Reliability-based optimization

The presence of uncertainty in several aspects of structural design, such as load modeling and structural and material properties characterization, requires approaching the design of structures from a probabilistic perspective. I have been working on the development of reliability-based design optimization frameworks in several fields, including vehicle crashworthiness, composite panels of aircraft fuselages, and bridge and wind engineering.

Vehicle crashworthiness

In the field of automotive safety, the lightweight design of crash absorbers is an important research topic with a direct effect on occupant safety levels. The design of these absorbers usually requires an optimization of their crashworthiness, which can include multi-objective and reliability-based optimization techniques. This process is very time-consuming, and in spite of the continuous growth of computational power, the problem needs a reliable solving scheme. The use of surrogate models and parallel computing are suitable alternatives to deal with this issue. However, the strongly non-linear response functions obtained from the finite element simulations need careful treatment. This work contributes with the application of a surrogate-based reliability-based design optimization method to an original design of a crash absorber made of metal and a glass-fiber-reinforced polymer (GFRP) which is subjected to a frontal impact.


Rendered view of a Dodge Neon body in white with the location of several important
regions for the constraint of the reliability-based design optimization. Cid Montoya et al. Struct Multidisc Optim, 52:827-843, 2015.
Comparison of the probabilistic and deterministic Pareto fronts obtained using different surrogate models. Cid Montoya et al. Struct Multidisc Optim, 52:827-843, 2015.

Composite panels of aircraft fuselage

The main factors governing the design of composite laminates are the geometrical dimensions, the stacking sequence –including ply thickness and orientation angles–, the mechanical properties of the materials, the applied loads, and the performance requirements. Most of these factors are commonly affected by uncertainty and this should be taken into account when designing these structures. Thus, uncertainty quantification should be used to evaluate the performance requirements and a reliability-based procedure is advisable when the design is optimized. However, these methods present several drawbacks, like the lack of trustworthy information about the uncertainty present in the variables of the model or the high computational cost required to apply the algorithms to medium to large models. This study evaluates several methodologies for the design optimization of composite panels under uncertainty.

Surrogate-based RBDO flowchart. Díaz et al. Adv Eng Soft 93, 9-21, 2016.
First buckling mode of an aircraft fuselage stiffened composite panel. Díaz et al. Adv Eng Soft 93, 9-21, 2016.
Evolution of the optimum design of the stacking sequence considering continuous and discrete random design variables and stochastic collocation to evaluate reliability constraints. Díaz et al. Adv Eng Soft 93, 9-21, 2016.

Bridge and wind engineering

Aeroelastic responses of long-span bridges are influenced by a large number of parameters. Most of these have an inherent probabilistic nature that necessitates the evaluation of these limit states from a probabilistic perspective. Reliability analyses in the aero-structural design of bridges are still rather limited. The large number of inputs, as well as outputs, makes this problem very challenging. The set of input parameters considered as random variables includes aleatory uncertainties stemming from wind and epistemic uncertainties resulting from structural characterization parameters as well as aerodynamic and aeroelastic characteristics of the deck cross-section. The objective of this work is twofold: to compute the probability of failure of long-span cable-stayed bridges against wind-induced loads, considering uncertainty in several parameters that significantly affect the limit state, and to investigate the influence of deck shape variations on the reliability of the structure. Then, a framework combining several numerical design techniques, including CFD analyses, surrogate models, global sensitivity analyses, and reliability analyses, is developed to carry out a reliability-based tailoring of the deck shape.

Flutter velocity Uf and reliability index of the Great Belt bridge for different deck shape geometries. Kusano et al. J Wind Eng Ind Aerodyn, 202: 104176, 2020.

Uncertainty propagation of the lateral, vertical, and torsional buffeting responses in terms of RMS of accelerations of a 3-DoF system. Cid Montoya et al. ASCE Structures Congress, 2020.

Journal papers

Kusano I, Cid Montoya M, Baldomir A, Nieto F, Jurado J. A and Hernández S (2020). Reliability based design optimization for bridge girder shape and plate thickness of long-span suspension bridges considering aeroelastic constraint. Journal of Wind Engineering and Industrial Aerodynamics, 202:104176.
DOI: j.jweia.2020.104176

Díaz J, Cid Montoya M, and Hernández S (2016) Efficient methodologies for reliability-based design optimization of composite panels. Advances in Engineering Software, 93: 9-21.
DOI: j.advengsoft.2015.12.001

Cid Montoya M, Costas M, Díaz J, Romera L and Hernández S (2015) A multi-objective reliability-based optimization of the crashworthiness of a metallic-GFRP impact absorber using hybrid approximations. Structural and Multidisciplinary Optimization, 52 (4): 827-843.
DOI: s00158-015-1255-7


Cid Montoya M, Nieto F, Hernández S, Kareem A, Ding F (2020) “Computational techniques for novel design of long span bridges considering aeroelastic phenomena” ASCE Structures Congress 2020, session: Novel Building and Bridge Design with Structural Optimization, St. Louis, Missouri, April 5-8, 2020. (Published, conference canceled because of COVID)
DOI: 10.1061/9780784482896.070

Cid Montoya M, Ding F, Kareem A, Hernández S, Nieto F (2020) “A reliability-based design optimization of bridge deck shape for buffeting response” BBAA IX 9th Int. Colloquium on Bluff Body Aerodynamics and Applications, University of Birmingham, UK, July 20-23, 2020. (Accepted, conference canceled because of COVID)

Cid Montoya M, Ding F, Kareem A, Hernández S, Nieto F, Baldomir A (2019) “A reliability based tailoring of bridge deck shape for buffeting response” The 15 th Int. Conference on Wind Eng. 2019, Sep 1-6, Beijing, China.

Kusano I, Cid Montoya M, Baldomir A, Nieto F, Jurado J A, Hernández S (2018) “Reliability based design optimization for single box deck shape and plate thickness of suspension bridges under flutter constraint” The 7 th International Symposium on Computational Wind Engineering 2018. June 18-22, Seoul, Republic of Korea.

Hernández S, Jurado J Á, Nieto F, Baldomir A, Kusano I and Cid Montoya M (2017) “The role of reliability analysis and optimization techniques in the aeroelastic design of long span bridges” Second International Bridges Congress – Chile 2017; Design, Construction and Maintenance. 18-20 October, Santiago, Chile.

Cid Montoya M, Díaz J, and Hernández S (2014) “Performance of surrogate models in reliability-based design optimization” HPSM/OPTI 2014. The 2014 International Conference on High Performance and Optimum Design ofStructures and Materials. Wessex Institute of Technology. 9-11 June 2014, Ostend, Belgium
DOI: 10.2495/HPSM140351

Díaz J, Hernández S and Cid M (2013) “Comparison of reliability based optimization methods applied to the design of composite panels” ICCS17: 17th Int. Conf. on Composite Structures. Univ. of Porto. Book of Abstracts, pp. 118.

Hernández S, Díaz J, Baldomir A, Cid M and López C (2013) “Comparison of reliability based structural optimization methodologies in the design of aircraft structures”. ICOSSAR 2013: 11th International Conference on Structural Safety & Reliability. Columbia University. CRC Press/Balkema, ISBN: 978-1-138-00086-5, pp. 755.

Hernández S, Díaz J, Cid M, Baldomir A and Romera L (2012) “Uncertainty and reliability in aircraft design and optimization”. OPTI 2012. 12th Int Conf on Optimum Design of Structures and Materials in Eng. Wessex Institute of Technology. Computer Aided Opt Design in Eng XII, WIT Press 2012, ISBN: 978-1-84564-598-4, pp. 219-230.
DOI: 10.2495/OP120191

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