The probability density evolution method (PDEM) is a versatile approach for analyzing stochastic dynamical systems. When combined with the change of probability measure (COM), it provides a tool to efficiently deal wi...
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The probability density evolution method (PDEM) is a versatile approach for analyzing stochastic dynamical systems. When combined with the change of probability measure (COM), it provides a tool to efficiently deal with the aleatory and epistemic uncertainties, where shifts of probability distributions are frequently encountered. However, when the shifts of distributions are too large, the PDEM-COM method can lead to increasing numerical errors. This paper aims to propose an extension of the PDEM-COM that can address the large shifts of distributions involving multiple random variables. In the proposed method, the concepts of the multi-dimensional augmented support and the augmented probability density function (PDF) are introduced based on the differences between the original and updated distributions. Then, an efficient numerical procedure is established for selecting a small set of additional representative points based on the augmented PDF. These additional representative points serve as a complement to the representative point set selected according to the original distributions. By incorporating the augmented representative point set and solving the generalized probability density evolution equation (GDEE), the stochastic response of the system considering the updated distributions can be evaluated. Numerical examples are presented to demonstrate the capability and effectiveness of the proposed approach. The results demonstrate that the proposed approach offers improved accuracy compared to the PDEM-COM method, particularly for large distribution shifts, while maintaining a relatively lower computational cost.
The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material *** order to ameliorate r...
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The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material *** order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this *** the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random ***,the failure modes were considered as the randomvariables of system response to obtain the distributed collaborative response surface model based on structure failure ***,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented *** the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation ***,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.
Based on the reliability and buckling analysis of the steel tanks with a stiffened dome-roof, a mathematical model with multiple random variables was established and a new method for calculating and analysing the reli...
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Based on the reliability and buckling analysis of the steel tanks with a stiffened dome-roof, a mathematical model with multiple random variables was established and a new method for calculating and analysing the reliability and stability of the tank-roof by minimum distance and Lagrange formulae is provided. The analysis result of the tank as an engineering example by the proposed method shows that the thickness of both dome-roof-plates and stiffened ribs would affect the reliability of the tank-roof under different external loads. It is demonstrated that decisive factors affecting tank-roof reliability may be analysed such as: material thickness and external load. A reliability assessment is also needed performed to prove the correctness of both model and method. The assessment results were consistent with those from the engineering example. A baseline, reference method, for tank design and operation is thus proposed. (C) 2013 Elsevier Ltd. All rights reserved.
A hybrid analytical-intelligent approach is proposed for fuzzy reliability analysis of the composite beams reinforced by zinc oxide (ZnO) nanoparticle. The fuzzy reliability index corresponding to buckling failure mod...
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A hybrid analytical-intelligent approach is proposed for fuzzy reliability analysis of the composite beams reinforced by zinc oxide (ZnO) nanoparticle. The fuzzy reliability index corresponding to buckling failure mode of nanocomposite beam under thickness-direction external voltage is computed based on three-levels: (1) fuzzy analysis, (2) reliability analysis and (3) analytical buckling analysis. In fuzzy analysis level, an improved gravitational search algorithm has been applied to determine uncertainty interval for membership levels of reliability index. The adaptive formulation with a dynamical self-adjusting process is used for reliability analysis level based on conjugate first-order reliability method (FORM). The self-adjusting term in conjugate sensitivity vector is used to satisfy the sufficient descent condition for controlling instability of FORM formula while the proposed conjugate scalar factor is computed less than the original conjugate FORM, thus it may be provided with the efficient results for the convex problem. The new and previous sensitivity vectors obtained by conjugate and steepest descent vectors dynamically adjusted the proposed conjugate factor. In the buckling analysis level, an exponential theory in conjunction with the method of energy is utilized. Fuzzy randomvariables including applied voltage, the volume fraction of ZnO, thickness of beam, spring constant and shear constant of the foundation are considered in studied nanocomposite beam. Survey results indicated that the proposed method can provide stable and acceptable fuzzy membership functions for parametric study. Moreover, the ratio of length to thickness and spring constant of foundation are the more sensitive parameters which affect fuzzy reliability index significantly.
This paper presents a failure probability assessment of compressive contact connectors due to tin whiskers caused leads bridging. Based on scanning electron microscope measurements, we establish probability distributi...
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This paper presents a failure probability assessment of compressive contact connectors due to tin whiskers caused leads bridging. Based on scanning electron microscope measurements, we establish probability distributions of four involved variables: whisker length, orientation, origin location, and counts. A failure probability model is developed and used to calculate the failure probability in terms of two types of failure definition: 1) National Electronics Manufacturing Initiative (NEMI) acceptance criteria, and 2) leads bridging caused by tin whiskers. Results indicate that, in terms of the NEMI criteria, there is more than a 50% chance that the connectors would fail to meet the maximum allowable whisker length for Class 2 products at six-month ambient storage, while the probability goes up to 74% for Class 2, or 62% for Class 3 at one year. However, the failure probability for tin whisker caused leads bridging is fairly low, only 0.0002% for six-month storage, 0.0074% for one-year storage, and even 0.0515% for five-year storage. Therefore, although the connectors may fail to meet NEMI acceptance criteria for maximum allowable whisker length, the whiskers do not pose significant field risk to cause leads bridging at ambient storage.
This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the tra...
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ISBN:
(纸本)9781424492701
This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the traditional Granger causality analysis, showing that it leads to false detection of causality when instantaneous and time-lagged effects coexist in the process structure. Then, we propose an improved algorithm for causal inference that combines the Granger framework with the approach proposed by Pearl for the study of causality among multiple random variables. This new approach is compared with the traditional one in theoretical and simulated examples of interacting processes, showing its ability to retrieve the correct structure of instantaneous and time-lagged interactions. These approaches for causal inference are then tested on the physiological variability series of heart period, arterial pressure and cerebral blood flow variability obtained in subjects with postural-related syncope during a tilt-test protocol.
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