Reliability analysis of polynomial systems subject to p-box uncertainties

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

doi:10.1016/j.ymssp.2012.08.012

Cited by 47 publications

(24 citation statements)

References 16 publications

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“…(8) provides only the means to test the membership of a candidate θ x 1 to Ω x 1 n d , but not the means to calculate mathematically the desired set. In order to do that, set bounding approaches, such as those presented in [26][27][28][29], should be adopted. On the other hand, it has to be also considered that this limitation does not absolutely impair the quality and validity of the results of the following subproblems of the challenge.…”

Section: Pedroni and Ziomentioning

confidence: 99%

“…Finally, tasks (C) and (D) are here tackled together by solving the (optimization) problem of identifying the values of the epistemically uncertain coefficients of the category (II) and (III) parameters that yield the smallest and largest values (i.e., the ranges) of the two performance metrics defined above [26][27][28][29]; during the optimization search the (aleatory) uncertainty described by probability distributions is propagated by standard Monte Carlo simulation (MCS) [30,31].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Uncertainty and Sensitivity Analysis of the Model of a Twin-Jet Aircraft

Pedroni

Zio

2015

Journal of Aerospace Information Systems

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International audienceThe mathematical models employed in the risk assessment of complex, safety-critical engineering systems cannot capture all the characteristics of the system under analysis, due to: (i) the intrinsically random nature of several of the phenomena occurring during system operation (aleatory uncertainty); (ii) the incomplete knowledge about some of the phenomena (epistemic uncertainty). In this work, we consider the model of a twin-jet aircraft, which includes twenty-one inputs and eight outputs. The inputs are affected by mixed aleatory and epistemic uncertainties represented by probability distributions and intervals, respectively. Within this context, we address the following issues: (A) improvement of the input uncertainty models (i.e., reduction of the corresponding epistemic uncertainties) based on experimental data; (B) sensitivity analysis to rank the importance of the inputs in contributing to output uncertainties; (C) propagation of the input uncertainties to the outputs; (D) extreme case analysis to identify those system configurations that prescribe extreme values of some system performance metrics of interest (e.g., the failure probability). All the tasks are tackled and solved by means of an efficient combination of: (i) Monte Carlo Simulation (MCS) to propagate the aleatory uncertainty described by probability distributions; (ii) Genetic Algorithms (GAs) to solve the numerous optimization problems related to the propagation of epistemic uncertainty by interval analysis, and (iii) fast-running Artificial Neural Network (ANN) regression models to reduce the computational time related to the repeated model evaluations required by uncertainty and sensitivity analyses

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Section: Pedroni and Ziomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybrid Uncertainty and Sensitivity Analysis of the Model of a Twin-Jet Aircraft

Pedroni

Zio

2015

Journal of Aerospace Information Systems

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“…For example, symbolic data analysis [1,2] has been proposed to extend the classical data models to take into account the interval-valued information. The representatives interval-valued data analysis approaches include point value replacement [3][4][5], p-Box [6][7][8][9][10][11], and Hausdorff distance methods [12,13].…”

Section: Related Workmentioning

confidence: 99%

Incremental Discriminant Analysis on Interval-Valued Parameters for Emitter Identification

Xiong

Wang

2015

Mathematical Problems in Engineering

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Emitter identification has been widely recognized as one crucial issue for communication, electronic reconnaissance, and radar intelligence analysis. However, the measurements of emitter signal parameters typically take the form of uncertain intervals rather than precise values. In addition, the measurements are generally accumulated dynamically and continuously. As a result, one imminent task has become how to carry out discriminant analysis of interval-valued parameters incrementally for emitter identification. Existing machine learning approaches for interval-valued data analysis are unfit for this purpose as they generally assume a uniform distribution and are usually restricted to static data analysis. To address the above problems, we bring forward an incremental discriminant analysis method on interval-valued parameters (IDAIP) for emitter identification. Extensive experiments on both synthetic and real-life data sets have validated the efficiency and effectiveness of our method.

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“…Its application areas include: the failure probability evaluation of fault system [2] , the uncertainty evaluation of vibration system dynamic responses [3] , The uncertainty of climate change [4] , Seawall risk modeling and reliability assessment [5][6] , Automobile gearbox reliability design [7] , finite element modeling and parameter optimization of rocket shell structure [8] , parameter uncertainty of damped oscillator [9] , multi-parameters uncertainty mathematical modeling [10] , Mechanical reliability system architecture and evaluation [11] , The flood control evaluation of water conservancy system [12] , The error accumulated expression and evaluation of the measuring system [13] , the sea level estimation in the further considering climate change [14] , etc. as its huge advantages in the express of uncertainties, the applcation of its theory may explore to many other fields.…”

Section: Introductionmentioning

confidence: 99%

A Probability Box Modeling Method of Dimensionless Mechanical Fault Features in Time Domain

Du¹,

Ding²,

Liu³

2014

Proceedings of the 2014 International Conference on Mechatronics, Control and Electronic Engineering

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Abstract-The simply multi-segment averages of mechanical fault features lead to the loss of signal uncertainty probability statistics which may contribute to fault diagnosis. To solve the problem, a probability box modeling method of mechanical fault features is proposed. Three similar dimensionless factors (peak factor，form factor， margin factor) in time domain were used to obtain probability boxes. The algorithm of modeling was then proposed. Firstly, the mechanical fault raw data was divided into several segments according to the sampling frequency. Secondly, the dimensionless features in time domain were obtained for every segment. After verifying the normal distribution probability distribution type, the row vector of features was divided into several sets. From these sets, the range of the mean and variance were obtained. Finally, the DSS of mean and variance were integrated into the probability modeling algorithm of normal distribution to get the probability box. The rolling bearing's faults raw data was used to verify this modeling method. The results show that the probability box modeling method can effectively reflect the uncertainties of fault state, which can be used for fault diagnosis.

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Reliability analysis of polynomial systems subject to p-box uncertainties

Cited by 47 publications

References 16 publications

Hybrid Uncertainty and Sensitivity Analysis of the Model of a Twin-Jet Aircraft

Hybrid Uncertainty and Sensitivity Analysis of the Model of a Twin-Jet Aircraft

Incremental Discriminant Analysis on Interval-Valued Parameters for Emitter Identification

A Probability Box Modeling Method of Dimensionless Mechanical Fault Features in Time Domain

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