Optimal Design With Non-Normally Distributed Random Parameters, Conditional Probability, and Joint Constraint Reliabilities: A Case Study in Vehicle Emissions Regulations to Achieve Ambient Air Quality Standards

2006 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
High Reliability ◽  
Ambient Air ◽  
Probabilistic Constraints ◽  
Model Complexity ◽  
Bayesian Probability ◽  
Vehicle Speed ◽  
Random Parameters ◽  
Active Set ◽  
Regulatory Constraints

Making appropriate environmental policy decisions requires considering various sources of uncertainty. An air pollution example is formulated as a design optimization problem with probabilistic constraints, also referred to as reliability-based design optimization (RBDO). Environmental applications with a large number of constraints and significant model complexity present special challenges. In this paper an efficient active set strategy is integrated with a reliability contour surface approach to solve probabilistic problems with non-normal variable probability distributions. Discrete random parameters, which result in Bayesian probability, are also present and they are incorporated using delta function approximations. Joint constraint reliability that considers satisfying all regulatory constraints is also discussed. A demonstration example of setting the optimal vehicle speed limit while maintaining high reliability for CO and NOx standards of a residential area near two highway systems is included.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2005 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on Reliability-Based Design Optimization (RBDO), i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with a numerical example.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on reliability-based design optimization, i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with numerical examples.

An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches

2002 ◽  
Author(s):  
Kyung K. Choi ◽  
Byeng D. Youn
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Probability Distributions ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Standard Normal

Deterministic optimum designs that are obtained without consideration of uncertainty could lead to unreliable designs, which call for a reliability approach to design optimization, using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mapping between X- and U-spaces for a various probability distributions. Therefore, the nonlinearity of RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity to reliability-based performance measures evaluated during the RBDO process. Evaluation of probabilistic constraints in RBDO can be carried out in two different ways: the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity of RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of highly nonlinear transformations involved. However, PMA is rather independent of probability distributions because of little involvement of the nonlinear transformation.

Reliability-based design optimization analysis of tube hydroforming process

SIMULATION ◽  
2012 ◽  
Vol 88 (9) ◽  
pp. 1129-1137 ◽  
Author(s):  
A El Hami ◽  
B Radi ◽  
A Cherouat
Keyword(s):  
Design Optimization ◽  
Failure Modes ◽  
High Reliability ◽  
Thickness Distribution ◽  
Tube Hydroforming ◽  
Probabilistic Constraints ◽  
Forming Limit ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Hydroforming Process

In this paper, we are interested particularly in the tube hydroforming process (THP). This process consists of applying an inner pressure combined with an axial displacement to manufacture the part. During the manufacturing phase, inappropriate choice of the load paths can lead to failure. Deterministic approaches are unable to optimize the process by taking into account the uncertainty. So we introduce the reliability-based design optimization (RBDO) to optimize the process under probabilistic constraints to ensure a high reliability level and stability during the manufacturing phase and avoid the occurrence of such plastic instability. Taking some uncertainties into account the process is very stable and associated with a low failure probability. The definition of the objective function and the probabilistic constraints take advantage of 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. To validate the proposed approach, the THP is then introduced as an example. The numerical results show the robustness and efficiency of the RBDO to improve thickness distribution and minimize the risk of potential failure modes.

An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches

2003 ◽  
Vol 126 (3) ◽  
pp. 403-411 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Probability Distributions ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Standard Normal

Because deterministic optimum designs obtained without taking uncertainty into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and a reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mappings between X- and U-spaces for various probability distributions. Therefore, the nonlinearity of the RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity into the reliability-based performance measures evaluated during the RBDO process. The evaluation of probabilistic constraints in RBDO can be carried out in two ways: using either the Reliability Index Approach (RIA), or the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity for RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of the highly nonlinear transformations that are involved. However, PMA is rather independent of probability distributions because it only has a small involvement with a nonlinear transformation.

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.

Reliability-Based Design Optimization of Robotic System Dynamic Performance

2006 ◽  
Vol 129 (4) ◽  
pp. 449-454 ◽  
Author(s):  
Alan P. Bowling ◽  
John E. Renaud ◽  
Jeremy T. Newkirk ◽  
Neal M. Patel ◽  
Harish Agarwal
Keyword(s):  
Design Optimization ◽  
Reference Point ◽  
High Reliability ◽  
Dynamic Performance ◽  
Performance Measure ◽  
Robotic System ◽  
Reliability Based Design Optimization ◽  
End Effector ◽  
Reliability Based Design ◽  
Reliable Design

In this investigation a robotic system’s dynamic performance is optimized for high reliability under uncertainty. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end effector (i.e., point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs with robust dynamic performance with respect to the end-effector reference point. In this work a unilevel performance measure approach is used to perform RBDO. This is important for the reliable design of robotic systems in which a solution to the DCE is required for each constraint call. The method is illustrated on a robot design problem.

Sign in / Sign up

Export Citation Format

Share Document