Hybrid Function-Based Moment Method for Luffing Angular Response of Dual Automobile Crane System With Random and Interval Parameters

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Bin Zi ◽  
Bin Zhou ◽  
Weidong Zhu ◽  
Daoming Wang
Keyword(s):  
Moment Method ◽  
Uncertain Parameters ◽  
Random Interval ◽  
Random Parameters ◽  
Interval Parameters ◽  
Angular Response ◽  
Novel Approach ◽  
Hybrid Function ◽  
Interval Perturbation Method ◽  
Dual Automobile Cranes System

A hybrid uncertain parameter model (HUPM) is introduced to predict the luffing angular response (LAR) field of the dual automobile cranes system (DACS) with random and interval parameters. In the model, all random parameters with specified probabilistic distributions comprise a random vector, while all interval parameters with determined bounds comprise an interval vector. A hybrid uncertain LAR equilibrium equation is established, and a novel approach named as hybrid perturbation compound function-based moment method is proposed based on the HUPM. In the hybrid perturbation compound function-based moment method, the expression of LAR is developed according to the random interval perturbation compound function-based method. More, by using the random interval compound function-based moment method and the monotonic technique, the expectations and variances of the bounds for LAR are calculated. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results on different uncertain cases of the DACS demonstrate the feasibility and efficiency of the proposed algorithm. The proposed method is proved to be an effective engineering method to quantify the effects of hybrid uncertain parameters on the LAR of DACS.

Multiple Dynamic Response Patterns of Flexible Multibody Systems With Random Uncertain Parameters

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Zhe Wang ◽  
Qiang Tian ◽  
Haiyan Hu
Keyword(s):  
Dynamic Response ◽  
Multibody System ◽  
Uncertain Parameters ◽  
Response Patterns ◽  
Algebraic Equations ◽  
Flexible Multibody System ◽  
Random Parameters ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Flexible Multibody

The mechanisms with uncertain parameters may exhibit multiple dynamic response patterns. As a single surrogate model can hardly describe all the dynamic response patterns of mechanism dynamics, a new computation methodology is proposed to study multiple dynamic response patterns of a flexible multibody system with uncertain random parameters. The flexible multibody system of concern is modeled by using a unified mesh of the absolute nodal coordinate formulation (ANCF). The polynomial chaos (PC) expansion with collocation methods is used to generate the surrogate model for the flexible multibody system with random parameters. Several subsurrogate models are used to describe multiple dynamic response patterns of the system dynamics. By the motivation of the data mining, the Dirichlet process mixture model (DPMM) is used to determine the dynamic response patterns and project the collocation points into different patterns. The uncertain differential algebraic equations (DAEs) for the flexible multibody system are directly transformed into the uncertain nonlinear algebraic equations by using the generalized-alpha algorithm. Then, the PC expansion is further used to transform the uncertain nonlinear algebraic equations into several sets of nonlinear algebraic equations with deterministic collocation points. Finally, two numerical examples are presented to validate the proposed methodology. The first confirms the effectiveness of the proposed methodology, and the second one shows the effectiveness of the proposed computation methodology in multiple dynamic response patterns study of a complicated spatial flexible multibody system with uncertain random parameters.

Reliability-Based Analysis of Frequency of Closed-Loop Vibration Control Systems with Interval Parameters

2014 ◽  
Vol 644-650 ◽  
pp. 53-57
Author(s):  
Jin Gang Liu ◽  
Shi Peng Wang ◽  
Zhong Jun Zhang ◽  
Da Wei Jin ◽  
Feng Xiao Huang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Vibration Control ◽  
Control Systems ◽  
Present Method ◽  
Closed Loop ◽  
Uncertain Parameters ◽  
Convex Model ◽  
Interval Parameters ◽  
Closed Loop Systems ◽  
Random Eigenvalues

Using the convex model theory, the reliability-based analysis of frequency of the vibration control problem of structures with Interval parameters is discussed. Based on the theory of perturbation method, reliability analysis, and PNET method, the method of reliability-based analysis of eigenvalues of closed-loop vibration control systems with uncertain parameters is studied. And the distribution function of the random eigenvalues will not be computed other than their means and variances. The standard deviations of eigenvalues of the uncertain closed-loop systems can be used to estimate the reliability of frequency. The numerical results show that the present method is effective.

Overestimation Analysis of Interval Finite Element for Structural Dynamic Response

2019 ◽  
Vol 11 (04) ◽  
pp. 1950035
Author(s):  
Tuanjie Li ◽  
Hangjia Dong ◽  
Xi Zhao ◽  
Yaqiong Tang
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Structural Parameters ◽  
Upper And Lower Bounds ◽  
Response Analysis ◽  
Uncertain Parameters ◽  
Engineering Structures ◽  
Structural Dynamic ◽  
Dynamic Response Analysis ◽  
Interval Parameters

Dynamic response analysis plays an important role for the structural design. For engineering structures, there exist model inaccuracies and structural parameters uncertainties. Consequently, it is necessary to express these uncertain parameters as interval variables and introduce the interval finite element method (IFEM), in which the elements in stiffness matrix, mass matrix and damping matrix are all the function of interval parameters. The dependence of interval parameters leads to overestimation of dynamic response analysis. In order to reduce the overestimation of IFEM, the element-based subinterval perturbation for static analysis is applied to dynamic response analysis. According to the interval range, the interval parameters are divided into different subintervals. With permutation and combination of each subinterval, the upper and lower bounds of displacement response are obtained. Because of the large number of degrees of freedom and uncertain parameters, the Laplace transform is used to evaluate the dynamic response for avoiding to frequently solve the interval finite element linear equations. The numerical examples illustrate the validity and feasibility of the proposed method.

Optimum Design of Mechanical Systems Involving Interval Parameters

2002 ◽  
Vol 124 (3) ◽  
pp. 465-472 ◽  
Author(s):  
S. S. Rao ◽  
Lingtao Cao
Keyword(s):  
Optimum Design ◽  
Mechanical Systems ◽  
Distribution Functions ◽  
Interval Methods ◽  
System Response ◽  
Uncertain Parameters ◽  
Engineering Systems ◽  
Interval Parameters ◽  
Computational Aspects ◽  
Range Of Values

The imprecision or uncertainty present in many engineering systems can be modeled using probabilistic, fuzzy or interval methods. This work presents the optimum design of uncertain mechanical systems using interval analysis for the prediction of system response. Each of the uncertain parameters is defined by a range of values. Since the interval ranges of response parameters is found to increase with an increase in the number and/or ranges of input interval parameters with the use of interval arithmetic operations, a truncation procedure is used to obtain approximate but reasonably accurate response of the system. This procedure is found to be simple, economical and fairly accurate. The optimum design of a brake is considered to illustrate the computational aspects of the methods. The procedures outlined in this work are quite general and can be used for the design of any uncertain mechanical system when either the probability distribution functions or the preference information of uncertain parameters are unknown.

Probabilistic Interval Perturbation Methods for Hybrid Uncertain Acoustic Field Prediction

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu ◽  
Jian Liu
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Perturbation Method ◽  
Moment Method ◽  
Sound Pressure ◽  
Perturbation Methods ◽  
Interval Matrix ◽  
Matrix Perturbation ◽  
Random Interval ◽  
Acoustic Cavity

For the hybrid uncertain acoustic field prediction with random and interval variables, the random interval dynamic equilibrium equation is established and two hybrid probabilistic interval perturbation methods, named as hybrid perturbation Monte Carlo method (HPMCM) and hybrid perturbation vertex method (HPVM), are present. In HPMCM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and Monte Carlo method. In HPVM, the intervals of expectation and variance of sound pressure are calculated by a combination of the random interval matrix perturbation method, the random interval moment method and the vertex method. Numerical results on a 2D acoustic tube, the 2D acoustic cavity of a car and a 3D acoustic cavity verify the effectiveness and the high efficiency of HPVM when compared with HPMCM. HPVM can be considered as an effective engineering method to quantify the effects of parametric uncertainty on the sound pressure response.

scholarly journals Computational Method and Simulation of Reliability for Series, Parallel, and k-Out-of-n Systems with Interval Parameters

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Yongfeng Fang ◽  
Kong Fah Tee ◽  
Zhengwei Cheng ◽  
Xu Yong
Keyword(s):  
System Reliability ◽  
Reliability Index ◽  
Computational Method ◽  
Voting Systems ◽  
Calculation Methods ◽  
Random Parameters ◽  
Interval Parameters ◽  
Reliability Calculation ◽  
Interval Reliability ◽  
Voting System

For series, parallel, and k-out-of-n voting system reliability calculation methods, the six σ principles have been proposed in this study to derive the interchange relationship between interval parameters and random parameters. The interval reliability index can be expressed in the function of the random reliability index. The interval reliability index can then be transformed into a random reliability index. The computational method of the reliability for series, parallel, and k-out-of-n voting systems with interval parameters is established. Finally, it has been shown that the proposed method is rational, practical, and applicable with two engineering practical simulations.

Static Response Analysis of Uncertain Structures With Large-Scale Unknown-But-Bounded Parameters

2021 ◽  
Vol 13 (01) ◽  
pp. 2150004
Author(s):  
Tonghui Wei ◽  
Feng Li ◽  
Guangwei Meng ◽  
Wenjie Zuo
Keyword(s):  
Large Scale ◽  
Taylor Series Expansion ◽  
Upper And Lower Bounds ◽  
Response Analysis ◽  
Original Structure ◽  
Uncertain Parameters ◽  
Static Response ◽  
Interval Parameters ◽  
Structural Problems ◽  
Function Decomposition

This paper proposes an interval finite element method based on function decomposition for structural static response problems with large-scale unknown-but-bounded parameters. When there is a large number of uncertain parameters, it will lead to the curse of dimensionality. The existing Taylor expansion-based methods, which is often employed to deal with large-scale uncertainty problems, need the sensitivity information of response function to uncertain parameters. However, the gradient information may be difficult to obtain for some complicated structural problems. To overcome this drawback, univariate decomposition expression (UDE) and bivariate decomposition expression (BDE) are deduced by the higher-order Taylor series expansion. The original structure function with [Formula: see text]-dimensional interval parameters is decomposed into the sum of several low-dimensional response functions by UDE or BDE, each of which has only one or two interval parameters while the other interval parameters are replaced by their midpoint values. Therefore, solving the upper and lower bounds of the [Formula: see text]-dimensional function can be converted into solving those of the one- or two-dimensional functions, which savethe calculation costs and can be easily implemented. The accuracy and efficiency of the new method are verified by three numerical examples.

A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 351-359
Author(s):  
Adel Ouannas ◽  
Samir Bendoukha ◽  
Abdulrahman Karouma ◽  
Salem Abdelmalek
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Projective Synchronization ◽  
The Novel ◽  
Fractional Order Systems ◽  
Function Projective Synchronization ◽  
Novel Approach ◽  
Full State ◽  
Hybrid Function ◽  
New Type

AbstractReferring to incommensurate fractional-order systems, this paper proposes a new type of chaos synchronization by combining full state hybrid function projective synchronization (FSHFPS) and inverse full state hybrid function projective synchronization (IFSHFPS). In particular, based on stability theory of linear integer-order systems and stability theory of linear fractional-order systems, the co-existence of FSHFPS and IFSHFPS between incommensurate fractional chaotic (hyperchaotic) systems is proved. To illustrate the capabilities of the novel approach proposed herein, numerical and simulation results are given.

scholarly journals Pseudo-Valid Cutting Planes for Two-Stage Mixed-Integer Stochastic Programs with Right-Hand-Side Uncertainty

2020 ◽  
Vol 68 (4) ◽  
pp. 1199-1217
Author(s):  
Ward Romeijnders ◽  
Niels van der Laan
Keyword(s):  
Cutting Planes ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Random Parameters ◽  
Two Stage ◽  
Stochastic Programs ◽  
Second Stage ◽  
Right Hand ◽  
Novel Approach ◽  
Decision Variables

Cutting planes need not be valid in stochastic integer optimization. Many practical problems under uncertainty, for example, in energy, logistics, and healthcare, can be modeled as mixed-integer stochastic programs (MISPs). However, such problems are notoriously difficult to solve. In “Pseudo-Valid Cutting Planes for Two-Stage Mixed-Integer Stochastic Programs with Right-Hand-Side Uncertainty,” Romeijnders and van der Laan introduce a novel approach to solve two-stage MISPs. Instead of using exact cuts that are always valid, they propose to use pseudo-valid cutting planes for the second-stage feasible regions that may cut away feasible integer second-stage solutions for some scenarios and may be overly conservative for others. The advantage of using such cutting planes is that the approximating problem remains convex in the first-stage decision variables and thus can be solved efficiently. Moreover, the performance of these cutting planes is good if the variability of the random parameters in the model is large enough.

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.

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