Surrogate-Assisted Multi-Objective Optimization of Stilling Basin Design: Integrating ANN Metamodeling with NSGA-II Using Real Experimental Data

Water rushing over a dam or down a spillway carries immense power. If that high-speed flow hits the riverbed below without warning, it acts like a relentless sandblaster, carving deep holes and threatening to undermine the very structure that holds back the water. To prevent this destruction, engineers build a specific pool at the bottom of these structures, known as a stilling basin. Its job is to force the water to slow down and lose its energy safely before it continues downstream. This happens through a chaotic, churning event called a hydraulic jump, where the fast, thin sheet of water suddenly crashes into a deeper, slower pool. The goal is to dissipate as much of that destructive energy as possible. However, there is a catch: the very turbulence that breaks up the energy also tends to scour, or dig out, the riverbed. Engineers have long faced a difficult balancing act: design a basin that stops the water's power without digging a hole so deep it collapses the foundation.

For decades, finding the perfect shape for these basins meant relying on trial and error, physical models in laboratories, or complex computer simulations that could take days to run for a single design. A new study, however, offers a faster, smarter way to solve this puzzle. Researchers from Northern Technical University and Karlstad University have developed a method that combines real-world experimental data with artificial intelligence to find the best possible designs in a matter of minutes. Instead of guessing or running thousands of slow computer simulations, they trained a digital brain to learn from actual measurements taken in previous experiments. This system then used a powerful search algorithm to explore thousands of potential designs, quickly identifying the perfect trade-offs between stopping the water's energy and protecting the riverbed.

The team started by gathering high-quality data from two separate, peer-reviewed studies where scientists had already tested how water behaved in different basin setups. They collected eighty distinct data points, each representing a specific combination of water depth, speed, basin length, and the height of small blocks placed inside the basin to disrupt the flow. These blocks, called baffles, are crucial because they help break up the water and create the turbulence needed to slow it down. The researchers fed this real data into an artificial neural network, a type of computer program modeled after the human brain that is excellent at spotting patterns in complex information. They taught this digital model to predict two things: how much energy the water would lose (efficiency) and how deep the riverbed would be dug out (scour depth). The model learned so well that it could predict the outcome of a new design with an accuracy of over 95 percent, a level of precision that made it a reliable substitute for running expensive physical tests or slow computer simulations.

Once the digital model was trained, the researchers set it loose on the problem of finding the best design. They asked the computer to solve a classic conflict: maximize the energy loss while simultaneously minimizing the digging of the hole. In the real world, you cannot have both at the same time; usually, making the water lose more energy means it digs a deeper hole. To navigate this, they used an algorithm called NSGA-II, which is designed specifically to handle such conflicting goals. Instead of giving a single answer, the algorithm generated a list of 123 different designs, each representing a unique compromise. Some designs were very good at stopping the energy but left a slightly deeper hole, while others were gentle on the riverbed but didn't stop the water's power as effectively. This collection of options, known as a Pareto front, gives engineers a menu of choices rather than a single forced solution, allowing them to pick the design that best fits their specific needs.

The study identified one particular design as the "best compromise," a solution that sits right in the middle of the trade-off curve. For this ideal setup, the water enters the basin at a depth of 0.064 meters and a speed of 0.812 meters per second. The basin itself is about 1.004 meters long, and the baffles inside stand 0.036 meters high. This specific configuration manages to dissipate 51.10 percent of the water's energy while keeping the scour depth to just 0.005 meters. The researchers also discovered which factors mattered most. They found that the speed of the incoming water was the single biggest driver of energy loss; changing the speed had a massive impact on how much power was dissipated. Conversely, the height of the baffles was the most critical factor for controlling how deep the riverbed would be dug out. By adjusting these two variables, engineers can fine-tune the basin to prioritize either safety from erosion or maximum energy reduction.

Perhaps the most significant finding of this work is the sheer speed at which these results were achieved. In the past, optimizing a design like this using detailed computer fluid dynamics simulations could take days or even weeks of computing time. By using the artificial intelligence model trained on real data, the researchers completed the entire optimization process, including ten separate runs to ensure reliability, in about 25 minutes total. This dramatic reduction in time means that engineers can now explore a much wider range of possibilities and find better solutions without being held back by computational limits. While the study notes that the specific results are valid only within the range of conditions tested, the method itself is a powerful new tool. It proves that by combining real experimental data with smart algorithms, we can solve complex hydraulic problems efficiently, ensuring that the structures protecting our rivers and cities are designed with both precision and practicality.