Background: Large engineering structures, such as space launch towers and suspension bridges, are subjected to extreme forces that cause high-speed 3D deformation and compromise safety. These structures typically operate under extreme illumination conditions. Traditional cameras often struggle to handle strong light intensity, leading to overexposure due to their limited dynamic range. Objective: Event cameras have emerged as a compelling alternative to traditional cameras in high dynamic range and low-latency applications. This paper presents an integrated method, from calibration to measurement, using a multi-event camera array for high-speed 3D deformation monitoring of structures in extreme illumination conditions. Methods: Firstly, the proposed method combines the characteristics of the asynchronous event stream and temporal correlation analysis to extract the corresponding marker center point. Subsequently, the method achieves rapid calibration by solving the Kruppa equations in conjunction with a parameter optimization framework. Finally, by employing a unified coordinate transformation and linear intersection, the method enables the measurement of 3D deformation of the target structure. Results: Experiments confirmed that the relative measurement error is below 0.08%. Field experiments under extreme illumination conditions, including self-calibration of a multi-event camera array and 3D deformation measurement, verified the performance of the proposed method. Conclusions: This paper addressed the critical limitation of traditional cameras in measuring high-speed 3D deformations under extreme illumination conditions. The experimental results demonstrate that, compared to other methods, the proposed method can accurately measure 3D deformations of structures under harsh lighting conditions, and the relative error of the measured deformation is less than 0.1%.