposed a parameterization method that based on class and shape transformation functions, which has the advantages of high precision and fewer variables. The CST method is a powerful and versatile means to describe complex aeronautical shapes ranging from 2D airfoils to 3D geometries of aircraft using analytical functions. Since it has been introduced, this parameterization method has been the subject of several studies [7]. Marco Ceze of the University of Michigan studied the characteristics of CST parameterization and found that the ill-conditioning of parameterization when fitting airfoil with high-order Bernstein polynomials [8]. Straathof et al. proposed a parameterization method that used a combination of Bernstein polynomials and B-splines to allow...

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“…overestimation phenomenon). In interval algorithm research, numerous proxy models [20][21][22][23]36 have been proposed to construct interval algorithms. The previous Taylor expansion function method involves the first-and second-order differentials of independent variables with respect to uncertain parameters.…”

Section: Chebyshev Interval Function Algorithmsmentioning

confidence: 99%

“…Fast modelling method is also called proxy model method, which includes polynomial proxy model, mobile least squares proxy model, radial basis function proxy model, Gauss process (or kriging) proxy model, neural network and support vector regression. In interval algorithm research, numerous proxy models [20][21][22][23][24] have been proposed to construct interval algorithms. Agent model, also known as approximation model, is an important tool in approximation modelling.…”

Section: Introductionmentioning

confidence: 99%

Kinematics uncertainty analysis of mine bolter manipulator based on Chebyshev interval algorithms

Zhang

Huang

Meng

et al. 2019

Advances in Mechanical Engineering

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A mine bolter is a fast, safe and economical support equipment, in which the manipulator is the key component for its parallel operation. In this study, the kinematics of mine bolter manipulator is selected as the research object. Aiming at the problem of the dynamic system response estimation of positive solution matrix with uncertain parameters, an interval estimation analysis method based on Chebyshev polynomial is proposed. The response envelope interval of the forward kinematics solution matrix of the manipulator with uncertain parameters is investigated using three types of surrogate models: scanning method, tensor product and collocation method. The feasibility and efficiency of the proposed algorithm are proved by a prototype test. The study of response interval with uncertain parameters has become a new method for predicting the spatial trajectory tracking and location of the manipulator to ensure that its prediction error is minimal.

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A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

Cited by 11 publications

References 27 publications

Novel Interval Parameter Identification Method Using Augmented Fourier Series-Based Polynomial Surrogate Model

Novel Interval Parameter Identification Method Using Augmented Fourier Series-Based Polynomial Surrogate Model

A General Integrated Method for Design Analysis and Optimization of Missile Structure

Kinematics uncertainty analysis of mine bolter manipulator based on Chebyshev interval algorithms

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