Sustainable bridge design by metamodel-assisted multi-objective optimization and decision-making under uncertainty

[EN] Today, bridge design seeks not only to minimize cost, but also to minimize adverse environmental and social impacts. This multi-criteria decision-making problem is subject to variability of the opinions of stakeholders regarding the importance of criteria for sustainability. As a result, this paper proposes a method for designing and selecting optimally sustainable bridges under the uncertainty of criteria comparison. A Pareto set of solutions is obtained using a metamodel-assisted multi-objective optimization. A new decision-making technique introduces the uncertainty of the decision-maker's preference through triangular distributions and thereby ranks the sustainable bridge designs. The method is illustrated by a case study of a three-span post-tensioned concrete box-girder bridge designed according to the embodied energy, overall safety and corrosion initiation time. In this particular case, 211 efficient solutions are reduced to two preferred solutions which have a probability of being selected of 81.6% and 18.4%. In addition, a sensitivity analysis validates the influence of the uncertainty regarding the decision making. The approach proposed allows actors involved in the bridge design and decision-making to determine the best sustainable design by finding the probability of a given design being chosen.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (Project: BIA2017-85098-R).García-Segura, T.; Penadés-Plà, V.; Yepes, V. (2018). Sustainable bridge design by metamodel-assisted multi-objective optimization and decision-making under uncertainty. Journal of Cleaner Production. 202:904-915. doi:10.1016/j.jclepro.2018.08.177S90491520

Multi-objective design of post-tensioned concrete road bridges using artificial neural networks

[EN] In order to minimize the total expected cost, bridges have to be designed for safety and durability. This paper considers the cost, the safety, and the corrosion initiation time to design post-tensioned concrete box-girder road bridges. The deck is modeled by finite elements based on problem variables such as the cross-section geometry, the concrete grade, and the reinforcing and post-tensioning steel. An integrated multi-objective harmony search with artificial neural networks (ANNs) is proposed to reduce the high computing time required for the finite-element analysis and the increment in conflicting objectives. ANNs are trained through the results of previous bridge performance evaluations. Then, ANNs are used to evaluate the constraints and provide a direction towards the Pareto front. Finally, exact methods actualize and improve the Pareto set. The results show that the harmony search parameters should be progressively changed in a diversification-intensification strategy. This methodology provides trade-off solutions that are the cheapest ones for the safety and durability levels considered. Therefore, it is possible to choose an alternative that can be easily adjusted to each need.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (BRIDLIFE Project: BIA2014-56574-R) and the Research and Development Support Program of Universitat Politecnica de Valencia (PAID-02-15).García-Segura, T.; Yepes, V.; Frangopol, D. (2017). Multi-objective design of post-tensioned concrete road bridges using artificial neural networks. Structural and Multidisciplinary Optimization. 56(1):139-150. doi:10.1007/s00158-017-1653-0S139150561Alberdi R, Khandelwal K (2015) Comparison of robustness of metaheuristic algorithms for steel frame optimization. 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Accelerated optimization method for low-embodied energy concrete box-girder bridge design

[EN] Structural optimization is normally carried out by means of conventional heuristic optimization due to the complexity of the structural problems. However, the conventional heuristic optimization still consumes a large amount of time. The use of metamodels helps to reduce the computational cost of the optimization and, along these lines, kriging-based heuristic optimization is presented as an alternative to carry out an accelerated optimization of complex problems. In this work, conventional heuristic optimization and kriging-based heuristic optimization will be applied to reach the optimal solution of a continuous box-girder pedestrian bridge of three spans with a low embodied energy. For this purpose, different penalizations and different initial sample sizes will be studied and compared. This work shows that kriging-based heuristic optimization provides results close to those of conventional heuristic optimization using less time. For the sample size of 50, the best solution differs about 2.54% compared to the conventional heuristic optimization, and reduces the computational cost by 99.06%. Therefore, the use of a kriging model in structural design problems offers a new means of solving certain structural problems that require a very high computational cost and reduces the difficulty of other problems.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness, along with FEDER funding (Project: BIA2017-85098-R).Penadés-Plà, V.; García-Segura, T.; Yepes, V. (2019). Accelerated optimization method for low-embodied energy concrete box-girder bridge design. Engineering Structures. 179:556-565. https://doi.org/10.1016/j.engstruct.2018.11.015S55656517

Efficient design of post-tensioned concrete box-girder road bridges based on sustainable multi-objective criteria

[EN] Bridges, as an important component of infrastructure, are expected to meet all the requirements for a modern society. Traditionally, the primary aim in bridge design has been to achieve the lowest cost while guaranteeing the structural efficiency. However, concerns regarding building a more sustainable future have change the priorities of society. Ecological and durable structures are increasingly demanded. Under these premises, heuristic optimization methods provide an effective alternative to structural designs based on experience. The emergence of new materials, structural designs and sustainable criteria motivate the need to create a methodology for the automatic and accurate design of a real post-tensioned concrete bridge that considers all these aspects. For the first time, this thesis studies the efficient design of post-tensioned concrete box-girder road bridges from a sustainable point of view. This research integrates environmental, safety and durability criteria into the optimum design of the bridge. The methodology proposed provides multiple trade-off solutions that hardly increase the cost and achieve improved safety and durability. Likewise, this approach quantifies the sustainable criteria in economic terms, and evaluates the effect of these criteria on the best values of the variables. In this context, a multi-objective optimization is formulated to provide multiple trade-off and high-performing solutions that balance economic, ecologic and societal goals. An optimization design program selects the best geometry, concrete type, reinforcement and post-tensioning steel that meet the objectives selected. A three-span continuous box-girder road bridge located in a coastal region is selected for a case study. This approach provides vital knowledge about this type of bridge in the sustainable context. The life-cycle perspective has been included through a lifetime performance evaluation that models the bridge deterioration process due to chloride-induced corrosion. The economic, environmental and societal impacts of maintenance actions required to extend the service life are examined. Therefore, the proposed goals for an efficient design have been switch from initial stage to life-cycle consideration. Faced with the large computational time of multi-objective optimization and finite-element analysis, artificial neural networks (ANNs) are integrated in the proposed methodology. ANNs are trained to predict the structural response based on the design variables, without the need to analyze the bridge response. The multi-objective optimization problem results in a set of trade-off solutions characterized by the presence of conflicting objectives. The final selection of preferred solutions is simplified by a decision-making technique. A rational technique converts a verbal pairwise comparison between criteria with a degree of uncertainty into numerical values that guarantee the consistency of judgments. This thesis gives a guide for the sustainable design of concrete structures. The use of the proposed approach leads to designs with lower life-cycle cost and emissions compared to general design approaches. Both bridge safety and durability can be improved with a little cost increment by choosing the correct design variables. In addition, this methodology is applicable to any type of structure and material.[ES] Los puentes, como parte importante de una infraestructura, se espera que reúnan todos los requisitos de una sociedad moderna. Tradicionalmente, el objetivo principal en el diseño de puentes ha sido lograr el menor coste mientras se garantiza la eficiencia estructural. Sin embargo, la preocupación por construir un futuro más sostenible ha provocado un cambio en las prioridades de la sociedad. Estructuras más ecológicas y duraderas son cada vez más demandadas. Bajo estas premisas, los métodos de optimización heurística proporcionan una alternativa eficaz a los diseños estructurales basados en la experiencia. La aparición de nuevos materiales, diseños estructurales y criterios sostenibles motivan la necesidad de crear una metodología para el diseño automático y preciso de un puente real de hormigón postesado que considere todos estos aspectos. Por primera vez, esta tesis estudia el diseño eficiente de puentes de hormigón postesado con sección en cajón desde un punto de vista sostenible. Esta investigación integra criterios ambientales, de seguridad estructural y durabilidad en el diseño óptimo del puente. La metodología propuesta proporciona múltiples soluciones que apenas encarecen el coste y mejoran la seguridad y durabilidad. Al mismo tiempo, se cuantifica el enfoque sostenible en términos económicos, y se evalúa el efecto que tienen dichos criterios en el valor óptimo de las variables. En este contexto, se formula una optimización multiobjetivo que proporciona soluciones eficientes y de compromiso entre los criterios económicos, ecológicos y sociales. Un programa de optimización del diseño selecciona la mejor combinación de geometría, tipo de hormigón, armadura y postesado que cumpla con los objetivos seleccionados. Se ha escogido como caso de estudio un puente continuo en cajón de tres vanos situado en la costa. Este método proporciona un mayor conocimiento sobre esta tipología de puentes desde un punto de vista sostenible. Se ha estudiado el ciclo de vida a través de la evaluación del deterioro estructural del puente debido al ataque por cloruros. Se examina el impacto económico, ambiental y social que produce el mantenimiento necesario para extender la vida útil del puente. Por lo tanto, los objetivos propuestos para un diseño eficiente han sido trasladados desde la etapa inicial hasta la consideración del ciclo de vida. Para solucionar el problema del elevado tiempo de cálculo debido a la optimización multiobjetivo y el análisis por elementos finitos, se han integrado redes neuronales en la metodología propuesta. Las redes neuronales son entrenadas para predecir la respuesta estructural a partir de las variables de diseño, sin la necesidad de analizar el puente. El problema de optimización multiobjetivo se traduce en un conjunto de soluciones de compromiso que representan objetivos contrapuestos. La selección final de las soluciones preferidas se simplifica mediante una técnica de toma de decisiones. Una técnica estructurada convierte los juicios basados en comparaciones por pares de elementos con un grado de incertidumbre en valores numéricos que garantizan la consistencia de dichos juicios. Esta tesis proporciona una guía que extiende y mejora las recomendaciones sobre el diseño de estructuras de hormigón dentro del contexto de desarrollo sostenible. El uso de la metodología propuesta lleva a diseños con menor coste y emisiones del ciclo de vida, comparado con diseños que siguen metodologías generales. Los resultados demuestran que mediante una correcta elección del valor de las variables se puede mejorar la seguridad y durabilidad del puente con un pequeño incremento del coste. Además, esta metodología es aplicable a cualquier tipo de estructura y material.[CA] Els ponts, com a part important d'una infraestructura, s'espera que reunisquen tots els requisits d'una societat moderna. Tradicionalment, l'objectiu principal en el disseny de ponts ha sigut aconseguir el menor cost mentres es garantix l'eficiència estructural. No obstant això, la preocupació per construir un futur més sostenible ha provocat un canvi en les prioritats de la societat. Estructures més ecològiques i durables són cada vegada més demandades. Davall estes premisses, els mètodes d'optimització heurística proporcionen una alternativa eficaç als dissenys estructurals basats en l'experiència. L'aparició de nous materials, dissenys estructurals i criteris sostenibles motiven la necessitat de crear una metodologia per al disseny automàtic i precís d'un pont real de formigó posttesat que considere tots estos aspectos. Per primera vegada, esta tesi estudia el disseny eficient de ponts de formigó posttesat amb secció en calaix des d'un punt de vista sostenible. Esta investigació integra criteris ambientals, de seguretat estructural i durabilitat en el disseny òptim del pont. La metodologia proposada proporciona múltiples solucions que a penes encarixen el cost i milloren la seguretat i durabilitat. Al mateix temps, es quantifica l'enfocament sostenible en termes econòmics, i s'avalua l'efecte que tenen els dits criteris en el valor òptim de les variables. En este context, es formula una optimització multiobjetivo que proporciona solucions eficients i de compromís entre els criteris econòmics, ecològics i socials. Un programa d'optimització del disseny selecciona la millor geometria, tipus de formigó, armadura i posttesat que complisquen amb els objectius seleccionats. S'ha triat com a cas d'estudi un pont continu en calaix de tres vans situat en la costa. Este mètode proporciona un major coneixement sobre esta tipologia de ponts des d'un punt de vista sostenible. S'ha estudiat el cicle de vida a través de l'avaluació del deteriorament estructural del pont a causa de l'atac per clorurs. S'examina l'impacte econòmic, ambiental i social que produïx el manteniment necessari per a estendre la vida útil del pont. Per tant, els objectius proposats per a un disseny eficient han sigut traslladats des de l'etapa inicial fins a la consideració del cicle de vida. Per a solucionar el problema de l'elevat temps de càlcul degut a l'optimització multiobjetivo i l'anàlisi per elements finits, s'han integrat xarxes neuronals en la metodologia proposada. Les xarxes neuronals són entrenades per a predir la resposta estructural a partir de les variables de disseny, sense la necessitat d'analitzar el pont. El problema d'optimització multiobjetivo es traduïx en un conjunt de solucions de compromís que representen objectius contraposats. La selecció final de les solucions preferides se simplifica per mitjà d'una tècnica de presa de decisions. Una tècnica estructurada convertix els juís basats en comparacions per parells d'elements amb un grau d'incertesa en valors numèrics que garantixen la consistència dels dits juís. Esta tesi proporciona una guia que estén i millora les recomanacions sobre el disseny d'estructures de formigó dins del context de desenrotllament sostenible. L'ús de la metodologia proposada porta a dissenys amb menor cost i emissions del cicle de vida, comparat amb dissenys que seguixen metodologies generals. Els resultats demostren que per mitjà d'una correcta elecció del valor de les variables es pot millorar la seguretat i durabilitat del pont amb un xicotet increment del cost. A més, esta metodologia és aplicable a qualsevol tipus d'estructura i material.García Segura, T. (2016). Efficient design of post-tensioned concrete box-girder road bridges based on sustainable multi-objective criteria [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/73147TESI

Pseudo-analytical solutions for stochastic options pricing using monte carlo simulation and breeding PSO-trained neural networks

We introduce a novel methodology for pricing options which uses a particle swarm trained neural network to approximate the solution of a stochastic pricing model. The performance of the network is compared to the analytical solution for European call options and the errors shown statistically comparable to Monte Carlo pricing. The work provides a proof of concept that can be extended to more complex options for which no analytical solutions exist, the pricing method presented here delivering results several orders of magnitude faster than the Monte Carlo pricing method used by default in the financial industry

Assessment and identification of concrete box-girder bridges properties using surrogate model calibration: case study: El Tablazo bridge

Dissertação de mestrado integrado em Engenharia CivilThis work consists in identifying and assessing the properties in a pre-stressed concrete bridge related to material, geometry and physic sources, through a surrogate model. The participation of this mathematical model allows to generate a relationship between bridge properties and its dynamic response, with the purpose of creating a tool to predict the analytical values of the studied properties from measured eigenfrequencies; in this case, it is introduced the identification of damage scenarios, giving the application for validate the generated metamodel (Artificial Neural Network - ANN). A FE model is developed to simulate the studied structure, a Colombian bridge called El Tablazo, one of the higher in the country of this type (box-girder bridge), with a total length of 560 meters, located on the Sogamoso riverbed in the region of Santander - Colombia. Once the damage scenarios are defined, this work allows to indicate the basis for futures plans of structural health monitoring.Este trabalho consiste em identificar e avaliar as propriedades de uma ponte em betão pré-esforçado em relação ao material, geometria e características físicas através de um metamodelo. A participação deste modelo matemático permite gerar uma relação entre as propriedades da ponte e sua resposta dinâmica, com o objetivo de criar uma ferramenta para prever os valores analíticos das propriedades estudadas a partir de frequências próprias medidas; neste caso, é introduzida a identificação de cenários de dano, dando uma aplicação para validar o metamodelo (Rede Neural Artificial - ANN). Um modelo de elemento finito é desenvolvido para simular a estrutura estudada, uma ponte colombiana chamada El Tablazo, uma das que apresenta maior altura do país em seu tipo (pontes em viga-caixão), com um comprimento total de 560 metros, localizada no rio Sogamoso, na região de Santander - Colômbia. Uma vez que os cenários de dano são definidos, a tese permite indicar a base para os planos futuros de monitoramento da saúde estrutural

Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge

[EN] The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a small variation of these initial uncertain parameters can have a big influence on the structural behavior. The objective of robust design optimization is to obtain an optimum design with the lowest possible variation of the objective functions. For this purpose, a probabilistic optimization is necessary to obtain the statistical parameters that represent the mean value and variation of the objective function considered. However, one of the disadvantages of the optimal robust design is its high computational cost. In this paper, robust design optimization is applied to design a continuous prestressed concrete box-girder pedestrian bridge that is optimum in terms of its cost and robust in terms of structural stability. Furthermore, Latin hypercube sampling and the kriging metamodel are used to deal with the high computational cost. Results show that the main variables that control the structural behavior are the depth of the cross-section and compressive strength of the concrete and that a compromise solution between the optimal cost and the robustness of the design can be reached.This research was funded by the Ministerio de Economia, Ciencia y Competitividad and FEDER funding grant number [BIA2017-85098-R].Penadés-Plà, V.; García-Segura, T.; Yepes, V. (2020). Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge. Mathematics. 8(3):1-14. https://doi.org/10.3390/math8030398S11483Lee, K.-H., & Kang, D.-H. (2006). A robust optimization using the statistics based on kriging metamodel. 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The impact of human errors on the performance to failure of concrete bridges

Programa doutoral em Engenharia CivilO colapso de pontes que tiveram lugar em todo o mundo nos últimos 50 anos destacou o erro humano como a principal causa do colapso de pontes. Dadas as implicações financeiras, sociais e psicológicas de tais eventos indesejados, a contribuição do erro humano no colapso de pontes deve ser investigada com o objetivo de compreender como é que a robustez e a segurança estrutural das pontes são afetadas pelos mesmos. A deterioração das pontes, leva à redução das margens de segurança, expondo muitas vezes deficiências causadas por erros de projeto e construção, realçando a importância do desenvolvimento de procedimentos de avaliação estrutural mais abrangentes, tendo em conta numerosas fontes de incertezas. Apesar destes factos conhecidos existem poucos trabalhos disponíveis investigando questões tão relevantes. Neste sentido este trabalho aborda a identificação dos erros humanos em suas inúmeras formas, ou seja, erros de projeto e erros de construção, de acordo com opiniões de especialistas e eventos de colapso de pontes registados. Diferentes erros representam diferentes ameaças à segurança estrutural; como tal o risco relativo dos erros também é investigado. O real impacto dos erros humanos na segurança estrutural é investigado através de três pontes de betão armado, considerando a probabilidade de falha perante um conjunto de incertezas como principal indicador de desempenho. Tal investigação é realizada em duas etapas, uma onde os erros de projeto e construção são introduzidos em cenários onde se entende que eles estão presentes e outra onde a possibilidade de ocorrência de erros de construção é investigada considerando a probabilidade do erro humano e a magnitude do erro. Ocorrências únicas e múltiplas de erros também são discutidas. Modelos de elementos finitos, considerada para fins de análise estrutural não linear, e modelos substitutos são introduzidos como a base das múltiplas análises de fiabilidade estrutural realizadas. Finalmente, a previsão da vida útil de pontes considerando a corrosão induzida por carbonatação e a redução da vida útil das pontes causada por erros de construção são questões também abordadas.The collapse of bridges that have taken place worldwide in the last 50 years has highlighted human error as the main cause of the collapse of bridges. Given the financial, social and phycological implications of such hazardous events, human errors' contribution to the collapse of bridges must be investigated, aiming to understand how their robustness and structural safety are affected. The ageing of bridges leads to safety margin reductions that often expose deficiencies caused by design and construction errors, underling the importance of developing more comprehensive frameworks that consider numerous sources of uncertainty for structural safety assessment purposes. Despite these facts and known needs, few works facing such relevant concerns are available. Accordingly, human errors are identified in their numerous forms, i.e., design errors and construction errors, according to expert opinions and real-world bridge collapse events. Different errors represent different threats to structural safety; thus, their relative risk is also investigated. The actual impact of human errors on structural safety is investigated through one reinforced and two prestressed concrete bridges, using their probability of failure, given a group of uncertainties, as the main performance indicator. Such investigation is performed on two fronts, one where design and construction errors are introduced under scenarios where they are understood to be present, and another where the possibility of occurrence of construction errors is investigated considering probabilistic models to describe human error probabilities and error magnitudes. Single and multiple occurrences of errors are also discussed. Finite element modelling, considered for non-linear structural analysis purposes, and surrogate models are introduced as the backbone of the multiple structural reliability analysis performed. Finally, the service life prediction of bridges considering carbonation-induced corrosion and the service life reduction of bridges due to construction errors are carefully addressed.This work was partially financed by (i) national funds through FCT - Foundation for Science and Technology, under grant agreement “PD/ BD/143003/2018” attributed to the PhD Candidate through the iRail Doctoral program; and (ii) FCT/MCTES through national funds (PIDDAC) under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB/04029/2020