ANN-Based Adaptive NMPC for Uranium Extraction-Scrubbing Operation in Spent Nuclear Fuel Treatment Process

TL;DR

The paper tackles the control of solvent saturation in the PUREX uranium extraction-scrubbing step, a problem complicated by a $128$-state nonlinear, stiff DAE model. It proposes an ANN-based predictor comprising $LSTM$, linear, and logistic components to estimate key outputs from measurement histories and integrates this predictor into an adaptive NMPC framework with an accompanying MHE for disturbance estimation, all solved via an enhanced PSO. The approach yields a tailored architecture predicting $y$ and a binary $\bar z$, reduces optimization complexity, and demonstrates effective startup stabilization, rapid tracking under set-point changes, and disturbance rejection in simulations. The results indicate strong potential for online implementation and experimental testing, with future work aimed at online learning, stability analysis, robustness, and real-world deployment.

Abstract

This paper addresses the particularities in optimal control of the uranium extraction-scrubbing operation in the PUREX process. The control problem requires optimally stabilizing the system at a desired solvent saturation level, guaranteeing constraints, disturbance rejection, and adapting to set point variations. A qualified simulator named PAREX was developed by the French Alternative Energies and Atomic Energy Commission (CEA) to simulate liquid-liquid extraction operations in the PUREX process. However, since the mathematical model is complex and is described by a system of nonlinear, stiff, high-dimensional differential-algebraic equations (DAE), applying optimal control methods will lead to a large-scale nonlinear programming problem with a huge computational burden. The solution we propose in this work is to train a neural network to predict the process outputs using the measurement history. This neural network architecture, which employs the long short-term memory (LSTM), linear regression and logistic regression networks, allows reducing the number of state variables, thus reducing the complexity of the optimization problems in the control scheme. Furthermore, nonlinear model predictive control (NMPC) and moving horizon estimation (MHE) problems are developed and solved using the PSO (Particle Swarm Optimization) algorithm. Simulation results show that the proposed adaptive optimal control scheme satisfies the requirements of the control problem and provides promise for experimental testing.

Figures (11)

• Figure 1: Uranium extraction-scrubbing operations using mixers-settlers (vo2023).
• Figure 2: Profile of aqueous uranium concentration in the mixer, as derived with the two-film theory (Dinh2008b).
• Figure 3: Mixer-settler model vo2023.
• Figure 4: Steady state relationship of feed solution flow rates and uranium concentrations. Note that ${[{U}]^\text{aD}_{9,s1}} \approx 37.5\% {[{U}]^\text{aD}_{9,s2}}$.
• Figure 5: Profiles of aqueous uranium concentration in nominal and critical cases.