A novel method for self-adaptive feature extraction using scaling crossover characteristics of signals and combining with LS-SVM for multi-fault diagnosis of gearbox

Vibration signals of defective gears are usually non-stationary and masked by noise. As a result, the feature extraction of gear fault data is always an intractable problem, especially for multi-fault couple system (two or more fault types simultaneously occur in mechanical systems). Recently, an interesting crossover characteristic of nonlinear data is used to diagnose the different severities of gear faults. Nonetheless, it lacks of self-adaptivity. Consequently, a novel method for self-adaptive feature extraction using scaling crossover characteristics of signals and combining with least square support vector machine (LS-SVM) for multi-fault diagnosis of gearbox is proposed. Firstly, detrended fluctuation analysis (DFA) is introduced to analyze fractal properties and multi-scaling behaviors of vibration signal from multi-fault gearbox. The scale exponents are abrupt changed with the gradual increasing of time scales, which can be observed in the scaling-law curve. Secondly, a criterion based on a Quasi-Monte Carlo algorithm is developed to uncover optimal scaling intervals of scaling-law curve. Several different scaling regions are objectively measured in each of which a single scale exponent can be estimated. Thirdly, a three-dimensional vector, containing three scale exponents which carry definite physical meaning, is used as the feature parameter to describe the underlying dynamic mechanism hidden in gearbox vibration data. Lastly, these vectors are classified by LS-SVM. Moreover, the method of statistical parameters is exploited to classify the multi-fault vibration data which have been investigated by proposed method. The results show that the proposed method is sensitive to multi-fault vibration data of gearbox with similar fault patterns and has a better performance than other methods

Modeling and analysis of a high-static-low-dynamic stiffness vibration isolator with experimental investigation

In order to attenuate low-frequency vibration, a novel nonlinear vibration isolator with high-static-low-dynamic stiffness (HSLDS) is developed in this paper by combining the negative stiffness corrector in parallel with a vertical linear spring. The force and stiffness characteristics are first derived by the static analysis. Then, the displacement transmissibility of the HSLDS system is obtained to evaluate the isolation performance using the harmonic balance method. The parametric analysis shows that the proposed HSLDS system can outperform the equivalent linear one in some aspects. Besides, the initial isolation frequency is defined and further investigated with the purpose of providing some useful guidelines for choosing parameter combinations conveniently. Finally, a prototype is developed and the experimental test is conducted to verify the isolation performance of the proposed HSLDS system

On the analysis of a piecewise nonlinear-linear vibration isolator with high-static-low-dynamic-stiffness under base excitation

A piecewise nonlinear vibration isolator with high-static-low-dynamic-stiffness (HSLDS) is presented in this paper. This nonlinear vibration isolator is comprised of a vertical spring and two pre-compressed cam-roller-spring mechanisms used as the stiffness correctors. Firstly, the static analysis of the vibration isolator is analyzed. The primary resonance of the system under harmonic base excitation is derived by applying the averaging method and further verified by the direct numerical integration. The effect of base excitation amplitude and damping ratio on the resonance frequency is considered. The stability analysis of the primary resonance is also studied. Then, the frequency island phenomenon is found and confirmed by numerical method. The parameter analysis on the appearance of frequency island is also considered. Finally, the absolute displacement transmissibility of the vibration isolator is defined and compared with the conventional HSLDS vibration isolator and the equivalent linear one. The results show that it exhibits a wider frequency range of vibration isolation than the equivalent linear vibration isolator. When the base excitation amplitude takes a larger value, the unbounded response which occurs in the conventional HSLDS vibration isolator can also be avoided, then a better isolation performance can be achieved

Response and performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness under shock excitations

A nonlinear vibration isolator with High-Static-Low-Dynamic-Stiffness (HSLDS) characteristic comprised of vertical spring and horizontal spring is presented in this paper. Response of the nonlinear vibration isolator under three different kinds of base shock excitations is considered, the dynamic motion can be approximately described by the classic Duffing equation. A transformation function and ultra-spherical polynomial approximation method are employed to determine the shock response and compared with numerical method. Then performance of the nonlinear vibration isolator under shock excitations is evaluated by three performance indicies (Maximum Absolute Displacement Ratio (MADR), Maximum Relative Displacement Ratio (MRDR) and Maximum Acceleration Ratio (MAR)), and also compared with a linear one. Results show that the analytic method suits for weak nonlinearity and the performance of the nonlinear vibration isolator under shock excitations is greatly influenced by the input shock magnitude and structural parameters

The Higher Educational Transformation of China and Its Global Implications

This paper documents the major transformation of higher education that has been underway in China since 1999 and evaluates its potential global impacts. Reflecting China's commitment to continued high growth through quality upgrading and the production of ideas and intellectual property as set out in both the 10th (2001-2005) and 11th (2006-2010) five-year plans, this transformation focuses on major new resource commitments to tertiary education and also embodies significant changes in organizational form. This focus on tertiary education differentiates the Chinese case from other countries who earlier at similar stages of development instead stressed primary and secondary education. The number of undergraduate and graduate students in China has been grown at approximately 30% per year since 1999, and the number of graduates at all levels of higher education in China has approximately quadrupled in the last 6 years. The size of entering classes of new students and total student enrollments have risen even faster, and have approximately quintupled. Prior to 1999 increases in these areas were much smaller. Much of the increased spending is focused on elite universities, and new academic contracts differ sharply from earlier ones with no tenure and annual publication quotas often used. All of these changes have already had large impacts on China's higher educational system and are beginning to be felt by the wider global educational structure. We suggest that even more major impacts will follow in the years to come and there are implications for global trade both directly in ideas, and in idea derived products. These changes, for now, seem relatively poorly documented in literature.

A Study on Defect Identification of Planetary Gearbox under Large Speed Oscillation

Rotational speed of a reference shaft is the key information for planetary gearbox condition monitoring under nonstationary conditions. As the time-variant speed and load of planetary gearboxes result in time-variant characteristic frequencies as well as vibration magnitudes, the conventional methods tracking time-frequency ridge perform a poor robustness, especially for large speed variations. In this paper, two schemes, time-frequency ridge fusion and logarithm transformation, are proposed to track the targeted ridge curve reliably. Meanwhile, the identified ridge curve by logarithm scheme can be further refined by the time-frequency ridge fusion scheme. Hence, a procedure involving the proposed ridge estimation methods is presented to diagnose the planetary gearbox defects. Two simulation signals and a vibration signal collected from a planetary gearbox in practical engineering (provided by the conference on condition monitoring of machinery in nonstationary operations (CMMNO)) are used to verify the proposed methods. It is validated that the proposed methods can well-track the targeted ridge curve compared with two conventional methods. As a result, the characteristic frequency of each component in the planetary gearbox is clearly demonstrated and the inner race defect of one of the planet bearings is successfully discovered in the order spectrum depending on the derived expression of planet bearing fault frequency

An intelligent fault diagnosis method of rotating machinery based on deep neural networks and time-frequency analysis

As the crucial part of the health management and condition monitoring of mechanical equipment, the fault diagnosis and pattern recognition using vibration signal are essential researching contents. The time-frequency representation method cannot identify the fault patterns from time-frequency representation effectively because of the complex work conditions of rotating machinery parts and the interference of strong background noise. Considering these disadvantages, a new reliable and effective method based on the time-frequency representation and deep convolutional neural networks is presented. In this method, the time-frequency features are calculated by the short time Fourier transform (STFT), and the pseudo-color map as the new identification objects. A novel feature learning method based on the sparse autoencode with linear decode is used to extract these time-frequency features, which is an unsupervised feature learning method with the goal of minimizing the loss function. The convoluting and pooling are applied to establish the hierarchical deep convolutional neural networks and filter the useful features layer by layer from the output of sparse autoencode. And a softmax classifier is used to obtain the faults classification. The experimental datasets from roller bearing and gearbox have been taken to verify the reliability and effectiveness of the proposed method for fault diagnosis and pattern recognition. The results show that the proposed method have excellent performance of the recognized objects

Pessimistic Portfolio Choice with One Safe and One Risky Asset and Right Monotone Probability Difference Order

As is well known, a first-order dominant deterioration in risk does not necessarily cause a risk-averse investor to reduce his holdings of that deteriorated asset under the expected utility framework, even in the simplest portfolio setting with one safe asset and one risky asset. The purpose of this paper is to derive conditions on shifts in the distribution of the risky asset under which the counterintuitive conclusion above can be overthrown under the rank-dependent expected utility framework, a more general and prominent alternative of the expected utility. Two new criterions of changes in risk, named the monotone probability difference (MPD) and the right monotone probability difference (RMPD) order, are proposed, which is a particular case of the first stochastic dominance. The relationship among MPD, RMPD, and the other two important stochastic orders, monotone likelihood ratio (MLR) and monotone probability ratio (MPR), is examined. A desired comparative statics result is obtained when a shift in the distribution of the risky asset satisfies the RMPD criterion

An automatic feature extraction method and its application in fault diagnosis

The main challenge of fault diagnosis is to extract excellent fault feature, but these methods usually depend on the manpower and prior knowledge. It is desirable to automatically extract useful feature from input data in an unsupervised way. Hence, an automatic feature extraction method is presented in this paper. The proposed method first captures fault feature from the raw vibration signal by sparse filtering. Considering that the learned feature is high-dimensional data which cannot achieve visualization, t-distributed stochastic neighbor embedding (t-SNE) is further selected as the dimensionality reduction tool to map the learned feature into a three-dimensional feature vector. Consequently, the effectiveness of the proposed method is verified using gearbox and bearing experimental datas. The classification results show that the hybrid method of sparse filtering and t-SNE can well extract discriminative information from the raw vibration signal and can clearly distinguish different fault types. Through comparison analysis, it is also validated that the proposed method is superior to the other methods