Machine component health prognostics with only truncated histories using geometrical metric approach

Prognostics plays a vital part in modern decision making for maintenance. Many related valuable approaches have been reported by scientists with both truncated and failure histories. However, for cases where the actual asserts have no failure histories, one important topic of prognostics is to focus on modeling with only truncated histories. Here we first describe an algorithm called time-continuous relevant isometric mapping (TRIM) to establish a manifold space where the health state evolutionary laws within truncated histories can be cognized. Unlike classical methods, such as isometric feature mapping, TRIM involves the vital element of state evolution (time), establishes a state evolutionary manifold space by utilizing both local geometrical structures and global isometric features of a given truncated data set. Meantime, two geometrical metrics, neighborhood geodesic distance (NGD) and cumulative geodesic distance, were defined and used in this study to indicate the health state of a given component. Then the feed-forward neural network (FFNN) was trained with inputs from the NGD series. The corresponding target vectors (survival probabilities) of FFNN were estimated by intelligent product limit estimator using truncation times and generated failure times. After validation, the FFNN was applied to predict the machine component health of individual component. To validate the proposed method, case study was conducted by using the degradation data generated by a bearing test rig. Results demonstrate that the proposed method can highlight the intrinsic health state evolutionary laws by TRIM even with only truncated histories. The more accuracy prognostics results can be consequently achieved based on the cognition of the evolutionary laws.