Design and Multi-Objective Optimization of a High-Sensitivity Miniaturized Multilayer Flexible Electric Field Sensor for Early Detection of Insulation Degradation

To address the difficulty of effectively sensing weakly distorted electric fields generated during the early stage of insulation degradation in power equipment, this paper proposes a miniaturized high-sensitivity multilayer flexible electric field sensor optimized using an improved GOOSE algorithm. First, based on the electric field coupling mechanism, the enhancement effect of the flexible arc-shaped structure on local distorted electric fields is analyzed, and an equivalent model that discretizes the flexible curved surface into parallel-plate micro-elements is established. Furthermore, a multilayer sensor equivalent circuit model considering the effects of parasitic capacitance and conductive ink electrode resistance is developed, and the relationship between sensor sensitivity and structural parameters is derived. Subsequently, an electric field–circuit-coupled simulation model is established in COMSOL Multiphysics to systematically investigate the influence of parameters such as electrode layer number, electrode thickness, dielectric layer thickness, and electrode side length on the output response. The results show that the multilayer structure can effectively improve the equivalent sensing capacitance and electric field coupling capability, while the electrode thickness and dielectric layer thickness exhibit significant nonlinear effects on the output voltage. To achieve the coordinated optimization of high sensitivity and miniaturization, Tent chaotic mapping initialization and nonlinear dynamic adaptive inertia weight are introduced to improve the traditional GOOSE algorithm, and a multi-objective optimization model is constructed with the objectives of maximizing the output voltage and minimizing the electrode area. The optimization results indicate that the improved GOOSE algorithm achieves faster convergence and better optimization stability. Among the Pareto solution sets with different electrode layer numbers, the seven-layer structure exhibits the best size–performance trade-off. The final optimized design achieves an electrode area of only 1.746 mm2 and an output voltage of 2.565 × 10−6 V. These results demonstrate that the proposed multilayer flexible structure and improved GOOSE optimization method can significantly enhance the response capability to weak electric fields while maintaining device miniaturization, providing a new sensor design concept and optimization approach for non-contact detection of early-stage insulation degradation in power equipment.