Assessment of uncertainty on structural dynamic responses with the short transformation method

Donders, Stijn; Vandepitte, Dirk; Peer, Joost Van de; Desmet, Wim

doi:10.1016/j.jsv.2005.07.003

Cited by 43 publications

(21 citation statements)

References 5 publications

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“…The core of the set is defined as the subset of elements for which µ=1, whilst the support is the subset for which µ>0. A fuzzy number is a fuzzy set that is convex 10 and normal, and whose membership function is piecewise continuous [7]. An example of a symmetric triangular fuzzy number is given in Fig.…”

Section: Fuzzy Arithmeticmentioning

confidence: 99%

“…One approach that has been adopted is to consider each fuzzy variable at different 'levels of membership', and to use interval arithmetic to calculate the corresponding model outputs. Alternatively, the response at each membership level can be approximated by performing multiple 'crisp' 25 calculations using standard arithmetic [7]; reassembling the results of these calculations leads to fuzzy number(s) that describe the output to the engineering model. One methodology for implementing this approach is the so-called transformation method [4].…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy stability analysis of regenerative chatter in milling

Sims

Manson

Mann

2010

Journal of Sound and Vibration

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During machining, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece.Consequently it is desirable to predict, and hence avoid the onset of this instability. Regenerative chatter is a function of empirical cutting coefficients, and the structural dynamics of the machine-tool system. There can be significant uncertainties in the underlying parameters, so the predicted stability limits do not necessarily agree with those found in practice.In the present study, fuzzy arithmetic techniques are applied to the chatter stability problem. It is first shown that techniques based upon interval arithmetic are not suitable for this problem due to the issue of recursiveness. An implementation of fuzzy arithmetic is then developed based upon the work of Hanss and Klimke. The arithmetic is then applied to two techniques for predicting milling chatter stability: the classical approach of Altintas, and the time-finite element method of Mann. It is shown that for some cases careful programming can reduce the computational effort to acceptable levels. The problem of milling chatter uncertainty is then considered within the framework of Ben-Haim's information-gap theory.It is shown that the presented approach can be used to solve process design problems with robustness to the uncertain parameters. The fuzzy stability bounds are then compared to previously published data, to investigate how uncertainty propagation techniques can offer more insight into the accuracy of chatter predictions.

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Section: Fuzzy Arithmeticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fuzzy stability analysis of regenerative chatter in milling

Sims

Manson

Mann

2010

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…Uncertainty can arise from variability in materials, manufacture, and assembly, and can be modelled deterministically [1][2][3], in a fuzzy sense [4][5], or statistically [6][7][8][9][10][11][12][13]. Focusing on statistical bound prediction, complexity depends on the defined frequency range, whether low, mid, or high frequency.…”

Section: Introductionmentioning

confidence: 99%

Accurate extreme-value-based frequency response bounding for structures with a small number of highly random parameters

Dunne

Cheepsomsong

2016

Journal of Sound and Vibration

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A modified extreme-value-based methodology is discussed for computing statistical bounds associated with the magnitude of the frequency response of a specified number of structures with high levels of random parameter uncertainty. The methodology, intended for small numbers of uncertain parameters, is capable of constructing accurate statistical bounds in terms of quantiles associated with the extreme value distribution. Quantiles can be constructed for an ensemble of structural responses across the entire frequency range without using Monte Carlo Simulation. To test the methodology, statistical bounds for the energy of an L-shaped structure with low and high levels of uniformly-distributed length and thickness variability are obtained: i) via direct integration using an ANSYS Finite Element model, and ii) via Statistical Energy Analysis (SEA). Comparisons are shown with bounds obtained using Monte Carlo simulation. The merit of direct integration for computing bounds associated with the responses of an ensemble of structures with high levels of random parameter uncertainty is demonstrated by its simplicity, high accuracy, and absence of statistical scatter.Keywords: ensemble analytical response bounds random parameters 11 main-section pages (double-spaced) 32 references Figures 1 -9 1 appendix 3

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“…In recent years, there is an increasing focus on the development of FFEM, first for static analysis and then extended in dynamics [1][2][3][4][5][6][7][8][9]. Fundamental strategies for FFEM can be categorized into two main groups: the interval arithmetic approach and the optimization strategy.…”

Section: Introductionmentioning

confidence: 99%

A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure

Tuan¹,

Huynh

Pham

2015

Vietnam J. Mech.

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Abstract. This paper introduces an improved response surface-based fuzzy finite element analysis of structural dynamics. The free vibration of structure is established using superposition method, so that fuzzy displacement responses can be presented as functions of fuzzy mode shapes and fuzzy natural frequencies. Instead of direct determination of these fuzzy quantities by modal analysis which will involve the calculation of the whole finite element model, the paper proposes a felicitous approach to design the response surface as surrogate model for the problem. In the design of the surrogate model, complete quadratic polynomials are selected with all fuzzy variables are transformed to standardized fuzzy variables. This methodology allows accurate determination of the fuzzy dynamic outputs, which is the major issue in response surface based techniques. The effectiveness of the proposed fuzzy finite element algorithm is illustrated through a numerical analysis of a linear two-storey shear frame structure.

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Assessment of uncertainty on structural dynamic responses with the short transformation method

Cited by 43 publications

References 5 publications

Fuzzy stability analysis of regenerative chatter in milling

Fuzzy stability analysis of regenerative chatter in milling

Accurate extreme-value-based frequency response bounding for structures with a small number of highly random parameters

A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure

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