One of the countless challenges facing the international community is the question of what to do with the radioactive waste produced from nuclear plants each year. In the United States alone, more than 2,000 metric tons of highly radioactive waste are produced yearly. While such waste can be stored in a pool on-site for several years, a permanent solution is necessary to protect human health and the environment in the long run.
This project utilizes machine learning models to optimize the properties of waste glass currently produced by the Pacific Northwest National Laboratory’s (PNNL) vitrification site in Hanford, Washington. Vitrification is the process of combining nuclear waste with glass-forming materials at extremely high temperatures to create a molten glass that is easily disposed of permanently and safely.
PNNL currently uses an optimization scheme with partial quadratic mixture (PQM) models to optimize properties of the waste glass with the help of additives - this might include maximizing waste loading and ensuring that safety constraints are met. Because real-world behavior does not directly match simulation, constraints such as prediction uncertainties that affect optimization must be taken into account to ensure that decisions are made with confidence.
In replacing or refining the models currently used in the optimization scheme with machine learning models, we hope to offer improvements that have the same prediction performance, provide a prediction uncertainty that affects optimization, run as fast as current PQM models, and are retained easily for new datasets. These models are used for the properties of the glass, including electrical conductivity, viscosity, and certain component solubilities. In this case, the models are used as a constraint of an optimization problem in order to replicate physics-based behavior.
Following is a more detailed explanation of the project logistics by project lead LaGrande Gunnell:
The optimization is done in the Gekko Optimization Suite, with IPOPT as the solver. These models need to be interfaced to Gekko and have second derivative information available to work with the gradient optimization method. So far, we have looked at Gaussian Process Regression (GPR), Support Vector Regression (SVR), and Neural Networks (NN) with packages like Sklearn, Tensorflow, and GPFlow. GPR uses Gaussian principles and Kernel functions to predict a solution by generating every possible function that could match the data and then taking the average of those functions. SVR draws a hyperplane between the data with kernel functions and tries to maximize the margins in order to be able to regress the data. NN uses different numbers of layers, neurons, weights, and biases to predict the value. Some of these methods, like GPR and some NN, have Gaussian uncertainties built in and can readily provide confidence intervals on the predictions; other models need to be retrained multiple times through bootstrapping, and used together to predict an ensemble prediction and uncertainty.”
Project Support
The authors are grateful for the support by the U.S. Department of Energy (DOE), Office of River Protection Waste Treatment and Immobilization Plant (WTP) Project. Pacific Northwest National Laboratory is a multi-program national laboratory operated for the U.S. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RL01830. This project was funded as a subcontract to Brigham Young University to develop machine learning methods for Gekko Optimization Suite in support of nuclear waste modeling and loading optimization.
Publications
Machine Learning in Gekko
Gunnell, L., Manwaring, K., Lu, X., Reynolds, J., Vienna, J., Hedengren, J.D., Machine Learning with Gradient-based Optimization of Nuclear Waste Vitrification with Uncertainties and Constraints, Processes, 10(11), 2365, Nov 2022, DOI: 10.3390/pr10112365. Article (Open Access) | Documentation
Abstract: Gekko is an optimization suite in Python that solves optimization problems involving mixed-integer, nonlinear, and differential equations. The purpose of this study is to integrate common ML algorithms such as Gaussian Process Regression (GPR), support vector regression (SVR), and artificial neural network (ANN) models into Gekko to solve data based optimization problems. Uncertainty quantification (UQ) is used alongside ML for better decision making. These methods include ensemble methods, model-specific methods, conformal predictions, and the Delta method. An optimization problem involving nuclear waste vitrification is presented to demonstrate the benefit of ML in this field. ML models are compared against the current Partial Quadratic Mixture (PQM) model in an optimization problem in Gekko. GPR with Conformal uncertainty was chosen as the best substitute model as it had a lower mean squared error of 0.0025 compared to 0.018 and more confidently predicted a higher waste loading of 37.5 wt% compared to 34 wt%. The example problem shows that these tools can be used in similar industry settings where easier use and better performance is needed over classical approaches. Future works with these tools include expanding them with other regression models and UQ methods, and exploration into other optimization problems or dynamic control.
