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Generally, the internal states of most engineering systems are inaccessible to sensors under operational conditions, permitting indirect measurements and failures to be observed discretely. For this type of system, a class of proportional hazard (PH) models with multistate process have been proposed for performing prognostics. However, existing studies use a constant degradation mechanism with a very limited number of states, which may fail to model the actual deterioration of the system. Therefore, this article presents a novel PH model that utilizes a nonconstant degradation mechanism with a large number of states to perform health prognostics. A matrix partition-based approximation method is developed to include all the possible state transitions and to estimate important health quantities of the system, such as conditional reliability (CR), mean remaining useful life (MRUL), and remaining useful life distribution (RULD). An online prognostic scheme based on this matrix approach is presented to provide an update with the latest health quantities of the system. The proposed approach provides appealing computational features and avoids difficulties in calculating uncountable transitions for PH model-based prognostics. The effectiveness of the proposed method is demonstrated via a case of helical gearboxes under indirect monitoring and random failure conditions. [ABSTRACT FROM AUTHOR]

Accurate identification of the tool wear states in machining of titanium alloys continues to be a thorny problem. Rapid construction of accurate and effective tool wear predictive models with regard to various titanium alloys is indispensable for promoting the development of intelligent manufacturing. This article presents a novel WOA-SVM model that integrates support vector machine (SVM) and whale optimization algorithm (WOA), which is utilized for accurate estimation of the tool wear in end milling of titanium alloy Ti-6Al-4V under variable cutting conditions. The signal features in three domains are extracted from the original cutting forces and constitute the “complete features” that are adopted as the monitoring features. Besides, neighborhood preserving embedding (NPE) is utilized to fuse the monitoring features and realize dimension reduction, which aims at improving the modeling efficiency of the novel WOA-SVM model. The experimental results show that under the premise of guaranteeing prediction accuracy, the utilization of NPE reduces the modeling time-consumption of WOA-SVM by more than 90%. In comparison with the commonly used methods (such as PSO-SVM and GSA-SVM), WOA-SVM takes on comparable prediction accuracy and can reduce the modeling time-consumption by more than 30% in most cases. Moreover, the WOA-SVM model has better prediction accuracy and stability than other classical methods, such as ${k}$ -nearest neighbor ($k$ -NN), feedforward neural network (FFNN), linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and classification and regression tree (CART). Therefore, the combination of NPE and WOA-SVM provides a guarantee for rapidly constructing accurate tool wear predictive models in machining of titanium alloys. [ABSTRACT FROM AUTHOR]