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, Anhui Province 230009 China binzi.cumt@163.com

Bin Zhou

Hefei, Anhui Province, 230009, China Hefei, Anhui Province 230009 China zhoubin13865923505@163.com

Weidong Zhu

Department of Mechanical Engineering 1000 Hilltop Circle Baltimore, MD 21250 wzhu@umbc.edu

1Corresponding author.

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

ASME 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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