A new compound faults detection method for rolling bearings based on empirical wavelet transform and chaotic oscillator

The rolling bearings often suffer from compound faults in practice. The concurrence of different faults increases the fault detection difficulty and the decoupling detection of compound faults is attracting considerable attentions. Recent publications report the application of the multiwavelets and empirical mode decomposition (EMD) for compound faults decoupling. However, due to limited adaptability they would induce mode mixing or/and overestimation problems in the signal processing. Particularly, the mode mixing would greatly degrade their performance on compound faults detection. To address this issue, this work presents a new method based on the empirical wavelet transform-duffing oscillator (EWTDO) for compound faults decoupling diagnosis of rolling bearings. The empirical wavelet transform (EWT) is able to extract intrinsic modes of a signal by fully adaptive wavelet basis. Hence, the mode mixing and overestimation can be resolved in decoupling processing and the compound faults can be correctly decomposed into different single faults in the form of empirical modes. Then, each single fault frequency was incorporated into a duffing oscillator to establish its corresponding fault isolator. By directly observing the chaotic motion from the Poincar mapping of the isolator outputs the single faults were identified one by one from the empirical modes. Experimental tests were carried out on a rolling bearing fault tester to examine the efficacy of the proposed EWTDO method on compound faults detection. The analysis results show attractive performance with respect to existing decoupling approaches based on the multiwavelets and EMD. In particular, our proposed method is much more reliable in decoupling the compound faults. Hence, the proposed method has practical importance in compound faults decoupling diagnosis for rolling bears.     

Dynamic analysis and experiment investigation of a cracked dual-disc bearing-rotor system based on orbit morphological characteristics

The paper is aimed to examine dynamic behaviors of a dual-disc bearing-rotor system in multi-fault state, and the crack detection based on the orbit morphological characteristics and vibration responses is proposed. Dynamic response and vibration signal analysis are two significant studies in rotor system. Most researchers have simulated the nonlinear dynamics and analyzed the fault signal using various methods separately. However, the fault feature from vibration signal is tightly connected with the dynamic mechanism in the rotor system, especially in rotor system with coupling multi-fault. In the paper, the dynamic model of the dual-disc bearing-rotor system is established, which takes into account the effects of crack, rub-impact and nonlinear oil-film forces. The vibration responses and the effect of crack on dual-disc rotor system with multi faults are investigated. The existence of crack and the coupling effect of multi faults enrich dynamic behavior of the dual-disc bearing-rotor system, and the response near the 1/2 subcritical speed provides a criterion for crack detection. Experiment investigation is attempted for the first time, which is based on the changes of crack depth and rotation speed for multi-fault dual-disc rotor system. The analysis of the dynamic response and the orbit morphological characteristics from experiment can effectively detect the crack information.     

Robust state estimation and fault diagnosis for uncertain hybrid systems

Robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems. In this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults. Model uncertainties, disturbances and faults are represented as structured unknown inputs. The robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling. Furthermore, the detectability and mode identifiability conditions are rigorously analyzed. On the basis of the robust hybrid observer, a robust fault detection and isolation scheme is presented also in the paper. Simulations of a hybrid four-tank system show the proposed approach is effective.     

Detection,isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: Application to a waste water treatment process

The goal in many fault detection and isolation schemes is to increase the isolation and identification speed. This paper, presents a new approach of a nonlinear model based adaptive observer method, for detection, isolation and identification of actuator and sensor faults. Firstly, we will design a new method for the actuator fault problem where, after the fault detection and before the fault isolation, we will try to estimate the output of the instrument. The method is based on the formation of nonlinear observer banks where each bank isolates each actuator fault. Secondly, for the sensor problem we will reformulate the system by introducing a new state variable, so that an augmented system can be constructed to treat sensor faults as actuator faults. A method based on the design of an adaptive observers’ bank will be used for the fault treatment. These approaches use the system model and the outputs of the adaptive observers to generate residues. Residuals are defined in such way to isolate the faulty instrument after detecting the fault occurrence. The advantages of these methods are that we can treat not only single actuator and sensor faults but also multiple faults, more over the isolation time has been decreased. In this study, we consider that only abrupt faults in the system can occur. The validity of the methods will be tested firstly in simulation by using a nonlinear model of waste water treatment process with and without measurement noise and secondly with the same nonlinear model but by using this time real data.     

Detection of incipient gear failures using statistical techniques

Gears are important components in most power transmission mechanisms.Failures of gears can cause heavy losses in industry. Conditionmonitoring and fault diagnosis of gears is therefore importantto improve safety and reliability of gearbox operations andreduce losses caused by gear failures. This research proposesa new diagnostic approach based on the statistical analysisof data. It investigates the use of Principal Components Analysis(PCA) to detect growing local faults in a two-stage industrialhelical gearbox. In this research, the vibration signal is usedto monitor fault conditions and a broken tooth is simulatedas a local fault. Since the early detection of faults is a challenge,small fault conditions were tested first as well as severe faultconditions. In order to examine the ability of the PCA to detectfault conditions, first the PCA-based model was created fornormal operating conditions. Any unexpected event such as afault condition causes a significant deviation from the PCAmodel, which is obtained from the normal condition data of thegearbox. The Square Prediction Error (SPE) was calculated todetect the fault conditions. When the vibration signal fromthe gearbox is representative of normal operation, the valueof the SPE shows very little fluctuation and remains under acertain threshold value. However, in the presence of the faultthe SPE fluctuates considerably beyond the threshold value.It is shown that the PCA-based statistical approach cannot onlybe used to detect severe fault conditions, but that it alsoreveals small growing fault conditions at very early stage.The technique also provides information about the state of thefault such as the location of the fault as well as its severity. Received 5 March 2001. Revised 12 December 2001. Accepted 17 January 2002.     

Robust state estimation and fault diagnosis for uncertain hybrid nonlinear systems

Robust state estimation and fault diagnosis are challenging problems in the research of hybrid systems. In this paper, a novel robust hybrid observer is proposed for a class of uncertain hybrid nonlinear systems with unknown mode transition functions, model uncertainties and unknown disturbances. The observer consists of a mode observer for discrete mode estimation and a continuous observer for continuous state estimation. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to unknown transition functions, model uncertainties and disturbances can be guaranteed by disturbance decoupling and selecting proper thresholds. The transition detectability and mode identifiability conditions are rigorously analyzed. Based on the robust hybrid observer, a robust fault diagnosis scheme is presented for faults modeled as discrete modes with unknown transition functions, and the analytical properties are investigated. Simulations of a hybrid three-tank system demonstrate that the proposed approach is effective.     

Fault diagnosis for a class of nonlinear uncertain hybrid systems

This paper presents a fault diagnosis architecture for a class of hybrid systems with nonlinear uncertain time-driven dynamics, measurement noise, and autonomous and controlled mode transitions. The proposed approach features a hybrid estimator based on a modified hybrid automaton framework. The fault detection scheme employs a filtering approach that attenuates the effect of the measurement noise and allows tighter mode-dependent thresholds for the detection of both discrete and parametric faults while guaranteeing no false alarms due to modeling uncertainty and mode mismatches. Both the hybrid estimator and the fault detection scheme are linked with an autonomous guard events identification (AGEI) scheme that handles the effects of mode mismatches due to autonomous mode transitions and allows effective mode estimation. Finally, the fault isolation scheme anticipates which fault events may have occurred and dynamically employs the appropriate isolation estimators for isolating the fault by calculating suitable thresholds and estimating the parametric fault magnitude through adaptive approximation methods. Simulation results from a five-tank hybrid system illustrate the effectiveness of the proposed approach.     

Modelling of Gearbox Vibration and Noise

The paper presents the methodology intended to the vibration and noise analysis of gearboxes or generally of large rotating systems. These systems are considered including their interior rotating shaft system and housing joined together by rollingelement bearings and gear couplings. The new developed bearing model respects real number of rolling bodies and roller contact forces acting between the journals and the outer housing. The model of a complete gearbox is created using the modal synthesis method. Steady state dynamic response of the whole gearbox excited by gear kinematic transmission errors is investigated. A noise radiated by the housing is calculated on the basis of the acoustic power density evaluation. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Early fault detection of rotating machinery through chaotic vibration feature extraction of experimental data sets

Fault detection of rotating machinery by the complex and non-stationary vibration signals with noise is very difficult, especially at the early stages. Also, many failure mechanisms and various adverse operating conditions in rotating machinery involve significant nonlinear dynamical properties. As a novel method, phase space reconstruction is used to study the effect of faults on the chaotic behavior, for the first time. Strange attractors in reconstructed phase space proof the existence of chaotic behavior. To quantify the chaotic vibration for fault diagnosis, a set of new features are extracted. These features include the largest Lyapunov exponent; approximate entropy and correlation dimension which acquire more fault characteristic information. The variations of these features for different healthy/faulty conditions are very good for fault diagnosis and identification. For the first time, a new chaotic feature space is introduced for fault detection, which is made from chaotic behavior features. In this space, different conditions of rotating machinery are separated very well. To obtain more generalized results, the features are introduced into a neural network to identify different faults in rotating machinery. The effectiveness of the new features based on chaotic vibrations is demonstrated by the experimental data sets. The proposed approach can reliably recognize different fault types and have more accurate results. Also, the performance of the new procedure is robust to the variation of load values and shows good generalization capability for various load values.     

Adjustable dimension descriptor observer based fault estimation for switched nonlinear systems with partially unknown nonlinear dynamics

This paper focuses on the fault estimation problem for switched systems with partially unknown nonlinear dynamics, actuator and sensor faults, simultaneously. The fault estimation observers are constructed, in which the observer dimension is not fixed and can be selected in a certain range. Both the disturbance decoupling and disturbance attenuation are considered, where the unknown nonlinear dynamics can be decoupled and the effect of modeling error and measurement disturbance is attenuated. Based on the average dwell time and the piecewise Lyapunov function, the observer parameter matrices can be calculated by solving LMIs and matrix equations. Finally, two examples are listed to verify the proposed fault estimation approach.     

Gain-scheduled fault detection on stochastic nonlinear systems with partially known transition jump rates

In this paper, the problem of continuous gain-scheduled fault detection (FD) is studied for a class of stochastic nonlinear systems which possesses partially known jump rates. Initially, by using gradient linearization approach, the nonlinear stochastic system is described by a series of linear jump models at some selected working points. Subsequently, observer-based residual generator is constructed for each jump linear system. Then, a new observer-design method is proposed for each re-constructed system to design H_∞ observers that minimize the influences of the disturbances, and to formulate a new performance index that increase the sensitivity to faults. Finally, continuous gain-scheduled approach is employed to design continuous FD observers on the whole nonlinear stochastic system. Simulation example is given to show the effectiveness and potential of the developed techniques.     

The fault detection problem in nonlinear systems using residual generators

In this work we study the fault detection problem using residualgenerators based upon high gain nonlinear observers in a differentialalgebraic framework. We analyse the stability of the residualgenerator when a fault occurs. We also consider two faults types:constant and time-varying faults. It is shown that under somemild conditions over the aforementioned faults the residualis different from zero.     

Volterra核函数法在轴承滚珠磨损中的特征提取及应用

针对滚动轴承滚珠磨损故障特征难以提取的问题,提出一种基于多脉冲激励法下的Volterra级数核的求解算法.该方法是一种非线性系统模型的“交叉”诊断法,利用轴承系统输入输出的采样信号,建立Volterra非线性辨识系统模型,并运用多脉冲激励Volterra低阶核求解算法,将得到的低阶核通过时域和频域进行对比来判断轴承当前所处的运行状态.该文以无心车床主轴轴承为例进行实验验证,并与传统的小波分析法对比得出:多脉冲激励法能够方便准确地提取轴承的故障特征,该方法对此类故障的诊断具有一定的借鉴意义.     

Hybrid linear and nonlinear complexity pursuit for blind source separation

Blind source separation (BSS) is an increasingly popular data analysis technique with many applications. Several methods for BSS using the statistical properties of original sources have been proposed; for a famous case, non-Gaussianity, this leads to independent component analysis (ICA). In this paper, we propose a hybrid BSS method based on linear and nonlinear complexity pursuit, which combines three statistical properties of source signals: non-Gaussianity, linear predictability and nonlinear predictability. A gradient learning algorithm is presented by minimizing a loss function. Simulations verify the efficient implementation of the proposed method.     

Qualitative fault tolerance analysis for a class of hybrid systems

This paper investigates the fault tolerance problem of hybrid systems with faults that affect the switching sequence. A hierarchical model is developed, which consists of four parts from bottom to top: hybrid automata, qualitative abstraction, discrete abstraction, and supervisor. Under this model, the reachability and fault tolerability properties of hybrid systems can be analyzed in a qualitative manner and from discrete-event system point of view. Sufficient conditions are given to maintain the system’s ideal (or acceptable) performance in spite of faults. Several numerical examples and an application to hose insertion task illustrate the efficiency of the proposed method.     

A fixed-point algorithm for blind source separation with nonlinear autocorrelation

This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective function based on the nonlinear autocorrelation of sources. Maximizing the objective function, we propose a fixed-point source separation algorithm. Furthermore, we give some mathematical properties of the algorithm. Computer simulations for sources with square temporal autocorrelation and the real-world applications in the analysis of the magnetoencephalographic recordings (MEG) illustrate the efficiency of the proposed approach. Thus, the presented BSS algorithm, which is based on the nonlinear measure of temporal autocorrelation, provides a novel statistical property to perform BSS.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

A Class of Learning/Estimation Algorithms Using Nominal Values: Asymptotic Analysis and Applications

A class of estimation/learning algorithms using stochastic approximation in conjunction with two kernel functions is developed. This algorithm is recursive in form and uses known nominal values and other observed quantities. Its convergence analysis is carried out; the rate of convergence is also evaluated. Applications to a nonlinear chemical engineering system are examined through simulation study. The estimates obtained will be useful in process operation and control, and in on-line monitoring and fault detection.     

Blind separation of vibration signals and source change detection – Application to machine monitoring

The paper presents a new approach for machine vibration analysis and health monitoring combining blind source separation (BSS) and change detection in source signals. So, the problem is transferred from the original space of the measurements to the space of independent sources, where the reduced number of components is going to simplify the monitoring problem while the change detection methods are going to be applied for scalar signals. The assessment of the approach on a real machine is presented in this paper.     

Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization

Chaos optimization algorithms (COAs) usually utilize the chaotic map like Logistic map to generate the pseudo-random numbers mapped as the design variables for global optimization. Many existing researches indicated that COA can more easily escape from the local minima than classical stochastic optimization algorithms. This paper reveals the inherent mechanism of high efficiency and superior performance of COA, from a new perspective of both the probability distribution property and search speed of chaotic sequences generated by different chaotic maps. The statistical property and search speed of chaotic sequences are represented by the probability density function (PDF) and the Lyapunov exponent, respectively. Meanwhile, the computational performances of hybrid chaos-BFGS algorithms based on eight one-dimensional chaotic maps with different PDF and Lyapunov exponents are compared, in which BFGS is a quasi-Newton method for local optimization. Moreover, several multimodal benchmark examples illustrate that, the probability distribution property and search speed of chaotic sequences from different chaotic maps significantly affect the global searching capability and optimization efficiency of COA. To achieve the high efficiency of COA, it is recommended to adopt the appropriate chaotic map generating the desired chaotic sequences with uniform or nearly uniform probability distribution and large Lyapunov exponent.