Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty

2004 ◽  
Author(s):  
Michael Kokkolaras ◽  
Zissimos P. Mourelatos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Probability Distributions ◽  
Mean Value ◽  
Design Problems ◽  
Propagation Of Uncertainty ◽  
Reliability Based Design ◽  
Multilevel Systems ◽  
Simulation Based Design ◽  
Engine Design ◽  
Advanced Mean Value

This paper presents a methodology for design optimization of decomposed systems in the presence of uncertainties. We extend the analytical target cascading (ATC) formulation to probabilistic design by treating stochastic quantities as random variables and parameters and posing reliability-based design constraints. We model the propagation of uncertainty throughout the multilevel hierarchy of elements that comprise the decomposed system by using the advanced mean value (AMV) method to generate the required probability distributions of nonlinear responses. We utilize appropriate metamodeling techniques for simulation-based design problems. A simple yet illustrative hierarchical bi-level engine design problem is used to demonstrate the proposed methodology.

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.

Hybrid Analysis Method for Reliability-Based Design Optimization

2003 ◽  
Vol 125 (2) ◽  
pp. 221-232 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi ◽  
Young H. Park
Keyword(s):  
Design Optimization ◽  
Mean Value ◽  
Performance Measure ◽  
Equality Constraint ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Function ◽  
Reliability Based Design ◽  
Advanced Mean Value

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the optimization process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the advanced mean value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the conjugate mean value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the hybrid mean value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.

A Methodology for Trading-Off Performance and Robustness Under Uncertainty

2005 ◽  
Vol 128 (4) ◽  
pp. 856-863 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Jinghong Liang
Keyword(s):  
Design Optimization ◽  
Pareto Frontier ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Mean Value ◽  
Preference Aggregation ◽  
Efficient Design ◽  
Reliability Based Design ◽  
Advanced Mean Value ◽  
Reliability And Robustness

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization, however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multiobjective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the advanced mean value method. A preference aggregation method converts the multiobjective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.

Hybrid Analysis Method for Reliability-Based Design Optimization

2001 ◽  
Author(s):  
Kyung K. Choi ◽  
Byeng D. Youn
Keyword(s):  
Design Optimization ◽  
Mean Value ◽  
Performance Measure ◽  
Equality Constraint ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Function ◽  
Reliability Based Design ◽  
Advanced Mean Value

Abstract Reliability-Based Design Optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the RBDO process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the Advanced Mean Value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the Conjugate Mean Value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the Hybrid Mean Value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.

The Performance Moment Integration Method for Reliability-Based Robust Design Optimization

2004 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi
Keyword(s):  
Design Optimization ◽  
Product Quality ◽  
Robust Design ◽  
Mean Value ◽  
Performance Measure ◽  
Robust Design Optimization ◽  
Integration Scheme ◽  
Quality Loss ◽  
Reliability Based Design ◽  
Different Types

Reliability-based robust design optimization deals with two objectives of structural design methodologies subject to various uncertainties: reliability-based design and robust design. A reliability-based design optimization deals with the probability of failure, while a robust design optimization minimizes the product quality loss. In general, the product quality loss is described by using the first two statistical moments: mean and standard deviation. In this paper, a performance moment integration (PMI) method is proposed by using numerical integration scheme for output response to estimate the product quality loss. For the reliability part of the reliability-based robust design optimization, the performance measure approach (PMA) and its numerical method, hybrid-mean value (HMV) method, are used. New formulations of reliability-based robust design optimization are presented for three different types of robust objectives, such as smaller-the-better, larger-the-better, and nominal-the-better types. Examples are used to demonstrate the effectiveness of reliability-based robust design optimization using the proposed PMI method for different types of robust objective.

Reliability-Based Design Optimization for Design Problems with Random Fuzzy and Interval Uncertainties

2019 ◽  
Vol 17 (06) ◽  
pp. 1950018 ◽  
Author(s):  
Li-Xiang Zhang ◽  
Xin-Jia Meng ◽  
He Zhang
Keyword(s):  
Design Optimization ◽  
Mechanical Design ◽  
Computational Cost ◽  
Reliability Based Design Optimization ◽  
Design Problems ◽  
Main Obstacle ◽  
Reliability Based Design ◽  
Interval Uncertainties ◽  
Mixed Uncertainties ◽  
Measurement Approach

Reliability-based design optimization (RBDO) has been widely used in mechanical design. However, the treatment of various uncertainties and associated computational burden are still the main obstacle of its application. A methodology of RBDO under random fuzzy and interval uncertainties (RFI-RBDO) is proposed in this paper. In the proposed methodology, two reliability analysis approaches, respectively named as FORM-[Formula: see text]-URA and interpolation-based sequential performance measurement approach (ISPMA), are developed for the mixed uncertainties assessment, and a parallel-computing-based SOMUA (PCSOMUA) method is proposed to reduce the computational cost of RFI-RBDO. Finally, two examples are provided to verify the validity of the methods.

Reliability-Based Design Optimization on Qualitative Objective With Limited Information

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Khaldon T. Meselhy ◽  
G. Gary Wang
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Probability Distributions ◽  
Random Variables ◽  
Limited Information ◽  
Reliability Based Design Optimization ◽  
Mathematical Formula ◽  
Reliability Based Design ◽  
Design Structure ◽  
Design Variables

Reliability-based design optimization (RBDO) algorithms typically assume a designer's prior knowledge of the objective function along with its explicit mathematical formula and the probability distributions of random design variables. These assumptions may not be valid in many industrial cases where there is limited information on variable variability and the objective function is subjective without mathematical formula. A new methodology is developed in this research to model and solve problems with qualitative objective functions and limited information about random variables. Causal graphs and design structure matrix are used to capture designer's qualitative knowledge of the effects of design variables on the objective. Maximum entropy theory and Monte Carlo simulation are used to model random variables' variability and derive reliability constraint functions. A new optimization problem based on a meta-objective function and transformed deterministic constraints is formulated, which leads close to the optimum of the original mathematical RBDO problem. The developed algorithm is tested and validated with the Golinski speed reducer design case. The results show that the algorithm finds a near-optimal reliable design with less initial information and less computation effort as compared to other RBDO algorithms that assume full knowledge of the problem.

A Methodology for Trading-Off Performance and Robustness Under Uncertainty

2005 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Jinghong Liang
Keyword(s):  
Design Optimization ◽  
Pareto Frontier ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Mean Value ◽  
Preference Aggregation ◽  
Efficient Design ◽  
Multi Objective ◽  
Reliability Based Design ◽  
Reliability And Robustness

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multi-objective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the Advanced Mean Value (AMV) method. A preference aggregation method converts the multi-objective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.

Reliability Based Design Optimization Modeling Future Redesign With Different Epistemic Uncertainty Treatments

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Taiki Matsumura ◽  
Raphael T. Haftka
Keyword(s):  
Design Optimization ◽  
Thermal Protection ◽  
Epistemic Uncertainty ◽  
Probability Distributions ◽  
Aleatory Uncertainty ◽  
Reliability Based Design Optimization ◽  
Worst Case ◽  
Reliability Based Design ◽  
The Future ◽  
Integrated Thermal Protection System

Design under uncertainty needs to account for aleatory uncertainty, such as variability in material properties, and epistemic uncertainty including errors due to imperfect analysis tools. While there is a consensus that aleatory uncertainty be described by probability distributions, for epistemic uncertainty there is a tendency to be more conservative by taking worst case scenarios or 95th percentiles. This conservativeness may result in substantial performance penalties. Epistemic uncertainty, however, is usually reduced by additional knowledge typically provided by tests. Then, redesign may take place if tests show that the design is not acceptable. This paper proposes a reliability based design optimization (RBDO) method that takes into account the effects of future tests possibly followed by redesign. We consider each realization of epistemic uncertainty to correspond to a different design outcome. Then, the future scenario, i.e., test and redesign, of each possible design outcome is simulated. For an integrated thermal protection system (ITPS) design, we show that the proposed method reduces the mass penalty associated with a 95th percentile of the epistemic uncertainty from 2.7% to 1.2% compared to standard RBDO, which does not account for the future. We also show that the proposed approach allows trading off mass against development costs as measured by probability of needing redesign. Finally, we demonstrate that the tradeoff can be achieved even with the traditional safety factor based design.

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