Feature extraction is crucial to efficiently diagnose fault. This paper discusses a number of time-domain statistical features, including Kurtosis or the Crest Factor, the Mean by Deviation Ratio (MDR), and Symbolized Sequence Shannon Entropy (SSSE). The SSSE reflects the spatial distribution of the signal which is complementary with the statistical features. A new feature, Normalized Normal Negative Likelihood (NNNL), is used to improve the Normal Negative Likelihood (NNL). A Separation Index (SI) called the Extended SI (ESI) evaluates the performance of each feature and to remove noise feature. The Multi-Class Support Vector Machine (MSVM) recognizes bearing defect patterns. A numerical case is presented to demonstrate these features, their feature subset selection method and the pattern recognition method. The MSVM is used to detect three different types of bearing defects: defects in the inner race, outer race and bearing ball

Fault detection is a crucial step in condition based maintenance requiring. The importance of fault diagnosis necessitates an efficient and effective failure pattern identification method. Artificial Neural Networks (ANN) and Support Vector Machines (SVM) emerging as prospective pattern recognition techniques in fault diagnosis have been showing its adaptability, flexibility and efficiency. Regardless of variants of the two techniques, this paper discusses the principle of the two techniques, and discusses their theoretical similarity and difference. Eventually using the commonest ANN, SVM, a case study is presented for fault diagnosis using a wide used bearing data. Their performances are compared in terms of accuracy, computational cost and stability

The Proportional Intensity Model (PIM) extends the classical Proportional Hazard Model (PHM) in order to deal with repairable systems. This paper develops a more general PIM model which uses the imperfect model as baseline function. By using the imperfect model, the effectiveness of repair has been taken into account, without assuming an "as-bad-as-old" or an "as-good-as-new" scheme. Moreover, the effectiveness of other factors, such as the environmental conditions and the repair history, is considered as covariant in this PIM. In order to solve the large number parameters estimation problem, a Bayesian inference method is proposed. The Markov Chain Monte Carlo (MCMC) method is used to compute the posterior distribution for the Bayesian method. The Bayesian Information Criterion (BIC) is employed to perform model selection, namely, selecting the baseline function and remove the nuisance factors in this paper. In the final, a numerical example is provided to demonstrate the proposed model and method. 

The proportional intensity model (PIM) has been used to model the intensity function of repairable systems taking non-time factors, such as operating conditions, and repair history, into consideration. This paper develops a kernelized PIM (KPIM) by combining the PIM and the kernel method to consider a scenario where a repairable system experiences piecewise operating conditions. The kernel method is used to approximate the PIM covariate function nonlinearly. An approach based on the regularized likelihood function is proposed to obtain the optimal parameters for the KPIM. A numerical example is provided to demonstrate the KPIM model, and the parameter estimation approach

With increasing amounts of data being generated by businesses and researchers, there is a need for fast, accurate and robust algorithms for data analysis. Improvements in database's technology, computing performance and artificial intelligence have contributed to the development of intelligent data analysis. The primary aim of data mining is knowledge discovery, i.e. patterns in the data that lead to better understanding of the data generating process and to useful predictions.

The knowledge that becomes available through data mining enables an asset owner to make important decisions about life cycle costs in advance. In maintenance field, CMMS (Computer maintenance management system) and CM (Condition Monitoring) are the most popular software available in the industries. Since first one stores all historical data, maintenance actions, events and ma nufacturer recommendations, second one collects and stores all critical physical parameters (vibration, temperature.) to be monitored in a regular time basis. However, converting these data into useful information is a challenge.

The degradation process of a system may be affected by many unknown factors, such as unidentified fault modes, unmeasured operational conditions, engineering variance, environmental conditions, etc. These unknown factors not only complicate the degradation behaviors of the system, but also make it difficult to collect quality data. Due to lack of knowledge and incomplete measurements, certain important con text information (e.g. fault modes, operational conditions) of the collected data will be missing. Therefore, historical data of the system with a large variety of degradation patterns will be mixed together. With such data, learning a global model for Remaining Useful Life (RUL) prediction becomes extremely hard since the end user does not have enough and good-quality data to model properly the system.

This has led us to look for advanced RUL prediction techniques beyond the traditional RUL prediction models. The degradation process for many engineering systems, especially mechanical systems, is irreversible unless the condition is recovered by effective maintenance actions. The irreversible degradation process does not necessarily imply that the observed features will exhibit a monotonic progression pattern during degradation. Such progression pattern is sometimes hard to model using parametric methods. Considering a degradation process involving no or limited maintenance, the process may compose of a sequence of irreversible stages (either discrete or continuous) from new to be worn out, which can be implicitly expressed by the trajectory of the measured condition data or features. Therefore, the RUL of the system can be estimated if its future degradation trend can be projected from those historical instances. In this paper, a novel RUL prediction method inspired by feature maps and SVM classifiers is proposed.

The historical instances of a system with life-time condition data are used to create a classification by SVM hyper planes. For a test instance of the same system, whose RUL is going to be estimated, degradation speed is evaluated by computing the minimal distance defined based on the degradation trajectories, i.e. the approach of the system to the hyper plane that segregates good and bad condition data at a different time horizon. Therefore, the final RUL of a specific component can be estimated, and global RUL information can then be obtained by aggregating the multiple RUL estimations using a density estimation method.

Proposed model develops an effective RUL prediction method that addresses multiple challenges in complex system prognostics, where many parameters are unknown. Similarities between degradation trajectories can be checked in order to enrich existing methodologies in prognostic's applications. Existing CM data for bearings will be used to verify the model.

In general, downtime of a system can be attributed due to multiple failure categories and repair costs for each failure categories can be different. Many of these failure types are repaired to a state which can be called as bad as old and such repair actions are termed as “minimal repair”. Many system or components are replaced after a certain number of such minimal repair actions. In this study, we intend to prove that if the system failure process can be described by NHPP (Non Homogenous Poisson Process), then each failure category can also be modelled by NHPP.

Based on this, a cost model is developed by using the decomposition of the NHPP and renewal theory. Using the cost model, a model is developed to obtain the optimal number of minimum repair action every failure category. Since it is not possible to find any analytical solution, solution to the renewal function, an approximate approach is introduced to obtain numerical solution. Finally, a numerical example is presented to demonstrate the method.

Support Vector Machine (SVM) is an artificial intelligence technique that has been successfully used in data classification problems, taking advantage of its learning capacity. In systems modelled as networks, SVM has been used to classify the state of a network as failed or operating to approximate the network reliability. Due to the lack of information, or high computational complexity, the complete analytical expression of system states may be impossible to obtain, that is to say, only incomplete data-set can be obtained.

Using these incomplete data-sets, depending on amount of missed data-set, this paper proposes two different approaches named rough approximation method and simulation based method to evaluate system reliability. SVM is used to make the incomplete data-set complete. Simulation technique is also employed in the so called simulation based approximation method. Several examples are presented to illustrate the approaches.

Failure diagnostics is an important part of condition monitoring aiming to identify incipient failures in early stages. Accurate and efficient failure diagnostics can guarantee that the operator makes the correct maintenance decision, thereby reducing the maintenance costs and improving system availability. The Support Vector Machine (SVM) is discussed in this thesis with the purpose of efficiently diagnosing failure. The SVM utilizes the kernel method to transform input data from a lower dimensional space to a higher dimensional space. In the higher dimensional space, the hitherto linearly non separable patterns can be linearly separated, without compromising the computational cost. This facilitates failure diagnostics as in the higher dimensional space, the existing failure or incipient failure is more identifiable.

The SVM uses the maximal margin method to overcome the “overfitting” problem. This problem makes the model fit special data sets. The maximal margin method also makes it suitable for solving small sample size problems. In this thesis, the SVM is compared with another well known technique, the Artificial Neural Network (ANN). In the comparative study, the SVM performs better than the ANN. However, as the performance of the SVM critically depends on the parameters of the kernel function, this thesis proposes using an Ant Colony Optimization (ACO) method to obtain the optimal parameters. The ACO optimized SVM is applied to diagnose the electric motor in a railway system. The Support Vector Regression (SVR) is an extension of the SVM.

In this thesis, SVR is combined with a time-series to forecast reliability. Finally, to improve the SVM performance, the thesis proposes a multiple kernel SVM. The SVM is an excellent pattern recognition technique. However, to obtain an accurate diagnostics performance, one has to extract the appropriate features. This thesis discusses the features extracted from the time domain and uses the SVM to diagnose failure for a bearing. Another case in this thesis is presented, namely failure diagnostics for an electric motor installed in a railway’s crossing and switching system; in this case, the features are extracted from the power consumption signal.

In short, the thesis discuses the use of the SVM in failure diagnostics. Theoretically, the SVM is an excellent classifier or regressor possessing a solid theoretical foundation. Practically, the SVM performs well in failure diagnostics, as shown in the cases presented. Finally, as failure diagnostics critically relies on feature extraction, this thesis considers feature extraction from the time domain.

Support Vector Machine (SVM) is a new but prospective technique which has been used in pattern recognition, data mining, etc. Taking the advantage of Kernel function, maximum margin and Lanrangian optimization method, SVM has high application potential in reliability data analysis. This paper introduces the principle and some concepts of SVM. One extension of regular SVM named Support Vector Regression (SVR) is discussed. SVR is dedicated to solve continuous problem. This paper uses SVR to predict reliability for repairable system. Taking an equipment from Swedish railway industry as a case, it is shown that the SVR can predict (Time to Failure) TTF accurately and its prediction performance can outperform Artificial Neural Network (ANN).