Techniques for Uncertainty Modeling and Data Fusion for High-Precision Installation of Large Insertion Device in the Particle Accelerators

With the increasing demands for installation accuracy in particle accelerators, accurately evaluating uncertainty throughout the complete installation chain has become a critical engineering challenge. Taking large-scale scientific facilities such as Hefei Advanced Light Facility (HALF) as an example, the complete installation chain involves multiple stages, including tunnel network measurement, component calibration, and equipment installation. These stages are influenced by various coupled error sources, and the complexity of on-site measurement environments further exacerbates the difficulty of accurately evaluating installation uncertainty. As a result, traditional methods that treat each step as an independent part for calculation fail to capture the true propagation paths of uncertainty, thereby severely limiting improvements in overall installation accuracy. Therefore, this article proposes symmetric transformation-based uncertainty data fusion (STDF) to construct the uncertainty model for the complete installation chain in particle accelerators. This model not only integrates environmental uncertainty, but also fully considers the random errors introduced jointly by the station coordinate system and the target coordinate system. It systematically addresses the problem of nonlinear error propagation across multiple stages under environmental disturbances. Once the installation uncertainty is accurately evaluated, we leverage the model to develop an efficient dual-laser system through data fusion to install a large insertion device in the particle accelerator, achieving a significant average accuracy improvement of more than 50% compared with traditional dual-laser systems that rely on simple averaging. The validity and accuracy improvement of STDF have been verified through simulation and measurement. The STDF method has been tested during the installation of the undulator at the HALF. STDF not only provides critical support for the high-precision installation of particle accelerator devices, but also offers a general methodological reference for uncertainty evaluation in other complex engineering systems, such as radio telescopes, precision astronomical instruments, and large-scale manufacturing systems.