Computationally Efficient Optimisation of Elbow-Type Draft Tube Using Neural Network Surrogates

TL;DR

This work tackles the design optimisation of an elbow-type draft tube for hydropower by introducing a data-driven workflow that uses Latin hypercube sampling to generate designs, CFD for evaluation, and deep neural network surrogates to predict $C_p$ and $C_d$ rapidly. It systematically compares single-objective and multi-objective evolutionary algorithms, finding that L-SHADE excels in single-objective tasks and MOEA/D provides robust, well-distributed Pareto fronts for multi-objective cases, with TOPSIS used to select the best compromise design. Validation shows surrogate predictions differ from CFD by less than $0.5\%$ for $C_p$ and $3\%$ for $C_d$, and the best MO solution achieves about $17\%$ drag reduction and $1.5\%$ pressure-recovery improvement relative to the reference. The approach offers a scalable path to efficient, data-driven draft-tube optimisation applicable to turbine revitalisation and new designs, while highlighting future directions such as velocity profiles, multi-point optimization, and cavitation considerations.

Abstract

This study aims to provide a comprehensive assessment of single-objective and multi-objective optimisation algorithms for the design of an elbow-type draft tube, as well as to introduce a computationally efficient optimisation workflow. The proposed workflow leverages deep neural network surrogates trained on data obtained from numerical simulations. The use of surrogates allows for a more flexible and faster evaluation of novel designs. The success history-based adaptive differential evolution with linear reduction and the multi-objective evolutionary algorithm based on decomposition were identified as the best-performing algorithms and used to determine the influence of different objectives in the single-objective optimisation and their combined impact on the draft tube design in the multi-objective optimisation. The results for the single-objective algorithm are consistent with those of the multi-objective algorithm when the objectives are considered separately. Multi-objective approach, however, should typically be chosen, especially for computationally inexpensive surrogates. A multi-criteria decision analysis method was used to obtain optimal multi-objective results, showing an improvement of 1.5% and 17% for the pressure recovery factor and drag coefficient, respectively. The difference between the predictions and the numerical results is less than 0.5% for the pressure recovery factor and 3% for the drag coefficient. As the demand for renewable energy continues to increase, the relevance of data-driven optimisation workflows, as discussed in this study, will become increasingly important, especially in the context of global sustainability efforts.

Figures (29)

• Figure 1: Changes@ColorredA proposed workflow combining LHS for geometry selecetion, CFD, DNN surrogate modelling and optimisation (left). CFD is used to generate data. The tuned DNNs are coupled with the SO and MO algorithms. The optimal MO solution is determined using the TOPSIS method. Typical optimisation process (right). First, the algorithm is initialised, and an initial set of candidates is generated. The fitness is calculated, and each algorithm performs algorithm-specific steps (crossover, mutation, location update, velocity and position updates, etc.). The process is repeated until the termination criterion is satisfied (number of iterations, generations).
• Figure 1: Changes@ColorredDistribution of values for each feature and targets in the dataset used in Scenario I.
• Figure 1: Convergence graphs for FWA, PSO and L-SHADE when optimising for $C_p$ (a) and $C_d$ (b) in test Scenario I.a. L-SHADE performs better than the competition. The differences for $C_p$ are negligible, while for $C_d$, a difference of $\approx 5\%$ can be observed.
• Figure 2: HPP Rijeka draft tube reference cross-sections.
• Figure 2: Changes@ColorredDistribution of values for each feature and targets in the dataset used in Scenario II.