ANN-based optimized design of doubly reinforced rectangular concrete beams based on multi-objective functions

Figures & data

Table 1. Nomenclature of design parameters.

Table 2. Design criteria for a design of ductile RC beams according to ACI 318–19 (2019).

Figure 1. Configuration of a doubly RC beam.

Table 3. Unit cost of reinforcement and concrete based on Korean unit (Hong et al. 2010).

Figure 2. AI-based Lagrange optimization algorithm of five steps based on unified functions of objectives (UFO).

Table 4. Optimization design scenario of a doubly RC beam.

Figure 3. A topology of an ANN for a design of doubly RC beams.

Figure 4. Flow of optimized designs based on AI-based Lagrange optimization algorithm.

Table 5. Design range to generate 100,000 data used for training ANNs.

Table 6. 100,000 datasets to train ANNs.

Table 7. Training accuracies obtained based on three, four, and five hidden layers, each of which contains 30, 40, and 50 neurons.

Table 8. Formulation of equality and inequality constraints.

Table 9. Optimized single-objective functions.

Table 10. Equally spaced fractions generated based on MATLAB function, $linspace$.

Figure 5. Equally spaced fractions generated based on MATLAB function.

Table 11. Optimized design parameters on a Pareto frontier illustrated in Figure 6.

Figure 6. A Pareto frontier based on 361 fractions for RC beams based on three objective functions.

Figure 7. Verification of a Pareto frontier by 1 million structural datasets.

Table 12. Design option with tradeoff ratios for an example shown in Fig. 8.

Table 13. Design parameters of two designs marked in blue color in Table 12.

Figure 8. Estimated design ranges for minimized $C{O}_2$ and $BW$ corresponding to a defined cost budget.

“ACI CODE 318-19: Building Code Requirements for Structural Concrete and Commentary”. 2019

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Hong, W.-K., J.-M. Kim, S.-C. Park, S.-G. Lee, S.-I. Kim, K.-J. Yoon, H.-C. Kim, and J. T. Kim. 2010. “A New Apartment Construction Technology with Effective CO2 Emission Reduction Capabilities.” Energy 35 (6): 2639–2646. doi:10.1016/j.energy.2009.05.036.

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