The Dynamic Analysis of Multibody Systems with Uncertain Parameters Using Interval Method

Wu, Jing; Zhang, Yunqing

doi:10.4028/www.scientific.net/amm.152-154.1555

Cited by 7 publications

(4 citation statements)

References 10 publications

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“…H Â q 1 , : : : , Â q k cos j 1 Â q 1 : : : cos j k Â q k .j 1 , : : : , j k D 0, 1 : : : n/, (47) where Â l denotes the interpolation points, which are determined by Equation (34). m is the order of Mehler integral.…”

Section: Chebyshev Methods For Solving Nonlinear Functions With Intervmentioning

confidence: 99%

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Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions

Luo

Zhang

et al. 2013

Numerical Meth Engineering

177

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SUMMARYThis study proposes a new uncertain analysis method for multibody dynamics of mechanical systems based on Chebyshev inclusion functions The interval model accounts for the uncertainties in multibody mechanical systems comprising uncertain‐but‐bounded parameters, which only requires lower and upper bounds of uncertain parameters, without having to know probability distributions. A Chebyshev inclusion function based on the truncated Chebyshev series, rather than the Taylor inclusion function, is proposed to achieve sharper and tighter bounds for meaningful solutions of interval functions, to effectively handle the overestimation caused by the wrapping effect, intrinsic to interval computations. The Mehler integral is used to evaluate the coefficients of Chebyshev polynomials in the numerical implementation. The multibody dynamics of mechanical systems are governed by index‐3 differential algebraic equations (DAEs), including a combination of differential equations and algebraic equations, responsible for the dynamics of the system subject to certain constraints. The proposed interval method with Chebyshev inclusion functions is applied to solve the DAEs in association with appropriate numerical solvers. This study employs HHT‐I3 as the numerical solver to transform the DAEs into a series of nonlinear algebraic equations at each integration time step, which are solved further by using the Newton–Raphson iterative method at the current time step. Two typical multibody dynamic systems with interval parameters, the slider crank and double pendulum mechanisms, are employed to demonstrate the effectiveness of the proposed methodology. The results show that the proposed methodology can supply sufficient numerical accuracy with a reasonable computational cost and is able to effectively handle the wrapping effect, as cosine functions are incorporated to sharpen the range of non‐monotonic interval functions. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Chebyshev Methods For Solving Nonlinear Functions With Intervmentioning

confidence: 99%

“…For the slider crank mechanism , both the geometry parameters and external force are considered as interval parameters. Firstly, we only consider the length of the crank as an interval parameter, with a view to obtaining the range of slider displacement in the problem.…”

Section: Numerical Applicationmentioning

confidence: 99%

Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions

Luo

Zhang

et al. 2013

Numerical Meth Engineering

177

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“…In recent years, some new research methods for interval analysis have been developed. Wu et al [84,85] studied the dynamic response by using the Chebyshev polynomial interval method. e advantage of this method is that it does not need to determine the probability distribution of parameters but only needs to determine the parameter interval range and obtain the system response interval by solving the parameter equation.…”

Section: Interval Analysismentioning

confidence: 99%

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

Zheng

Deng

et al. 2019

Shock and Vibration

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Statistical energy analysis (SEA) can accurately describe the average vibration characteristics through system energy flow and transmission feedback. It is a powerful tool to solve the problem of high-frequency acoustics-vibration. SEA is widely used in vehicles, ships, aviation, and other transportation engineering fields. However, the expansion of SEA, based on the assumption of modal equipartition and weak coupling, is limited to the intermediate frequency. Although the SEA basic theory can be extended by relaxing the hypothesis conditions or the analysis of the medium-frequency acoustics-vibration can be carried out using the finite element method (FEM) and SEA mixing method, there are still many challenges associated with these options. To improve the basic theory of SEA and knowledge of intermediate frequency extension methods, as well as attract the attention of domestic scholars, this paper describes classical SEA and intermediate frequency extension methods. First, coupling loss factor (CLF) error propagation and parameter acquisition in classical SEA are introduced, and the three relative error calculation methods of CLF are compared. Then, the method of obtaining parameters is described from three aspects of energy transfer, input load, and modal density. Second, SEA intermediate frequency extension technology (experimental statistical energy analysis (ESEA), finite element statistical energy analysis (FE-SEA), statistical modal energy distribution analysis (SMEDA), and waveguide analysis (WGA)) are introduced. Neutron structure assembly and modeling, interval and mixed interval analysis, interval variable and mixed interval variable response are also described, so as to justify the development of a hybrid, large-scale interval algorithm. Finally, the engineering application of the above method is introduced, the limitations and shortcomings of SEA and intermediate frequency extension methods are reviewed, and unsolved problems are further discussed.

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“…To address these shortcomings, various approaches are used [26][27][28][29][30][31][32]. The control constructed for the deterministic system is applied to the interval system.…”

Section: Literature Reviewmentioning

confidence: 99%

Research of controllability of dynamical systems with constraints on control using interval mathematics

Jomartova

Nikulin

Karymsakova

2019

JMMCS

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The article is devoted to the actual problem of the mathematical theory of controllability. It investigated the mathematical model of control, described by ordinary differential equations, taking into account the restrictions on the control. As is known, the problem of finding controllability of dynamic systems with phase and control constraints is still relevant. There are many approaches to solving the determined problem. The classical control theory is being modified today and it finds new methods for solving problems of controllability, optimal control and stability, the solutions obtained. In the course of studying the controllability of a dynamic system, the authors applied interval mathematics, which made it possible to obtain an effective controllability criterion for dynamic systems with phase and control constraints. This method is applicable for a certain class of problems in which the data are described by the normal distribution law. The constructiveness of the proposed criterion is demonstrated in two examples. The first is a model problem described by 2-nd order equations. The second is an electromechanical tracking system of an automatic manipulator, described by equations of the 3rd order. Thus, for dynamic systems, we obtained a sufficient condition for controllability.

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The Dynamic Analysis of Multibody Systems with Uncertain Parameters Using Interval Method

Cited by 7 publications

References 10 publications

Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions

Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

Research of controllability of dynamical systems with constraints on control using interval mathematics

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