Decision-Based Approach for Reliability Design

2006 ◽  
Vol 129 (5) ◽  
pp. 466-475 ◽  
Author(s):  
Efstratios Nikolaidis
Keyword(s):  
Probabilistic Models ◽  
Epistemic Uncertainty ◽  
Reliability Based Design Optimization ◽  
Insufficient Information ◽  
Design Problems ◽  
Reliability Design ◽  
Reliability Based Design ◽  
Trade Offs ◽  
New Formulation ◽  
Robust Reliability

We propose a decision-based approach for reliability design when there is insufficient information for constructing probabilistic models. The approach enables a designer to perform reliability-cost trade-offs and to assess the importance of variability and epistemic uncertainty. A method for decision under epistemic uncertainty is first presented and justified by presenting axioms on a decision maker’s (DM’s) preferences and by assuming that the DM’s goal is to find the most immune act (in terms of having undesirable consequences) to deviations of the state of the world from an expected state. Thus, the philosophy of the method is similar to that of robust reliability (Ben Haim, Y., 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin). A new formulation of reliability design problems is proposed based on the above decision method and is compared to two reliability-based design optimization formulations that minimize cost given a maximum acceptable failure probability or maximize expected utility. The method is demonstrated on a decision where a designer has to choose between two materials for a structure.

Reliability-Based Design Optimization for Nonlinear Energy Harvesters

2015 ◽  
Author(s):  
Sumin Seong ◽  
Christopher Mullen ◽  
Soobum Lee
Keyword(s):  
Energy Harvesting ◽  
Design Optimization ◽  
Reliability Based Design Optimization ◽  
Vibration Energy Harvester ◽  
Reliability Design ◽  
Energy Harvesters ◽  
Reliability Based Design ◽  
Stable Characteristic ◽  
Tip Mass ◽  
Nonlinear Energy

This paper presents reliability-based design optimization (RBDO) and experimental validation of the purely mechanical nonlinear vibration energy harvester we recently proposed. A bi-stable characteristic was embodied with a pre-stressed curved cantilever substrate on which piezoelectric patches were laminated. The curved cantilever can be simply manufactured by clamping multiple beams with different lengths or by connecting two ends of the cantilever using a coil spring. When vibrating, the inertia of the tip mass activates the curved cantilever to cause snap-through buckling and makes the nature of vibration switch between two equilibrium positions. The reliability-based design optimization study for maximization of power density and broadband energy harvesting performance is performed. The benefit of the proposed design in terms of excellent reliability, design compactness, and ease of implementation is discussed. The prototype is fabricated based on the optimal design result and energy harvesting performance between the linear and nonlinear energy harvesters is compared. The excellent broadband characteristic of the purely mechanical harvester will be validated.

scholarly journals Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

2021 ◽  
Author(s):  
Yoshihiro Kanno
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Structural Reliability ◽  
Reliability Based Design Optimization ◽  
Input Distribution ◽  
Reliability Based Design ◽  
Optimal Value ◽  
Reliability Constraint ◽  
Distributionally Robust ◽  
Robust Reliability

AbstractThis study considers structural optimization under a reliability constraint, in which the input distribution is only partially known. Specifically, when it is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, it is required that the failure probability of a structure should be no greater than a specified target value for any realization of the input distribution. We demonstrate that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can handle a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization; in particular, nonlinear semidefinite programming. Two numerical examples are solved to demonstrate the relation between the optimal value and either the target reliability or the uncertainty magnitude.

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 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.

Model Uncertainty Approximation Using a Copula-Based Approach for Reliability Based Design Optimization

2016 ◽  
Author(s):  
Hao Pan ◽  
Zhimin Xi ◽  
Ren-Jye Yang
Keyword(s):  
Design Optimization ◽  
Model Uncertainty ◽  
Design Space ◽  
Epistemic Uncertainty ◽  
Minimum Cost ◽  
Vehicle Design ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Model Inadequacy

Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting defined reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias which indicates the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty characterization in a defined product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias correction approach is proposed and results are demonstrated by two vehicle design case studies.

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

2012 ◽  
Author(s):  
Taiki Matsumura ◽  
Raphael T. Haftka ◽  
Bhavani V. Sankar
Keyword(s):  
Design Optimization ◽  
Epistemic Uncertainty ◽  
Single Point ◽  
Probabilistic Approach ◽  
Probability Of Failure ◽  
Aleatory Uncertainty ◽  
Engineering Systems ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Analysis Models

The design of engineering systems is often based on analysis models with substantial errors in predicting failures, that is epistemic uncertainty. The epistemic uncertainty is reduced by post design tests, and the safety of unsafe designs restored by redesign. When this process of design, test and redesign is to be based on probabilistic analysis, there is some controversy on whether uncertainty associated with variability (aleatory uncertainty) should be treated differently than the epistemic uncertainty. In this paper we compare several approaches to design and redesign and treatments of the epistemic uncertainties. These include safety factors, probabilistic approach disregarding redesign and regarding redesign, treating epistemic uncertainty and aleatory uncertainty the same, and more conservative treatment of the epistemic uncertainty. We demonstrate that the proposed approach can allow tradeoff of system performance against development cost (probability of redesign), while a standard reliability based design optimization, which does not take into account future redesign, provides only a single point on the tradeoff curve. We also show that the tradeoff can be achieved even with the traditional safety factor approach, without any probabilistic optimization. Furthermore, we investigate different treatments of epistemic error for probability of failure calculation. We find that it is possible to design to the 95th percentile of the probability of failure with modest mass penalty compared to treating epistemic and aleatory uncertainty alike.

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