Academic literature on the topic 'Reliability Design Optimization methods (RBDO)'
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Journal articles on the topic "Reliability Design Optimization methods (RBDO)":
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Chiralaksanakul, Anukal, and Sankaran Mahadevan. "First-Order Approximation Methods in Reliability-Based Design Optimization." Journal of Mechanical Design 127, no. 5 (October 8, 2004): 851–57. http://dx.doi.org/10.1115/1.1899691.
Abstract:
Efficiency of reliability-based design optimization (RBDO) methods is a critical criterion as to whether they are viable for real-world problems. Early RBDO methods are thus based primarily on the first-order reliability method (FORM) due to its efficiency. Recently, several first-order RBDO methods have been proposed, and their efficiency is significantly improved through problem reformulation and/or the use of inverse FORM. Our goal is to present these RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO reformulations. Through the formalization, their relationships are revealed. Using reported numerical studies, we discuss their numerical efficiency, convergence, and accuracy.
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Li, Xiaoke, Qingyu Yang, Yang Wang, Xinyu Han, Yang Cao, Lei Fan, and Jun Ma. "Development of surrogate models in reliability-based design optimization: A review." Mathematical Biosciences and Engineering 18, no. 5 (2021): 6386–409. http://dx.doi.org/10.3934/mbe.2021317.
Abstract:
<abstract> <p>Reliability-based design optimization (RBDO) is applied to handle the unavoidable uncertainties in engineering applications. To alleviate the huge computational burden in reliability analysis and design optimization, surrogate models are introduced to replace the implicit objective and performance functions. In this paper, the commonly used surrogate modeling methods and surrogate-assisted RBDO methods are reviewed and discussed. First, the existing reliability analysis methods, RBDO methods, commonly used surrogate models in RBDO, sample selection methods and accuracy evaluation methods of surrogate models are summarized and compared. Then the surrogate-assisted RBDO methods are classified into global modeling methods and local modeling methods. A classic two-dimensional RBDO numerical example are used to demonstrate the performance of representative global modeling method (Constraint Boundary Sampling, CBS) and local modeling method (Local Adaptive Sampling, LAS). The advantages and disadvantages of these two kinds of modeling methods are summarized and compared. Finally, summary and prospect of the surrogate–assisted RBDO methods are drown.</p> </abstract>
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Deng, Siyang, Stéphane Brisset, and Stephane Clénet. "Comparative study of methods for optimization of electromagnetic devices with uncertainty." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 2 (March 5, 2018): 704–17. http://dx.doi.org/10.1108/compel-11-2016-0502.
Abstract:
PurposeThis paper compares six reliability-based design optimization (RBDO) approaches dealing with uncertainties for a simple mathematical model and a multidisciplinary optimization problem of a safety transformer to highlight the most effective. Design/methodology/approachThe RBDO and various approaches to calculate the probability of failure are is presented. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems. FindingsThe mathematical example shows that the six RBDO approaches have almost the same results except the approximate moment approach that is less accurate. The optimization of the safety transformer highlights that not all the methods can converge to the global solution. Performance measure approach, single-loop approach and sequential optimization and reliability assessment (SORA) method appear to be more stable. Considering both numerical examples, SORA is the most effective method among all RBDO approaches. Originality/valueThe comparison of six RBDO methods on the optimization problem of a safety transformer is achieved for the first time. The comparison in terms of precision and number of evaluations highlights the most effective ones.
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Zou, T., and S. Mahadevan. "Versatile Formulation for Multiobjective Reliability-Based Design Optimization." Journal of Mechanical Design 128, no. 6 (November 22, 2005): 1217–26. http://dx.doi.org/10.1115/1.2218884.
Abstract:
This paper develops a multiobjective optimization methodology for system design under uncertainty. Model-based reliability analysis methods are used to compute the probabilities of unsatisfactory performance at both component and system levels. Combined with several multiobjective optimization formulations, a versatile reliability-based design optimization (RBDO) approach is used to achieve a tradeoff between two objectives and to generate the Pareto frontier for decision making. The proposed RBDO approach uses direct reliability analysis to decouple the reliability and optimization iterations, instead of inverse first-order reliability analysis as other existing decoupled approaches. This helps to solve a wide variety of RBDO problems with competing objectives, especially when system-level reliability constraints need to be considered. The approach also allows more accurate methods to be used for reliability analysis, and reliability terms to be included in the objective function. Two important automotive quality objectives, related to the door closing effort (evaluated using component reliability analysis) and the wind noise (evaluated using system reliability analysis), are used to illustrate the proposed method.
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Zhang, Li-Xiang, Xin-Jia Meng, and He Zhang. "Reliability-Based Design Optimization for Design Problems with Random Fuzzy and Interval Uncertainties." International Journal of Computational Methods 17, no. 06 (April 4, 2019): 1950018. http://dx.doi.org/10.1142/s021987621950018x.
Abstract:
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.
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Albuquerque, Carla Simone de, and Mauro de Vasconcelos Real. "Comparative analysis of deterministic and reliability-based structural optimization methods." Ciência e Natura 45, esp. 3 (December 1, 2023): e74335. http://dx.doi.org/10.5902/2179460x74335.
Abstract:
Optimization is the act of obtaining the best possible result under established conditions. Usually, the optimization of a structural design is done considering the structure's dimensions, the materials' properties, and the loads as deterministic values. This way, the optimization process can lead to a more economical design without guaranteeing that this structure is safe. In practice, there are always uncertainties about the final dimensions of the built structure, material properties, and loads. Then, the need arises to use design optimization techniques based on reliability to guarantee a project that is both economical and safe. This objective is achieved by including uncertainties in the optimization process. This article evaluates the parameters that determine the global minimum of the optimization methods DDO (Deterministic Design Optimization) and RBDO (Reliability-Based Design Optimization). This work aims to compare the structural optimization methods of DDO and RBDO through an example. The results are obtained through the codes of the methods implemented in the Python language and show that when comparing the two optimization methods, the presence of uncertainties alters the optimal solution.
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El Hami, A., and Bouchaib Radi. "Comparison Study of Different Reliability-Based Design Optimization Approaches." Advanced Materials Research 274 (July 2011): 113–21. http://dx.doi.org/10.4028/www.scientific.net/amr.274.113.
Abstract:
In this paper, we present a new method based on Optimal Safety Factors (OSF) in the context of the Reliability-Based Design Optimization (RBDO) analysis of ultrasonic motors with traveling wave taking into account the contact between the different components (stator and rotor). We will underline also the different methods of the RBDO analysis and we highlight the advantage of our approach based on OSF. Numerical results are given to illustrate the proposed method.
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Chen, Zhen Zhong, Hao Bo Qiu, Hong Yan Hao, and Hua Di Xiong. "A Reliability Index Based Decoupling Method for Reliability-Based Design Optimization." Advanced Materials Research 544 (June 2012): 223–28. http://dx.doi.org/10.4028/www.scientific.net/amr.544.223.
Abstract:
Reliability-based design optimization (RBDO) evaluates variation of output induced by uncertainties of design variables and results in an optimal design while satisfying the reliability requirements. However, its use in practical applications is hindered by the huge computational cost during the evaluation of structure reliability. In this paper, the reliability index based decoupling method is developed to improve the efficiency of probabilistic optimization. The reliability index is used to calculate the shifting vector in the decoupling process, due to its efficiency in evaluating violated probabilistic constraints. The computation capability of the proposed method is demonstrated using two examples, which are widely used to test RBDO methods. The comparison results show that the proposed method has the same accuracy as the existing methods, and it is also very efficient.
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Chun, Junho. "Reliability-Based Design Optimization of Structures Using Complex-Step Approximation with Sensitivity Analysis." Applied Sciences 11, no. 10 (May 20, 2021): 4708. http://dx.doi.org/10.3390/app11104708.
Abstract:
Structural optimization aims to achieve a structural design that provides the best performance while satisfying the given design constraints. When uncertainties in design and conditions are taken into account, reliability-based design optimization (RBDO) is adopted to identify solutions with acceptable failure probabilities. This paper outlines a method for sensitivity analysis, reliability assessment, and RBDO for structures. Complex-step (CS) approximation and the first-order reliability method (FORM) are unified in the sensitivity analysis of a probabilistic constraint, which streamlines the setup of optimization problems and enhances their implementation in RBDO. Complex-step approximation utilizes an imaginary number as a step size to compute the first derivative without subtractive cancellations in the formula, which have been observed to significantly affect the accuracy of calculations in finite difference methods. Thus, the proposed method can select a very small step size for the first derivative to minimize truncation errors, while achieving accuracy within the machine precision. This approach integrates complex-step approximation into the FORM to compute sensitivity and assess reliability. The proposed method of RBDO is tested on structural optimization problems across a range of statistical variations, demonstrating that performance benefits can be achieved while satisfying precise probabilistic constraints.
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Zhang, Chun-Yi, Ze Wang, Cheng-Wei Fei, Zhe-Shan Yuan, Jing-Shan Wei, and Wen-Zhong Tang. "Fuzzy Multi-SVR Learning Model for Reliability-Based Design Optimization of Turbine Blades." Materials 12, no. 15 (July 24, 2019): 2341. http://dx.doi.org/10.3390/ma12152341.
Abstract:
The effectiveness of a model is the key factor of influencing the reliability-based design optimization (RBDO) of multi-failure turbine blades in the power system. A machine learning-based RBDO approach, called fuzzy multi-SVR learning method, was proposed by absorbing the strengths of fuzzy theory, support vector machine of regression (SVR), and multi-response surface method. The model of fuzzy multi-SVR learning method was established by adopting artificial bee colony algorithm to optimize the parameters of SVR models and considering the fuzziness of constraints based on fuzzy theory, in respect of the basic thought of multi-response surface method. The RBDO model and procedure with fuzzy multi-SVR learning method were then resolved and designed by multi-objective genetic algorithm. Lastly, the fuzzy RBDO of a turbine blade with multi-failure modes was performed regarding the design parameters of rotor speed, temperature, and aerodynamic pressure, and the design objectives of blade stress, strain, and deformation, and the fuzzy constraints of reliability degree and boundary conditions, as well. It is revealed (1) the stress and deformation of turbine blade are reduced by 92.38 MPa and 0.09838 mm, respectively. (2) The comprehensive reliability degree of the blade was improved by 3.45% from 95.4% to 98.85%. (3) It is verified that the fuzzy multi-SVR learning method is workable for the fuzzy RBDO of complex structures just like a multi-failure blade with high modeling precision, as well as high optimization, efficiency, and accuracy. The efforts of this study open a new research way, i.e., machine learning-based RBDO, for the RBDO of multi-failure structures, which expands the application of machine learning methods, and enriches the mechanical reliability design method and theory as well.
Dissertations / Theses on the topic "Reliability Design Optimization methods (RBDO)":
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Cho, Hyunkyoo. "Efficient variable screening method and confidence-based method for reliability-based design optimization." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/4594.
Abstract:
The objectives of this study are (1) to develop an efficient variable screening method for reliability-based design optimization (RBDO) and (2) to develop a new RBDO method incorporated with the confidence level for limited input data problems. The current research effort involves: (1) development of a partial output variance concept for variable screening; (2) development of an effective variable screening sequence; (3) development of estimation method for a confidence level of a reliability output; and (4) development of a design sensitivity method for the confidence level.
In the RBDO process, surrogate models are frequently used to reduce the number of simulations because analysis of a simulation model takes a great deal of computational time. On the other hand, to obtain accurate surrogate models, we have to limit the dimension of the RBDO problem and thus mitigate the curse of dimensionality. Therefore, it is desirable to develop an efficient and effective variable screening method for reduction of the dimension of the RBDO problem. In this study, it is found that output variance is critical for identifying important variables in the RBDO process. A partial output variance, which is an efficient approximation method based on the univariate dimension reduction method (DRM), is proposed to calculate output variance efficiently. For variable screening, the variables that has larger partial output variances are selected as important variables. To determine important variables, hypothesis testing is used so that possible errors are contained at a user-specified error level. Also, an appropriate number of samples is proposed for calculating the partial output variance. Moreover, a quadratic interpolation method is studied in detail to calculate output variance efficiently. Using numerical examples, performance of the proposed variable screening method is verified. It is shown that the proposed method finds important variables efficiently and effectively.
The reliability analysis and the RBDO require an exact input probabilistic model to obtain accurate reliability output and RBDO optimum design. However, often only limited input data are available to generate the input probabilistic model in practical engineering problems. The insufficient input data induces uncertainty in the input probabilistic model, and this uncertainty forces the RBDO optimum to lose its confidence level. Therefore, it is necessary to consider the reliability output, which is defined as the probability of failure, to follow a probability distribution. The probability of the reliability output is obtained with consecutive conditional probabilities of input distribution type and parameters using the Bayesian approach. The approximate conditional probabilities are obtained under reasonable assumptions, and Monte Carlo simulation is applied to practically calculate the probability of the reliability output. A confidence-based RBDO (C-RBDO) problem is formulated using the derived probability of the reliability output. In the C-RBDO formulation, the probabilistic constraint is modified to include both the target reliability output and the target confidence level. Finally, the design sensitivity of the confidence level, which is the new probabilistic constraint, is derived to support an efficient optimization process. Using numerical examples, the accuracy of the developed design sensitivity is verified and it is confirmed that C-RBDO optimum designs incorporate appropriate conservativeness according to the given input data.
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Mansour, Rami. "Reliability Assessment and Probabilistic Optimization in Structural Design." Doctoral thesis, KTH, Hållfasthetslära (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-183572.
Abstract:
Research in the field of reliability based design is mainly focused on two sub-areas: The computation of the probability of failure and its integration in the reliability based design optimization (RBDO) loop. Four papers are presented in this work, representing a contribution to both sub-areas. In the first paper, a new Second Order Reliability Method (SORM) is presented. As opposed to the most commonly used SORMs, the presented approach is not limited to hyper-parabolic approximation of the performance function at the Most Probable Point (MPP) of failure. Instead, a full quadratic fit is used leading to a better approximation of the real performance function and therefore more accurate values of the probability of failure. The second paper focuses on the integration of the expression for the probability of failure for general quadratic function, presented in the first paper, in RBDO. One important feature of the proposed approach is that it does not involve locating the MPP. In the third paper, the expressions for the probability of failure based on general quadratic limit-state functions presented in the first paper are applied for the special case of a hyper-parabola. The expression is reformulated and simplified so that the probability of failure is only a function of three statistical measures: the Cornell reliability index, the skewness and the kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the MPP. In the last paper, an approximate and efficient reliability method is proposed. Focus is on computational efficiency as well as intuitiveness for practicing engineers, especially regarding probabilistic fatigue problems where volume methods are used. The number of function evaluations to compute the probability of failure of the design under different types of uncertainties is a priori known to be 3n+2 in the proposed method, where n is the number of stochastic design variables.QC 20160317
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Ndashimye, Maurice. "Accounting for proof test data in Reliability Based Design Optimization." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/97108.
Abstract:
Thesis (MSc)--Stellenbosch University, 2015.ENGLISH ABSTRACT: Recent studies have shown that considering proof test data in a Reliability Based Design Optimization (RBDO) environment can result in design improvement. Proof testing involves the physical testing of each and every component before it enters into service. Considering the proof test data as part of the RBDO process allows for improvement of the original design, such as weight savings, while preserving high reliability levels. Composite Over-Wrapped Pressure Vessels (COPV) is used as an example application of achieving weight savings while maintaining high reliability levels. COPVs are light structures used to store pressurized fluids in space shuttles, the international space station and other applications where they are maintained at high pressure for extended periods of time. Given that each and every COPV used in spacecraft is proof tested before entering service and any weight savings on a spacecraft results in significant cost savings, this thesis put forward an application of RBDO that accounts for proof test data in the design of a COPV. The method developed in this thesis shows that, while maintaining high levels of reliability, significant weight savings can be achieved by including proof test data in the design process. Also, the method enables a designer to have control over the magnitude of the proof test, making it possible to also design the proof test itself depending on the desired level of reliability for passing the proof test. The implementation of the method is discussed in detail. The evaluation of the reliability was based on the First Order Reliability Method (FORM) supported by Monte Carlo Simulation. Also, the method is implemented in a versatile way that allows the use of analytical as well as numerical (in the form of finite element) models. Results show that additional weight savings can be achieved by the inclusion of proof test data in the design process.
AFRIKAANSE OPSOMMING: Onlangse studies het getoon dat die gebruik van ontwerp spesifieke proeftoets data in betroubaarheids gebaseerde optimering (BGO) kan lei tot 'n verbeterde ontwerp. BGO behels vele aspekte in die ontwerpsgebied. Die toevoeging van proeftoets data in ontwerpsoptimering bring te weë; die toetsing van 'n ontwerp en onderdele voor gebruik, die aangepaste en verbeterde ontwerp en gewig-besparing met handhawing van hoë betroubaarsheidsvlakke. 'n Praktiese toepassing van die BGO tegniek behels die ontwerp van drukvatte met saamgestelde materiaal bewapening. Die drukvatontwerp is 'n ligte struktuur wat gebruik word in die berging van hoë druk vloeistowwe in bv. in ruimtetuie, in die internasionale ruimtestasie en in ander toepassings waar hoë druk oor 'n tydperk verlang word. Elke drukvat met saamgestelde materiaal bewapening wat in ruimtevaartstelsels gebruik word, word geproeftoets voor gebruik. In ruimte stelselontwerp lei massa besparing tot 'n toename in loonvrag. Die tesis beskryf 'n optimeringsmetode soos ontwikkel en gebaseer op 'n BGO tegniek. Die metode word toegepas in die ontwerp van drukvatte met saamgestelde materiaal bewapening. Die resultate toon dat die gebruik van proeftoets data in massa besparing optimering onderhewig soos aan hoë betroubaarheidsvlakke moontlik is. Verdermeer, die metode laat ook ontwerpers toe om die proeftoetsvlak aan te pas om sodoende by ander betroubaarheidsvlakke te toets. In die tesis word die ontwikkeling en gebruik van die optimeringsmetode uiteengelê. Die evaluering van betroubaarheidsvlakke is gebaseer op 'n eerste orde betroubaarheids-tegniek wat geverifieer word met talle Monte Carlo simulasie resultate. Die metode is ook so geskep dat beide analitiese sowel as eindige element modelle gebruik kan word. Ten slotte, word 'n toepassing getoon waar resultate wys dat die gebruik van die optimeringsmetode met die insluiting van proeftoets data wel massa besparing kan oplewer.
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Zhao, Liang. "Reliability-based design optimization using surrogate model with assessment of confidence level." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1194.
Abstract:
The objective of this study is to develop an accurate surrogate modeling method for construction of the surrogate model to represent the performance measures of the compute-intensive simulation model in reliability-based design optimization (RBDO). In addition, an assessment method for the confidence level of the surrogate model and a conservative surrogate model to account the uncertainty of the prediction on the untested design domain when the number of samples are limited, are developed and integrated into the RBDO process to ensure the confidence of satisfying the probabilistic constraints at the optimal design. The effort involves: (1) developing a new surrogate modeling method that can outperform the existing surrogate modeling methods in terms of accuracy for reliability analysis in RBDO; (2) developing a sampling method that efficiently and effectively inserts samples into the design domain for accurate surrogate modeling; (3) generating a surrogate model to approximate the probabilistic constraint and the sensitivity of the probabilistic constraint with respect to the design variables in most-probable-point-based RBDO; (4) using the sampling method with the surrogate model to approximate the performance function in sampling-based RBDO; (5) generating a conservative surrogate model to conservatively approximate the performance function in sampling-based RBDO and assure the obtained optimum satisfy the probabilistic constraints.
In applying RBDO to a large-scale complex engineering application, the surrogate model is commonly used to represent the compute-intensive simulation model of the performance function. However, the accuracy of the surrogate model is still challenging for highly nonlinear and large dimension applications. In this work, a new method, the Dynamic Kriging (DKG) method is proposed to construct the surrogate model accurately. In this DKG method, a generalized pattern search algorithm is used to find the accurate optimum for the correlation parameter, and the optimal mean structure is set using the basis functions that are selected by a genetic algorithm from the candidate basis functions based on a new accuracy criterion. Plus, a sequential sampling strategy based on the confidence interval of the surrogate model from the DKG method, is proposed. By combining the sampling method with the DKG method, the efficiency and accuracy can be rapidly achieved.
Using the accurate surrogate model, the most-probable-point (MPP)-based RBDO and the sampling-based RBDO can be carried out. In applying the surrogate models to MPP-based RBDO and sampling-based RBDO, several efficiency strategies, which include: (1) using local window for surrogate modeling; (2) adaptive window size for different design candidates; (3) reusing samples in the local window; (4) using violated constraints for surrogate model accuracy check; (3) adaptive initial point for correlation parameter estimation, are proposed.
To assure the accuracy of the surrogate model when the number of samples is limited, and to assure the obtained optimum design can satisfy the probabilistic constraints, a conservative surrogate model, using the weighted Kriging variance, is developed, and implemented for sampling-based RBDO.
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Gaul, Nicholas John. "Modified Bayesian Kriging for noisy response problems and Bayesian confidence-based reliability-based design optimization." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1322.
Abstract:
The objective of this study is to develop a new modified Bayesian Kriging (MBKG) surrogate modeling method that can be used to carry out confidence-based reliability-based design optimization (RBDO) for problems in which simulation analyses are inherently noisy and standard Kriging approaches fail. The formulation of the MBKG surrogate modeling method is presented, and the full conditional distributions of the unknown MBKG parameters are derived and coded into a Gibbs sampling algorithm. Using the coded Gibbs sampling algorithm, Markov chain Monte Carlo is used to fit the MBKG surrogate model.
A sequential sampling method that uses the posterior credible sets for inserting new design of experiment (DoE) sample points is proposed. The sequential sampling method is developed in such a way that the new DoE sample points added will provide the maximum amount of information possible to the MBKG surrogate model, making it an efficient and effective way to reduce the number of DoE sample points needed. Therefore, it improves the posterior distribution of the probability of failure efficiently.
Finally, a confidence-based RBDO method using the posterior distribution of the probability of failure is developed. The confidence-based RBDO method is developed so that the uncertainty of the MBKG surrogate model is included in the optimization process.
A 2-D mathematical example was used to demonstrate fitting the MBKG surrogate model and the developed sequential sampling method that uses the posterior credible sets for inserting new DoE. A detailed study on how the posterior distribution of the probability of failure changes as new DoE are added using the developed sequential sampling method is presented. Confidence-based RBDO is carried out using the same 2-D mathematical example. Three different noise levels are used for the example to compare how the MBKG surrogate modeling method, the sequential sampling method, and the confidence-based RBDO method behave for different amounts of noise in the response. A comparison of the optimization results for the three different noise levels for the same 2-D mathematical example is presented.
A 3-D multibody dynamics (MBD) engineering block-car example is presented. The example is used to demonstrate using the developed methods to carry out confidence-based RBDO for an engineering problem that contains noise in the response. The MBD simulations for this example were done using the commercially available MBD software package RecurDyn. Deterministic design optimization (DDO) was first done using the MBKG surrogate model to obtain the mean response values, which then were used with standard Kriging methods to obtain the sensitivity of the responses. Confidence-based RBDO was then carried out using the DDO solution as the initial design point.
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Dersjö, Tomas. "Methods for reliability based design optimization of structural components." Doctoral thesis, KTH, Hållfasthetslära (Avd.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-90753.
Abstract:
Cost and quality are key properties of a product, possibly even the two most important. Onedefinition of quality is fitness for purpose. Load-bearing products, i.e. structural components,loose their fitness for purpose if they fail. Thus, the ability to withstand failure is a fundamentalmeasure of quality for structural components. Reliability based design optimization(RBDO) is an approach for development of structural components which aims to minimizethe cost while constraining the probability of failure. However, the computational effort ofan RBDO applied to large-scale engineering problems has prohibited it from employment inindustrial applications. This thesis presents methods for computationally efficient RBDO.A review of the work presented on RBDO algorithms reveals that three constituentsof an RBDO algorithm has rendered significant attention; i ) the solution strategy for andnumerical treatment of the probabilistic constraints, ii ) the surrogate model, and iii) theexperiment design. A surrogate model is ”a model of a model”, i.e. a computationally cheapapproximation of a physics-based but computationally expensive computer model. It is fittedto responses from the physics-motivated model obtained via a thought-through combinationof experiments called an experiment design.In Paper A, the general algorithm for RBDO employed in this work, including the sequentialapproximation procedure used to treat the probabilistic constraints, is laid out. A singleconstraint approximation point (CAP) is used to save computational effort with acceptablelosses in accuracy. The approach is used to optimize a truck component and incorporatesthe effect that production related design variables like machining and shot peening have onfatigue life.The focus in Paper B is on experiment design. An algorithm employed to construct anovel experiment design for problems with multiple constraints is presented. It is based onan initial screening and uses the specific problem structure to combine one-factor-at-a-timeexperiments to a several-factors-at-a-time experiment design which reduces computationaleffort.In Paper C, a surrogate model tailored for RBDO is introduced. It is motivated by appliedsolid mechanics considerations and the use of the first order reliability method to evaluate theprobabilistic constraint. An optimal CAP is furthermore deduced from the surrogate model.In Paper D, the paradigm to use sets of experiments rather than one experiment at atime is challenged. A new procedure called experiments on demand (EoD) is presented. TheEoD procedure utilizes the core of RBDO to quantify the demand for new experiments andaugments it by a D-optimality criterion for added robustness and numerical stability.QC 20120229
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Chen, Qing. "Reliability-based structural design: a case of aircraft floor grid layout optimization." Thesis, Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39630.
Abstract:
In this thesis, several Reliability-based Design Optimization (RBDO) methods and algorithms for airplane floor grid layout optimization are proposed. A general RBDO process is proposed and validated by an example. Copula as a mathematical method to model random variable correlations is introduced to discover the correlations between random variables and to be applied in producing correlated data samples for Monte Carlo simulations. Based on Hasofer-Lind (HL) method, a correlated HL method is proposed to evaluate a reliability index under correlation. As an alternative method for computing a reliability index, the reliability index is interpreted as an optimization problem and two nonlinear programming algorithms are introduced to evaluate reliability index. To evaluate the reliability index by Monte Carlo simulation in a time efficient way, a kriging-based surrogate model is proposed and compared to the original model in terms of computing time. Since in RBDO optimization models the reliability constraint obtained by MCS does not have an analytical form, a kriging-based response surface is built. Kriging-based response surface models are usually segment functions that do not have a uniform expression over the design space; however, most optimization algorithms require a uniform expression for constraints. To solve this problem, a heuristic gradient-based direct searching algorithm is proposed. These methods and algorithms, together with the RBDO general process, are applied to the layout optimization of aircraft floor grid structural design.
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Mahadevan, Sankaran. "Stochastic finite element-based structural reliability analysis and optimization." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/19517.
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Bouguila, Maissa. "Μοdélisatiοn numérique et οptimisatiοn des matériaux à changement de phase : applicatiοns aux systèmes cοmplexes." Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMIR05.
Abstract:
Les matériaux à changement de phase MCP révèlent des performances importantes dans le domaine de la gestion thermique. Ces matériaux ont une capacité importante de stockage thermique. L’excès de la chaleur dissipée par les composantes électroniques peut causer des graves défaillances. Un système de refroidissement développé basé sur les matériaux à changement de phase est l’une des solutions les plus recommandées afin d’assurer un fonctionnement sécurisé de ces composants microélectroniques. Bien que la faible conductivité de ces matériaux soit considérée comme la limitation majeure de leurs utilisations dans les applications de gestion thermique. L’objectif principal de cette thèse est l’amélioration de la conductivité thermique de ces matériaux et l’optimisation des dissipateurs thermiques. Dans les premiers chapitres, des modélisations numériques sont effectuées afin de déterminer la configuration optimale d’un dissipateur à partir de l’étude de plusieurs paramètres comme l’insertion des ailettes, la dispersion des nanoparticules et l’utilisation de multiples matériaux à changement de phase. L’innovation de cette étude est la modélisation du transfert thermique des matériaux à changement de phase avec une concentration des nanoparticules relativement importante par rapport à la littérature et plus précisément les travaux scientifiques expérimentaux. Des conclusions intéressantes sont extraites de cette étude paramétrique qui va nous permettre parla suite de proposer un nouveau modèle basé sur des multiples des matériaux à changement de phase améliorés avec les nanoparticules. Des études d’optimisation fiabiliste sont après réalisées.En premier lieu, une étude d’optimisation fiabiliste mono-objective a été réalisé dans le but est de proposer un modèle du dissipateur fiable à multiple NANOMCPS avec des dimensions optimales. Donc l’objectif est d'optimiser (minimiser) le volume total du dissipateur tout en considérant les différents contraintes géométriques et fonctionnels. La méthode hybride robuste (RHM) montre une efficacité à proposer un modèle fiable et optimal comparant à la méthode d’optimisation déterministe (DDO) et les différentes méthodes d’optimisation de la conception basée sur la fiabilité (RBDO) considérées. En plus de la nouveauté de modèle proposée basé sur des multiples NANOMCPs, l’intégration d’une méthode de RBDO développée (RHM) pour l’application de gestion thermique est considérée comme une innovation dans la littérature récente.En deuxième lieu, une étude d’optimisation fiabiliste multi objective est proposée. Deux objectives sont considérées : le volume total du dissipateur et le temps de décharge pour atteindre la température ambiante. De plus, l’utilisation d’une méthode d’optimisation RHM, et l’algorithme génétique de tri non dominée, sont adoptées afin de chercher le modèle optimal et fiable qui offre le meilleur compromis entre les deux objectifs. En outre, un modèle de substitution avancée est établi dans le but de réduire le temps de simulation vu que le nombre important des itérations jusqu'à aboutir à un modèle optimalPhase-change materials exhibit considerable potential in the field of thermal management.These materials offer a significant thermal storage capacity. Excessive heat dissipated by miniature electronic components could lead to serious failures. A cooling system based on phase-change materials is among the most recommended solutions to guarantee the reliable performance of these microelectronic components. However, the low conductivity of these materials is considered a major limitation to their use in thermal management applications. The primary objective of this thesis is to address the challenge of improving the thermal conductivity of these materials. Numerical modeling is conducted, in the first chapters, to determine the optimal configuration of a heat sink, based on the study of several parameters such as fin insertion, nanoparticle dispersion, and the use of multiple phase-change materials. The innovation in this parametric study lies in the modeling of heat transfer from phase-change materials with relatively high nanoparticle concentration compared to the low concentration found in recent literature (experimental researchs). Significant conclusions are deducted from this parametric study, enabling us to propose a new model based on multiple phase-change materials improved with nanoparticles (NANOMCP). Reliable optimization studies are then conducted. Initially, a mono-objective reliability optimization study is carried out to propose a reliable and optimal model based on multiple NANOMCPs. The Robust Hybrid Method (RHM)proposes a reliable and optimal model, compared with the Deterministic Design Optimization method (DDO) and various Reliability Design Optimization methods (RBDO). Furthermore,the integration of a developed RBDO method (RHM) for the thermal management applicationis considered an innovation in recent literature. Additionally, a reliable multi-objective optimization study is proposed, considering two objectives: the total volume of the heat sink and the discharge time to reach ambient temperature. The RHM optimization method and the non-dominated sorting genetics algorithm (C-NSGA-II) were adopted to search for the optimal and reliable model that offers the best trade-off between the two objectives. Besides, An advanced metamodel is developed to reduce simulation time, considering the large number of iterations involved in finding the optimal model
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Patel, Jiten. "Optimal design of mesostructured materials under uncertainty." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31829.
Abstract:
Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2010.Committee Chair: Choi, Seung-Kyum; Committee Member: Muhanna, Rafi; Committee Member: Rosen, David. Part of the SMARTech Electronic Thesis and Dissertation Collection.
Books on the topic "Reliability Design Optimization methods (RBDO)":
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Zhang, J. C. Yield and variability optimization of integrated circuits. Boston: Kluwer Academic Publishers, 1995.
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Dodson, Bryan. Probabilistic design for optimization and robustness for engineers. 2014.
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Li, Xin, Jiayong Le, and Lawrence T. Pileggi. Statistical Performance Modeling and Optimization. Now Publishers Inc, 2007.
Book chapters on the topic "Reliability Design Optimization methods (RBDO)":
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Tahir, Arslan, and Claus Kunz. "Reliability Based Rehabilitation of Existing Hydraulic Structures." In Lecture Notes in Civil Engineering, 578–90. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-6138-0_50.
Abstract:
AbstractExisting hydraulic structures may show damage with increasing age and operation, so structural verification is crucial. In case of structural deficits, repair measures must be planned, and their effectiveness demonstrated. The advent of improved structural analysis methods and subsequent standardization processes facilitate the verification of existing structures to ensure sufficient reliability of infrastructure. Among the existing inland navigation hydraulic structures, older ship locks had been constructed with primitive construction materials such as damped plain concrete. At times, the structure exhibited neither any severe damages nor an indication of failure but failed to satisfy the limit states prescribed by the latest standards. This contribution considers a similar ship lock built in 1922 as a case study. The ship lock has a half-frame structural system with plain concrete gravity walls and a lightly transverse reinforced base slab. Cross-section based static verification revealed that the structure does not provide sufficient resistance in case of sliding and overturning limit states which could be attributed to crack and pore-water pressures in the cross-section. Consequently, rehabilitation of the lock walls with a vertical anchoring system was proposed to conform to required standards. Similar problems are expected for other existing locks in the German waterway system. Therefore, a methodology was developed to verify and to optimize the structural reliability of similar structures using full probabilistic methods while considering standard-based limit state functions. This involved uncertainty quantification of parameters for relevant loads (self-weight, water pressure, earth/ groundwater pressure, temperature, etc.) and materials (concrete, steel). To calculate the probability of failure and reliability indexes First Order Reliability Methods (FORM) was applied, considering its computational efficiency and more suitable for the presented Reliability-Based Design Optimization (RBDO) scheme. The contribution provides a probabilistic framework to study the influence of three aspects on the reliability of existing hydraulic structures, crack and pore-water pressures, operational conditions and lastly, the effect and optimization of rehabilitation in the form of anchoring.
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Kharmanda, Ghias, Abedelkhalak El Hami, and Eduardo Souza De Cursi. "Reliability-based Design Optimization (RBDO)." In Multidisciplinary Design Optimization in Computational Mechanics, 425–58. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2013. http://dx.doi.org/10.1002/9781118600153.ch11.
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Majumder, Rohan, and Sudib K. Mishra. "Reliability Based Design Optimization (RBDO) of Randomly Imperfect Thin Cylindrical Shells Against Post-Critical Drop." In Recent Developments in Structural Engineering, Volume 1, 47–55. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-9625-4_5.
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Vu-Quoc, Loc, and Alexander Humer. "Stochastic Optimization Methods in Machine Learning." In Reliability-Based Analysis and Design of Structures and Infrastructure, 315–32. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003194613-21.
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Torng, T. Y., and R. J. Yang. "Robust Structural System Design Using A System Reliability-Based Design Optimization Method." In Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, 534–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-85092-9_35.
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Sohouli, A., M. Yildiz, and A. Suleman. "Design Optimization and Reliability Analysis of Variable Stiffness Composite Structures." In Computational Methods in Applied Sciences, 245–65. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44507-6_13.
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Quagliarella, Domenico, Giovanni Petrone, and Gianluca Iaccarino. "Reliability-Based Design Optimization with the Generalized Inverse Distribution Function." In Computational Methods in Applied Sciences, 77–92. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11541-2_5.
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Georgioudakis, Manolis, Nikos D. Lagaros, and Manolis Papadrakakis. "Reliability-Based Shape Design Optimization of Structures Subjected to Fatigue." In Computational Methods in Applied Sciences, 451–88. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18320-6_24.
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Makhloufi, Abderahman, and Abdelkhalak El Hami. "Reliability-Based Design Optimization and Its Applications to Interaction Fluid Structure Problems." In Numerical Methods for Reliability and Safety Assessment, 623–46. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07167-1_24.
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Hejazi, Taha-Hossein, Mirmehdi Seyyed-Esfahani, and Iman Soleiman-Meigooni. "Robust Design of Accelerated Life Testing and Reliability Optimization: Response Surface Methodology Approach." In Numerical Methods for Reliability and Safety Assessment, 329–64. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07167-1_11.
Conference papers on the topic "Reliability Design Optimization methods (RBDO)":
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Chiralaksanakul, Anukal, and Sankaran Mahadevan. "Reliability-Based Design Optimization Methods." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57456.
Abstract:
Reliability-based design optimization (RBDO) methods are optimization algorithms that utilize reliability methods to evaluate probabilistic constraints and/or objective functions used to prescribe reliability. For practical applications, it is important that RBDO methods are efficient, i.e, they only require a manageable number of numerical evaluations of underlying functions since each one can be computationally expensive. The type of reliability methods and the manner in which they are used in conjunction with optimization algorithms strongly affect computational efficiency. The first order reliability method (FORM) and its inverse are proved to be efficient and widely accepted for reliability analysis. RBDO methods have therefore employed FORM or inverse FORM to numerically evaluate probabilistic constraints and objective functions. During the last decade, the efficiency of RBDO methods has been further improved through problem reformulation. Our goal is to present RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO formulations. This new perspective helps not only to clearly reveal their close relationships but also provides a common ground for understanding different types of RBDO methods. Using numerical studies reported in the literature, we indicate the numerical efficiency, convergence, and accuracy of existing RBDO methods.
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Zou, Tong, Sankaran Mahadevan, and Akhil Sopory. "A Reliability-Based Design Method Using Simulation Techniques and Efficient Optimization Approach." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57457.
Abstract:
A novel reliability-based design optimization (RBDO) method using simulation-based techniques for reliability assessments and efficient optimization approach is presented in this paper. In RBDO, model-based reliability analysis needs to be performed to calculate the probability of not satisfying a reliability constraint and the gradient of this probability with respect to each design variable. Among model-based methods, the most widely used in RBDO is the first-order reliability method (FORM). However, FORM could be inaccurate for nonlinear problems and is not applicable for system reliability problems. This paper develops an efficient optimization methodology to perform RBDO using simulation-based techniques. By combining analytical and simulation-based reliability methods, accurate probability of failure and sensitivity information is obtained. The use of simulation also enables both component and system-level reliabilities to be included in RBDO formulation. Instead of using a traditional RBDO formulation in which optimization and reliability computations are nested, a sequential approach is developed to greatly reduce the computational cost. The efficiency of the proposed RBDO approach is enhanced by using a multi-modal adaptive importance sampling technique for simulation-based reliability assessment; and by treating the inactive reliability constraints properly in optimization. A vehicle side impact problem is used to demonstrate the capabilities of the proposed method.
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Cho, Hyunkyoo, K. K. Choi, and David Lamb. "Confidence-Based Method for Reliability-Based Design Optimization." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34644.
Abstract:
An accurate input probabilistic model is necessary to obtain a trustworthy result in the reliability analysis and the reliability-based design optimization (RBDO). However, the accurate input probabilistic model is not always available. Very often only insufficient input data are available in practical engineering problems. When only the limited input data are provided, uncertainty is induced in the input probabilistic model and this uncertainty propagates to the reliability output which is defined as the probability of failure. Then, the confidence level of the reliability output will decrease. To resolve this problem, the reliability output is considered to have a probability distribution in this paper. The probability of the reliability output is obtained as a combination of consecutive conditional probabilities of input distribution type and parameters using Bayesian approach. The conditional probabilities that are obtained under certain assumptions and Monte Carlo simulation (MCS) method is used to calculate the probability of the reliability output. Using the probability of the reliability output as constraint, a confidence-based RBDO (C-RBDO) problem is formulated. In the new probabilistic constraint of the C-RBDO formulation, two threshold values of the target reliability output and the target confidence level are used. For effective C-RBDO process, the design sensitivity of the new probabilistic constraint is derived. The C-RBDO is performed for a mathematical problem with different numbers of input data and the result shows that C-RBDO optimum designs incorporate appropriate conservativeness according to the given input data.
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Choi, Kyung K., Yoojeong Noh, and Liu Du. "Reliability Based Design Optimization With Correlated Input Variables Using Copulas." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35104.
Abstract:
For the performance measure approach (PMA) of RBDO, a transformation between the input random variables and the standard normal random variables is necessary to carry out the inverse reliability analysis. For reliability analysis, Rosenblatt and Nataf transformations are commonly used. In many industrial RBDO problems, the input random variables are correlated. However, often only limited information such as the marginal distribution and covariance could be practically obtained, and the input joint probability distribution function (PDF) is very difficult to obtain. Thus, in literature, most RBDO methods assume all input random variables are independent. However, in this paper, it is found that the RBDO results can be significantly different when the input variables are correlated. Thus, various transformation methods are investigated for development of a RBDO method for problems with correlated input variables. It is found that Rosenblatt transformation is impractical for problems with correlated input variables due to difficulty of constructing a joint PDF from the marginal distributions and covariance. On the other hand, Nataf transformation can construct the joint CDF using the marginal distributions and covariance, and thus applicable to problems with correlated random input variables. The joint CDF is Nataf model, which is called a Gaussian copula in the copula family. Since the Gaussian copula can describe a wide range of the correlation coefficient, Nataf transformation can be widely used for various types of correlated input variables. In this paper, Nataf transformation is used to develop a RBDO method for design problems with correlated random input variables. Numerical examples are used to demonstrate the proposed method. Also, it is shown that the correlated random input variables significantly affect the RBDO results.
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Oza, Kunjal, and Hae Chang Gea. "Two-Level Approximation Method for Reliability-Based Design Optimization." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57463.
Abstract:
In order to model uncertainties and achieve the required reliability, Reliability Based Design Optimization (RBDO) has evolved as a dominant design tool. Many methods have been introduced in solving the RBDO problem. However, the computational expense associated with the probabilistic constraint evaluation still limits the applicability of the RBDO to practical engineering problems. In this paper, a Two-Level Approximation method (TLA) is proposed. At the first level, a reduced second order approximation is used for better optimization solution; at the second level a linear approximation is used for faster reliability assessment. The optimal solution is obtained interatively. The proposed method is tested on certain numerical examples, and results obtained are compared to evaluate the cost-effectiveness.
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Mansour, Rami, and Mårten Olsson. "The Response Surface Single Loop Reliability-Based Design Optimization Method With Reliability Requirement on System Failure." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60505.
Abstract:
In reliability-based design optimization (RBDO), an optimal design which minimizes an objective function while satisfying a number of probabilistic constraints is found. As opposed to deterministic optimization, statistical uncertainties in design variables and design parameters have to be taken into account in the design process in order to achieve a reliable design. In the most widely used RBDO approaches, the First-Order Reliability Method (FORM) is used in the probability assessment. This involves locating the Most Probable Point (MPP) of failure, or the inverse MPP, either exactly or approximately. If exact methods are used, an optimization problem has to be solved, typically resulting in computationally expensive double loop or decoupled loop RBDO methods. On the other hand, locating the MPP approximately typically results in highly efficient single loop RBDO methods since the optimization problem is not necessary in the probability assessment. However, since all these methods are based on FORM, which in turn is based on a linearization of the deterministic constraints at the MPP, they may suffer inaccuracies associated with neglecting the nonlinearity of deterministic constraints. In a previous paper presented by the authors, the Response Surface Single Loop (RSSL) Reliability-based design optimization method was proposed. The RSSL-method takes into account the non-linearity of the deterministic constraints in the computation of the probability of failure and was therefore shown to have higher accuracy than existing RBDO methods. The RSSL-method was also shown to have high efficiency since it bypasses the concept of an MPP. In RSSL, the deterministic solution is first found by neglecting uncertainties in design variables and parameters. Thereafter quadratic response surface models are fitted to the deterministic constraints around the deterministic solution using a single set of design of experiments. The RBDO problem is thereafter solved in a single loop using a closed-form second order reliability method (SORM) which takes into account all elements of the Hessian of the quadratic constraints. In this paper, the RSSL method is used to solve the more challenging system RBDO problems where all constraints are replaced by one constraint on the system probability of failure. The probabilities of failure for the constraints are assumed independent of each other. In general, system reliability problems may be more challenging to solve since replacing all constraints by one constraint may strongly increase the non-linearity in the optimization problem. The extensively studied reliability-based design for vehicle crash-worthiness, where the provided deterministic constraints are general quadratic models describing the system in the whole region of interest, is used to demonstrate the capabilities of the RSSL method for problems with system reliability constraints.
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Sopory, Akhil, Sankaran Mahadevan, Zissimos P. Mourelatos, and Jian Tu. "Decoupled and Single Loop Methods for Reliability-Based Optimization and Robust Design." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57404.
Abstract:
Several procedures have been developed in the literature for reliability-based design optimization (RBDO), including the Reliability Index Approach (RIA), the Performance Measure Approach (PMA), and more recent techniques wherein the reliability and optimization calculations are decoupled. This paper extends the decoupled approach to include standard deviations as design parameters and wherein simulation or other methods can replace the traditional first order analytical method for reliability assessment. The methods are extended to robust design and their applicability is investigated. The paper also investigates a single loop method and extends it for the robust design problem. The accuracy and computational efficiency of the various RBDO methods are compared.
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Choi, Kyung K., and Byeng D. Youn. "Hybrid Analysis Method for Reliability-Based Design Optimization." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21044.
Abstract:
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.
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Wang, Pingfeng, Byeng D. Youn, and Lee J. Wells. "Bayesian Reliability Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35524.
Abstract:
In the last decade, considerable advances have been made in Reliability-Based Design Optimization (RBDO). It is assumed in RBDO that statistical information of input uncertainties is completely known (aleatory uncertainty), such as a distribution type and its parameters (e.g., mean, deviation). However, this assumption is not valid in practical engineering applications, since the amount of uncertainty data is restricted mainly due to limited resources (e.g., man-power, expense, time). In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, this paper proposes an integration of RBDO with Bayes Theorem, referred to as Bayesian Reliability-Based Design Optimization (Bayesian RBDO). However, when a design problem involves a large number of epistemic variables, Bayesian RBDO becomes extremely expensive. Thus, this paper presents a more efficient and accurate numerical method for reliability method demanded in the process of Bayesian RBDO. It is found that the Eigenvector Dimension Reduction (EDR) Method is a very efficient and accurate method for reliability analysis, since the method takes a sensitivity-free approach with only 2n+1 analyses, where n is the number of aleatory random parameters. One mathematical example and an engineering design example (vehicle suspension system) are used to demonstrate the feasibility of Bayesian RBDO. In Bayesian RBDO using the EDR method, random parameters associated with manufacturing variability are considered as the aleatory random parameters, whereas random parameters associated with the load variability are regarded as the epistemic random parameters. Moreover, a distributed computing system is used for this study.
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Liang, Jinghong, Zissimos P. Mourelatos, and Jian Tu. "A Single-Loop Method for Reliability-Based Design Optimization." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57255.
Abstract:
Reliability-Based Design Optimization (RBDO) can provide optimum designs in the presence of uncertainty. It can therefore, be a powerful tool for design under uncertainty. The traditional, double-loop RBDO algorithm requires nested optimization loops, where the design optimization (outer) loop, repeatedly calls a series of reliability (inner) loops. Due to the nested optimization loops, the computational effort can be prohibitive for practical problems. A single-loop RBDO algorithm is proposed in this paper for both normal and non-normal random variables. Its accuracy is the same with the double-loop approach and its efficiency is almost equivalent to deterministic optimization. It collapses the nested optimization loops into an equivalent single-loop optimization process by imposing the Karush-Kuhn-Tucker optimality conditions of the reliability loops as equivalent deterministic equality constraints of the design optimization loop. It therefore, converts the probabilistic optimization problem into an equivalent deterministic optimization problem, eliminating the need for calculating the Most Probable Point (MPP) in repeated reliability assessments. Several numerical applications including an automotive vehicle side impact example, demonstrate the accuracy and superior efficiency of the proposed single-loop RBDO algorithm.
Reports on the topic "Reliability Design Optimization methods (RBDO)":
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L51816 Reliability-Based Prevention of Mechanical Damage to Pipelines. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), August 2000. http://dx.doi.org/10.55274/r0010429.
Abstract:
Most pipeline incidents� resulting in the loss of life, production and/or environmental damage is caused by third party damage. A need for recommendations regarding the most cost effective third party damage prevention approach and/or plan was identified by the Pipeline Research Council International, Inc. (PRCI). This project and resulting study used a reliability-based methodology from a previous PRCI sponsored project (PR-224-9519) "Reliability-Based Planning of Inspection and Maintenance of Pipeline Systems". The focus of this project and resulting study was to collect the data and develop the models required to apply the methodology to the optimization of mechanical damage prevention. The resulting reliability model consists of two components: a) an impact probability model that calculates the frequency of mechanical interference by excavation equipment as a function of line attributes and damage prevention practices; and b) the puncture failure model that calculates the probability of puncture for a given impact as a function of the pipeline design parameters. The reliability model detailed in this study provides a quantitative tool to estimate the probability of failure due to mechanical damage and to evaluate the effectiveness of different design and maintenance methods.