Progressive advanced-mean-value method for CDF and reliability analysis

2002 ◽  
Vol 17 (5/6) ◽  
pp. 303 ◽  
Author(s):  
Y.-T. (Justin) Wu ◽  
C.R. Shah ◽  
A.K. Deb Baruah
Keyword(s):  
Reliability Analysis ◽  
Mean Value ◽  
Advanced Mean Value ◽  
Mean Value Method

Some Important Issues on First-Order Reliability Analysis With Nonprobabilistic Convex Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
C. Jiang ◽  
G. Y. Lu ◽  
X. Han ◽  
R. G. Bi
Keyword(s):  
Reliability Analysis ◽  
Reliability Index ◽  
Probability Model ◽  
Mean Value ◽  
Convex Model ◽  
First Order ◽  
Reliability Method ◽  
Complex Engineering ◽  
Mean Value Method ◽  
Form Type

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the well-established techniques in probability-based reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used first-order reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convex-model-based reliability analysis. Two FORM-type approximations, namely, the mean-value method and the design-point method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.

Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty

2005 ◽  
Vol 128 (2) ◽  
pp. 503-508 ◽  
Author(s):  
Michael Kokkolaras ◽  
Zissimos P. Mourelatos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Uncertainty Propagation ◽  
Mean Value ◽  
Multilevel Systems ◽  
System A ◽  
Engine Design ◽  
Advanced Mean Value ◽  
Mean Value Method ◽  
Propagation Technique ◽  
Bottom To Top

This paper presents a methodology for design optimization of hierarchically decomposed systems under uncertainty. We propose an extended, probabilistic version of the deterministic analytical target cascading (ATC) formulation by treating uncertain quantities as random variables and posing probabilistic design constraints. A bottom-to-top coordination strategy is used for the ATC process. Given that first-order approximations may introduce unacceptably large errors, we use a technique based on the advanced mean value method to estimate uncertainty propagation through the multilevel hierarchy of elements that comprise the decomposed system. A simple yet illustrative hierarchical bilevel engine design problem is used to demonstrate the proposed methodology. The results confirm the applicability of the proposed probabilistic ATC formulation and the accuracy of the uncertainty propagation technique.

Structural/Acoustic Sensitivity Analysis of a Panel With Manufacturing Variability

2002 ◽  
Author(s):  
Sameer B. Mulani ◽  
Michael J. Allen
Keyword(s):  
Sensitivity Analysis ◽  
Mean Value ◽  
Design Parameters ◽  
Sound Power ◽  
Deterministic System ◽  
Acoustic Response ◽  
Element Analysis ◽  
Advanced Mean Value ◽  
Mean Value Method ◽  
Acoustic Sensitivity

Sensitivity analysis is an essential component in the design of structural/acoustic systems. Current structural/acoustic sensitivity algorithms assume deterministic system design parameters and therefore predict changes in the deterministic response of the system. Due to variability associated with manufacturing tolerances most structural/acoustic systems consist of random and deterministic structural design parameters and therefore produce a probabilistic acoustic response. In this work, a structural/acoustic sensitivity algorithm is presented that considers systems comprised of random and deterministic design parameters. The new sensitivity algorithm calculates the change in the probabilistic vibro-acoustic response of a system due to a change in a deterministic design parameter. The new algorithm uses boundary element analysis, finite element analysis, and an advanced mean value method. An elastically supported panel subject to a non-uniform load is used to illustrate the algorithm. Variability is considered in the elastic support while structural sizing parameters are taken to be deterministic. The response of the panel is defined in terms of probabilistic radiated sound power. Probabilistic sound power sensitivity results are calculated and used to predict new sound power values via finite difference analysis. These results are compared successfully to results obtained through re-analysis.

Reliability Analysis of Stiffened Aircraft Panels Using Adjusting Mean Value Method

AIAA Journal ◽  
2020 ◽  
Vol 58 (12) ◽  
pp. 5448-5458
Author(s):  
Behrooz Keshtegar ◽  
Mi Xiao ◽  
Reza Kolahchi ◽  
Nguyen-Thoi Trung
Keyword(s):  
Reliability Analysis ◽  
Mean Value ◽  
Mean Value Method ◽  
Aircraft Panels

Numerical Probabilistic Analysis of Structural/Acoustic Systems

2001 ◽  
Author(s):  
Michael Allen ◽  
Nickolas Vlahopoulos
Keyword(s):  
Probabilistic Analysis ◽  
Mean Value ◽  
Cumulative Distribution ◽  
Acoustic Response ◽  
Element Analysis ◽  
Performance Function ◽  
The Difference ◽  
Advanced Mean Value ◽  
Mean Value Method ◽  
Viable Method

Abstract A formulation that accounts for manufacturing variability in the analysis of structural/acoustic systems is presented. The methodology incorporates the concept of fast probability integration with finite element (FEA) and boundary element analysis (BEA) for producing the probabilistic acoustic response of a structural/acoustic system. The advanced mean value method is used for integrating the system probability density function. FEA and BEA are combined for producing the acoustic response that constitutes the performance function. The probabilistic acoustic response is calculated in terms of a cumulative distribution function. The new methodology is used to illustrate the difference between the results from a probabilistic analysis that accounts for manufacturing uncertainty, and an equivalent deterministic simulation through applications. The probabilistic computations are validated by comparison to Monte Carlo simulations. Based on its computational efficiency and its accuracy the new methodology is concluded to be a viable method of calculating numerically the probabilistic response of structural/acoustic systems due to manufacturing variability.

scholarly journals Sensitivity of a Subject-specific Ankle Sprain Simulation to Extrinsic Versus Intrinsic Biomechanical Factors

2021 ◽  
Vol 9 ◽  
Author(s):  
Adam J. Yoder ◽  
Anthony J. Petrella ◽  
Shawn Farrokhi
Keyword(s):  
Monte Carlo ◽  
Ankle Sprain ◽  
Deterministic Model ◽  
Mean Value ◽  
Ankle Sprains ◽  
Probabilistic Simulation ◽  
Subject Specific ◽  
Advanced Mean Value ◽  
Mean Value Method ◽  
Biomechanical Factors

Ankle sprains are the most common musculoskeletal injury in sport and military activity, despite existing prophylactic strategies. The purpose of this report was to develop a probabilistic simulation of lateral ankle sprains during single-limb drop landing, towards accelerating innovation in ankle sprain prevention. A deterministic, subject-specific musculoskeletal model was extended with automation and probabilistic distributions on sprain-related biomechanical factors. Probabilistic simulations were generated using traditional Monte Carlo techniques and the advanced mean value method, a more computationally-efficient approach. Predicted distributions of peak ankle joint rotations, velocities, and moments borne by supporting passive structures agreed favorably with the deterministic model and with reports of real sprain biomechanics. Parameter sensitivities identified that predictions were most strongly influenced by drop height, subtalar joint posture at contact, invertor/evertor co-activation, and passive ankle stiffness. The advanced mean value method predicted confidence bounds comparable to a 1000-trial Monte Carlo simulation, and required only 14 model evaluations and 4-min processing time. The extended probabilistic simulation may be useful to virtually test new prophylactic strategies for ankle sprains, and is made available for open-source use (https://simtk.org/projects/sprain-sim).

scholarly journals A Mean Extragradient Method for Solving Variational Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 462
Author(s):  
Apichit Buakird ◽  
Nimit Nimana ◽  
Narin Petrot
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Mean Value ◽  
Inequality Problem ◽  
The Mean ◽  
Mean Value Method

We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates. We show weak convergence of the mean value iterate to a solution of the variational inequality problem, provided that a condition on the corresponding averaging matrix is fulfilled. Some numerical experiments are given to show the effectiveness of the obtained theoretical result.

scholarly journals Parameter Estimation of a Class One-Dimensional Discrete Chaotic System

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Lidong Liu ◽  
Jinfeng Hu ◽  
Huiyong Li ◽  
Jun Li ◽  
Zishu He ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Chaotic System ◽  
Chaos Control ◽  
Mean Value ◽  
Unknown Parameters ◽  
Tent Map ◽  
One Dimensional ◽  
Chebyshev Map ◽  
Mean Value Method ◽  
Control And Synchronization

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method (MVM). It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exact than MVM. Finally, numerical simulations on Chebyshev map and Tent map show that the proposed method has better performance of parameter estimation than MVM.

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