Systems and methods compute dysfunctions via mapping of tri-axial accelerations of drill pipe into drill-string motions. The methods remove gravitational and centripetal accelerations to yield corrected acceleration data due to the vibration only, transform the corrected acceleration data, and maps resulting transformed acceleration data into continuous drill-string positions. The maps provide 2D/3D visualization of drill-string motions to enable real-time optimization and control of well drilling operations and other scenarios where proactive detection of temporal events in automated systems may aid in avoiding failures.