Luffing angular response field prediction of the DACS with narrowly random payload parameters based on a modified hybrid random method

Deterministic kinematic modeling and stochastic luffing angular response field prediction of the dual automobile cranes system (DACS) are studied in this paper. For the response analysis of the DACS with deterministic information, the inverse kinematics are analyzed. For the prediction of luffing angular response field of the DACS with narrowly random payload parameters, a narrowly random model is introduced. In the narrowly random model, the payload parameters with certain probability distribution are modeled as random variables. Based on the narrowly random model, the equilibrium equation of luffing angular response vector of the DACS with random parameters is derived. Then a perturbation-based random composite function method (PRCFM) is proposed. Based on the PRCFM, the first-order Neumann series expansion and the proposed random variable functional moment method, a modified hybrid random method (MHRM) for the luffing angular response field prediction of the DACS with narrowly random payload parameters is proposed. In the MHRM, the statistical characteristics of luffing angular response vector are determined. Numerical results show the feasibility and efficiency of the MHRM for solving the narrowly stochastic DACS problems compared with the Monte Carlo method. The effects of different random parameters (y, z, \(\theta \)) on the DACS luffing angular response field are also investigated deeply, and numerical results indicate the impact on the variances made by the randomness in the random payload parameter y is larger than those made by random payload parameters z and \(\theta \).