Uncertainty in rockmass and in situ stress parameters poses a critical design challenge in geotechnical engineering. This uncertainty stems from natural variability (aleatory) due to the complex history of formation and continual reworking of geological materials as well as knowledge-based uncertainty (epistemic) due to a lack of site specific information and the introduction of errors during the testing and design phases. While such uncertainty can be dealt with subjectively through the use of conservative design parameters, this leads to a lack of understanding of the variable ground response and the selection of an over-conservative design that can have a negative impact on both the project cost and schedule. Reliability methods offer an alternative approach that focuses on quantifying the uncertainty in ground conditions and utilizing it directly in the design process. By doing so, a probability of failure can be calculated with respect to a prescribed limit state, providing a measure of design performance. When multiple design options are considered, reliability methods can be paired with a quantitative risk analysis to determine the optimum design on the basis of safety and minimum cost rather than subjective conservatism. Despite the inherent benefits of such an approach, the adoption of reliability methods has been slow in geotechnical engineering due to a number of technical and conceptual challenges. The research conducted pertaining to this thesis aims to address these issues and remove the perceived “cloak of mystery” that surrounds the use of reliability methods. The scientific and engineering research in this thesis was divided into four sections: (1) the assessment of uncertainty in geotechnical input parameters, (2) a review of reliability methods in the context of geotechnical problems, (3) the development of a reliability-based, quantitative risk approach for underground support design and (4) the application of such a method to existing case studies. The completion of these areas is critical to the design of underground structures and may bring about a shift in design philosophy in the geotechnical industry. / Thesis (Ph.D, Geological Sciences & Geological Engineering) -- Queen's University, 2013-09-18 10:35:26.265

There is a large amount of geotechnical data. By putting it into a database, it can be applied to design reliable offshore foundations. The goal of this research is to improve the efficiency and transparency of the implementation of the previously developed reliability-based framework to streamline the process for analyzing and developing an offshore site in the Gulf of Mexico by looking at spatial variations among data sets. This thesis documents how to store soil behavior information in the database and how to use that information for offshore foundation design. The process is illustrated through observing the steps with figures provided directly from the database so the user can more readily use the database to produce results. This makes the database more transparent for the user to follow the flow of information from input to analysis and to follow the calculation process as well. Enhancements were also made to the database to provide a more readily accessible interface. There is now an allowance of data to streamline the data input process. There is also a set amount of fifty data points to be used in each spatially conditioned analysis. These detailed explanations and consistencies in data collection help the user to understand the models. This database provides a synthetic image of the site using both physical and statistical parameters where there might not be exact data at a desired foundation location. By providing the industry with a database that uses reliability-based design from actual data and spatial variation analysis, this project will continue to provide a more efficient design process. / text

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.

Les premières étapes d'une conception fiabiliste impliquent la formulation de critères de performance et de contraintes de fiabilité d'une part, et le choix d'une représentation des incertitudes d'autre part. Force est de constater que, le plus souvent, des aspects de performance ou de fiabilité conditionnant la solution optimale ne seront pas connus ou seront négligés lors des premières phases de conception. De plus, les techniques de réduction des incertitudes telles que les tests additionnels et la reconception ne sont pas pris en compte dans les calculs de fiabilité initiaux. Le travail exposé dans ce manuscrit aborde la conception optimale de systèmes sous deux angles : 1) le compromis entre performance et coût généré par les tests supplémentaires et les reconceptions et, 2) l'identification de multiples solutions optimales (dont certaines locales) en tant que stratégie contre les erreurs initiales de conception. Dans la première partie de notre travail, une méthodologie est proposée pour estimer l'effet sur la performance et le coût d'un produit d'un test supplémentaire et d'une éventuelle reconception. Notre approche se base, d'une part, sur des distributions en probabilité des erreurs de calcul et des erreurs expérimentales et, d'autre part, sur une rêgle de reconception a priori. Ceci permet d'estimer a posteriori la probabilité et le coût d'un produit. Nous montrons comment, à travers le choix de politiques de prochain test et de re-conception, une entreprise est susceptible de contrôler le compromis entre performance et coût de développement.Dans la seconde partie de notre travail, nous proposons une méthode pour l'estimation de plusieurs solutions candidates à un problème de conception où la fonction coût et/ou les contraintes sont coûteuses en calcul. Une approche pour aborder de tels problèmes est d'utiliser un métamodèle, ce qui nécessite des évaluations de points en diverses régions de l'espace de recherche. Il est alors dommage d'utiliser cette connaissance seulement pour estimer un optimum global. Nous proposons une nouvelle approche d'échantillonnage à partir de métamodèles pour trouver plusieurs optima locaux. Cette méthode procède par partitionnement adaptatif de l'espace de recherche et construction de métamodèles au sein de chaque partition. Notre méthode est testée et comparée à d'autres approches d'optimisation globale par métamodèles sur des exemples analytiques en dimensions 2 à 6, ainsi que sur la conception d'un bouclier thermique en 5 dimensions. / 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.

Computational design has become a predominant element of various engineering tasks. However, the ever increasing complexity of numerical models creates the need for efficient methodologies. Specifically, computational design under uncertainties remains sparsely used in engineering settings due to its computational cost. This dissertation proposes a coherent framework for various branches of computational design under uncertainties, including model update, reliability assessment and reliability-based design optimization. Through the use of machine learning techniques, computationally inexpensive approximations of the constraints, limit states, and objective functions are constructed. Specifically, a novel adaptive sampling strategy allowing for the refinement of any approximation only in relevant regions has been developed, referred to as generalized max-min. This technique presents various computational advantages such as ease of parallelization and applicability to any metamodel. Three approaches tailored for computational design under uncertainties are derived from the previous approximation technique. An algorithm for reliability assessment is proposed and its efficiency is demonstrated for different probabilistic settings including dependent variables using copulas. Additionally, the notion of fidelity map is introduced for model update settings with large number of dependent responses to be matched. Finally, a new reliability-based design optimization method with local refinement has been developed. A derivation of sampling-based probability of failure derivatives is also provided along with a discussion on numerical estimates. This derivation brings additional flexibility to the field of computational design. The knowledge acquired and techniques developed during this Ph.D. have been synthesized in an object-oriented MATLAB toolbox. The help and ergonomics of the toolbox have been designed so as to be accessible by a large audience.

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.

abstract: This dissertation is to address product design optimization including reliability-based design optimization (RBDO) and robust design with epistemic uncertainty. It is divided into four major components as outlined below. Firstly, a comprehensive study of uncertainties is performed, in which sources of uncertainty are listed, categorized and the impacts are discussed. Epistemic uncertainty is of interest, which is due to lack of knowledge and can be reduced by taking more observations. In particular, the strategies to address epistemic uncertainties due to implicit constraint function are discussed. Secondly, a sequential sampling strategy to improve RBDO under implicit constraint function is developed. In modern engineering design, an RBDO task is often performed by a computer simulation program, which can be treated as a black box, as its analytical function is implicit. An efficient sampling strategy on learning the probabilistic constraint function under the design optimization framework is presented. The method is a sequential experimentation around the approximate most probable point (MPP) at each step of optimization process. It is compared with the methods of MPP-based sampling, lifted surrogate function, and non-sequential random sampling. Thirdly, a particle splitting-based reliability analysis approach is developed in design optimization. In reliability analysis, traditional simulation methods such as Monte Carlo simulation may provide accurate results, but are often accompanied with high computational cost. To increase the efficiency, particle splitting is integrated into RBDO. It is an improvement of subset simulation with multiple particles to enhance the diversity and stability of simulation samples. This method is further extended to address problems with multiple probabilistic constraints and compared with the MPP-based methods. Finally, a reliability-based robust design optimization (RBRDO) framework is provided to integrate the consideration of design reliability and design robustness simultaneously. The quality loss objective in robust design, considered together with the production cost in RBDO, are used formulate a multi-objective optimization problem. With the epistemic uncertainty from implicit performance function, the sequential sampling strategy is extended to RBRDO, and a combined metamodel is proposed to tackle both controllable variables and uncontrollable variables. The solution is a Pareto frontier, compared with a single optimal solution in RBDO. / Dissertation/Thesis / Ph.D. Industrial Engineering 2012

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24575号 / 工博第5081号 / 新制||工||1973(附属図書館) / 京都大学大学院工学研究科建築学専攻 / (主査)教授 大崎 純, 教授 池田 芳樹, 准教授 藤田 皓平 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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This dissertation addresses the ultimate strength analysis of nonlinear beam-columns under axial compression, the sensitivity of the ultimate strength, structural optimization and reliability analysis using ultimate strength analysis, and Reliability-Based Design Optimization (RBDO) of the nonlinear beam-columns. The ultimate strength analysis is based on nonlinear beam theory with material and geometric nonlinearities. Nonlinear constitutive law is developed for elastic-perfectly-plastic beam cross-section consisting of base plate and T-bar stiffener. The analysis method is validated using commercial nonlinear finite element analysis. A new direct solving method is developed, which combines the original governing equations with their derivatives with respect to deformation matric and solves for the ultimate strength directly. Structural optimization and reliability analysis use a gradient-based algorithm and need accurate sensitivities of the ultimate strength to design variables. Semi-analytic sensitivity of the ultimate strength is calculated from a linear set of analytical sensitivity equations which use the Jacobian matrix of the direct solving method. The derivatives of the structural residual equations in the sensitivity equation set are calculated using complex step method. The semi-analytic sensitivity is more robust and efficient as compared to finite difference sensitivity. The design variables are the cross-sectional geometric parameters. Random variables include material properties, geometric parameters, initial deflection and nondeterministic load. Failure probabilities calculated by ultimate strength reliability analysis are validated by Monte Carlo Simulation. Double-loop RBDO minimizes structural weight with reliability index constraint. The sensitivity of reliability index with respect to design variables is calculated from the gradient of limit state function at the solution of reliability analysis. By using the ultimate strength direct solving method, semi-analytic sensitivity and gradient-based optimization algorithm, the RBDO method is found to be robust and efficient for nonlinear beam-columns. The ultimate strength direct solving method, semi-analytic sensitivity, structural optimization, reliability analysis, and RBDO method can be applied to more complicated engineering structures including stiffened panels and aerospace/ocean structures. / Ph. D. / This dissertation presents a Reliability-Based Design Optimization (RBDO) procedure for nonlinear beam-columns. The beam-column cross-section has asymmetric I shape and the nonlinear material model allows plastic deformation. Structural optimization minimizes the structural weight while maintaining an ultimate strength level, i.e. the maximum load it can carry. In reality, the geometric parameters and material properties of the beam-column vary from the design value. These uncertain variations will affect the strength of the structure. Structural reliability analysis accounts for the uncertainties in structural design. Reliability index is a measurement of the structure’s probability of failure by considering these uncertainties. RBDO minimizes the structural weight while maintaining the reliability level of the beam-column. A novel numerical method is presented which solves an explicit set of equations to obtain the maximum strength of the beam-column directly. By using this method, the RBDO procedure is found to be efficient and robust.