Optimization approaches for reinforced concrete structures considering polymorphic uncertainties

For the numerical design of reinforced concrete structures, a framework combining optimization algorithms with polymorphic uncertainty models has been developed, see Figure 1a and [1]. The particle swarm optimization algorithm in combination with stochastic and interval uncertainty models has been implemented and different objectives for uncertain quantities of interest have been formulated. To reduce the computation time of the optimization, a space subdividing technique (see Figure 1b) for the consideration of inequality constraints has been adopted in [2]. A surrogate modelling strategy has been developed to replace the nonlinear finite element simulations, where the deterministic simulation as well as the stochastic analysis are approximated by sequentially trained artificial neural networks, see Figure 1c. In [3], this approach has been extended to a multilevel surrogate modelling strategy, where also the interval analysis is approximated by a third artificial neural network.

Figure 1: Framework for optimization with constraints considering polymorphic uncertainties and efficient neural network based surrogate models: a) Computational scheme; b) Space subdividing technique for constraint limit state approximation; c) Approximation of the surrogate objective function by an artificial neural network based surrogate modelling strategy.

Exemplified, the concrete cover of the lower and upper reinforcement layer of a reinforced concrete bridge structure has been optimized by minimizing the exposed lateral surface of the reinforcement crossing a crack, see [2]. The design parameters have been modelled as intervals with different radii to account for construction imprecision, while the material parameters of concrete (Young’s modulus and fully correlated tension and compression strength) and the traffic load are modelled as a priori stochastic variables. As a constraint, the accepted failure probability with respect to the load bearing capacity has been defined. Nine combinations of rebar arrangements have been analysed in [1], followed by further investigations of the best rebar arrangement [2] with respect to the sensitivity of the interval radii and the standard deviation of the load. It was found, that the optimal value of the objective function is exponentially increasing with increasing interval radius. It was observed, that slight variations of the standard deviation of the traffic load lead to large changes of the constraint limit state and to variations of the objective function and the optimal designs, see Figure 2.

Figure 2: Optimization of the concrete cover of a reinforced concrete bridge structure: a) Structural system; b) Cross section with interval design parameters htop and hbottom (positions of the rebar layers); c) Stochastic a priori parameters Q (traffic load) and E (Young’s modulus of concrete); d) Objective functions µ(M) with optimal designs (midpoints are marked by asterisks and interval bounds are marked by white boxes for three different interval radii 0, 5, 10 mm) and constraint limit state for three different standard deviations of the traffic load.


M.Sc. Philipp Edler
+49 234 / 32-29069


  • [1] P. Edler, S. Freitag, K. Kremer, and G. Meschke
    Optimization of durability performance of reinforced concrete structures under consideration of polymorphic uncertain data
    In Proceedings of the joint ICVRAM ISUMA UNCERTAINTIES conference, pages 1—19, Florianopolis, Brazil, April 2018

  • [2] P. Edler, S. Freitag, K. Kremer, and G. Meschke
    Optimization approaches for the numerical design of structures under consideration of polymorphic uncertain data
    ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part B: Mechanical Engineering, 5(4):041013 (12 pages), 2019

  • [3] S. Freitag, P. Edler, K. Kremer, and G. Meschke
    Multilevel surrogate modeling approach for optimization problems with polymorphic uncertain parameters
    International Journal of Approximate Reasoning, 119:81--91, 2020
    Special Issue Reliable Computing

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