The early detection of structural malfunctions requires the installation of real-time monitoring systems ensuring continuous access to the damage-sensitive information; nevertheless, it can generate bottlenecks in terms of bandwidth and storage. Deploying data reduction techniques at the edge is recognized as a proficient solution to reduce the system's network traffic. However, the most effective solutions currently employed for the purpose are based on memory and power-hungry algorithms, making their embedding on resource-constrained devices very challenging; this is the case of vibration data reduction based on System Identification models. This paper presents PARSY-VDD, a fully optimized PArallel end-to-end software framework based on SYstem identification for Vibration-based Damage Detection, as a suitable solution to perform damage detection at the edge in a time and energy-efficient manner, avoiding streaming raw data to the cloud. We evaluate the damage detection capabilities of PARSY-VDD with two benchmarks: a bridge and a wind turbine blade, showcasing the robustness of the end-to-end approach. Then, we deploy PARSY-VDD on both commercial single-core and a specific multi-core edge device. We introduce an architecture-agnostic algorithmic optimization for SysId, improving the execution by 90x and reducing the consumption by 85x compared with the state-of-the-art SysId implementation on GAP9. Results show that by utilizing the unique parallel computing capabilities of GAP9, the execution time is 751μs with the high-performance multi-core solution operating at 370MHz and 0.8V, while the energy consumption is 37μJ with the low-power solution operating at 240MHz and 0.65V. Compared with other single-core implementations based on STM32 microcontrollers, the GAP9 high-performance configuration is 76x faster, while the low-power configuration is 360x more energy efficient.