Keywords: machineryproduct, acceleratedtesting, fuzzy regression, uncertainty, reliability. 1. Introduction
In many engineering applications, such as airplanes, wind turbines and automobiles, rotatingmachinery parts are widely used and play a key role in their functions. Two commonly used machinery products are bearing and gear, which must have the attribute of high reliability . The health monitoring of their status will not only prevent the unscheduled system downtime but also save related personnel and property losses. Thus, the research of condition-based maintenance (CBM) [1, 2] and prognostics and health management (PHM)  have being studied during the past decades. The purpose of the health monitoring is to tell that how far is the current state to system/component failure, i.e. remaining useful life (RUL), and make corresponding maintenance policy. A host of methods have been provided to conduct RUL prediction which are model-based, data-driven and hybrid models [1, 2, 4, 5].
The lifetime knowledge of components or a complex system is fundamental both for consumers and manufacturers. Manufacturers can evaluate ex-ante the efficiency of their products (i.e. machines and equipment), provide effective maintenance policies to maintain the targeted efficiency levels and also design the after-sales maintenance policies and network [7, 10]. Core of Accelerated Life Testing (ALT) analysis is identification of the working-load stress levels of a system (or sub-system or component) and then the increase levels of stresses to use during the analyses . In fact, during these tests, the system is stress with higher levels of loads or different environmental factors in order to accelerate the failure mechanisms, which must represent the normal conditions. Accelerated conditions allow to reduce the testing time and so estimate behavioral characteristics of the product in normal conditions . After different high stress levels tests, life data are extrapolated to estimate the life distribution at the use condition by employing an appropriate acceleration model. To minimize the statistical error of extrapolation, reliability experts have developed numerous accelerated life test plans , nowadays implemented with specific models. Main goal of the ALT applications is to build a model of the real behavior of the components under analysis to obtain reliabilityprediction in a shorter time. Difficult of the analysis is to be able to extrapolate life duration at standard stress conditions from the accelerated test lifetime. During years, researchers proposed many different approaches both for the accelerate tests design and for the following statistical analysis of the data obtained, [3,5,8]. From a statistical point of view, the prediction of the reliability of a component deals with the determination of the distribution assumed by its time to failure variable . Three most used and well-known distributions are the Weibull, the Exponential and the Log-normal distribution. The most frequently applied is the Weibull distribution [2,4,14]. Weibull distribution, applied to the random variable called x, is based on the pdf function
Abstract. This paper proposes a novel method of fuzzy analysis for bearing accelerated degradation testing, which extracts degradation index from bearing vibration signals under different accelerated levels and obtains fuzzy failure time based on fuzzy regression model in consideration of uncertainties. Identification of accelerated model is conducted through linear mixture model. The proposed method provides a methodology to do accelerated vibration analysis for rotatingmachinery products. An industrial application is used to verify its effectiveness. Keywords: bearing, vibration data, accelerated degradation testing, fuzzy method, uncertainty. 1. Introduction
Traditional reliabilitydata have consisted of failure times for units that failed and running times for units that had not failed. Although laboratory reliabilitytesting is of- ten used to make product design decisions, the “real” reliabilitydata come from the field, often in the form of warranty returns (for consumer products) and field tracking studies (e.g., for company-owned assets and medical devices). The field data often exhibit more variability in component or product failure-times than the data from the laboratory test- ing. This important difference between carefully controlled laboratory accelerated test experiments and field reliability results is due to uncontrolled field variation (unit-to- unit and temporal) in variables, such as use-rate, load, vibration, temperature, humidity, UV intensity, and UV spectrum. Thus, incorporating use-rate/environmental data into our analyses can be expected to provide stronger statistical methods and more accurate inferences or predictions. Historically, however, use-rate/environmental data have, in most applications, not been available to reliability analysts.
(Received 26 November 2013; received in revised form 19 December 2013; accepted 26 December 2013)
Abstract. Shaft orbit is a significant diagnosis criterion, and its identification plays an important role in the fault diagnosis of large rotatingmachinery. The main difficulty of shaft orbit identification is how to extract the shape features automatically and effectively. Therefore, in this paper, a novel method named statistical fuzzy vector chain code (SFVCC) is proposed for the feature extraction of shaft orbit, which has such advantages as invariance, simple calculation and high separability. Furthermore, taking the extracted feature vectors as input, support vector machine (SVM) is utilized to identify various kinds of shaft orbits for rotatingmachinery. Comparative experiments are implemented, the results reveal that, compared with previous methods, the proposed method can identify the shaft orbit more effectively and efficiently with satisfactory accuracy.
As illustrated in Figure 5.1 two screws of 10.2-gram were added in the threaded hole of the left side rotor for simulating an unbalanced operating condition. Additional mass in the form of screws was removed from the rotor disk to simulate normal operating condition. Before extracting healthy operating condition data, the shaft was also aligned perfectly. The system was set to operate at various motor speeds by changing the frequency to 10 Hz, 15 Hz, 20 Hz, and 25 Hz successively. The signals were extracted and further processed using MATLAB (version: R2016a) and NI Sound and Vibration Assistant Software after recording data. Hanning window was selected during data acquisition to minimize the leakage in the non-periodic signal. Similarly, as shown in Figure 5.2, the alignment jack bolt was used to misalign the shaft angularly to 10 milli inches.
Fault localization in rotatingmachinery is an important topic of research for future condition-based monitoring systems. Knowing not only what type of fault has occurred, but also where in the system is an important consideration which can influence maintenance procedures in complex machinery. It is worth noting from the literature surveyed for this paper that many studies have focused on diagnosis and prognosis of single rotor/bearing systems. Often for legitimate reasons – simplification for computing speed, for example. Few studies, however, have taken into account the localization of faults across whole systems. This problem is not limited to modeling and simulation-based research. Many newly-developed data-driven techniques for diagnostics and prognostics claim good results by heavily instrumenting specific components of a test system. In many industrial cases this is not possible, practical or cost effective.
Abstract: This paper presents a technique to find the different conditions of rotatingmachinery through data obtained by vibration analyses. The various earlier researchers work is also elaborated in this paper. The major focus of the proposed work is to analyses all obtained data from the milling machines vibrations using wavelet transform. The vibration data is obtained by experiment done on milling machine. The faulty signals give the condition of that Milling machine component. The results will be also going to test by FEM analysis. It is general thinking at this stage that comparisons of FEM analysis and experiment result give better solution for faults occur in rotatingmachinery.
Abstract: Condition-based maintenance (CBM) presently plays an important role in avoiding unexpected failures, improving machine reliability, and providing accurate maintenance records and activities for rotatingmachinery. Traditional wired sensors commonly used for gathering data are costly and of limited value in industry. Recently, together with the advancement of sensor technology and communication networks, sensors have been virtually metamorphosed into smaller, cheaper, and more intelligent ones. These sensors are equipped with wireless interface that can communicate with others to form a network. This enables the sensors to be flexibly applicable and the hard cables from the sensors to the data acquisition/analysis system to be eliminated, hence, lead to reduction of the capital and maintenance costs. In this study, a wireless CBM system comprised hardware and software components is proposed to deal with the maintenance issues of rotatingmachinery. The hardware component consists of wireless sensors and networks used for receiving, processing, and transmitting signals obtained from the machine. The software component is a Matlab graphic user interface which is implemented for data processing and analysis, condition monitoring, diagnostics, and prognostics. The viability of the wireless CBM system for industrial application is presented using the water pump system as a case-study to evaluate the reliability and applicability of this system.
Some key differences distinguish GOFCM from these similar methods. The first difference is GOFCM’s use of Thompson’s method to derive the initial sample size. The second is that GOFCM reuses the information from each sample (PDA). This is so because the cluster centers obtained from a PDA are weighted, combined with the next PDA, and used as the starting cluster centers. These differences have benefits that decrease the runtime of the algorithm. The initial cluster center estimates are generated using the minimum amount of sampled data. The cluster center estimates represent, using weights, all previously processed data. This reduces the number of iterations needed by each PDA until termination .
It is well known that the in-cylinder pressure technique can provide comprehensive information for engine combustion performance. However, the comparison between the synchronous averaged Cylinder 1 pressure signals in crank angle domain (averaged over several hundred engine cycles to eliminate the data variation) for the normal and the defective engine with a faulty injector at different loading locations does not provide a clear indication for this type of fault. This is particularly so at the unloaded condition. Fig. 5 shows the synchronous averaged pressure of Cylinder 1 at full loaded condition for the normal and the faulty injector cases. It is seen that the faulty injector has led to a small increase of the combustion pressure in the cylinder. However, the difference is insignificant, which implies that the time domain (or crank angle domain) pressure signal would not be a good indicator to diagnosing this type of injector fault.
Abstract. The vibration signals acquired from rotatingmachinery are often complex, and fault features are masked by background noise. Feature extraction and denoising are the key for rotatingmachinery fault detection, and advanced signal processing method is needed to analyze such vibration signals. In this paper, an optimal lifting multiwavelet denoising method is developed for rotatingmachinery fault detection. Minimum energy entropy is used as the metric optimize the lifting multiwavelet coefficients, and the optimal lifting multiwavelet is constructed to capture the vibration signal characteristics. The improved denoising threshod method is used to remove the background noise. The proposed method is applied to turbine generator and rolling bearing fault detection to verify the effectiveness. The results show that the method is a robust approach to reveal the impulses from background noise, and it performs well for rotatingmachinery fault detection.
The problem of a micropolar fluid about an accelerated disk rotating with angular velocity Ω proportional to time has been studied. By means of the usual similarity transformations, the governing equations are reduced to ordinary non-linear differential equations and then solved numerically, using SOR method and Simpson’s (1/3) rule for s ≥ 0, where s is non-dimensional parameter which measures unsteadiness. The calculations have been carried out using three different grid sizes to check the accuracy of the results. The results have been improved by using Richardson’s extrapolation.
Extracting time-domain features. After the fault root- cause variables are identified among all process vari- ables, multiple time-domain features will be extracted so as to better reveal the deterioration process. Time- domain analysis is employed to extract mean, root mean square, standard deviation, variance, skewness, kurtosis, crest factor and peak value (see Appendix 1) from the root-cause variables. Normally, vibration signals/current measurements require a much higher sampling rate than conventional process measurements (e.g. pressure, flow rate or temperature) due to the fast dynamics of vibration and current measurements. With such high sampling rates, frequency domain features could be extracted after windowing the vibration/cur- rent signals and performing a short Fourier trans- form. 17 Then, ‘signature’ frequency domain features that correspond to different mechanical faults can be used to diagnose fault conditions and predict fault evo- lution. 28 Similarly, time-frequency domain features can be extracted over selected frequency bands across the samples. 29 However, the data used in this study were process measurements captured by the monitoring sys- tem of the plant. The sampling rate for all measure- ments was one sample per hour (e.g. 1/3600 Hz). Considering the low sampling rate of the data,
The imbalanced data sets shown in Fig. 6 are adopted as the training samples. The testing samples are composed of 300 samples. 150 samples are from normal gear data while another 150 samples are from full failure data. Meanwhile, decision tree models are also trained for comparing with the proposed fault diagnosis model. Table 2 and Fig. 7 show the classification accuracy comparisons between proposed fault diagnosis model and other methods. We can see that pruning has no effect on the improvement of decision tree classification accuracy for the imbalanced data set. To show the advantage of the fast clustering algorithm for extracting the core samples, K-means clustering algorithm is also adopted for comparing. Since K-means clustering algorithm is a similarity measure method based on Euclidean distance, so the algorithm is suitable for clusters of spherical shapes. Thus, the core samples extracted by K-means clustering algorithm are mostly gathered together. Therefore, the decision tree trained by these gathered core samples is not suitable to the entire imbalance data set. It is clear that the classification accuracy of the K-means clustering algorithm is less than other methods in Table 2.
With the increasing popularity of using Service-Oriented Systems (SOS), the reliability is becoming a signiﬁcant concern for SOS. SOS are mainly built by Web services, hence prediction of reliability of Web service(s) leads to major concern in SOS. In this paper, Hidden Markov Model (HMM) and Fuzzy logic prediction model are used to predict reliability of Web service(s). The experiments are often conducted on real time Web services. The maximum likelihood value in HMM are calculated by Estimation- Maximization algorithm. Viterbi algorithm is used to restore the hidden states in HMM. The throughput, response time, and successful invocation of Web service are used to form rules in Fuzzy logic model. This helps to model highly complex problems that have multi-dimensional data. These experimental results prove better prediction method as compared to other conventional methods.
Since reliability is a critical parameter in the design of electronic components, manufacturers keep track of it through different parameters. An accurate assessment of the reliability can be achieved through the periodic analysis of products on service and by accounting for failed products, but this is not predictive and takes a long time. Therefore, other methods are required to reduce the evaluation time, which should also be able to provide an indication of the reliability prior to the commercial release of the components. Accelerated test conditions must be designed to obtain the most accurate prediction possible of the lifetime of capacitors under service conditions. The most common tests for the reliability of MLCCs are the insulation resistance and combined stress measurements, which is also known as the Highly Accelerated Life Test (HALT) [ 7 ].
Thermal image, or thermogram, becomes a new type of signal for machine condition monitoring and fault diagnosis due to the capability to display real-time temperature distribution and possibility to indicate the machine’s operating condition through its temperature. In this paper, an investigation of using the second-order statistical features of thermogram in association with minimum redundancy maximum relevance (mRMR) feature selection and simplified fuzzy ARTMAP (SFAM) classification is conducted for rotatingmachinery fault diagnosis. The thermograms of different machine conditions are firstly preprocessed for improving the image contrast, removing noise, and cropping to obtain the regions of interest (ROIs). Then, an enhanced al- gorithm based on bi-dimensional empirical mode decomposition is imple- mented to further increase the quality of ROIs before the second-order statis- tical features are extracted from their gray-level co-occurrence matrix (GLCM). The highly relevant features to the machine condition are selected from the total feature set by mRMR and are fed into SFAM to accomplish the fault diagnosis. In order to verify this investigation, the thermograms acquired from different conditions of a fault simulator including normal, misalign- ment, faulty bearing, and mass unbalance are used. This investigation also provides a comparative study of SFAM and other traditional methods such as back-propagation and probabilistic neural networks. The results show that the second-order statistical features used in this framework can provide a plausi- ble accuracy in fault diagnosis of rotatingmachinery.
41 according to the severity of parallel and angular misalignment. They concluded that (i) nonlinear effects are evident in both types of misalignment and (ii) the ratio between the higher harmonic components and the 1X component in angular misalignment is greater than parallel misalignment. Hili et al.  carried out a study of angular misalignment characterization and developed a theoretical model. They found three characteristic peak frequencies in the shaft behaviour: (i) the most prominent being at 1X; (ii) a smaller peak at 2X; and (iii) the last peak corresponding to the natural frequency of the system. Sidebands of the rotation frequency around it were also visible. Al-Hussain  presented a study of the effect of angular misalignment of two rigid rotors connected through a flexible mechanical coupling. The results showed that an increase in angular misalignment, or mechanical coupling stiffness terms, leads to an increase of the model stability region. However, the variability of the signature, produced by misalignment at different operational conditions of load and speed in the vibration spectrum, is one of the main drawbacks of vibration analysis . Toth and Ganeriwala  studied the vibration signature for misalignment under a varying operating and design conditions such as speed, type and level of misalignment, coupling types and machinery dynamic stiffness. The aim was to develop a misalignment model and diagnostics procedure. Measurements were performed at three different shaft speeds, using three types of couplings, rigid, spiral and rubber, three shaft diameters and multiple misalignment configurations which include parallel and angular types with three different severity levels. The results indicated that the rotor speed, the coupling and shaft stiffness, have high impact on the vibration signature. The authors concluded that the signature of misalignment produced in vibration spectrum was unsteady for different operational conditions.
The fault detection technique proposed in this work incorporates a picture preparing segment, which is connected to upgrade data that is removed from numerical pictures. This area shows a short depiction of two fundamental picture handling strategies utilized as a part of this examination: limit separating and network calculations. Limit sifting changes over a nonstop dim scale picture into a two-or-more-level picture with the end goal that the concerned shapes are isolated from the foundation. Shape pictures acquired from genuine working frameworks are frequently ruined with commotion, and accordingly the shape got from the edge as a rule has clamor around its limit. A de-noising process is along these lines connected utilizing a traditional wavelet change to break down the flag, expel commotion from parts and after that remake it . This wipes out detached pixels and little confined districts or fragments.