Redundancy-Aware Sensor Layout Optimization for Robust Regional Active Magnetic Compensation System

Regional active magnetic compensation (AMC) systems are essential for providing stable magnetic environments in precision applications such as frontier physics and bio-magnetic measurements. However, conventional feedback-sensor placement strategies remain largely empirical, often neglecting spatial observability, numerical conditioning, and redundancy against sensor failures. This paper presents a multi-stage sensor layout optimization framework for regional AMC systems, which is intended as a simulation level pre-design approach under a fixed coil model and quantified disturbance/noise assumptions. Based on a global three-axis random background-fluctuation model, the sensor density is first screened through Monte Carlo (MC) simulations with ridge-regularized feedback compensation. For a fixed sensor budget, a multi-objective optimization problem is then formulated by integrating the conditional value-at-risk of the scalar compensation error, CVaR_0.95(E_sca), the observation matrix condition number, and the average top-2 single-sensor-failure CVaR metric. A posterior MC simulation is further introduced to validate the closed-loop robustness of the candidate Pareto solutions. Optimization in a 1 m³ target volume with 13 optimized sensors shows that the balanced layout solution achieves CVaR_0.95(E_sca) =6.19%, a condition number of 3.35, and an average top-2 single-sensor-failure CVaR of 10.7%. The posterior re-evaluation further shows that the mean relative error of the stochastic objectives is 6.49%, confirming the reliability of the optimization. Results demonstrate that the proposed framework can provide an interpretable, robust, and fault-tolerant sensor deployment strategy for the pre-design of regional AMC systems.