Finite element analysis with uncertain probabilities

Quaranta, Giuseppe

doi:10.1016/j.cma.2010.07.018

Cited by 21 publications

(8 citation statements)

References 50 publications

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“…Thus, to capture the real dynamic response of a physical practical multibody system, the parameter uncertainty should be considered in the dynamics model. There are two main types of methods to describe the uncertain parameters [470][471][472], namely the probabilistic methods and the non-probabilistic methods. The probabilistic methods are usually considered to describe the random parameters with known probability density functions, while the nonprobabilistic methods are mainly utilized to solve the uncertain problems with uncertain, but bounded parameters.…”

Section: Uncertainty Of Mechanisms With Clearance Jointsmentioning

confidence: 99%

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Tian

Flores

Lankarani

2018

Mechanism and Machine Theory

306

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A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960's. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links' flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.

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Section: Uncertainty Of Mechanisms With Clearance Jointsmentioning

confidence: 99%

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

Tian

Flores

Lankarani

2018

Mechanism and Machine Theory

306

View full text Add to dashboard Cite

show abstract

“…Artificial neural network (ANN) has the property to approximate non‐linear models by adjusting the weights of connections 33 . To establish the LSF of cycloid gear at acceptable computational cost, 118 design points is solved by the ANSYS Workbench, which is a widespread finite element analysis 34 (FEA) software. And back propagation artificial neural network 35 (BPANN) is adopted to establish output response

g^{\prime}{r_{rp}},{r_p},a,f

with 100 design points as train set and 18 design points as test set.…”

Section: Numerical Examplementioning

confidence: 99%

An improved reliability index based on regional equivalent conversion

Wang

Liu

Zhao

et al. 2022

Quality & Reliability Eng

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Aiming at the accuracy and efficiency of traditional reliability method for solving highly nonlinear problem, this paper proposes the regional equivalent conversion index (RECI) to compute reliability under arbitrary boundary and number of subdomains of limit state function. Firstly, we establish the model of RECI and the corresponding sampling method. Furthermore, the RECI of a series of parallel linear performance functions are computed by the proposed method. Besides the advanced first order and second moment method (AFOSM) are used to compute the reliability. Finally, the mapping relationship between RECI and reliability is established. Influence of sampling parameters on relative error is studied and optimal value is given. The parameters are optimized by analyzing the influence of the parameters on the precision. This method is also suitable for multiple failure modes without changing any process. Numerical examples are employed to demonstrate the feasibility of the proposed method for solving highly nonlinear problem in dimension 1–4.

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“…Thus the structure evaluation of this method is often accelerated by techniques such as importance sampling [1,2], subset simulation [3,4]. Stochastic finite element method is based on series expansion (such as perturbation technique, Taylor expansion and Neumann expansion), which leads stochastic finite element method to be very complex in theory, difficult in programming, as well as time-consuming in computation [5]. Due to the inherent rigidity of quadratic polynomial, it is not suitable for highly non-linear and complex problem [6].…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis for highly non-linear and complex model using ANN-MCM simulation

Xiao

Shi

2018

J Braz. Soc. Mech. Sci. Eng.

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To predict reliability for highly non-linear and complex model efficiently and accurately, an artificial neural network (ANN) based Monte Carlo method (MCM) is proposed. In this method, ANN trained by backpropagation (BP) algorithm is developed to establish the relationship between inputs and outputs. The trained ANN model is then connected to MCM to predict reliability and reliability sensitivity of structure. To examine the accuracy and efficiency of the proposed method, results obtained by polynomial-FOSM (first-order second moment) method and ANN-AFOSM (advanced first-order second moment) method are provided. Compared with the traditional Monte Carlo method, the time consumed by ANN-MCM, polynomial-FOSM and ANN-AFOSM methods only accounts for 0.14% of the traditional MCM. The reliability analysis and reliability sensitivity analysis results of ANN-MCM method are very close to traditional MCM, polynomial-FOSM method yields large errors, ANN-AFOSM is in between. It shows that the proposed method is of high accuracy and efficiency.

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Finite element analysis with uncertain probabilities

Cited by 21 publications

References 50 publications

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

An improved reliability index based on regional equivalent conversion

Reliability analysis for highly non-linear and complex model using ANN-MCM simulation

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