Academic literature on the topic 'RBDO (Reliability Based Design Optimisation)'
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Journal articles on the topic "RBDO (Reliability Based Design Optimisation)":
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Al-Juboori, Muqdad, and Bithin Datta. "Optimum design of hydraulic water retaining structures incorporating uncertainty in estimating heterogeneous hydraulic conductivity utilizing stochastic ensemble surrogate models within a multi-objective multi-realisation optimisation model." Journal of Computational Design and Engineering 6, no. 3 (December 24, 2018): 296–315. http://dx.doi.org/10.1016/j.jcde.2018.12.003.
Abstract:
Abstract In order to find optimum and reliable designs for hydraulic water retaining structures (HWRSs), a reliability based optimum design (RBOD) model was used to quantify uncertainty in estimates of seepage characteristics due to uncertainty in heterogeneous hydraulic conductivity (HHC). This included incorporating reliability measures into minimum-cost HWRS designs and utilising a multi-realisation optimisation technique based on various stochastic ensemble surrogate models. To improve the efficiency of the RBOD model and the direct search optimisation solver, a multi-objective multi-realisation optimisation (MOMRO) model was employed. Some of the stochastic optimisation constraints could be formulated as a second objective function to be minimised in the MOMRO model. This can significantly improve the search efficiency of the multi-objective non-dominated sorting genetic algorithm-II (NSGA-II) that was used, and help determine more feasible candidate solutions in the search space. Gaussian process regression was used to develop the surrogate models, which were trained on numerous datasets created from numerical seepage simulations. The effect of uncertainty was also considered for other HWRS safety factors and conditions, such as overturning, flotation, sliding and eccentric loading. The results demonstrate that uncertainty in HHC estimates significantly impacts optimum HWRS design. Therefore, deterministic optimum solutions that are created based on expected values of hydraulic conductivity are not adequate for reliable HWRS design. The developed MOMRO model, which was based on an ensemble approach, addresses some of the uncertainty in HHC values that affects HWRS design. Also, the MOMRO technique improves the efficiency of the optimisation search process and facilitates a direct search process to provide many optimum alternatives. Highlights The uncertainty in HHC affects the optimum HWRS design. MOMR is used to quantify the reliability based on stochastic ensemble surrogate models. The MOMR technique improves the direct search optimization process based NSGA-II. Exit gradient is influenced by the uncertainty of HHC and affects the HWRS optimum designs.
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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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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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Youn, Byeng D., and Kyung K. Choi. "An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches." Journal of Mechanical Design 126, no. 3 (October 1, 2003): 403–11. http://dx.doi.org/10.1115/1.1701880.
Abstract:
Because deterministic optimum designs obtained without taking uncertainty into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and a reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mappings between X- and U-spaces for various probability distributions. Therefore, the nonlinearity of the RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity into the reliability-based performance measures evaluated during the RBDO process. The evaluation of probabilistic constraints in RBDO can be carried out in two ways: using either the Reliability Index Approach (RIA), or the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity for RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of the highly nonlinear transformations that are involved. However, PMA is rather independent of probability distributions because it only has a small involvement with a nonlinear transformation.
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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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Youn, Byeng D., Kyung K. Choi, and Young H. Park. "Hybrid Analysis Method for Reliability-Based Design Optimization." Journal of Mechanical Design 125, no. 2 (June 1, 2003): 221–32. http://dx.doi.org/10.1115/1.1561042.
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 optimization process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the advanced mean value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the conjugate mean value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the hybrid mean value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.
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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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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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Elhami, Norelislam, Mhamed Itmi, and Rachid Ellaia. "Reliability-Based Design and Heuristic Optimization MPSO-SA of Structures." Advanced Materials Research 274 (July 2011): 91–100. http://dx.doi.org/10.4028/www.scientific.net/amr.274.91.
Abstract:
In this paper, we present a probability study about spring of clutch structure. In the structure problems, the randomness and the uncertainties of the distribution of the structural parameters are a crucial problem. In the case of Reliability Based Design Optimization (RBDO), it is the objective is to play a dominant role in the structural optimization problem introducing the reliability concept. The RBDO problem is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. This paper proposes a new method for a modified particle swarm optimization algorithm (MPSO) combined with a simulated annealing algorithm (SA) and RBDO. MPSO is known as an efficient approach with a high performance of solving optimization problems in many research fields. It is a population intelligence algorithm inspired by social behavior simulations of bird flocking. Numerical results show the robustness of the MPSO-SA algorithm and RBDO.
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Tu, J., K. K. Choi, and Y. H. Park. "A New Study on Reliability-Based Design Optimization." Journal of Mechanical Design 121, no. 4 (December 1, 1999): 557–64. http://dx.doi.org/10.1115/1.2829499.
Abstract:
This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields singularity in some cases.
Dissertations / Theses on the topic "RBDO (Reliability Based Design Optimisation)":
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Chakchouk, Mohamed. "Conceptiοn d'un détecteur de système mécatronique mobile intelligent pour observer des molécules en phase gazeuse en ΙR." Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMIR06.
Abstract:
Ce travail anticipe que, dans un monde technologique numérique en constante expansion, les percées technologiques dans l'analyse des données collectées par des dispositifs spectroscopiques permettront l'identification presque instantanée d'espèces connues observées in-situ dans un environnement spécifique, laissant l'analyse approfondie nécessaire aux espèces non observées. La méthode dérivée de la technologie RBDO (Reliability Based Design Optimisation) sera utilisé pour implémenter une procédure d’intelligence artificielle afin d'identifier les espèces observées à partir d'un capteur IR mobile. Afin d'analyser avec succès les données obtenues, il est nécessaire d'assigner de manière appropriée les espèces moléculaires à partir des données IR observées en utilisant les modèles théoriques appropriés. Ce travail se concentre sur l'observation à partir d'appareils mobiles équipés de capteurs, d'antennes et d'électronique appropriés pour capturer et envoyer des données brutes ou analysées à partir d'un environnement spectroscopique IR intéressant. Il est donc intéressant voir indispensable de se concentrer sur les outils théoriques basés sur la symétrie pour l'analyse spectroscopique des molécules, ce qui permet d'identifier les fenêtres IR à choisir pour l'observation dans la conception de l'appareil. Ensuite, en ajustant les paramètres théoriques spectroscopiques aux fréquences observées, le spectre d'une espèce moléculaire peut être reconstruit. Une déconvolution des spectres observés est nécessaire avant l'analyse en termes d'intensité, de largeur et de centre de raie caractérisant une forme de raie. Une stratégie adéquate est donc nécessaire lors de la conception pour inclure l'analyse des données pendant la phase d'observation, qui peut bénéficier d'un algorithme d'intelligence artificielle pour tenir compte des différences dans la signature spectrale IR à cet égard, le pouvoir analytique des données de l'instrument peut être amélioré en utilisant la méthodologie d'optimisation de la conception basée sur la fiabilité (RBDO). Basée sur le comportement multiphysique de la propagation des incertitudes dans l'arbre hiérarchique du système, la RBDO utilise une modélisation probabiliste pour analyser l'écart par rapport à la sortie souhaitée comme paramètres de rétroaction pour optimiser la conception au départ. Le but de cette thèse est de traiter les paramètres de fenêtres d'observation IR, afin de traiter les questions de fiabilité au-delà de la conception mécatronique, pour inclure l'identification des espèces par l'analyse des données collectéesThis work anticipates that, in an ever-expanding digital technology world, technological breakthroughs in the analysis of data collected by spectroscopic devices will allow the almost instantaneous identification of known species observed in-situ in a specific environment, leaving the necessary in-depth analysis of unobserved species. The method derived from RBDO (Reliability Based Design Optimization) technology will be used to implement an artificial intelligence procedure to identify observed species from a mobile IR sensor. To successfully analyze the obtained data, it is necessary to appropriately assign molecular species from the observed IR data using appropriate theoretical models. This work focuses on the observation from mobile devices equipped with appropriate sensors, antennas, and electronics to capture and send raw or analyzed data from an interesting IR spectroscopic environment. It is therefore interesting if not essential to focus on symmetry-based theoretical tools for the spectroscopic analysis of molecules, which allows to identify the IR windows to be chosen for observation in the design of the device. Then, by fitting the theoretical spectroscopic parameters to the observed frequencies, the spectrum of a molecular species can be reconstructed. A deconvolution of the observed spectra is necessary before the analysis in terms of intensity, width and line center characterizing a line shape. Therefore, an adequate strategy is needed in the design to include data analysis during the observation phase, which can benefit from an artificial intelligence algorithm to account for differences in the IR spectral signature. In this regard, the analytical power of the instrument data can be improved by using the reliability-based design optimization (RBDO) methodology. Based on the multi-physics behavior of uncertainty propagation in the hierarchical system tree, RBDO uses probabilistic modeling to analyze the deviation from the desired output as feedback parameters to optimize the design in the first place. The goal of this thesis is to address IR observation window parameters to address reliability issues beyond mechatronic design to include species identification through analysis of collected data
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Zhang, Peipei. "Diffuse response surface model based on advancing latin hypercube patterns for reliability-based design optimization of ultrahigh strength steel NC milling parameters." Compiègne, 2011. http://www.theses.fr/2011COMP1949.
Abstract:
Puisque les incertitudes des paramètres de systèmes mécaniques entrainent la variabilité de la performance du produit, les systèmes optimisés sans prendre en compte les incertitudes peuvent présenter le risque de défaillance. L'optimisation fiabiliste (RBDO) focalise ainsi l'attention des ingénieurs et des chercheurs. Cependant, les méthodes habituelles de RBDO présentent un coût informatique excessif. Donc, afin d'améliorer l'efficacité informatique de la résolution de problèmes de RBDO, il est naturel de faire appel à des approches basées sur les surfaces de réponse (RSM). Dans ce travail, nous nous concentrons sur une Méthodologie de Surface de Réponse adaptée à la conception optimale dans le contexte fiabiliste. Nous proposons une variante de l'Approximation Diffuse, basée sur un modèle d'échantillonnage progressif et couplée à l'estimation de la fiabilité par FORM. La méthode proposée utilise simultanément des points dans l'espace normal standard U ainsi que dans l'espace physique X. Les deux réseaux forment un « plan d'expériences virtuel » défini par deux jeux de points dans les deux espaces de conception, qui sont évalués seulement quand nécessaire pour réduire au minimum le nombre d'évaluations « exactes » et ainsi diminuer le coût informatique. Dans chaque nouvelle itération, le pattern de points est mis à jour avec des points du design virtuel convenablement choisis afin d'effectuer l'approximation. Nous étendons ici l'idée d'Hypercube Latin (LHS) pour réutiliser au maximum des points précédemment calculés en ajoutant un nombre minimal de nouveaux points voisins à chaque étape, nécessaires pour l'approximation au voisinage du design actuel. Nous proposons des opérateurs de translation, de zoom avant et arrière, étendant ainsi le modèle LHS et le rendant récursif tout en contrôlant la qualité d'exploration de l'espace de conception et en maximisant le conditionnement de l'approximation. Dans la partie applicative de ce travail, nous examinons l'optimisation des paramètres du processus de fraisage à commande numérique (NC) de l'acier à haute limite élastique. Le succès de l'opération d'usinage dépend de la sélection des paramètres tels que le taux d'alimentation, la vitesse de coupe, les profondeurs axiales et radiales de coupe. Les contraintes d'optimisation sont exprimées comme des fonctions des indices de fiabilité calculés par FORM diffusSince variances in the input parameters of engineering systems cause subsequent variations in the product performance, and deterministic optimum designs that are obtained without taking uncertainties into consideration could lead to unreliable designs. Reliability-Based Design Optimization (RBDO) is getting a lot of attention recently. However, RBDO is computationally expensive. Therefore, the Response Surface Methodology (RSM) is often used to improve the computational efficiency in the solution of problems in RBDO. In this work, we focus on a Response Surface Methodology (RSM) adapted to the Reliability-Based Design Optimization (RBDO). The Diffuse Approximation (DA), a variant of the well-known Moving Least Squares (MLS) approximation based on a progressive sampling pattern is used within a variant of the First Order Reliability Method (FORM). The proposed method simultaneously uses points in the standard normal space (U-space) as well as the physical space (X-space). The two grids form a “virtual design of experiments” defined by two sets of points in the two design spaces, that are evaluated only when needed in order to minimize the number of ‘exact’ thus computationally expensive function evaluations. In each new iteration, the pattern of points is updated with points appropriately selected from the “virtual design of experiments”, in order to perform the approximation. As an original contribution, we introduce the concept of « advancing Latin Hypercube Sampling (LHS) » which extends the idea of Latin Hypercube Sampling (LHS) to maximally reuse previously computed points while adding a minimal number of new neighboring points at each step, necessary for the approximation in the vicinity of the current design. We propose panning, expanding and shrinking Latin hypercube patterns of sampling points and we analyze the influence of this specific kind of patterns on the quality of the approximation. Next we calculate the minimal number of data points required in order to get a well-conditioned approximation system. In the application part of this work, we investigate the optimization of the process parameters for Numerical Control (NC) milling of ultrahigh strength steel. The success of the machining operation depends on the selection of machining parameters such as the feed rate, cutting speed, and the axial and radial depths of cut. A variant of the First Order Reliability Method (FORM) is chosen to calculate the reliability index. The optimization constraints are expressed as functions of the computed reliability indices
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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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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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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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Ezzati, Ghasem. "Reliability-based design optimisation methods in large scale systems." Thesis, Federation University Australia, 2015. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/99881.
Abstract:
Doctor of PhilosophyStructural optimisation is an important field of applied mathematics, which has proved useful in engineering projects. Reliability-based design optimisation (RBDO) can be considered a branch of structural optimisation. Different RBDO approaches have been applied in real world problems (e.g. vehicle side impact model, short column design, etc.). Double-loop, single-loop, and decoupled approaches are three categories in RBDO. This research focuses on double-loop approaches, which consider reliability analysis problems in their inner loops and design optimisation calculations in their outer loops. In recent decades, double-loop approaches have been studied and modified in order to improve their stability and efficiency, but many shortcomings still remain, particularly regarding reliability analysis methods. This thesis will concentrate on development of new reliability analysis methods that can be applied to solve RBDO problems. As a local optimisation algorithm, the conjugate gradient method will be adopted. Furthermore, a new method will be introduced to solve a reliability analysis problem in the polar space. The reliability analysis problem must be transformed into an unconstrained optimisation problem before solving in the polar space. Two methods will be introduced here and their stability and efficiency will be compared with the existing methods via numerical experiments. Next, we consider applications of RBDO models to electricity networks. Most of the current optimisation models of these networks are categorised as deterministic design optimisation models. A probabilistic constraint is introduced in this thesis for electricity networks. For this purpose, a performance function must be defined for a network in order to define safety and failure conditions. Then, new non-deterministic design optimisation models will be formulated for electricity networks by using the mentioned probabilistic constraint. These models are designed to keep failure probability of the network below a predetermined and accepted safety level.
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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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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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Villanueva, Diane. "Reliability Based Design Including Future Tests and Multi-Agent Approaches." Phd thesis, Saint-Etienne, EMSE, 2013. http://tel.archives-ouvertes.fr/tel-00862355.
Abstract:
The initial stages of reliability-based design optimization involve the formulation of objective functions and constraints, and building a model to estimate the reliability of the design with quantified uncertainties. However, even experienced hands often overlook important objective functions and constraints that affect the design. In addition, uncertainty reduction measures, such as tests and redesign, are often not considered in reliability calculations during the initial stages. This research considers two areas that concern the design of engineering systems: 1) the trade-off of the effect of a test and post-test redesign on reliability and cost and 2) the search for multiple candidate designs as insurance against unforeseen faults in some designs. In this research, a methodology was developed to estimate the effect of a single future test and post-test redesign on reliability and cost. The methodology uses assumed distributions of computational and experimental errors with re-design rules to simulate alternative future test and redesign outcomes to form a probabilistic estimate of the reliability and cost for a given design. Further, it was explored how modeling a future test and redesign provides a company an opportunity to balance development costs versus performance by simultaneously designing the design and the post-test redesign rules during the initial design stage.The second area of this research considers the use of dynamic local surrogates, or surrogate-based agents, to locate multiple candidate designs. Surrogate-based global optimization algorithms often require search in multiple candidate regions of design space, expending most of the computation needed to define multiple alternate designs. Thus, focusing on solely locating the best design may be wasteful. We extended adaptive sampling surrogate techniques to locate multiple optima by building local surrogates in sub-regions of the design space to identify optima. The efficiency of this method was studied, and the method was compared to other surrogate-based optimization methods that aim to locate the global optimum using two two-dimensional test functions, a six-dimensional test function, and a five-dimensional engineering example.
Book chapters on the topic "RBDO (Reliability Based Design Optimisation)":
1
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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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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"Reliability-Based Design Optimization (RBDO)." In Structural Design Optimization Considering Uncertainties, 1–2. Taylor & Francis, 2008. http://dx.doi.org/10.1201/b10995-2.
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"Reliability Based Design Optimization (RBDO)." In Encyclopedia of Ocean Engineering, 1451. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-10-6946-8_300642.
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Rahmani, Shima, Elyas Fadakar, and Masoud Ebrahimi. "An Efficient Quantile-Based Adaptive Sampling RBDO with Shifting Constraint Strategy." In Avantgarde Reliability Implications in Civil Engineering [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.110442.
Abstract:
There is an increasing demand for the performance optimization under the reliability constraints in various engineering problems. These problems are commonly known as reliability-based design optimization (RBDO) problems. Among different RBDO frameworks, the decoupled methods are widely accepted for their high efficiency and stability. However, when facing problems with high nonlinearity and nonnormally distributed random variables, they lose their computational performance. In this study, a new efficient decoupled method with two level quantile-based sampling strategy is presented. The strategies introduced for two level sampling followed by information reuse of nearby designs are intended to enhance the sampling from failure region, thus reducing the number of samples to improve the efficiency of sampling-based methods. Compared with the existing methods which decouples RBDO in the design space and thus need to struggle with searching for most probable point (MPP), the proposed method decouples RBDO in the probability space to further make beneficial use of an efficient optimal shifting value search strategy to reach an optimal design in less iterations. By comparing the proposed method with crude MCS and other sampling-based methods through benchmark examples, our proposed method proved to be competitive in dramatically saving the computational cost.
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Hurtado, Jorge. "Optimal Reliability-Based Design Using Support Vector Machines and Artificial Life Algorithms." In Intelligent Computational Paradigms in Earthquake Engineering, 59–79. IGI Global, 2007. http://dx.doi.org/10.4018/978-1-59904-099-8.ch004.
Abstract:
Reliability-based optimization is considered by many authors as the most rigorous approach to structural design, because the search for the optimal solution is performed with consideration of the uncertainties present in the structural and load variables. The practical application of this idea, however, is hindered by the computational difficulties associated to the minimisation of cost functions with probabilistic constraints involving the computation of very small probabilities computed over implicit threshold functions, that is, those given by numerical models such as finite elements. In this chapter, a procedure intended to perform this task with a minimal amount of calls of the finite element code is proposed. It is based on the combination of a computational learning method (the support vector machines) and an artificial life technique (particle swarm optimisation). The former is selected because of its information encoding properties as well as for its elitist procedures that complement hose of the a-life optimisation method. The later has been chosen du to its advantages over classical genetic algorithms. The practical application of the procedure is demonstrated with earthquake engineering examples.
Conference papers on the topic "RBDO (Reliability Based Design Optimisation)":
1
Coffey, Tiarnan, Christopher Rai, John Greene, and Stephen O’Brien Bromley. "Subsea Spare Parts Analysis Optimisation." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-96100.
Abstract:
Abstract The main objective of this paper is to present a fully quantitative methodology combining reliability, availability and maintainability (RAM) analysis and cost-benefit analysis (CBA) approaches to determine the optimum sparing strategy for subsea components considering reliability data, lead times, availability and cost. This methodology can be utilized at any stage of an asset lifecycle, from design to operation and can be adjusted to reflect modifications throughout the life of field. Using commercially available RAM analysis software, Maros [2], a reliability block diagram (RBD) is constructed to represent the reliability structure and logic of the system being analyzed. Retrievable components, for which spares would be suitable, are then identified within the model to review and update the failure modes and reliability information for each component. Reliability information can be based on project specific data or from industry-wide sources such as OREDA. The RAM analysis software uses the Monte-Carlo simulation technique to determine availability. A sensitivity analysis is then performed to determine maximum availability while holding the minimum required stock level of spare components. A sparing priority factor (SPF) analysis is then performed in addition to the RAM sensitivity analysis to support those results and consider spare purchase, storage and preservation costs. The SPF gives a weighting to the storage cost against the potential impact on production. The SPF is a number used to determine a component’s need to have a spare. A high SPF indicates an increased requirement to hold a spare.
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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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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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Moon, Min-Yeong, K. K. Choi, Hyunkyoo Cho, Nicholas Gaul, David Lamb, and David Gorsich. "Reliability-Based Design Optimization Using Confidence-Based Model Validation for Insufficient Experimental Data." 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/detc2016-60155.
Abstract:
The conventional reliability-based design optimization (RBDO) methods assume that a simulation model is able to represent the real physics accurately. However, the simulation model could be biased. Accordingly, when the conventional RBDO design is manufactured, the product may not satisfy the target reliability. Therefore, model validation, which corrects model bias, should be integrated in the RBDO process by incorporating experimental data. The challenge is that only a limited number of experimental data is usually available due to the cost of actual product testing. Consequently, model validation for RBDO needs to account for the uncertainty induced by insufficient experimental data as well as variability inherently existing in the products. In this paper, a confidence-based model validation process that captures the uncertainty and corrects model bias at user-specified target conservativeness level is developed. Thus, RBDO can be performed using confidence-based model validation to obtain conservative RBDO design. It is found that RBDO with model bias correction becomes a moving-target problem because the feasible domain changes as the design moves. Consequently, the RBDO optimum may not be easily found due to the convergence problem. To resolve the issue, an efficient process is proposed by carrying out deterministic design optimization (DDO) and RBDO without validation, followed by RBDO with confidence-based model validation. Finally, we demonstrate that the proposed RBDO approach can achieve a conservative and practical optimum design given a limited number of experimental data.
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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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Choi, Kyung K., and Byeng D. Youn. "An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dac-34128.
Abstract:
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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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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Pugazhendhi, K., and A. K. Dhingra. "Reliability Based Design Optimization Using Automatic Differentiation." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65912.
Abstract:
Typically, a reliability based design optimization (RBDO) problem is solved as a nested optimization problem because an evaluation of the probabilistic constraint(s) involves solving a minimization problem. Over the years, a number of algorithms have been developed to solve the RBDO problem efficiently. All of these approaches involve an evaluation of derivatives of the responses. In this paper, a decoupled approach using automatic differentiation (AD) is presented to solve the RBDO problem. The proposed approach employs AD to evaluate the reliability, as well as to evaluate the sensitivity of the most probable point (MPP) with respect to the design variables. Since these evaluations involve a computation of the Jacobian and the Hessian, a use of AD improves the accuracy while simultaneously reducing the required number of response evaluations. The applicability of the proposed approach is shown through examples of increasing complexity ranging from problems where closed form solutions are available for evaluation of response to situations where finite element analysis is needed to compute the system response.
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Pan, Hao, Zhimin Xi, and Ren-Jye Yang. "Model Uncertainty Approximation Using a Copula-Based Approach for Reliability Based Design Optimization." 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/detc2016-60071.
Abstract:
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.
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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.