I. Antoniadis

Rolling element bearing fault diagnosis using wavelet packets

Abstract A method is proposed for the analysis of vibration signals resulting from bearings with localized defects using the wavelet packet transform (WPT) as a systematic tool. A time–frequency decomposition of vibration signals is provided and the components carrying the important diagnostic information are selected for further processing. The proposed method is designed in such a way that it can exploit the underlying physical concepts of the modulation mechanism, present in the vibration response of faulty bearings. The flexibility of the WPT and the systematic parameter selection criteria, help in the minimization of interventions by the end user. The method is evaluated using simulated and experimental signals.

A Support Vector Machine approach based on physical model training for rolling element bearing fault detection in industrial environments

A hybrid two stage one-against-all Support Vector Machine (SVM) approach is proposed for the automated diagnosis of defective rolling element bearings. The basic concept and major advantage of the method, is that its training can be performed using simulation data, which result from a well established model, describing the dynamic response of defective rolling element bearings. Then, vibration measurements, resulting from the machine under condition monitoring, can be imported and processed directly by the already trained SVM, eliminating thus the need of training the SVM with experimental data of the specific defective bearing. A key aspect of the method is the data preprocessing approach, which among others, includes order analysis, in order to overcome problems related to sudden changes of the shaft rotating speed. Moreover, frequency domain features both from the raw signal as well as from the demodulated signal are used as inputs to the SVM classifiers for a two-stage recognition and classification procedure. At the first stage, a SVM classifier separates the normal condition signals from the faulty signals. At the second stage, a SVM classifier recognizes and categorizes the type of the fault. The effectiveness of the method tested in one literature established experimental test case and in three different industrial test cases, including a total number of 34 measurements. Each test case includes successive measurements from bearings under different types of defects, different loads and different rotation speeds. In all cases, the method presents 100% classification success.

Rolling element bearing fault detection in industrial environments based on a K-means clustering approach

A K-means clustering approach is proposed for the automated diagnosis of defective rolling element bearings. Since K-means clustering is an unsupervised learning procedure, the method can be directly implemented to measured vibration data. Thus, the need for training the method with data measured on the specific machine under defective bearing conditions is eliminated. This fact consists the major advantage of the method, especially in industrial environments. Critical to the success of the method is the feature set used, which consists of a set of appropriately selected frequency-domain parameters, extracted both from the raw signal, as well as from the signal envelope, as a result of the engineering expertise, gained from the understanding of the physical behavior of defective rolling element bearings. Other advantages of the method are its ease of programming, simplicity and robustness. In order to overcome the sensitivity of the method to the choice of the initial cluster centers, the initial centers are selected using features extracted from simulated signals, resulting from a well established model for the dynamic behavior of defective rolling element bearings. Then, the method is implemented as a two-stage procedure. At the first step, the method decides whether a bearing fault exists or not. At the second step, the type of the defect (e.g. inner or outer race) is identified. The effectiveness of the method is tested in one literature established laboratory test case and in three different industrial test cases. Each test case includes successive measurements from bearings under different types of defects. In all cases, the method presents a 100% classification success. Contrarily, a K-means clustering approach, which is based on typical statistical time domain based features, presents an unstable classification behavior.

Wavelet Based Demodulation of Vibration Signals Generated by Defects in Rolling Element Bearings

Vibration signals resulting from roller bearing defects, present a rich content of physical information, the appropriate analysis of which can lead to the clear identification of the nature of the fault. The envelope detection or demodulation methods have been established as the dominant analysis methods for this purpose, since they can separate the useful part of the signal from its redundant contents. The paper proposes a new effective demodulation method, based on the wavelet transform. The method fully exploits the underlying physical concepts of the modulation mechanism, present in the vibration response of faulty bearings, using the excellent time-frequency localization properties of the wavelet analysis. The choice of the specific wavelet family is marginal to their overall effect, while the necessary number of wavelet levels is quite limited. Experimental results and industrial measurements for three different types of bearing faults confirm the validity of the overall approach.

Maximally Robust Input Preconditioning for Residual Vibration Suppression Using Low-Pass FIR Digital Filters

A method for suppressing residual vibrations in flexible systems is presented and experimentally demonstrated. The proposed method is based on the preconditioning of the inputs to the system using low-pass Finite Impulse Response (FIR) digital filters. Provided that the cutoff frequency of FIR filters is selected lower than the lowest expected natural frequency of the system and their stop-band is maximized, we show that these filters can be designed to exhibit maximally robust behavior with respect to changes of the system natural frequencies. To perform the proper design of FIR filters for robust vibration suppression, this paper introduces a series of dimensionless performance indexes and the Delay-Error-Order (DEO) curves that represent graphically the delay time introduced by the filter as a function of the remaining residual vibrations, and the filter order. Several classes of FIR filters such as: a) Parks-McClellan; b) Window-based methods (using Chebyshev window); and c) Constrained Least Squares method, are shown to present maximally robust behavior, almost identical to the theoretically predicted. Parallel, they demonstrate excellent vibration suppression while they introduce the minimum possible delay. Further advantages offered by the proposed method, is that no modeling of the flexible system is required, the method can be used in a variety of systems exhibiting vibrations, it is independent of the guidance function and it is simple to implement in practical applications. The results are experimentally verified on a flexible aluminum beam with a significantly varying mass, attached to the end-effector of a robot manipulator The beam is rotated, using one joint of the manipulator from an initial to a final position. It is shown that the preconditioned inputs to the flexible system induce very little amount of residual vibrations compared to the inputs with no preconditioning.

A PEAK ENERGY CRITERION (P. E.) FOR THE SELECTION OF RESONANCE BANDS IN COMPLEX SHIFTED MORLET WAVELET (CSMW) BASED DEMODULATION OF DEFECTIVE ROLLING ELEMENT BEARINGS VIBRATION RESPONSE

Complex Shifted Morlet Wavelets (CSMW) present a number of advantages when used for the demodulation of the vibration response of defective rolling element bearings: (A) They present the optimally located window simultaneously in the time and in the frequency domains; (B) They allow for the maximal time-frequency resolution; (C) The magnitudes of the complex wavelet coefficients in the time domain lead directly to the required envelope; (D) They allow for the optimal selection of both the center frequency and the bandwidth of the requested filter. A Peak Energy criterion (P. E.) is proposed in this paper for the simultaneous automatic selection of both the center frequency and the bandwidth of the relevant wavelet window to be used. As shown in a number of application cases, this criterion presents a more effective behavior than other criteria used (Crest Factor, Kurtosis, Smoothness Index, Number of Peaks), since it combines the advantages of energy based criteria, with criteria characterizing the spikiness of the response.

Performance assessment of a morphological index in fault prediction and trending of defective rolling element bearings

Frequency domain based signal processing methods have been shown to present a quite effective behaviour in the detection of defects, when applied to the analysis of vibration signals, resulting from rolling element bearings. However, these methods typically require some complex and sophisticated analysis, which renders their application cumbersome for applications requiring unskilled personnel or automated fault detection and trending. Parallel, a number of traditional methods exist, such as the root mean square (RMS), the crest factor (CF), the kurtosis (KU), the impulse factor (IF) and the shape factor (SF), requiring only direct processing in the time domain. Alternatively to these methods, a morphological index (MI) for processing vibration signals has been proposed, addressing the issues of how to quantify the shape and the size of the signals directly in the time domain. In this paper, based on a model for the dynamic behaviour of defective rolling bearings, the sensitivity of the MI is assessed, compared to the previous five traditional time domain indices, with respect to the effect of the added noise, the impulse repetition period, as well as the natural period and the damping ratio of the excited resonance, both in the case of an inner and an outer race defect. The results clearly indicate the superiority of the MI over all the other time domain indices compared. This fact is then further verified in three different cases from industrial installations, presenting fault trending analysis of bearings under various defects.

Symmetric variational principles and modal methods in fluid-structure interaction problems

Two new symmetric variational principles for “acoustoelastic” fluid-structure interaction problems are first derived, with simultaneous use of three variables: the structural displacements and accelerations and the fluid pressure. Thus, a total of four three-field symmetric formulations is obtained. As is then shown, these formulations can be reduced to four two-field symmetric variational principles. Each of them can lead to a single-field “limit case” formulation, which is the formulation of the “in vaccum” structure or of the “acoustic” fluid plus a frequency independent term, expressing an “added” property in its general form: the “incompressible” fluid (“in vacuum” structure plus “added mass”), the “hypercompressible” fluid (“in vacuum” structure plus “added stiffness”), the “hyperlight” structure (“acoustic” fluid plus “added compressibility”) and the “hyperflexible” structure (“acoustic” fluid plus “added rigidity”). Combinations of the above “limit case” formulations are also of interest. The impact of these formulations on the construction of modal methods is significant. A large number of methods can be constructed, since the modes of the “in vacuum”, of the “acoustic” and of the several “limit case” eigenproblems can provide basis functions for the structure and for the fluid variables, not only in the formulations of the full problem, but also in the “limit case” formulations. To demonstrate this, some new methods are proposed for the solution of the full and of the “incompressible” eigenproblems. Then, the methods based on the non-symmetric or on the three-field symmetric formulations are shown to have disadvantages, compared to the methods based on the two-field symmetric formulations. The examples provided demonstrate analytical expressions of “added properties” and verify the efficiency or the disadvantages of the model methods described. Finally, in the Appendices, the free surface conditions and the damping forces are incorporated in the various formulations and “singular cases” are treated (e.g., free bodies, “wall bounded” fluids).

DIESYS?dynamically non-linear dielectric elastomer energy generating synergetic structures: perspectives and challenges

Dielectric elastomer based generators (DEGs) offer some unique properties over energy generators based on other materials. These properties include high energy density, high efficiency over a broad range of frequencies, low compliance, the ability to produce high strain, large area, low cost films with no toxic materials and wide range environmental tolerance. As further shown in this paper, DEG materials can also exhibit a non-linear dynamic behavior, enhancing broad-band energy transfer. More specifically, dielectric elastomer (DE) energy generating synergetic structures (DIESYS) are considered as dynamic energy absorbers. Two elementary characteristic DIESYS design concepts are examined, leading to a typical antagonistic configuration for in-plane oscillations and a typical synagonistic configuration for out-of-plane oscillations. Originally, all the DE elements of the structure are assumed to be always in tension during all the phases of the harvesting cycle, conforming to the traditional concept of operation of DE structures. As shown in this paper, the traditional always-in-tension concept results in a linear dynamic system response, despite the fact that the implemented (DE) parts are considered to have been made of a non-linear (hyperelastic) material. In contrast, the proposed loose-part concept ensures the appearance of a non-linear broad-band system response, enhancing energy transfer from the environmental source.

Guidance Preconditioning by an Impulse Sequence for Robust Residual Vibration Suppression

In order to suppress residual vibrations, a general method is presented for preconditioning any guidance function prior to its application to a dynamic system, by convolving it with a sequence of impulses. The approach includes first the development of the necessary design specifications for the impulse sequence, so that the robustness properties cover the widest possible variation of the system natural frequencies. Three solution methods are proposed then, with special emphasis in the achievement of the minimum possible duration time of the impulse sequence. Numerical experiments verify the effectiveness of the robustness, not only with respect to variations of the natural frequency, but also with respect to variations of a range of other linear and non-linear variables.