Classical and imprecise probability methods for sensitivity analysis in engineering: A case study

Oberguggenberger, Michael; King, Julian; Schmelzer, Bernhard

doi:10.1016/j.ijar.2008.09.004

Cited by 70 publications

(39 citation statements)

References 23 publications

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“…Along with the uncertainty project' advancement of American Sandia Country Laboratory in 2004, the project promotions in finance risk analysis, biogeography and mechanical reliability and so on are getting more and more widespread [6]. The application of p-box theory successively involves the fault system failure probability assessment [7], dynamic responses of the vibration system uncertainty evaluation [8], the expression of uncertainty about climate change [9], Many parameters of seawall risk modeling and reliability assessment [10,11], the lack of experimental data under the condition of automobile gearbox reliability design [12], rocket edge shell structure finite element modeling and parameter optimization [13] Currently SVM has been widely used in face recognition, fault classification, nonlinear system modeling and identification and other fields [14]. …”

Section: Imentioning

confidence: 99%

Fault Diagnosis of Power Transformer based on Probability-box Theory

Ding¹,

Du²,

Wang³

et al. 2014

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

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ABSTRACT-In practice, fault diagnosis of power transformer is often performed on the basis of limited data and many various uncertainties factors. Under this circumstance, there are practical difficulties in identifying unique distributions as input for fault diagnosis. In order to solve the problem and improve the diagnosis ability of power transformer by analyzing the dissolved gas, a new method based on probability boxes theory was proposed. Firstly, the raw percentages of dissolved gas were used as the information source to construct the tow pboxes about H 2 and C 2 H 6 gas content. Then, to take advantage of the complementation of the information source, the tow pboxes about H 2 and C 2 H 6 gas content were fused. Finally, the SVM features database was established by extracting different types of cumulative uncertainty measures from p-boxes. The analysis result shows that the proposed method has high degree of diagnosis accuracy and is characterized by fast diagnosis and good real-time, demonstrating the model is practical and effective.; Power transformer; Uncertainty; Probability box; Fusion

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Section: Imentioning

confidence: 99%

Fault Diagnosis of Power Transformer based on Probability-box Theory

Ding¹,

Du²,

Wang³

et al. 2014

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

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“…Augustin and Hable (2010) claim that building a relationship between the theory of imprecise probabilities and robust statistics is promising. Oberguggenberger et al (2009) have applied imprecise probability to deal with sensitivity analysis. An aerospace engineering example is used to compare the results obtained using random sets, fuzzy sets and interval spreads simulated with the aid of the Cauchy distribution.…”

Section: Application and Advances Of Imprecise Probability Theoriesmentioning

confidence: 99%

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

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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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Classical and imprecise probability methods for sensitivity analysis in engineering: A case study

Cited by 70 publications

References 23 publications

Fault Diagnosis of Power Transformer based on Probability-box Theory

Fault Diagnosis of Power Transformer based on Probability-box Theory

Possibility and Evidence-Based Reliability Analysis and Design Optimization

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

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