Probability Theory and Mathematical Statistics

Watanabe, Satoshi; Fukushima, Masao; Prohorov, Yu. V.; Shiryaev, Albert N.

doi:10.1142/9789814532181

Cited by 16 publications

(18 citation statements)

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“…The comparison indicates that the GA-optimized BP neural network provides better training results for the samples. According to statistical definitions [15], a smaller MSE between predicted values and outcomes indicates a smaller disparity between the estimated value and the sample data, which in turn suggests higher accuracy of the trained model. The genetically optimized BP neural network exhibits a smaller MSE, indicating more precise model training compared to the standard BP neural network.…”

Section: Resultsmentioning

confidence: 99%

“…It is noticeable that both the BP neural network's sample data and the model-predicted data converge to the optimal training value around the 12th cycle, with the mean squared error dropping below 10 -3 . The genetically optimized BP neural network's sample data and model prediction achieve their best training value in the 15th cycle, with the mean squared error decreasing below 10 -4 .According to statistical definitions[15], a smaller MSE between predicted values and outcomes indicates a smaller disparity between the estimated value and the sample data, which in turn suggests higher accuracy of the trained model. The genetically optimized BP neural network exhibits a smaller MSE, indicating more precise model training compared to the standard BP neural network.Figure11is a comparison of the predicted and actual values of the test set.…”

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confidence: 99%

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Defect Recognition Method for Magnetic Leakage Detection in Oil and Gas Steel Pipes Based on Improved Neural Networks

Mohd. Shah

2024

JMechE

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The aging infrastructure of petroleum and natural gas pipelines poses a threat to national economies, necessitating precise defect detection for safety and efficiency. To enhance the accuracy of predicting pipeline defect sizes, this study introduces a magnetic leakage detection system, employing Backpropagation (BP) neural networks optimized with genetic algorithms. Traditional BP networks face challenges, including parameter determination and slow convergence, addressed through genetic algorithms' global search capabilities. Simulated data are generated using ANSYS software by using models of semi-circular defects in steel pipes, producing magnetic leakage signals of varying intensities. MATLAB was used to construct both standard BP and genetically optimized BP neural networks. Results show that the latter significantly reduces computational errors, demonstrating improved accuracy in defect dimension prediction. The approach contributes to overcoming non-uniqueness in the recognition process and the complex nonlinear relationship between magnetic signals and defect size parameters. The study offers a guided approach for selecting BP neural network parameters, enhancing practicality. Simulations validate the method's effectiveness, indicating low workload and high reliability. This research provides a meaningful advancement in the detection of defects in long-distance pipelines, impacting the safety and efficiency of petroleum and natural gas transportation.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Defect Recognition Method for Magnetic Leakage Detection in Oil and Gas Steel Pipes Based on Improved Neural Networks

Mohd. Shah

2024

JMechE

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“…(3) (4) where PS(x) and PV(x) are the probabilities of the presence of defect-active impulses of elastic deformation waves in a sufficiently thin analyzed surface layer of the material, and in the general case of fluctuations of the SSS that can lead to critical growth of surface and subsurface defects respectively; CS and CV are the average "concentrations" of these defectcritical ultrajet pulses impacting the surface and subsurface layer of the OA material Based on the informative-physical logic of the above relations, it is not difficult to notice that (1) and ( 2) are the necessary, and ( 2) and ( 3) are the sufficient conditions for the material particle separation due to ultrajet erosion of the surface layer of the diagnosed OA due to the critical growth of the surface and/or subsurface defect. Therefore, according to the addition theorem of probability [13], we have: (5) where is the probability of erosion particle separation with a characteristic geometrical size x.…”

Section: Probabilistic Modelingmentioning

confidence: 99%

Hydroerosion probabilistic modeling during surface layer quality ultrajet mesodiagnostics of aviation, rocket, and space equipment

Galinovskiy

Barzov²,

Yanko³

et al. 2023

E3S Web of Conf.

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At present, deterministic approaches to the hydroerosion processes modeling, which is the informative-physical basis of ultrajet mesodiagnostics (UJM), significantly prevail over other methods of analysis. This contradicts the probabilistic nature of local hydroerosion, which is caused by the formation of an array of eroded particles with highly variable mass-geometric parameters reflecting the realities of the initial microdefects distribution in the surface layer of the analyzed object (OA). Therefore, probabilistic modeling is a physically more reasonable tool for describing multi-factor processes in the ultrajet interactions zone, including the peculiarities of ultrajet hydroerosion. Hence, this paper proposes a probabilistic approach to modeling the process of hydroerosion damage, based on the separation of the particle from the material surface as a result of the interaction of necessary and sufficient conditions for dispersion. The obtained calculation data (probabilistic analysis) are close to the results of live experiments, which, in turn, allows recommending this approach of mathematical formalization of the minimally invasive quality control method using complicated configuration parts surface properties ultrajet mesodiagnostics, and also OA produced from anisotropic materials, widely used in aviation, rocket, and space technology.

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“…Assume that Ω is the sample space of a random test, if for any sample point ω ∈ Ω , there is a unique real numbers X = X ( ω ) corresponding to ω , and X takes different values (or values in different ranges) with a certain probability, then X is called a random variable (Chen, 2009).…”

Section: General Uncertainty Data and General Uncertainty Variablementioning

confidence: 99%

On general uncertainty data and general uncertainty variable for reliability growth analysis of major aerospace equipment

Liu

Tang

2022

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PurposeThe purpose of this paper is to explore new ways and lay a solid foundation to solve the problem of reliability growth analysis of major aerospace equipment with various uncertainty data through propose new concepts of general uncertainty data (GUD) and general uncertainty variable (GUV) and build the operation system of GUVs.Design/methodology/approachThe characteristics of reliability growth data of major aerospace equipment and the limitations of current reliability growth models have been analyzed at first. The most commonly used uncertainty system analysis methods of probability statistics, fuzzy mathematics, grey system theory and rough set theory have been introduced. The concepts of GUD and GUV for reliability growth data analysis of major aerospace equipment are proposed. The simplified form of GUV based on the “kernel” and the degree of uncertainty of GUV is defined. Then an operation system of GUVs is built.Findings(1) The concept of GUD; (2) the concept of GUV; (3) The novel operation rules of GUVs with simplified form.Practical implicationsThe method exposed in this paper can be used to integrate complex reliability growth data of major aerospace equipment. The reliability growth models based on GUV can be built for reliability growth evaluation and forecasting of major aerospace equipment in practice. The reliability evaluation example of a solid rocket motor shows that the concept and idea proposed in this paper are feasible. The research of this paper opens up a new way for the analysis of complex uncertainty data of reliability growth of major aerospace equipment. Moreover, the operation of GUVs could be extended to the case of algebraic equation, differential equation and matrix which including GUVs.Originality/valueThe new concepts of GUD and GUV are given for the first time. The novel operation rules of GUVs with simplified form were constructed.

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Probability Theory and Mathematical Statistics

Cited by 16 publications

References 0 publications

Defect Recognition Method for Magnetic Leakage Detection in Oil and Gas Steel Pipes Based on Improved Neural Networks

Defect Recognition Method for Magnetic Leakage Detection in Oil and Gas Steel Pipes Based on Improved Neural Networks

Hydroerosion probabilistic modeling during surface layer quality ultrajet mesodiagnostics of aviation, rocket, and space equipment

On general uncertainty data and general uncertainty variable for reliability growth analysis of major aerospace equipment

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