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

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Bin Zi ◽  
Bin Zhou ◽  
Weidong Zhu
Keyword(s):  
Perturbation Method ◽  
High Order ◽  
Field Problem ◽  
Interval Model ◽  
First Order ◽  
Angular Response ◽  
Interval Variables ◽  
Bounded Uncertainty ◽  
Interval Perturbation Method ◽  
The Impact

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.

Hybrid Compound Function/Subinterval Perturbation Method for Kinematic Analysis of a Dual-Crane System With Large Bounded Uncertainty

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Bin Zhou ◽  
Bin Zi ◽  
Yuan Li ◽  
Weidong Zhu
Keyword(s):  
Perturbation Method ◽  
Kinematic Analysis ◽  
Neumann Series ◽  
Large Interval ◽  
Hybrid Compound ◽  
Numerical Examples ◽  
First Order ◽  
The Monte Carlo Method ◽  
Interval Variables ◽  
Interval Perturbation Method

Abstract By introducing the subinterval perturbation method (SIPM), a hybrid compound function/subinterval perturbation method (HCFSPM) is presented for a dual-crane system (DCS) with large interval variables. The HCFSPM employs the SIPM to decompose a large interval variable into several subinterval variables with small uncertain levels. The interval kinematic compound function vectors and their inverses are approximated by the first-order Taylor and Neumann series, respectively. Based on the monotonic technique, the bounds of original luffing angle vectors are derived. Compared with the first-order compound function/interval perturbation method and the Monte Carlo method, numerical examples verify the effectiveness of the HCFSPM at conducting uncertain kinematic analysis of the DCS, especially when it comes to large uncertain levels.

STOCHASTIC POST-BUCKLING OF FRAMES USING KOITER'S METHOD

2006 ◽  
Vol 06 (03) ◽  
pp. 333-358 ◽  
Author(s):  
B. W. SCHAFER ◽  
L. GRAHAM-BRADY
Keyword(s):  
Monte Carlo ◽  
Perturbation Method ◽  
Perturbation Expansion ◽  
Random Variable ◽  
Order Perturbation ◽  
Initial Slope ◽  
First Order ◽  
Post Buckling ◽  
The Impact ◽  
First Order Perturbation

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

Interval Perturbation Method to Structural Non-Probabilistic Reliability Analysis

2013 ◽  
Vol 712-715 ◽  
pp. 1527-1530 ◽  
Author(s):  
Zuo Zhen Sun ◽  
Guang Wei Meng ◽  
Feng Li ◽  
Li Ming Zhou
Keyword(s):  
Lower Bound ◽  
Perturbation Method ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Structural Parameters ◽  
Probability Model ◽  
Uncertain Variable ◽  
Interval Model ◽  
Interval Parameters ◽  
Interval Perturbation Method

In structural non-probabilistic reliability analysis, the uncertain structural parameters are assumed to be the interval parameters. The commonly used probability model will lose accuracy when there is not enough experimental date for the reliability analysis. Conversely, the interval model only requires the upper and lower bound of the uncertain variable, which is more reasonable compared with the probabilistic model. The interval perturbation method is applied in this paper to compute the non-probabilistic reliability index, where the interval expansion problem has been effectively controlled. The precision of computing the reliability index is effectively improved, solving the problem of the non-probabilistic reliability index in a new way. The numerical results prove that this method is effective and feasible.

Interval XFEM and its Application to Fracture Mechanics Problems

2012 ◽  
Vol 562-564 ◽  
pp. 1007-1011
Author(s):  
Tian Tang Yu ◽  
Lu Yang Shi
Keyword(s):  
Fracture Mechanics ◽  
Perturbation Method ◽  
Linear Elastic Fracture Mechanics ◽  
Uncertain Parameters ◽  
Linear Elastic ◽  
Interval Variables ◽  
Elastic Fracture ◽  
Interval Perturbation Method

This paper presents the results of a combination of interval perturbation method and the XFEM (IXFEM) to analyze Linear Elastic Fracture Mechanics problem. Uncertain parameters were expressed as interval variables and sub-intervals perturbation for the elements employed in the analysis. The IXFEM method proved very robust in handling parameters uncertainties in fracture problems.

VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

2001 ◽  
Vol 09 (04) ◽  
pp. 1259-1286 ◽  
Author(s):  
MIGUEL R. VISBAL ◽  
DATTA V. GAITONDE
Keyword(s):  
Three Dimensional ◽  
Radiation Condition ◽  
Higher Order ◽  
High Order ◽  
High Frequencies ◽  
Decomposition Strategies ◽  
The Impact ◽  
Spurious Modes ◽  
Very High ◽  
Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

Optimal Capacitors Placement of Distribution Systems Using 2nd Order Power Loss Sensitivity Analysis and Hierarchical Clustering

2014 ◽  
Vol 986-987 ◽  
pp. 377-382 ◽  
Author(s):  
Hui Min Gao ◽  
Jian Min Zhang ◽  
Chen Xi Wu
Keyword(s):  
Sensitivity Analysis ◽  
Hierarchical Clustering ◽  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Reactive Power ◽  
Digital Simulation ◽  
Second Order ◽  
First Order ◽  
The Impact

Heuristic methods by first order sensitivity analysis are often used to determine location of capacitors of distribution power system. The selected nodes by first order sensitivity analysis often have virtual high by first order sensitivities, which could not obtain the optimal results. This paper presents an effective method to optimally determine the location and capacities of capacitors of distribution systems, based on an innovative approach by the second order sensitivity analysis and hierarchical clustering. The approach determines the location by the second order sensitivity analysis. Comparing with the traditional method, the new method considers the nonlinear factor of power flow equation and the impact of the latter selected compensation nodes on the previously selected compensation location. This method is tested on a 28-bus distribution system. Digital simulation results show that the reactive power optimization plan with the proposed method is more economic while maintaining the same level of effectiveness.

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