Rigid multibody system dynamics with uncertain rigid bodies

Batou, Anas; Soize, Christian

doi:10.1007/s11044-011-9279-2

Cited by 40 publications

(18 citation statements)

References 29 publications

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“…The problem of stochastic excitation is adressed in [14] using generalized polynomial chaos. A MBS containing uncertain rigid bodies is evaluated in [15] by random number and random matrix theory, applying the Monte Carlo method.…”

Section: Fuzzy Arithmetic -The Transformation Methodsmentioning

confidence: 99%

Fuzzy Arithmetical Analysis of Multibody Systems with Uncertainties

Walz¹,

Hanss²

2013

Archive of Mechanical Engineering

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The consideration of uncertainties in numerical simulation is generally reasonable and is often indicated in order to provide reliable results, and thus is gaining attraction in various fields of simulation technology. However, in multibody system analysis uncertainties have only been accounted for quite sporadically compared to other areas.The term uncertainties is frequently associated with those of random nature, i.e. aleatory uncertainties, which are successfully handled by the use of probability theory. Actually, a considerable proportion of uncertainties incorporated into dynamical systems, in general, or multibody systems, in particular, is attributed to so-called epistemic uncertainties, which include, amongst others, uncertainties due to a lack of knowledge, due to subjectivity in numerical implementation, and due to simplification or idealization. Hence, for the modeling of epistemic uncertainties in multibody systems an appropriate theory is required, which still remains a challenging topic. Against this background, a methodology will be presented which allows for the inclusion of epistemic uncertainties in modeling and analysis of multibody systems. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, where the uncertain values of the model parameters are represented by socalled fuzzy numbers, reflecting in a rather intuitive and plausible way the blurred range of possible parameter values. As a result of this advanced modeling technique, more comprehensive system models can be derived which outperform the conventional, crisp-parameterized models by providing simulation results that reflect both the system dynamics and the effect of the uncertainties.The methodology is illustrated by an exemplary application of multibody dynamics which reveals that advanced modeling and simulation techniques using some well-thought-out inclusion of the presumably limiting uncertainties can provide significant additional benefit.

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Section: Fuzzy Arithmetic -The Transformation Methodsmentioning

confidence: 99%

Fuzzy Arithmetical Analysis of Multibody Systems with Uncertainties

Walz¹,

Hanss²

2013

Archive of Mechanical Engineering

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“…If one has in the relation that: p 3 is the probability of satisfying FR 3 with DP 3 p 2 is the probability of satisfying FR 2 …”

Section: Numerical Examplementioning

confidence: 99%

“…Multibody systems represent a special class of mechanical systems made of rigid and/or flexible bodies, mutually interconnected by joint constraints, and subjected to external force fields [1][2][3][4][5][6][7][8][9][10]. Several examples of such complex systems can be found in industrial engineering applications [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Entropic Measure of Epistemic Uncertainties in Multibody System Models by Axiomatic Design

Villecco

Pellegrino

2017

Entropy

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Abstract:In this paper, the use of the MaxInf Principle in real optimization problems is investigated for engineering applications, where the current design solution is actually an engineering approximation. In industrial manufacturing, multibody system simulations can be used to develop new machines and mechanisms by using virtual prototyping, where an axiomatic design can be employed to analyze the independence of elements and the complexity of connections forming a general mechanical system. In the classic theories of Fisher and Wiener-Shannon, the idea of information is a measure of only probabilistic and repetitive events. However, this idea is broader than the probability alone field. Thus, the Wiener-Shannon's axioms can be extended to non-probabilistic events and it is possible to introduce a theory of information for non-repetitive events as a measure of the reliability of data for complex mechanical systems. To this end, one can devise engineering solutions consistent with the values of the design constraints analyzing the complexity of the relation matrix and using the idea of information in the metric space. The final solution gives the entropic measure of epistemic uncertainties which can be used in multibody system models, analyzed with an axiomatic design.

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“…The final solution gives an entropic measure of epistemic uncertainties which can be then used in multibody system models analyzed by means of the axiomatic design. Multibody systems are the class of mechanical systems composed of rigid and/or flexible bodies interconnected by kinematic joints [1][2][3][4][5][6][7][8][9][10]. They are subjected to nonlinear external force fields and undergo large, finite translations and rotations [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Uncertainties in the Design Process of Complex Mechanical Systems

Villecco

Pellegrino

2017

Entropy

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Abstract:In this paper, the problem of the evaluation of the uncertainties that originate in the complex design process of a new system is analyzed, paying particular attention to multibody mechanical systems. To this end, the Wiener-Shannon's axioms are extended to non-probabilistic events and a theory of information for non-repetitive events is used as a measure of the reliability of data. The selection of the solutions consistent with the values of the design constraints is performed by analyzing the complexity of the relation matrix and using the idea of information in the metric space. Comparing the alternatives in terms of the amount of entropy resulting from the various distribution, this method is capable of finding the optimal solution that can be obtained with the available resources. In the paper, the algorithmic steps of the proposed method are discussed and an illustrative numerical example is provided.

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Rigid multibody system dynamics with uncertain rigid bodies

Cited by 40 publications

References 29 publications

Fuzzy Arithmetical Analysis of Multibody Systems with Uncertainties

Fuzzy Arithmetical Analysis of Multibody Systems with Uncertainties

Entropic Measure of Epistemic Uncertainties in Multibody System Models by Axiomatic Design

Evaluation of Uncertainties in the Design Process of Complex Mechanical Systems

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