T. Y. Wu

Misalignment diagnosis of rotating machinery through vibration analysis via the hybrid EEMD and EMD approach

The objective of this research is to investigate the feasibility of utilizing the hybrid method of ensemble empirical mode decomposition (EEMD) and pure empirical mode decomposition (EMD) to efficiently decompose the complicated vibration signals of rotating machinery into a finite number of intrinsic mode functions (IMFs), so that the fault characteristics of the misaligned shaft can be examined in the time–frequency Hilbert spectrum as well as the marginal Hilbert spectrum. The intrawave frequency modulation (FM) phenomenon, which indicates the nonlinear vibration behavior of a misaligned shaft, can be observed in the time–frequency Hilbert spectrum through the Hilbert–Huang transform (HHT) technique. The fault characteristic of shaft misalignment is also featured in terms of the amplitude modulation (AM) phenomenon in the information-containing IMF components that are extracted by the significance test. Through performing the envelope analysis on the information-containing IMF, the marginal Hilbert spectrum of the envelope signal of this IMF component exhibits that the level of shaft misalignment is presented by the level of AM in the IMF. A test bed of a rotor-bearing system is performed experimentally to illustrate both the parallel and angular shaft misalignment conditions as well as the healthy condition. The analysis results show that the proposed approach is capable of diagnosing the misaligned fault of the shaft in rotating machinery and providing a more meaningful physical insight compared with the conventional methods.

Multi-Scale Analysis Based Ball Bearing Defect Diagnostics Using Mahalanobis Distance and Support Vector Machine

The objective of this research is to investigate the feasibility of utilizing the multi-scale analysis and support vector machine (SVM) classification scheme to diagnose the bearing faults in rotating machinery. For complicated signals, the characteristics of dynamic systems may not be apparently observed in a scale, particularly for the fault-related features of rotating machinery. In this research, the multi-scale analysis is employed to extract the possible fault-related features in different scales, such as the multi-scale entropy (MSE), multi-scale permutation entropy (MPE), multi-scale root-mean-square (MSRMS) and multi-band spectrum entropy (MBSE). Some of the features are then selected as the inputs of the support vector machine (SVM) classifier through the Fisher score (FS) as well as the Mahalanobis distance (MD) evaluations. The vibration signals of bearing test data at Case Western Reserve University (CWRU) are utilized as the illustrated examples. The analysis results demonstrate that an accurate bearing defect diagnosis can be achieved by using the extracted machine features in different scales. It can be also noted that the diagnostic results of bearing faults can be further enhanced through the feature selection procedures of FS and MD evaluations.

A looseness identification approach for rotating machinery based on post-processing of ensemble empirical mode decomposition and autoregressive modeling:

The purpose of this research is to investigate the feasibility of utilizing the post-processing of Ensemble Empirical Mode Decomposition (EEMD) and Autoregressive (AR) modeling to identify the looseness faults at different mechanical components of rotating machinery. The post-processing of EEMD is employed to decompose the complicated vibration signals of rotating machinery into a finite number of Intrinsic Mode Functions (IMFs) which represent the mono-oscillated components of different frequency bands. The AR modeling process reveals the fault features of the information-contained IMF components. The characteristic vectors derived from the AR modeling process can be utilized for identifying the locations of looseness faults in the operating machinery. A rotor-bearing test rig is performed to illustrate the looseness faults at different mechanical components. The analysis results show that the proposed approach is capable of identifying the locations of looseness faults at the rotating machinery.

Periodic Isolator Design Enhancement via Vibration Confinement through Eigenvector Assignment and Piezoelectric Circuitry

The objective of this research is to investigate the feasibility of utilizing eigenvector assignment and piezoelectric circuitry for enhancing vibration isolation performance of periodic isolators. For a classical periodic structure, stop bands are created due to material discontinuity so that wave propagation of external excitation can be suppressed within the stop band frequency range. While effective, such a method cannot always create wide enough stop bands such that all disturbance frequencies are covered. In this study, the eigenvector assignment technique and piezoelectric circuitry are utilized to reduce the transmissibility of the isolator modes near the boundary of the stop bands, and therefore widen the effective frequency range of vibration suppression of the periodic isolator. The principle of eigenvector assignment is to alter the mode shapes of the system so that the modal components corresponding to the concerned coordinates are as small as possible. By applying the eigenvector assignment method on the spatially tailored periodic isolator structure, the response amplitude of the attenuated end (the end of the isolator designed to have small vibration) at resonant frequencies near the stop band can be reduced, which enhances the vibration isolation performance in the frequency range of interest. On the other hand, piezoelectric circuits connecting to the isolator structure increase the degrees of freedom of the integrated system, and enlarge the design space for achievable eigenvectors. The eigenvectors of this integrated system are selected such that the modal energy in the concerned coordinates is minimized by using the Rayleigh Principle. The integrated system with assigned eigenvectors will re-distribute vibratory energy of the complete electromechanical system. Small vibration at the attenuated end of the isolator is achieved since the energy is confined in the circuitry and other parts of the isolator. Numerical simulations are performed to evaluate the effectiveness of the proposed method on vibration confinement for isolator designs. An integrated closed-loop system with state estimator is developed to realistically implement the proposed algorithm. It is shown that with the piezoelectric circuitry and eigenvector assignment, the system energy is redistributed and confined in the unconcerned regions, which can greatly enhance the performance of the vibration isolation system.

Looseness Diagnosis of Rotating Machinery Via Vibration Analysis Through Hilbert–Huang Transform Approach

The objective of this research in this paper is to investigate the feasibility of utilizing the Hilbert–Huang transform method for diagnosing the looseness faults of rotating machinery. The complicated vibration signals of rotating machinery are decomposed into finite number of intrinsic mode functions (IMFs) by integrated ensemble empirical mode decomposition technique. Through the significance test, the information-contained IMFs are selected to form the neat time-frequency Hilbert spectra and the corresponding marginal Hilbert spectra. The looseness faults at different components of the rotating machinery can be diagnosed by measuring the similarities among the information-contained marginal Hilbert spectra. The fault indicator index is defined to measure the similarities among the information-contained marginal Hilbert spectra of vibration signals. By combining the statistical concept of Mahalanobis distance and cosine index, the fault indicator indices can render the similarities among the marginal Hilbert spectra to enhanced and distinguishable quantities. A test bed of rotor-bearing system is performed to illustrate the looseness faults at different mechanical components. The effectiveness of the proposed approach is evaluated by measuring the fault indicator indices among the marginal Hilbert spectra of different looseness types. The results show that the proposed diagnosis method is capable of classifying the distinction among the marginal Hilbert spectra distributions and thus identify the type of looseness fault at machinery.

Vibration isolator design via energy confinement through eigenvector assignment and piezoelectric networking

The objective of this research is to investigate the feasibility of utilizing eigenvector assignment and piezoelectric networking for enhancing vibration isolator design through energy confinement. For a classical periodic isolator structure, the material discontinuity creates stop bands that could suppress the wave propagation of external excitation in a particular frequency range. While effective, such method can not always create wide enough stop bands such that all the disturbance frequencies are covered. In this study, the eigenvector assignment technique and piezoelectric networks are utilized to reduce the transmissibility of the isolator modes near the boundary of the stop bands, and therefore widen the effective frequency range and enhance the performance of the isolator. The eigenvector assignment principle is to alter the mode shapes of the system so that the modal components have smaller amplitude in concerned coordinates than in other parts of the system. By applying the eigenvector assignment method on the spatially tailored periodic isolator structure, the attenuated end (the end of the isolator designed to have small vibration) response amplitude at resonant frequencies near the stop band can be reduced, which enhances the vibration isolation performance in the frequency range of interest. On the other hand, piezoelectric networks connecting to the isolator structure increase the degrees of freedom of the integrated system, and enlarge the design space for achievable eigenvectors. The right eigenvectors of this integrated system are selected such that the modal energy in the concerned area is minimized by using the Rayleigh Principle. The integrated system with assigned eigenvectors will re-distribute vibratory energy of the complete electromechanical system. Small vibration at the attenuated end of the isolator is achieved since the energy is confined in the circuitry and other parts of the isolator. Numerical simulations are performed to evaluate the effectiveness of the proposed method on vibration confinement for isolator designs. Frequency responses of the different generalized coordinates in the selected frequency range are illustrated. It is shown that with the piezoelectric networking and eigenvector assignment, the system energy is redistributed and confined in the unconcerned areas, which can greatly enhance the performance of the vibration isolation system.

Reduction of Structural Acoustic Radiation Via Left and Right Eigenvector Assignment Approach

The objective of this research is to investigate the feasibility of utilizing a new left—right eigenvector tailoring method in reducing the acoustical radiations of flexible structures. The structural sound pressure radiation can be expressed in terms of a combination of vibration modes, where its magnitude is also a function of the external disturbance distribution. In other words, the radiated sound pressure level depends on both the right eigenvectors (related to the structural mode shapes) and left eigenvectors (related to the system disturbance rejection ability) of the vibrating structure. The basic idea of the proposed approach is to simultaneously modify the structural modal velocity distribution and the system capability of disturbance rejection through active left—right eigenvector assignment control actions, so that the sound pressure radiated from the vibrating structure can be reduced. Numerical simulations are performed to evaluate the effectiveness of the proposed method on structural noise reduction. Frequency responses of sound pressure at a receiver in the selected frequency range are illustrated. It is shown that with the proposed active control method, one can re-shape the modal velocity distribution and enhance disturbance rejection, and hence can effectively minimize the structural sound pressure radiation.

Active vibration isolation via simultaneous left?right eigenvector assignment

The objective of this research is to synthesize a simultaneous left and right eigenvector assignment (SLREA) method for active vibration isolation. It is a pioneering effort to utilize such an eigenvector assignment concept for active isolator design, where the approach can provide good physical insight into the problem. In this investigation, a new algorithm for the synthesis of the desired left eigenvectors is developed, which is an improvement over the classical methods. The purpose of the right eigenvector assignment method is to alter the closed-loop system modes such that the modal components corresponding to the concerned region (isolation area of the isolator) have relatively small vibration amplitude. Correspondingly, the design goal of the left eigenvector assignment is to alter the left eigenvectors of the closed-loop system so that they are as closely orthogonal to the systems forcing vectors as possible. With the proposed approach, one can achieve both disturbance rejection and modal confinement concurrently for the purpose of vibration isolation. In this research, a new formulation is developed so that the desired left eigenvectors of this integrated system are selected through solving a generalized eigenvalue problem, where the orthogonality indices between the forcing vectors and the left eigenvectors are minimized. The components of the right eigenvectors corresponding to the concerned region are minimized concurrently. It is shown that, with the SLREA technique, both disturbance rejection and modal confinement can be achieved, and thus vibration amplitude in the isolated region can be suppressed significantly.

The bearing fault diagnosis of rotating machinery by using Hilbert-Huang transform

Based on improve the drawbacks of Ensemble Empirical Mode Decomposition (EEMD), such as mode mixing and end effect problem, post-processing of EEMD which was improved with HHT approach to solve the problem in this paper. Once the Intrinsic Mode Functions (IMFs) are obtained from the decomposition process, the crucial step is to extract the fault features from the information-contained IMFs. The amplitude modulation (AM) phenomenon can be discovered in the IMFs with fault information. In this paper, we not only classify the types of bearing fault but also identify the level of the fault.

An adaptive left?right eigenvector evolution algorithm for vibration isolation control

The purpose of this research is to investigate the feasibility of utilizing an adaptive left and right eigenvector evolution (ALREE) algorithm for active vibration isolation. As depicted in the previous paper presented by Wu and Wang (2008 Smart Mater. Struct. 17 015048), the structural vibration behavior depends on both the disturbance rejection capability and mode shape distributions, which correspond to the left and right eigenvector distributions of the system, respectively. In this paper, a novel adaptive evolution algorithm is developed for finding the optimal combination of left–right eigenvectors of the vibration isolator, which is an improvement over the simultaneous left–right eigenvector assignment (SLREA) method proposed by Wu and Wang (2008 Smart Mater. Struct. 17 015048). The isolation performance index used in the proposed algorithm is defined by combining the orthogonality index of left eigenvectors and the modal energy ratio index of right eigenvectors. Through the proposed ALREE algorithm, both the left and right eigenvectors evolve such that the isolation performance index decreases, and therefore one can find the optimal combination of left–right eigenvectors of the closed-loop system for vibration isolation purposes. The optimal combination of left–right eigenvectors is then synthesized to determine the feedback gain matrix of the closed-loop system. The result of the active isolation control shows that the proposed method can be utilized to improve the vibration isolation performance compared with the previous approaches.