An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels

Wu, Jinglai; Luo, Zhen; Zhang, Yunqing; Zhang, Nong

doi:10.1016/j.apm.2014.02.012

Cited by 80 publications

(46 citation statements)

References 20 publications

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“…Recently, there have been some published papers which consider the uncertainty in the analysis or optimization of multi-body systems [31][32][33][34]. The proposed method in this paper can also be extended for use in uncertain multi-body dynamics systems governed using differential algebraic equations (DAEs).…”

Section: Discussionmentioning

confidence: 89%

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

Liu

2015

Sci. China Phys. Mech. Astron.

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This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing approximation interval methods. We consider trigonometric approximation polynomials of three types: both cosine and sine functions, the sine function, and the cosine function. Thus, special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results. The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method. non-intrusive interval method, dynamic response analysis, uncertain nonlinear systems, trigonometric polynomial approximation, interval arithmetic PACS number(s): 05.10.-a, 05.45.-a, 05.45.Tp, 45.10.-b, 45.40.-f Citation: Liu Z Z, Wang T S, Li J F. A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems. Sci China-Phys Mech Astron, 2015, 58: 044501,

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Section: Discussionmentioning

confidence: 89%

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

Liu

2015

Sci. China Phys. Mech. Astron.

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“…In this section, a new sampling method will be proposed, based on both the tensor product method and the zeros of Chebyshev polynomials (Wu et al 2013(Wu et al , 2014, termed the Chebyshev tensor product (CTP) method. As discussed above, the Chebyshev polynomials can be used to improve numerical accuracy with a relatively small number of samples.…”

Section: Chebyshev Tensor Product Methodsmentioning

confidence: 99%

“…A continuous function can be expanded by the Chebyshev series (Wu et al 2013(Wu et al , 2014, which has higher numerical accuracy than the truncated Taylor series. For a one-dimensional problem, it requires (n + 1) sampling points to construct a polynomial model with degree n, which corresponds to the zeros of an (n + 1)-order Chebyshev polynomial.…”

Section: Introductionmentioning

confidence: 99%

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

Luo

Zhang

et al. 2014

Engineering Optimization

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The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the 'hypercube' polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the 'simplex' polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

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“…A new design optimization framework for suspension systems considering the kinematic characteristics, such as the camber angle, caster angle, kingpin inclination angle, and toe angle in the presence of uncertainties is proposed (Wu, et al, 2014). A general method of the kinematic synthesis of suspension mechanisms is presented (Suh, 1989).…”

Section: Introductionmentioning

confidence: 99%

On the analysis of double wishbone suspension regarding steering input and anti-dive/lift effect

Tanık

Parlaktaş

2016

JAMDSM

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In this study, a novel kinematic analysis procedure of the double wishbone suspension mechanism regarding steering input is proposed. In the previous study, published by the authors, the double wishbone mechanism was investigated disregarding steering input. To the best of our knowledge, there is no analytical method available in the literature for the analysis of double wishbone suspension mechanism regarding steering input. Initially, analysis of the mechanism for variable steering input, while keeping wheel travel fixed is considered. Then, kinematic analysis is performed analytically for the ultimate case of two inputs. Analysis simultaneously for both variable steering and variable wheel travel is presented. The essential parameters; camber, caster, kingpin angles are defined according to the kinematic model. For verification, a synthesized mechanism is established in Catia software and same results with the analytical model are obtained. Another presented novel analytical approach is anti-dive/lift analysis of the double wishbone mechanism.

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An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels

Cited by 80 publications

References 20 publications

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

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

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

On the analysis of double wishbone suspension regarding steering input and anti-dive/lift effect

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