M. El Badaoui

Cyclostationary modelling of rotating machine vibration signals

Abstract This paper is dedicated to modelling rotating machine signals as cyclostationary processes, with strong emphasis on the peculiarities and pitfalls that this issue implies. The objective is to demonstrate that machine signals require specific processing that are much more subtle than for communication signals—from which the paradigm of cyclostationarity was originally issued from and developed for. First, different types of cyclostationarity embracing a multitude of rotating machine signals are distinguished. In particular, the importance of considering pure rather than impure cyclostationarity is stressed out. Next, the relationships between angle and time cyclostationarity are investigated and some useful results are derived. It is shown that vibration signals exhibit cyclostationarity if and only if the random speed fluctuation of the machine is periodic, stationary or cyclostationary. Finally, a comprehensive methodology is proposed for processing actual cyclostationary signals: three typical examples dealing with vibration signals of an IC engine, a gearbox and a rolling element bearing are presented, each of them being characterised by a different type of cyclostationarity. The methodology proposed in this paper is general enough and may serve as a guideline for modelling and analysing other types of rotating machine signals, such as pressure signals, electric signals, etc.

Blind separation of convolved cyclostationary processes

A non-parametric method is presented for the blind separation of convolved cyclostationary processes such as those typically observed at the output of MIMO systems driven by periodically modulated random processes. The approach is formulated in the frequency domain and is deductive in the sense that it follows the lines of optimal supervised filtering--from which the relationships to be used in the unsupervised situation are derived. This leads to an algorithm where the successive diagonalisations of some cyclic spectral density matrices give rise to unique separating filters. One important result concerns the proposal of solutions to unambiguously recover the exact source permutation at each frequency. A statistical performance analysis of the method is also conducted, with the results suggesting some strategies to increase the robustness of the separation. Examples of successful separation are finally provided on realistic convolutive mixtures, both synthetic and from the real world, where impulse responses of several thousands of coefficients are dealt with.

A frequency domain-based approach for blind MIMO system identification using second-order cyclic statistics

This article introduces a new frequency domain approach for either MIMO system identification or source separation of convolutive mixtures of cyclostationary signals. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency bin up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency-dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each input signal has a different and specific cyclic frequency. Simulation examples are presented to illustrate the effectiveness of this approach.

Robotic High Speed Machining of Aluminum Alloys

The robotic machining is one of the most versatile manufacturing technologies. Its emerging helped to reduce the machining cost of complex parts. However, its application is sometimes limited due to the low rigidity of the robot. This low stiffness leads to high level of vibrations that limit the quality and the precision of the machined parts. In the present study, the vibration response of a robotic machining system was investigated. To do so, a new method based on the variation of spindle speed was introduced for machining operation and a new process stability criterion (CS) based on acceleration energy distribution and force signal was proposed for analysis. With the proposed method the vibrations and the cutting force signals were collected and analyzed to find a reliable dynamic stability machining domain. The proposed criterion and method were validated using data obtained during high speed robotic machining of 7075-T6 blocks. It was found that the ratio of the periodic energy on the total energy (either vibrations or cutting forces) is a good indicator for defining the degree of stability of the machining process. Besides, it was observed that the spindle speed with the highest ratio stability criterion is the one that has the highest probability to generate the best surface finish. The proposed method is rapid and permits to avoid trial-error tests during robot programming.

Chatter Detection in CNC Milling Processes Based on Wiener-SVM Approach and Using Only Motor Current Signals

The CNC milling is one of the most common processes in modern manufacturing, which characterized by highly nonlinear behavior and chatter problems. As other complex processes, Chatter detection in this situation is a crucial step for improving surface quality and reducing both noise and rapid wear of the cutting tool. This paper proposes a new methodology for chatter detection in computer numerical control milling machines. The originality of this method consists for using only motor current signals picked from electrical cabinet of machine and artificial intelligent. The methodology can be decomposed into four general tasks: (1) data acquisition, (2) signal processing, (3), features generation and selection, (4) classification. In signal processing task, electrical signals are resynchronized according to the electrical cycle (60 Hz) by exploiting the cyclostationarity of electrical signals through their cyclic statistics. After that, synchronous average is computed and subtracted from original signals in order to obtain the residual part. Wiener filter is then applied on residual signals by taking as reference the residual electrical signals acquired in spindle free rotation. This procedure allows estimating a signals corresponding to the electrical part and extracting the mechanical part, which linked to a chatter phenomenon and cutting mechanism. The signal processing task is primordial in order to decrease the dynamics of the electrical fundamental component and its harmonics and also to increase the contribution of mechanical parts. Extracted features computed from mechanical parts are then ranked based on theirs entropies in which only best features are selected and presented to the system for classification. At the classification step, the selected features are classified into two classes: stable and unstable utilizing a support vector machine (SVM). The intelligent chatter detection has accuracy above 96 % for the identification of cutting state after being trained by experimental data. The results show that it is possible to monitor chatter behavior in milling process by using motor current signal.

Techniques to estimate the instantaneous frequency with an aim of diagnosis induction machines faults

In this work we present a new techniques to detect a mechanical faults in asynchronous machines by exploiting the instantaneous frequencies estimated starting from an accelerometer sensor, optical encoder and stator current. Bearing damages cause a torque oscillations as well as a disturbance in the velocity signal which can be detected by a mechanical measurements. These fluctuations will be reflected on the stator currents and cause a phase modulation. Where, the idea to exploit the instantaneous frequency in order to find informations related to the defect. An experimental data were used to verify the validity of the different techniques. Data were collected through an accelerometer sensor to measure the mechanical vibrations, an optical encoder fixed on rotor shaft and by electrical measurements. The results, in presence of natural raceway bearing fault, illustrate the very good performance of the proposed methods.

On blind MIMO system identification based on second-order cyclic statistics

This letter introduces a new frequency domain approach for either MIMO System Identification or Source Separation of convolutive mixtures in cyclostationary context. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each input has a different and specific cyclic frequency. A comparison with an existing MIMO method is proposed.

Deterministic/cyclostationary Signal Separation Using Bootstrap

Abstract Cyclostationarity (CS) is relatively a new technique that offers diagnostic advantages for analysis of faults related to a studied system. The aim of this paper is to address the issue of separating the second-order cyclostationary (CS2) component from the first-order cyclostationary component (CS1) of a signal when low speed fluctuations exist. A bootstrap-based method called Generalized Seasonal Block Bootstrap (GSBB) is applied on walking signals coming from elderly in order to characterize walking in this population and possible age-related walking disturbance, in one hand, and to explore and analyze the influence of low speed fluctuations on the first and second orders cyclostationary properties of signals, on the other hand. Two GSBB-based indicators have also been proposed to characterize the quality of the CS1 and CS2 estimates.

Cyclostationarity analysis of instantaneous angular speeds for monitoring chatter in high speed milling

The detection of chatter is crucial in machining process and its monitoring is a key issue, so as to insure a better surface quality, to increase productivity and to protect both the machine and the workpiece. An investigation of chatter monitoring in high speed machining process on the basis of cyclostationary analysis of the instantaneous angular speeds is presented in this paper. Experimental cutting tests were carried out on slot milling operations of aluminum alloy. Our experimental set-up allows for the measurement of instantaneous angular speed by using the signal delivered by the standard encoder mounted on the spindle motors. Monitoring chatter in high speed milling, made particularly call to the cyclostationary character of instantaneous angular speeds signals. The cyclostationarity appears on average properties (first order) of signals and on the energetic properties (second order). We show the importance of the utilization of these two kinds of cyclostationarity, particularly to distinguish between stable and unstable machining conditions. The results show that stable machining generates only very few cyclostationary components of second order. The appearance of the chatter, which is characterized by unstable, chaotic motion of the tool and by a strong anomalous fluctuations of cutting forces, makes growing strongly the level of cyclostationary components of second order.

Gear Signal Separation by Exploiting the Spectral Diversity and Cyclostaionarity

This paper deals with the problem concerning the framework of rotating machines diagnostics by using signal processing advanced tools and more precisely blind source separation (BSS) methods. An application on gear box is given, the objective is to separate gear mesh signals corresponding to each reducers wheel. It enables us to diagnose and separate each defect in the event of degradation. The proposed method exploits the information redundancy around the meshing frequency and its harmonics resulting from cyclostationarity properties. This redundancy allows us to separate the contribution of each wheel from only one sensor, by tacking advantage of the non-uniformity of the mechanical structure frequency response (MSFR) connecting the exciting source to the sensor