On probabilistic constraints with multivariate truncated Gaussian and lognormal distributions

2015 ◽  
Vol 8 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andre Luiz Diniz ◽  
René Henrion
Keyword(s):  
Probabilistic Constraints ◽  
Lognormal Distributions ◽  
Truncated Gaussian

Gauss is Not Mocked: Power Laws and Lognormal Distributions in Performance Data

2013 ◽  
Author(s):  
Seth M. Spain ◽  
P. D. Harms ◽  
Marcus Credé ◽  
Bradley Brummel
Keyword(s):  
Power Laws ◽  
Performance Data ◽  
Lognormal Distributions

Optimization of Tube Hydroforming Process Using Probabilistic Constraints on Failure Modes

2011 ◽  
Vol 62 ◽  
pp. 21-35 ◽  
Author(s):  
Anis Ben Abdessalem ◽  
A. El Hami
Keyword(s):  
Failure Modes ◽  
High Reliability ◽  
Thickness Distribution ◽  
Tube Hydroforming ◽  
Forming Limit Diagram ◽  
Plastic Instability ◽  
Probabilistic Constraints ◽  
Forming Limit ◽  
Reliability Based Design ◽  
Hydroforming Process

In metal forming processes, different parameters (Material constants, geometric dimensions, loads …) exhibits unavoidable scatter that lead the process unreliable and unstable. In this paper, we interest particularly in tube hydroforming process (THP). This process consists to apply an inner pressure combined to an axial displacement to manufacture the part. During the manufacturing phase, inappropriate choice of the loading paths can lead to failure. Deterministic approaches are unable to optimize the process with taking into account to the uncertainty. In this work, we introduce the Reliability-Based Design Optimization (RBDO) to optimize the process under probabilistic considerations to ensure a high reliability level and stability during the manufacturing phase and avoid the occurrence of such plastic instability. Taking account of the uncertainty offer to the process a high stability associated with a low probability of failure. The definition of the objective function and the probabilistic constraints takes advantages from the Forming Limit Diagram (FLD) and the Forming Limit Stress Diagram (FLSD) used as a failure criterion to detect the occurrence of wrinkling, severe thinning, and necking. A THP is then introduced as an example to illustrate the proposed approach. The results show the robustness and efficiency of RBDO to improve thickness distribution and minimize the risk of potential failure modes.

Dynamic Optimization of Steel Catenary Risers Based on Reliability Using Metamodel

2010 ◽  
Author(s):  
Wenqing Zheng ◽  
Hezhen Yang
Keyword(s):  
Dynamic Optimization ◽  
Computational Cost ◽  
Minimum Cost ◽  
Probabilistic Constraints ◽  
Optimization Approach ◽  
Element Analysis ◽  
Steel Catenary Riser ◽  
Reliability Based Design ◽  
Minimum Cost Design ◽  
Steel Catenary Risers

Reliability based design optimization (RBDO) of a steel catenary riser (SCR) using metamodel is investigated. The purpose of the optimization is to find the minimum-cost design subjecting to probabilistic constraints. To reduce the computational cost of the traditional double-loop RBDO, a single-loop RBDO approach is employed. The performance function is approximated by using metamodel to avoid time consuming finite element analysis during the dynamic optimization. The metamodel is constructed though design of experiments (DOE) sampling. In addition, the reliability assessment is carried out by Monte Carlo simulations. The result shows that the RBDO of SCR is a more rational optimization approach compared with traditional deterministic optimization, and using metamodel technique during the dynamic optimization process can significantly decrease the computational expense without sacrificing accuracy.

Estimation of Lognormal Distributions

1981 ◽  
Vol 1 (2) ◽  
pp. 139-153 ◽  
Author(s):  
A. Clifford Cohen ◽  
Betty Jones Whitten
Keyword(s):  
Lognormal Distributions

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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