An interval perturbation method for exterior acoustic field prediction with uncertain-but-bounded parameters

2014 ◽  
Vol 49 ◽  
pp. 441-449 ◽  
Author(s):  
Chong Wang ◽  
Zhiping Qiu
Keyword(s):  
Perturbation Method ◽  
Acoustic Field ◽  
Interval Perturbation Method

An Iterative Dimension-Wise Approach to the Structural Analysis with Interval Uncertainties

2018 ◽  
Vol 15 (06) ◽  
pp. 1850044 ◽  
Author(s):  
Menghui Xu ◽  
Jianke Du ◽  
Jianbin Chen ◽  
Chong Wang ◽  
Yunlong Li
Keyword(s):  
Structural Analysis ◽  
Perturbation Method ◽  
Interval Analysis ◽  
Acoustic Analysis ◽  
Interval Uncertainties ◽  
Interval Perturbation Method ◽  
Current Interval ◽  
Interval Response ◽  
Expansion Point ◽  
Maximal Points

The structural analysis is inevitably surrounded with uncertainties and the interval analysis is a favorable method if insufficient data is available on uncertainties. The accuracy of current interval analysis methods including the interval perturbation method (IPM), subinterval perturbation method (SIPM) and dimension-wise approach (DWA) depends on a reference point (RP), e.g., the expansion point in IPM, for some problems due to ignoring the co-operative effects of multiple interval inputs on the response. To this end, an iterative dimension-wise approach (IDWA) is proposed. Either the minimal or maximal input vector of the response is identified as an RP by a global update in which a novel RP is dimension-wisely assembled by the minimal or maximal points of all sectional curves of the response surface at a previous RP through a local update. The interval response is calculated by deterministic solvers at the minimal and maximal input vectors. An acoustic analysis problem is studied eventually to validate the effectiveness of the proposed method, from which conclusions are drawn.

Evidence-theory-based kinematic uncertainty analysis of a dual crane system with epistemic uncertainty

2021 ◽  
pp. 1-29
Author(s):  
Bin Zhou ◽  
Bin Zi ◽  
Yishang Zeng ◽  
Weidong Zhu
Keyword(s):  
Uncertainty Analysis ◽  
Perturbation Method ◽  
Epistemic Uncertainty ◽  
Evidence Theory ◽  
Taylor Series Expansion ◽  
Computational Time ◽  
Evidence Based ◽  
Interval Equations ◽  
Basic Probability ◽  
Interval Perturbation Method

Abstract An evidence-theory-based interval perturbation method (ETIPM) and an evidence-theory-based subinterval perturbation method (ETSPM) are presented for the kinematic uncertainty analysis of a dual cranes system (DCS) with epistemic uncertainty. A multiple evidence variable (MEV) model that consists of evidence variables with focal elements (FEs) and basic probability assignments (BPAs) is constructed. Based on the evidence theory, an evidence-based kinematic equilibrium equation with the MEV model is equivalently transformed to several interval equations. In the ETIPM, the bounds of the luffing angular vector (LAV) with respect to every joint FE are calculated by integrating the first-order Taylor series expansion and interval algorithm. The bounds of the expectation and variance of the LAV and corresponding BPAs are calculated by using the evidence-based uncertainty quantification method. In the ETSPM, the subinterval perturbation method is introduced to decompose original FE into several small subintervals. By comparing results yielded by the ETIPM and ETSPM with those by the evidence theory-based Monte Carlo method, numerical examples show that the accuracy and computational time of the ETSPM are higher than those of the ETIPM, and the accuracy of the ETIPM and ETSPM can be significantly improved with the increase of the number of FEs and subintervals.

Response Analysis of Acoustic Field With Convex Parameters

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Baizhan Xia ◽  
Dejie Yu
Keyword(s):  
Perturbation Method ◽  
Acoustic Field ◽  
Taylor Series ◽  
Optimization Method ◽  
Second Order ◽  
Response Analysis ◽  
Engineering Practice ◽  
Local Optima ◽  
First Order ◽  
Convex Perturbation

The acoustic field with convex parameters widely exists in the engineering practice. The vertex method and the anti-optimization method are not considered as appropriated approaches for the response analysis of acoustic field with convex parameters. The shortcoming of the vertex method is that the local optima out of vertexes cannot be identified. The disadvantage of the anti-optimization method is that the analytical formulation of response may be not obtained. To analyze the acoustic field with convex parameters efficiently and effectively, a first-order convex perturbation method (FCPM) and a second-order convex perturbation method (SCPM) are presented. In FCPM, the response of the acoustic field with convex parameters is expanded with the first-order Taylor series. In SCPM, the response of the acoustic field with convex parameters is expanded with the second-order Taylor series neglecting the nondiagonal elements of Hessian matrix. The variational bounds of the expanded responses in FCPM and SCPM are yielded by the Lagrange multiplier method. The accuracy and efficiency of FCPM and SCPM are investigated by numerical examples.

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.

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.

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.

scholarly journals Efficient Midfrequency Analysis of Built-Up Structure Systems with Interval Parameters

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Hui Yin ◽  
Dejie Yu ◽  
Shengwen Yin ◽  
Baizhan Xia
Keyword(s):  
Perturbation Method ◽  
Perturbation Methods ◽  
Energy Analysis ◽  
Extreme Values ◽  
Search Algorithm ◽  
Second Order ◽  
Order Interval ◽  
Interval Parameters ◽  
Hybrid Finite Element ◽  
Interval Perturbation Method

To improve the efficiency of midfrequency analysis of built-up structure systems with interval parameters, the second-order interval and subinterval perturbation methods are introduced into the hybrid finite element/statistical energy analysis (FE/SEA) framework in this paper. Based on the FE/SEA for built-up structure systems and the second-order interval perturbation method, the response variables are expanded with the second-order Taylor series and nondiagonal elements of the Hessian matrices are neglected. Extreme values of the expanded variables are searched by using efficient search algorithm. For large parameter intervals, the subinterval perturbation method is introduced. Numerical results verify the effectiveness of the proposed methods.

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