Dissertations / Theses on the topic 'Reliability Design Optimization methods (RBDO)'

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.

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

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.

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.

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.

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

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.

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 optimal
Phase-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

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.

The primary objective of this study is to develop new computational methods for robust design optimization (RDO) and reliability-based design optimization (RBDO) of high-dimensional, complex engineering systems. Four major research directions, all anchored in polynomial dimensional decomposition (PDD), have been defined to meet the objective. They involve: (1) development of new sensitivity analysis methods for RDO and RBDO; (2) development of novel optimization methods for solving RDO problems; (3) development of novel optimization methods for solving RBDO problems; and (4) development of a novel scheme and formulation to solve stochastic design optimization problems with both distributional and structural design parameters. The major achievements are as follows. Firstly, three new computational methods were developed for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random inputs. The first method represents a novel integration of PDD of a multivariate stochastic response function and score functions, leading to analytical expressions of design sensitivities of the first two moments. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD approximation and score functions. For all three methods developed, both the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Secondly, four new methods were developed for RDO of complex engineering systems. The methods involve PDD of a high-dimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. The methods, depending on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompass direct, single-step, sequential, and multi-point single-step design processes. Thirdly, two new methods were developed for RBDO of complex engineering systems. The methods involve an adaptive-sparse polynomial dimensional decomposition (AS-PDD) of a high-dimensional stochastic response for reliability analysis, a novel integration of AS-PDD and score functions for calculating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point, single-step design process. The two methods, depending on how the failure probability and its design sensitivities are evaluated, exploit two distinct combinations built on AS-PDD: the AS-PDD-SPA method, entailing SPA and score functions; and the AS-PDD-MCS method, utilizing the embedded MCS of the AS-PDD approximation and score functions. In addition, a new method, named as the augmented PDD method, was developed for RDO and RBDO subject to mixed design variables, comprising both distributional and structural design variables. The method comprises a new augmented PDD of a high-dimensional stochastic response for statistical moment and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms, leading to a multi-point, single-step design process. The innovative formulations of statistical moment and reliability analysis, design sensitivity analysis, and optimization algorithms have achieved not only highly accurate but also computationally efficient design solutions. Therefore, these new methods are capable of performing industrial-scale design optimization with numerous design variables.

System Safety and Reliability are fundamental to system design and involve a quantitative assessment prior to system development. An accurate prediction of reliability and system safety in a new product before it is manufactured and marketed is necessary as it allows us to forecast accurately the support costs, warranty costs, spare parts requirements, etc. On the other hand, it can be argued that an accurate prediction implies knowledge about failures that is rarely there in early design phases. Furthermore, while predictions of system performance can be made with credible precision, within reasonable tolerances, reliability and system safety are seldom predicted with high accuracy and confidence. How well a product meets its performance requirements depends on various characteristics such as quality, reliability, availability, safety, and efficiency. But to produce a reliable product we may have to incur increased cost of design and manufacturing. Balancing such requirements, that are often contradictory, is also a necessary step in product development. This step can be performed using different optimization techniques. This thesis is an attempt to develop a methodology for analysis and optimization of system safety and reliability in early design phases. A theoretical framework and context are presented in the first part of the thesis, including system safety and reliability methods and optimization techniques. Each of these topics is presented in its own chapter. The second and third parts are dedicated to contributions and papers. Three papers are included in the third part; the first evaluates the applicability of reliability methods in early design phases, the second is a proposed guideline for how to choose the right reliability method, and the third suggests a method to balance the safety requirements, reliability goals, and costs.

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 diffus
Since 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

Au stade de projet amont, les ingénieurs utilisent souvent des modèles de basse fidélité possédant de larges erreurs. Les approches déterministes prennent implicitement en compte les erreurs par un choix conservatif des paramètres aléatoires et par l'ajout de facteurs de sécurité dans les contraintes de conception. Une fois qu'une solution est proposée, elle est analysée par un modèle haute fidélité (test futur): une re-conception peut s'avérer nécessaire pour restaurer la fiabilité ou améliorer la performance, et le modèle basse fidélité est calibré pour prendre en compte les résultats de l'analyse haute-fidélité. Mais une re-conception possède un coût financier et temporel. Dans ce travail, les effets possibles des tests futurs et des re-conceptions sont intégrés à une procédure de conception avec un modèle basse fidélité. Après les Chapitres 1 et 2 qui donnent le contexte de ce travail et l'état de l'art, le Chapitre 3 analyse le dilemme d'une conception initiale conservatrice en terme de fiabilité ou ambitieuse en termes de performances (avec les re-conceptions associées pour améliorer la performance ou la fiabilité). Le Chapitre 4 propose une méthode de simulation des tests futurs et de re-conception avec des erreurs épistémiques corrélées spatialement. Le Chapitre 5 décrit une application à une fusée sonde avec des erreurs à la fois aléatoires et de modèles. Le Chapitre 6 conclut le travail
At the initial design stage, engineers often rely on low-fidelity models that have high uncertainty. In a deterministic safety-margin-based design approach, uncertainty is implicitly compensated for by using fixed conservative values in place of aleatory variables and ensuring the design satisfies a safety-margin with respect to design constraints. After an initial design is selected, high-fidelity modeling is performed to reduce epistemic uncertainty and ensure the design achieves the targeted levels of safety. High-fidelity modeling is used to calibrate low-fidelity models and prescribe redesign when tests are not passed. After calibration, reduced epistemic model uncertainty can be leveraged through redesign to restore safety or improve design performance; however, redesign may be associated with substantial costs or delays. In this work, the possible effects of a future test and redesign are considered while the initial design is optimized using only a low-fidelity model. The context of the work and a literature review make Chapters 1 and 2 of this manuscript. Chapter 3 analyzes the dilemma of whether to start with a more conservative initial design and possibly redesign for performance or to start with a less conservative initial design and risk redesigning to restore safety. Chapter 4 develops a generalized method for simulating a future test and possible redesign that accounts for spatial correlations in the epistemic model error. Chapter 5 discusses the application of the method to the design of a sounding rocket under mixed epistemic model uncertainty and aleatory parameter uncertainty. Chapter 6 concludes the work

This thesis presents the reader the importance of optimization and probabilistic assessment of structures for civil engineering problems. Chapter 2 further investigates the combination between previously proposed optimization techniques and probabilistic assessment in the form of optimization constraints. Academic software has been developed for the purposes of demonstrating the effectiveness of the suggested methods and their statistical testing. 3th chapter summarizes the results of testing previously described optimization method (called Aimed Multilevel Sampling), including a comparison with other optimization techniques. In the final part of the thesis, described procedures have been demonstrated on the selected optimization and reliability problems. The methods described in text represents engineering approach to optimization problems and aims to introduce a simple and transparent optimization algorithm, which could serve to the practical engineering purposes.

碩士
中原大學
機械工程研究所
104
Reliability-Based Design Optimization (RBDO) algorithms have been developed to solve design optimization problems with existence of uncertainties. Traditionally, the original random design space is transformed to the standard normal design space, where the reliability index can be measured in a standardized unit. In the standard normal design space, the Modified Reliability Index Approach (MRIA) measured the minimum distance from the design point to the failure region to represent the reliability index; on the other hand, the Performance Measure Approach (PMA) performed inverse reliability analysis to evaluate the target function performance in a distance of reliability index away from the design point. MRIA was able to provide stable and accurate reliability analysis while PMA showed greater efficiency and was widely used in various engineering applications. However, the existing methods cannot properly perform reliability analysis in the standard normal design space if the transformation to the standard normal space does not exist or is difficult to determine. Especially, in image processing application, the transformation is hard to determine because of arbitrarily distribution in CIELAB space. The program speed is important while image processing application algorithm developed. To this end, a new algorithm, Parallelized Ensemble of Gaussian Reliability Analyses (PEoGRA), was developed to estimate the failure probability using Gaussian-based Kernel Density Estimate (KDE) in the original design space. The probabilistic constraints were formulated based on each kernel reliability analysis for the optimization processes. And Muti-Thread shared memory framework, including data access layer, assigned task layer and layer of estimation of reliability index layer, is used to acceleration program. This paper proposed an efficient way to estimate the constraint gradient and linearly approximate the probabilistic constraints with fewer function evaluations. Some numerical examples with various random distributions are studied to investigate the numerical performances of the proposed method. The program speed is investigated with EoGRA and PEoGRA in numerical examples also. Above of all, the results showed PEoGRA is capable of finding correct solutions in some problems that cannot be solved by traditional methods. PEoGRA is capable to operate image processing application in acceptable speed.

A practical engineering design problem is used to examine the over-conservativeness of designs obtained using deterministic optimization with worst-case parameter assumptions and a safety factor. Additionally, an attempted application of reliability-based design optimization (RBDO) demonstrates the limits of RBDO for practical problems. The design problem considered here is TESCO's Internal Casing Drive System (ICDS), which is used in feeding pipeline, or casing, into predrilled holes. After developing a finite element model of the ICDS, experimental data is used to successfully validate modeling methods and assumptions. The validated model is then subjected to multiple analyses to determine an appropriate design configuration to be used as the starting point for optimization. Worst-case, safety factor-based design optimization (SFBDO) is then applied considering two and three design variables, and is successful in increasing the critical load of the ICDS, Pcrit, by 35% and 45%, respectively. An efficient and recognized RBDO method, Sequential Optimization and Reliability Assessment, is selected for application to the design problem to determine an optimum design based on reliability. Due to the optimization formulation, however, SORA cannot be applied. The ICDS design problem represents a practical example that demonstrates the difficulties and limits in applying RBDO to practical engineering design problems. To evaluate the over-conservativeness of worst-case SFBDO, structural reliability analysis is performed on the deterministic optimum designs. It is found that the value of Pcrit for both the two and three variable optimum designs can be increased by 53% while maintaining acceptable probability of failure, demonstrating the over-conservativeness of the worst-case SFBDO.
Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2008-09-05 10:51:26.273

碩士
國立臺灣科技大學
營建工程系
105
Reliability-based Design Optimization (RBDO) produces optimal design with minimal cost and ensures a more reliable performance of the structure by explicitly incorporating uncertainties in its optimization algorithm. Expensive computational cost, accuracy of reliability assessment, as well as nonlinearity and non-differentiability of performance function are the main challenges in performing RBDO in real engineering problems. The promising accuracy and efficiency of Methods of Moments such as simplified third-moment (3M), fourth-moment (4M) and Pearson’s Distribution System-based fourth-moment (4M-P) for probabilistic analysis in combination with a metaheuristic optimization algorithm (i.e. Particle Swarm Optimization, PSO) is explored for RBDO implementation. The proposed methodology was able to search for the optimal design having linear, highly nonlinear, and implicit performance functions considered in the probabilistic constraints which were demonstrated in several numerical examples. To emphasize the applicability of the proposed algorithm in practical engineering problems, a two bay three story steel structure were solved, in which an equivalent stick model was developed to further lessen the computational cost in nonlinear time history analyses. The results were validated and compared from gathered related literature. The limitation on the applicable range of the simplified Methods of Moments produced incorrect optimal design in the RBDO for highly nonlinear limit state functions and non-normal random variables. However, for normally distributed random variables, simplified Methods of Moments formulations showed improved accuracy in structural reliability at optimal design compared to other existing reliability methods. Also, by increasing the number of variates in dimension reduction method, more accurate estimation of the moments of the performance function was observed. Finally, the implications of the results and limitations of the methodology are discussed