Reliability-Based Design With the Mixture of Random and Interval Variables

2005 ◽  
Vol 127 (6) ◽  
pp. 1068-1076 ◽  
Author(s):  
Xiaoping Du ◽  
Agus Sudjianto ◽  
Beiqing Huang
Keyword(s):  
Reliability Analysis ◽  
Probability Distributions ◽  
Case Scenario ◽  
Worst Case ◽  
Uncertain Variables ◽  
Reliability Based Design ◽  
Interval Variables ◽  
Practical Engineering ◽  
Loop Procedure ◽  
Precise Distribution

In reliability-based design (RBD), uncertainties are usually treated stochastically, and nondeterministic variables are assumed to follow certain probability distributions. However, in many practical engineering applications, distributions of some random variables may not be precisely known or uncertainties may not be appropriately represented with distributions. The possible values of those nondeterministic variables are often only known to lie within specified intervals without precise distribution information. In this paper, we attempt to address this issue by proposing a RBD method to deal with the uncertain variables characterized by the mixture of probability distributions and intervals. The reliability is considered under the condition of the worst case combination of interval variables. The computational demand of RBD with the mixture of random and interval variables may increase dramatically due to the need for identifying the worst case interval variables. To alleviate the computational burden, a sequential single-loop procedure is employed to replace the computationally expensive double-loop procedure when the worst case scenario is applied directly. With the proposed method, the RBD is conducted within a series of cycles of deterministic optimization and reliability analysis. The optimization model in each cycle is built based on the most probable point under the worst case combination of the interval variables obtained from the reliability analysis in the previous cycle. Since the optimization is decoupled from the probabilistic analysis, the computational amount for reliability analysis is decreased to the minimum extent. The proposed method is demonstrated with two examples.

Reliability-Based Design With the Mixture of Random and Interval Variables

2003 ◽  
Author(s):  
Xiaoping Du ◽  
Agus Sudjianto
Keyword(s):  
Reliability Analysis ◽  
Structural Design ◽  
Probability Distributions ◽  
Case Scenario ◽  
Worst Case ◽  
Uncertain Variables ◽  
Reliability Based Design ◽  
Previous Cycle ◽  
Interval Variables ◽  
Loop Procedure

In Reliability-Based Design (RBD), uncertainties usually imply for randomness. Nondeterministic variables are assumed to follow certain probability distributions. However, in real engineering applications, some of distributions may not be precisely known or uncertainties associated with some uncertain variables are not from randomness. These nondeterministic variables are only known within intervals. In this paper, a method of RBD with the mixture of random variables with distributions and uncertain variables with intervals is proposed. The reliability is considered under the condition of the worst combination of interval variables. In comparison with traditional RBD, the computational demand of RBD with the mixture of random and interval variables increases dramatically. To alleviate the computational burden, a sequential single-loop procedure is developed to replace the computationally expensive double-loop procedure when the worst case scenario is applied directly. With the proposed method, the RBD is conducted within a series of cycles of deterministic optimization and reliability analysis. The optimization model in each cycle is built based on the Most Probable Point (MPP) and the worst case combination obtained in the reliability analysis in previous cycle. Since the optimization is decoupled from the reliability analysis, the computational amount for MPP search is decreased to the minimum extent. The proposed method is demonstrated with a structural design example.

scholarly journals A Time-Variant Reliability Analysis Method Based on the Stochastic Process Discretization under Random and Interval Variables

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 568
Author(s):  
Fangyi Li ◽  
Jie Liu ◽  
Yufei Yan ◽  
Jianhua Rong ◽  
Jijun Yi
Keyword(s):  
Stochastic Process ◽  
Reliability Analysis ◽  
Random Variables ◽  
Static System ◽  
Reliability Problem ◽  
Uncertain Variables ◽  
Discrete Random Variables ◽  
Interval Variables ◽  
Practical Engineering ◽  
Hybrid Reliability

In practical engineering, it is a cost-consuming problem to consider the time-variant reliability of both random variables and interval variables, which usually requires a lot of calculation. Therefore, a time-variant reliability analysis approach with hybrid uncertain variables is proposed in this paper. In the design period, the stochastic process is discretized into random variables. Simultaneously, the original random variables and the discrete random variables are converted into independent normal variables, and the interval variables are changed into standard variables. Then it is transformed into a hybrid reliability problem of static series system. At different times, the limited state functions are linearized at the most probable point (MPP) and at the most unfavorable point (MUP). The transformed static system reliability problem with hybrid uncertain variables can be solved effectively by introducing random variables. To solve the double-loop nested optimization in the hybrid reliability calculation, an effective iterative method is proposed. Two numerical examples and an engineering example demonstrate the validity of the present approach.

Reliability-Based Design Optimization of Microstructures With Analytical Formulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Pinar Acar
Keyword(s):  
Design Optimization ◽  
Material Properties ◽  
Optimization Problem ◽  
Optimization Under Uncertainty ◽  
Reliability Based Design Optimization ◽  
Case Scenario ◽  
Worst Case ◽  
Analytical Formulation ◽  
Reliability Based Design ◽  
Safe Approach

Microstructures are stochastic by their nature. These aleatoric uncertainties can alter the expected material performance substantially and thus they must be considered when designing materials. One safe approach would be assuming the worst case scenario of uncertainties in design. However, design under the worst case conditions can lead to over-conservative solutions that provide less effective material properties. Here, a more powerful design approach can be developed by implementing reliability constraints into the optimization problem to achieve superior material properties while satisfying the prescribed design criteria. This is known as reliability-based design optimization (RBDO), and it has not been studied for microstructure design before. In this work, an analytical formulation that models the propagation of microstructural uncertainties to the material properties is utilized to compute the probability of failure. Next, the analytical uncertainty solution is integrated into the optimization problem to define the reliability constraints. The presented optimization under uncertainty scheme is exercised to maximize the yield stress of α-Titanium and magnetostriction of Galfenol, respectively.

scholarly journals A New SORM Method for Structural Reliability with Hybrid Uncertain Variables

2020 ◽  
Vol 11 (1) ◽  
pp. 346
Author(s):  
Pidong Wang ◽  
Lechang Yang ◽  
Ning Zhao ◽  
Lefei Li ◽  
Dan Wang
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Random Variables ◽  
State Function ◽  
Strong Nonlinearity ◽  
Limit State Function ◽  
Practical Applications ◽  
Uncertain Variables ◽  
Practical Engineering

(1) Background: in practical applications, probabilistic and non-probabilistic information often simultaneously exit. For a complex system with a nonlinear limit-state function, the analysis and evaluation of the reliability are imperative yet challenging tasks. (2) Methods: an improved second-order method is proposed for reliability analysis in the presence of both random and interval variables, where a novel polar transformation is employed. This method enables a unified reliability analysis taking both random variables and bounded intervals into account, simplifying the calculation by transforming a high-dimension limit-state function into a bivariate state function. The obtained nonlinear probability density functions of two variables in the function inherit the statistic characteristics of interval and random variables. The proposed method does not require any strong assumptions and so it can be used in various practical engineering applications. (3) Results: the proposed method is validated via two numerical examples. A comparative study towards a contemporary algorithm in state-of-the-art literature is carried out to demonstrate the benefits of our method. (4) Conclusions: the proposed method outperforms existing methods both in efficiency and accuracy, especially for cases with strong nonlinearity.

scholarly journals System Reliability Based Design Optimization of Truss Structures with Interval Variables

2019 ◽  
Author(s):  
Mohammad Zaeimi ◽  
Ali Ghoddosain
Keyword(s):  
Design Optimization ◽  
System Reliability ◽  
Truss Structures ◽  
Equivalent Model ◽  
Reliability Based Design Optimization ◽  
Uncertain Variables ◽  
Reliability Based Design ◽  
Interval Variables ◽  
Reliability Method ◽  
Process Reliability

New products ranging from simple components to complex structures should be designed to be optimal and reliable. In this paper, for the first time, a hybrid uncertain model is applied to system reliability based design optimization (RBDO) of trusses. All uncertain variables are described by random distributions but those lack information are defined by variation intervals. For system RBDO of trusses, the first order reliability method, as well as an equivalent model and the branch and bound method, are utilized to determine the system failure probability; and Improved (μ + λ) constrained differential evolution (ICDE) is employed for the optimization process. Reliability assessment of some engineering examples is proposed to verify our results. Moreover, the effect interval variables on the optimum weight of the truss structures are investigated. The results indicate that the optimal weight depends not only on the uncertainty level but also on the equivalent standard deviation; and a falling-rising behavior is observed.

scholarly journals Multi-Objective, Reliability-Based Design Optimization of a Steering Linkage

2020 ◽  
Vol 10 (17) ◽  
pp. 5748
Author(s):  
Suwin Sleesongsom ◽  
Sujin Bureerat
Keyword(s):  
Design Optimization ◽  
Double Loop ◽  
Reliability Based Design Optimization ◽  
Case Scenario ◽  
Worst Case ◽  
Multi Objective ◽  
Reliability Based Design ◽  
Linkage Design ◽  
A New Technique ◽  
Optimization Loop

Reliability-based design optimization (RBDO) of a mechanism is normally based on the non-probabilistic model, which is viewed as failure possibility constraints in each optimization loop. It leads to a double-loop nested problem that causes a computationally expensive evaluation. Several methods have been developed to solve the problem, which are expected to increase the realization of optimum results and computational efficiency. The purpose of this paper was to develop a new technique of RBDO that can reduce the complexity of the double-loop nested problem to a single-loop. This involves using a multi-objective evolutionary technique combined with the worst-case scenario and fuzzy sets, known as a multi-objective, reliability-based design optimization (MORBDO). The optimization test problem and a steering linkage design were used to validate the performance of the proposed technique. The proposed technique can reduce the complexity of the design problem, producing results that are more conservative and realizable.

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.

A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Zequn Wang ◽  
Pingfeng Wang
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Limit State ◽  
Time Dependent ◽  
Probabilistic Constraints ◽  
State Function ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Extreme Response ◽  
Practical Engineering

A primary concern in practical engineering design is ensuring high system reliability throughout a product's lifecycle, which is subject to time-variant operating conditions and component deteriorations. Thus, the capability of dealing with time-dependent probabilistic constraints in reliability-based design optimization (RBDO) is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. This approach employs the kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization (EGO) technique is integrated with the NERS approach to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation (ARPMM) mechanism is developed based on the mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis, and existing advanced reliability analysis and design methods can be used. The NERS approach is compared with existing time-dependent reliability analysis approaches and integrated with RBDO for engineered system design with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

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.

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