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Highlights • Novel approach to the cost-optimal early fault detection of CNC equipment. • VAR modeling of multivariate positioning data and residual testing for control purposes. • Estimation of the remaining useful life of CNC equipment using Bayesian approach. • Presented method outperforms previously published method based on HMM. Abstract The goal of a computer numerically controlled (CNC) equipment is to guarantee high specified performance and to maintain it effectively over its life cycle time. Thus, the assessment of health condition is crucial for industrial systems. However, very few papers have dealt with the cost-optimal early fault detection and remaining useful life prediction of CNC equipment using multivariate positioning data. The novel approach presented here is based on vector autoregressive (VAR) degradation modeling and hidden semi-Markov modeling using the optimal Bayesian control technique. System condition is modeled using a continuous time semi-Markov chain with three states, i.e. unobservable healthy state 1, unobservable warning state 2 and observable failure state 3. Model parameter estimates are calculated using the expectation-maximization (EM) algorithm. The optimal control policy for the three-state model is represented by a Bayesian control chart for a multivariate observation process. The optimization problem is formulated and solved in the semi-Markov decision process (SMDP) framework. A formula for the mean residual life (MRL) is also derived based on Bayesian approach, which enables the estimation of the remaining useful life and early maintenance planning based on the observed data. The validation of the proposed methodologies is carried out using actual multivariate degradation data obtained from a CNC equipment. A comparison with the multivariate Bayesian control chart based on a hidden Markov model (HMM) is given, which illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers an integrated framework for health measures prediction and optimal maintenance policy for mechanical systems subject to condition monitoring (CM) and random failure. We propose the proportional hazards model (PHM) to consider CM information as well as the age of the mechanical systems. Although the form of health prediction for the mechanical systems under periodic monitoring in the PHM with Markov chain was developed previously, the case of the continuous-state degradation process allowing possible degradation between the inspections still has not appeared. To this aim, the paper allows the use of Gamma process with non-constant degradation, which broadens the application area of PHM. A matrix-based approximation method is employed to compute health measures of the machine, such as condition reliability, mean residual life, residual life distribution. Based on the health measures, the optimal maintenance policy, which considers both hazard rate control limit and age control limit, is proposed and the optimization problem is formulated and solved in a semi-Markov decision process (SMDP) framework. The objective is to minimize the long-run expected average cost. The method is illustrated using two real data sets obtained from feed subsystem of a boring machine and GaAs lasers collected at regular time epochs, respectively. A comparison with other methods is given, which illustrates the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

• Dynamic Bayesian control scheme for adaptive monitoring and detection. • Multivariate hidden semi-Markov model to describe the deterioration process. • SMDP approach to formulate and optimize the dynamic Bayesian scheme. • Considerably better fault detection compared with published results. • Development of case studies using multivariate data. Due to restrictions of mechanical structure and sensor installation, the actual status of modern engineered machine is unobservable and only partial observations can be indirectly collected. For this type of machine, existing research works used several measurable variables with fixed thresholds to monitor and detect the failures of the system, which leads to suboptimal results. This paper proposes a dynamic monitoring and detection approach for partially observed machines under discrete multivariate observations. The actual status of the partially observed machine system is modeled as a multivariate hidden semi-Markov process with unobservable operational states and an observable failure state under a general sojourn time structure. The process parameters are estimated using expectation maximization (EM) algorithm. Based on the dynamics of the hidden state of machine deterioration, a dynamic Bayesian control chart is formulated to monitor the posterior probability of system in warning state and adaptively switches the monitoring frequency according to risks of potential failures. As the posterior probability statistic exceeds a certain level, full inspection is initiated to detect the impending failures. The objective of the dynamic Bayesian control scheme is to achieve the maximum long-run system average availability, and the optimal control problem of monitoring and detection is formulated and solved by a computational algorithm in a semi-Markov decision process (SMDP) framework. The entire procedure is illustrated using multivariate data from case studies of mechanical generators and feed systems. Comparison with other advanced methods is also given, which demonstrates a considerably better performance of the proposed dynamic Bayesian approach. [ABSTRACT FROM AUTHOR]

• A new two-stage feature-fusion method by combining PCA and KLPP is presented. • A unique approach for determining the model parameters of KLPP is presented. • KLPP is comprehensively analyzed under three weighting methods. • KLPP helps to improve the prediction accuracy and compress the CI of Standard_SBLR. • Under the support of KLPP, Standard_SBLR shows superior predictive performance. To further improve the prediction accuracy of surface roughness in milling process, this paper presents a new two-stage feature-fusion method by combining principal component analysis (PCA) and kernel locality preserving projection (KLPP). PCA is utilized for dimension-reduction while KLPP is utilized for dimension-increment. Vibration information of the workpiece, fixture and spindle is adopted as the monitoring signal. Firstly, the commonly-used time-domain features are extracted from the vibration signals. Then, the presented two-stage feature-fusion method is carried out for extracting more effective signal features. Besides, two types of Bayesian linear regression (BLR) model (Standard_BLR and Standard_SBLR) are utilized for model construction. Before the two-stage feature-fusion, Standard_BLR is utilized to determine the optimum dimension of PCA-based fusion features and the model parameters of KLPP. After the two-stage feature-fusion, Standard_SBLR is utilized to construct the BLR-based surface roughness predictive model. Two types of milling experiment (down milling and up milling) are carried out to show the influence of the presented two-stage feature-fusion method on the predictive performance of Standard_SBLR. Experimental results show that KLPP is highly effective in improving the prediction accuracy and compressing the confidence interval (CI) of Standard_SBLR. Moreover, the comparison results show that the effectiveness of KLPP is not inferior to kernel principal component analysis (KPCA). This paper lays the foundation for accurate monitoring of surface roughness in real industrial settings. [ABSTRACT FROM AUTHOR]

• A method of extracting effective features for monitoring surface roughness is presented. • KPCA_IRBF is re-derivated according to the derivation of PCA. • A new kind of BLR model abbreviated as Standard_SBLR is firstly proposed. • KPCA_IRBF helps to improve the prediction accuracy and ameliorate the CI of BLR. • Under the support of KPCA_IRBF, Standard_SBLR shows superior predictive performance. To improve the prediction accuracy of surface roughness in milling process, this paper provides an unique feature extraction method and comprehensively analyzes four types of Bayesian linear regression (BLR) model (Standard_BLR, Gaussian_BLR, Standard_SBLR and Gaussian_SBLR). Among them, Standard_SBLR is firstly proposed. Vibration information of the workpiece, fixture and spindle is adopted as the monitoring signal. The unique feature extraction method consists of three stages: extraction of time-domain features from the vibration signals, dimension-reduction by principal component analysis (PCA) and dimension-increment by the integrated radial basis function based kernel principal component analysis (KPCA_IRBF). The BLR models can provide both the predicted value and the corresponding confidence interval (CI). Two types of milling experiment (down milling and up milling) are conducted to reveal the influence of dimension-increment process of KPCA_IRBF on the predictive performance of the BLR models. Experimental results show that when combined with KPCA_IRBF, Standard_SBLR has the best predictive performance among the four BLR models. This also shows that KPCA_IRBF is highly effective in improving the prediction accuracy and compressing the CI of Standard_SBLR. To further prove the superiority of Standard_SBLR, other powerful machine learning methods such as partial least squares regression (PLS), artificial neural network (ANN) and support vector machine (SVM) are also utilized to realize surface roughness prediction under the support of KPCA_IRBF. This paper lays the foundation for accurate monitoring of surface roughness in real industrial settings. [ABSTRACT FROM AUTHOR]

• A novel tool wear predictive model based on KPCA_IRBF and RVM is developed. • KPCA_IRBF helps to improve the prediction accuracy of RVM. • KPCA_IRBF helps to ameliorate the confidence interval (CI) of RVM. • CI is an extra advantage over the traditional methods such as PLS, ANN and SVM. • In comparison with SVM, RVM has high sparseness and comparable prediction accuracy. In order to realize real-time and accurate monitoring of the tool wear in machining process, this paper presents a tool wear predictive model based on the integrated radial basis function based kernel principal component analysis (KPCA_IRBF) and relevance vector machine (RVM). The traditional methods such as partial least squares regression (PLS), artificial neural network (ANN) and support vector machine (SVM) can only provide predicted values which have no probabilistic significance. As a sparse probabilistic model, RVM can provide both the predicted value and the corresponding confidence interval (CI). However, the existence of process noises and redundancy will seriously affect the prediction accuracy and the stability of CI. As a new dimension-increment technique, KPCA_IRBF helps to weaken the negative effects of process noises and redundancy by increasing the dimensionality of monitoring features. The fused features obtained by KPCA_IRBF are more sensitive to the change of tool wear. Two different cutting experiments are carried out to verify the effectiveness of KPCA_IRBF in improving the prediction accuracy and ameliorating the CI of RVM. The experimental results show that KPCA_IRBF can reduce the root mean square error (RMSE) of RVM by more than 30% and compress the average width of CI by more than 90%. To further show the advantages of RVM, the traditional methods such as PLS, ANN and SVM are also utilized to realize tool wear prediction. This paper lays the foundation for the application of RVM to industrial field. [ABSTRACT FROM AUTHOR]