Adaptive B-spline curve fitting with minimal control points using an improved sparrow search algorithm for geometric modeling of aero-engine blades

In Industry 4.0 and advanced manufacturing, producing high-precision, complex products such as aero-engine blades involves sophisticated processes. Digital twin technology enables the creation of high-precision, real-time 3D models, optimizing manufacturing processes and improving product qualification rates. Establishing geometric models is crucial for effective digital twins. Traditional methods often fail to meet precision and efficiency demands. This paper proposes a fitting method based on an improved sparrow search algorithm (SSA) for high-precision curve fitting with minimal control points. This enhances modeling precision and efficiency, creating models suitable for digital twin environments and improving machining qualification rates. The SSA’s position update function is enhanced, and an internal node vector update range prevents premature convergence and improves global search capabilities. Through automatic iterations, optimal control points are calculated using the least squares method. Fitness values, based on local and global errors, are iteratively calculated to achieve target accuracy. Validation with aero-engine blade data showed fitting accuracies of 1e−3 mm and 1e−5 mm. Efficiency in searching for minimal control points improved by 34.7%–49.6% compared to traditional methods. This SSA-based fitting method significantly advances geometric modeling precision and efficiency, addressing modern manufacturing challenges with high-quality, real-time production capabilities.