Using Unbiased Autocorrelation to Enhance Kurtogram and Envelope Analysis Results for Rolling Element Bearing Diagnostics

Envelope analysis is one of the most advantageous methods for rolling element bearing diagnostics but finding the suitable frequency band for demodulation has been a substantial challenge for a long time. Introduction of spectral kurtosis (SK) mostly solved this problem but in situations where signal to noise ratio is very low or in presence of non-Gaussian noise this method will fail. This major drawback may noticeably decrease the effectiveness of the SK and goal of this paper is to overcome this problem. Vibration signals from rolling element bearings exhibit high levels of 2nd order cyclostationarity, especially in the presence of localised faults. A second-order cyclostationary signal is one whose autocovariance function is a periodic function of time: the proposed method, named Autogram by the authors, takes advantage of this property to enhance the conventional spectral kurtosis. First, a maximal overlap discrete wavelet packet transform (MODWPT) is adopted to split a signal in different frequency bands and central frequencies. Second, unbiased autocorrelation of the squared envelope is calculated to reduce the level of uncorrelated random noise. Third, kurtosis of the autocorrelation is computed and a two dimensional colormap, named Autogram, is presented in order to locate the optimal frequency band for demodulation. The purpose is to increase the detection and characterization of transients in the temporal signal, which contains the bearing defect frequencies as well as appropriate frequency at which the fault impulses are modulated. Finally, the Fourier transform is used to obtain a frequency domain representation of the envelope signal so to identify the defect frequencies of the bearing. The proposed method has been tested on experimental data and compared with literature results so to assess its performances in rolling element bearing diagnostics. The results are very positive, and bearing characteristic frequencies from signals masked by Gaussian and non-Gaussian background noise can be extracted

External condition removal in bearing diagnostics through EMD and One-Class SVM

The removal of the running conditions influencing data acquisitions in rotating machinery is a very important task because it could avoid some misunderstandings when diagnostic techniques are applied. This paper introduces a new parameter that could be able to identify damage in a rotating element of a roller bearing removing the effect of speed and external load. The parameter proposed in this paper is evaluated through Empirical Mode Decomposition (EMD). Our algorithm proposes firstly the decomposition of the acceleration vibration signals into a finite number of Intrinsic Mode Functions (IMFs) and then the evaluation of the energy for each one of these. Data are acquired both for a healthy bearing and for one with a 450 μm large indentation on a rolling element. Three different speeds and three radial loads are monitored for both cases, so nine conditions can be evaluated for each type of bearing overall. The parameters obtained, namely energy evaluated for a certain number of IMFs, are then used to train a One-Class Support Vector Machine (OCSVM). Healthy data belonging to the nine different conditions are taken into account and OCSVM is trained while other acquisitions are given to the classifier as test object. Since the real class membership is known, we consider how many errors the labelling produces. We compare these results with those obtained by considering a wavelet decomposition. Energies are evaluated for each level of decomposition and the previous approach is then applied to these parameter

Nonlinear dynamics of a negative stiffness oscillator: experimental identification and model updating

Systems exhibiting a negative stiffness region are often used as vibration isolators, due to their enhanced damping properties. The device tested in this paper is part of a damping system and it acts like an asymmetric double-well Duffing oscillator, with two stable and one unstable equilibrium positions. The range of motion can either be bounded around one stable position (in-well oscillations) or include all the three positions (cross-well oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics, and chaotic motion as well. Due to its asymmetrical design, the two linearized systems associated to small-amplitude oscillations around one stable equilibrium position are different. In this work, the dynamical behavior of the system is first investigated in the case of linear and nonlinear in-well oscillations and then in the case of cross-well oscillations with chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven through several excitation levels with both harmonic and random inputs. An experimental bifurcation tracking analysis is also carried out to understand the possible response scenarios. Afterwards, the nonlinear identification is performed using nonlinear subspace algorithms to extract the restoring force of the system. Eventually, the physically-based model of the device is updated to match the identified characteristics via genetic algorithms

Assessment of a high-resolution candidate detector for prostate time-of-flight positron emission tomography

We report on the measurements performed using a 22Na source on a detector element for an MRI-compatible TOF-PET endorectal prostate probe, with Depth-Of-Interaction sensitivity. It is made from a LYSO scintillator crystal, wrapped with Lumirror, readout at both ends by means of Silicon Photomultipliers. With a detailed description of the data analysis procedure we show that our results point to a 400 ps coincidence resolving time and, at the same time, to a Depth-Of-Interaction resolution of 1 mm. These appealing features, along with the tiny 1.5 mm x 1.5 mm x 10 mm crystal size, are quite promising in view of the realization of a prototype probe.Comment: 27 pages, 28 figures. arXiv admin note: substantial text overlap with arXiv:1203.004

New Separation Techniques for Output-Only Modal Analysis

The paper is devoted to the problem of discriminating between operational and natural modes of structures excited by generic inputs. This case often occurs when the system under analysis holds rotating parts and is contemporary excited by ambient noise; in this case the output-only techniques may fail being easily trapped in a misinterpretation of the system eigenvalues. A survey of the methods available in literature is given, together with the explanation of their failures. To solve this problem, two new techniques are introduced and their capabilities are checked with numerical and experimental data from a paper machine

Multi-Scale Wind Turbine Bearings Supervision Techniques Using Industrial SCADA and Vibration Data

Timely damage diagnosis of wind turbine rolling elements is a keystone for improving availability and eventually diminishing the cost of wind energy: from this point of view, it is a priority to integrate high-level practices into the real-world operation and maintenance of wind farms. On this basis, the present study is devoted to the formulation of reliable methodologies for the supervision of wind turbine bearings, which possibly can be integrated in the industrial practice. For this reason, this study is a collaboration between a company (ENGIE Italia), the University of Perugia and the Politecnico di Torino. The analysis is based on the exploitation of the data types which are available to wind farm managers from industrial control systems: SCADA (Supervisory Control And Data Acquisition) and TCM (Turbine Condition Monitoring). Due to the intrinsic sampling time difference between SCADA and TCM data (a few minutes the former, up to the millisecond for the latter), the proposed methodology is designed as multi-scale. At first, historical SCADA data are processed and the behavior of the oil filter pressure is analyzed for all the wind turbines in the farm: this provides preliminary advice for identifying presumably healthy wind turbines from those suspected of damage. A second step for the SCADA analysis is then represented by the study of the temperature trends of the bearings through a Support Vector Regression: the incoming damage is individuated from the analysis of the mismatch between measurements and estimates provided by the normal behavior model. Finally, the healthy units are selected as the reference and the faulty as the target for the analysis of TCM vibration data in the time domain: statistical features are computed on independent chunks of the signals and, using a Novelty Index, it was possible to distinguish the damaged wind turbines with respect to the reference ones. In light of the interest in application of the proposed methodology, good practice criteria in selecting and managing the data are discussed as well

ANOVA and other statistical tools for bearing damage detection

The aim of the paper is to exhaustively exploit and test some statistical tools, such as ANOVA and Linear Discriminant Analysis, to investigate a massive amounts of data collected over a rig available @DIRG Lab, specifically conceived to test high speed aeronautical bearings; the rig permits the control of rotational speed (6000 – 30000 RPM), radial load (0 to 1800 N) and temperature, and allows monitoring vibrations by means of 4 tri-axial accelerometers. Fifteen different damages have been realised on the bearing but, for simplicity, this papers only treats those cases where simple identification methods have failed or not demonstrated to be fully affordable. The damages have been inferred on rolls or on the internal ring, with different severities, which are reported as a function of their extension, i.e. 150, 250, 450 μm. A total number of 17 combinations of load and speed have been analysed per each damaged bearing. Although ANOVA rigorously applies when some conditions are respected on the probability distribution of the responses, such as Independence of observations, Normality (normal distribution of the residuals) and Homoscedasticity (homogeneity of variances – equal variances), the paper exploits the robustness of the technique even when data do not fully fall into the requisites. Analyses are focused on the best features to be taken into account, trying to seek for the most informative, but also trying to extract a “best choice” for the acceleration direction and the most informative point to be monitored over the simple structure. Wanting to focus on the classification of the single observation, Linear Discriminant Analysis has been tested, demonstrating to be quite effective as the number of misclassification is not very high, (at least considering the widest damages). All these classifications have unfortunately the limit of requiring labelled examples. Acquisitions in un- damaged and damaged conditions are in fact essential to guarantee their applicability, which is quite often impossible for real industrial plants. The target can be anyway reached by adopting distances from un-damaged conditions which, conversely, must be known as a reference. Advantages of the statistical methods are quickness, simplicity and full independence from human interaction

Big Data management: A Vibration Monitoring point of view

Vibration Monitoring is a particular kind of Condition Monitoring meant to infer the state of health of a machine from accelerometric measurements. From a practical point of view, the scope is then to extract from the acceleration data some valuable diagnostic information which could be used to detect the presence of possible damages (i.e., to produce knowledge about the state of health). When the monitoring is implemented online, in a continuous way, the raw accelerometric data sets can be very large and complex to be dealt with, as usually involve multiple channels (i.e., multiple locations and directions) and high sample rates (i.e., order of ksps - 103 samples per second), but the final knowledge about the state of health can, in principle, be summarized by a single binary information (i.e., healthy – 0 vs damaged – 1). This is commonly called Damage Detection. In this work, the big data management challenge is tackled from the point of view of statistical signal processing, so as to aggregate the multivariate data and condense them into single information of distance with respect to a healthy reference condition (i.e., the Novelty). When confounding influences (such as the work condition or the environmental condition) can be disregarded, the novelty information has a direct correspondence to the health information, so that an alarm indicating the detection of damage can be triggered upon exceeding a selected threshold for the limit novelty. Many different ways of solving such a binary classification problem can be found in the literature. Starting from the simplest, some of the more effective are compared in the present analysis, to finally select a reliable procedure for the big data management in vibration monitoring