Research Papers

Modified First-Order Compound Function-Based Interval Perturbation Method for Luffing Angular Response of Dual Automobile Crane System With Interval Variables

[+] Author and Article Information
Bin Zi

School of Mechanical Engineering,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: binzi.cumt@163.com

Bin Zhou

School of Mechanical Engineering,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China;
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: zhoubin13865923505@163.com

Weidong Zhu

Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
e-mail: wzhu@umbc.edu

1Corresponding author.

Manuscript received November 17, 2018; final manuscript received February 18, 2019; published online June 10, 2019. Assoc. Editor: Kristina Wärmefjord.

J. Comput. Inf. Sci. Eng 19(4), 041013 (Jun 10, 2019) (12 pages) Paper No: JCISE-18-1305; doi: 10.1115/1.4043041 History: Received November 17, 2018; Accepted February 19, 2019

The accuracy of conventional crane engineering problems with bounded uncertainty is limited to cases where only first-order terms are retained. However, the impact of high-order terms on the luffing angular response (LAR) may be significant when it comes to compound functions. A modified first-order compound-function-based interval perturbation method (MFCFIPM) is proposed for the prediction of the LAR field of a dual automobile crane system (DACS) with narrowly bounded uncertainty. In an interval model, all uncertain variables with bounded uncertainty comprise an interval vector. The equilibrium equations of the interval LAR vectors of the DACS are established based on the interval model. The MFCFIPM employs the surface rail generation method to expand the compound-function-based vectors. A modified Sherman–Morrison–Woodbury formula is introduced to analyze the impact of the high-order terms of the Neumann series expansion on the LAR field. Several numerical examples are presented to verify the accuracy and the feasibility of the MFCFIPM. The results show that the MFCFIPM can achieve a better accuracy than the first-order compound-function-based interval perturbation method and a higher efficiency than the Monte Carlo method for the LAR field problem with narrow interval variables. The effects of different numbers of interval variables on the LAR field by the MFCFIPM are also investigated.

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Grahic Jump Location
Fig. 1

Schematic of a planar DACS

Grahic Jump Location
Fig. 2

Lower and upper bounds of the LAR of the crane 1 with the four-interval-variable model

Grahic Jump Location
Fig. 3

Lower and upper bounds of the LAR of the crane 2 with the four-interval-variable model



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