Constrained optimization of sensor placement for nuclear digital twins

TL;DR

This paper tackles the challenge of placing a limited number of sensors in nuclear systems under spatial constraints to enable accurate reconstruction of flow and temperature fields for nuclear digital twins. It introduces a data-driven, constraint-aware sensor placement framework built on reduced-order modeling and a greedy, column-pivoted QR design that optimizes the D-optimal information criterion while enforcing region, distance, or predefined sensor-location constraints. Uncertainty quantification is integrated via confidence ellipsoids to bound reconstruction error under noisy measurements, enabling robust prospective planning and anomaly detection in digital twins. The approach is validated on a low-dimensional random system, a 2D heat diffusion model, and the OPTI-TWIST prototype, showing near-optimal sensor configurations, significantly reduced reconstruction error compared with random placements, and actionable uncertainty bounds for model recalibration in nuclear engineering contexts.

Abstract

The deployment of extensive sensor arrays in nuclear reactors is infeasible due to challenging operating conditions and inherent spatial limitations. Strategically placing sensors within defined spatial constraints is essential for the reconstruction of reactor flow fields and the creation of nuclear digital twins. We develop a data-driven technique that incorporates constraints into an optimization framework for sensor placement, with the primary objective of minimizing reconstruction errors under noisy sensor measurements. The proposed greedy algorithm optimizes sensor locations over high-dimensional grids, adhering to user-specified constraints. We demonstrate the efficacy of optimized sensors by exhaustively computing all feasible configurations for a low-dimensional dynamical system. To validate our methodology, we apply the algorithm to the Out-of-Pile Testing and Instrumentation Transient Water Irradiation System (OPTI-TWIST) prototype capsule. This capsule is electrically heated to emulate the neutronics effect of the nuclear fuel. The TWIST prototype that will eventually be inserted in the Transient Reactor Test facility (TREAT) at the Idaho National Laboratory (INL), serves as a practical demonstration. The resulting sensor-based temperature reconstruction within OPTI-TWIST demonstrates minimized error, provides probabilistic bounds for noise-induced uncertainty, and establishes a foundation for communication between the digital twin and the experimental facility.

Figures (12)

• Figure 1: Digital twins in nuclear power plants. Digital twin frameworks consist of a real/physical space containing physical assets, a virtual digital space containing computer-aided design (CAD) replicas, simulations and Artificial Intelligence (AI), a data space and a decision space grieves2015digitalgrieves2017digital; all of which are enabled by sensors providing two-way communication between the virtual (ROMs and simulations) and the physical spaces. This digital twin characterizes the lifecycle of OPTI-TWIST capsule, which is inserted into the TREAT reactor at Idaho National Laboratory (INL) to test fuel compositions.
• Figure 2: Greedy selection of the next sensor involves choosing the next pivot column of $\mathbf{\Psi}^T$ from the set of allowable sensor locations specified by the constraint.
• Figure 3: Enumeration of $\log \det(\mathbb{S}\boldsymbol{\Psi_r})^T(\mathbb{S}\boldsymbol{\Psi_r})$ (X-axis) over all possible placements of 7 out of 25 candidate locations (100,000-500,000 possible placements binned into histograms). The introduction of constraints into QR optimization results in a log determinant that is near optimal (optimum shown in red) for the three types of constraints.
• Figure 4: Reconstruction error comparison. Proximity between the brute-force optimum and QR selected sensors for unconstrained, region-constrained, and predetermined sensor placement leads to orders of magnitude lower reconstruction error ($\epsilon \sim \mathcal{O}(10^{-15})$) compared to random placements. Incorporating constraints results in accuracy comparable to that of the optimal placement (red stars).
• Figure 5: Reconstruction of the temperature field through selected sensors along with uncertainty in reconstruction. Uncertainty heatmaps (e,f,g) correspond to placements/reconstructions (b,c,d) respectively. Reconstruction of the temperature field at $t = 1000$, based on the different constraints demonstrate that constraining sensors far away from the heater region result in higher reconstruction error (c,d) and higher uncertainty (f,g) than unconstrained optimization (b,e) respectively, which favors sensors adjacent to the heat source.