SGL-PCA: Health Index Construction With Sensor Sparsity and Temporal Monotonicity for Mixed High-Dimensional Signals

With advancements in sensor technology, high dimensional signals such as functional curves and images are typically collected from multiple sensors to characterize the degradation of a system. Data fusion methods are employed to integrate multisensor signals generated from the system into a scalar health index (HI) to understand the degradation status of the system. This paper develops sparse group LASSO-principal component analysis (SGL-PCA), a method that constructs HIs for image and profile data. First, we remove the smooth background from each sensor signal. Then, we solve the degradation patterns and the degradation paths through a rank-one matrix approximation problem, with the consideration of the sparsity of the measurements related to the degradation process and the monotonicity of the degradation paths. Results from a simulation study and a case study illustrate that the HI constructed by the proposed method outperforms the benchmark methods in identifying the measurements subject to the degradation process and predicting the remaining useful life of the system. Note to Practitioners - In practice, sensors generating multiple high-dimensional curves and images are often installed in systems to characterize their degradation status. Compared with scalar sensor signals, the information that associates with the degradation process often appears in sparse regions from the sensor signals. Therefore, identifying the degradation information accurately is important in the health index (HI) construction for degradation modeling and prognostic analysis. This article proposes a method that simultaneously selects the degradation information and estimates the optimal weights for integrating multi-sensor signals in constructing the HI. The proposed method is applicable in the case where the systems degrade under a single failure mode, and multiple sensors are used to monitor the degradation processes. Practitioners can implement our method to predict the remaining useful lives of in-service systems through three steps: (1) estimate the backgrounds of each sensor and derive data-fusion model using a historical dataset; (2) construct the HIs of in-service systems; (3) predict the remaining useful lives of these systems based on the developed HIs.