This invention teaches a multi-sensor quality inference system for additive manufacturing. This invention still further teaches a quality system that is capable of discerning and addressing three quality issues: i) process anomalies, or extreme unpredictable events uncorrelated to process inputs; ii) process variations, or difference between desired process parameters and actual operating conditions; and iii) material structure and properties, or the quality of the resultant material created by the Additive Manufacturing process. This invention further teaches experimental observations of the Additive Manufacturing process made only in a Lagrangian frame of reference. This invention even further teaches the use of the gathered sensor data to evaluate and control additive manufacturing operations in real time.