Margenau-Hill Distribution Research Articles

Exploring quasiprobability approaches to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution.

In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general way to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.

Discriminating the lubrication condition from the rotor bearing fault in induction motors using Margenau-Hill frequency distribution and artificial neural networks

PurposeAbout 13 to 44 per cent of motor faults are caused by bearing failures in induction motors (IMs), where lubrication plays a significant role in maintaining rotating equipment because it minimizes friction and prevents wear by separating parts that move next to each other, and more than 35 per cent of bearing failures can be attributed to improper lubrication. An excessive amount of grease causes the rollers or balls to slide along the race instead of turning, and the grease will actually churn. This churning action will eventually wear down the base oil of the grease and all that will be left to lubricate the bearing is a thickener system with little or no lubricating properties. The heat generated from the churning, insufficient lubricating oil will begin to harden the grease, and this will prevent any new grease added to the bearing from reaching the rolling elements, with the consequence of bearing failure and equipment downtime. Regarding the case of grease excess in bearings, this case has not been sufficiently studied. This work aims to present an effective methodology applied to the detection and automatic classification of mechanical bearing faults and bearing excessively lubricated conditions in an IM through the Margenau-Hill distribution (MHD) and artificial neural networks (ANNs), where the obtained results demonstrate the correct classification of the studied cases.Design/methodology/approachThis work proposed an effective methodology applied to the detection and automatic classification of mechanical bearing faults and bearing excessively lubricated conditions in an IM through the MHD and ANNs.FindingsIn this paper, three cases of study for a bearing in an IM are studied, detected and classified correctly by combining some methods. The marginal frequency is obtained from the MHD, which in turn is achieved from the stator current signal, and a total of six features are estimated from the power spectrum, and these features are forwarded to the designed ANN with three output neurons, where each one represents a condition in the IM: healthy bearing, mechanical bearing fault and excessively lubricated bearing.Practical implicationsThe proposed methodology can be applied to other applications; it could be useful to use a time–frequency representation through the MHD for obtaining the energy density distribution of the signal frequency components through time for analysis, evaluation and identification of faults or conditions in the IM for example; therefore, the proposed methodology has a generalized nature that allows its application for detecting other conditions or even multiple conditions under different working conditions by a proper calibration.Originality/valueThe lubrication plays a significant role in maintaining rotating equipment because it minimizes friction and prevents wear by separating parts that move next to each other, and more than 35 per cent of bearing failures can be attributed to improper lubrication and it negatively affects the efficiency of the motor, resulting in higher operating costs. Therefore, in this work, a new methodology is proposed for the detection and automatic classification of mechanical bearing faults and bearing excessively lubricated conditions in an IM through the MHD and ANNs. The proposed methodology uses a total of six features estimated from the power spectrum, and these features are sent to the designed ANN with three output neurons, where each one represents a condition in the IM: healthy bearing, mechanical bearing fault and excessively lubricated bearing. From the obtained results, it was demonstrated that the proposed approach achieves higher classification performance, compared to short-time Fourier transform, Gabor transform and Wigner-Ville distribution methods, allowing to identify mechanical bearing faults and bearing excessively lubricated conditions in an IM, with a remarkable 100 per cent effectiveness during classification for treated cases. Also, the proposed methodology has a generalized nature that allows its application for detecting other conditions or even multiple conditions under different working conditions by a proper calibration.

A Non-Stationary Analysis of Low-Frequency Electromechanical Oscillations Based on a Refined Margenau-Hill Distribution

This paper focuses on the use of quadratic time-frequency distributions (QTFDs) to characterize the temporal variation of low-frequency electromechanical oscillations (LFEOs) using ringdown data. A refined Margenau-Hill distribution (MHD) and a procedure to extract the instantaneous frequencies and damping factors as well as initial phase angles of system low-frequency modes when the analyzed signal is multi-component are proposed. The refinement process enjoys a fast-converging iterative algorithm and without loss of generality it can be applied to other QTFDs for using in other applications. A non-stationary synthetic signal as well as simulated ringdown data of a 5-area, 16-machine power system and real measured data of Western Systems Coordinating Council (WSCC) system are used to demonstrate the efficiency of the proposed method in the presence of measurement noise.

Damage detection based on the propagation of longitudinal guided wave in a bimetal composite pipe

This paper investigates the damage detection based on the propagation of guided wave in bimetal composite pipes, which can identify damage locations in both axial and circumferential directions. The feasibility of the method is showed by numerical simulations using FEM code ANSYS. Mode analysis is used to evaluate the guided wave mode and its structure, which can provide the basis of the mode selection in measurements scheme. The guided wave propagation in a damaged pipe is computed by transient analysis. 16 nodes around the pipe wall, as probes, are used to record the guided wave signal. When Pseudo Margenau—Hill distribution (PMHD) for each signal is carried out, three types of modes could be found, which are led mode, excited mode and lag mode in sequences. Based on the results, the arrival time of the excited mode could be used to locate damage in axial direction, and the energy distribution around the pipe of lag mode is consistent with the damage in circumferential direction. The simulation illustrated the possibility of detecting damage location in both axial and circumferential directions based on longitudinal ultrasonic guided waves only.

Nonclassical properties of coherent states

It is demonstrated that a weak measurement of the squared quadrature observable may yield negative values for coherent states. This result cannot be reproduced by a classical theory where quadratures are stochastic c-numbers. The nonclassicality of coherent states can be associated with negative values of the Terletsky–Margenau–Hill distribution.

A TF distribution for disturbed and undisturbed speech signals and its application to noise reduction

All quadratic time–frequency (TF) representations that provide the TF-shift covariance property belong to the well-known Cohen class. In recent years, several publications have dealt with the problem of choosing the kernel function with respect to the signal to be analyzed. This paper investigates a solution for disturbed and undisturbed speech signals aimed at achieving a good TF analysis for the noise reduction problem. First, we introduce a speech model that defines a certain class of signals. Based on the speech model we develop a new compound kernel consisting of the Margenau–Hill and the Smoothed Pseudo-Wigner distribution and demonstrate its superior performance compared with some popular distributions (Zhang–Sato distribution, Pseudo-Wigner distribution, Smoothed Pseudo-Wigner distribution, S-method). Finally, the so-called ‘Smoothed Margenau–Hill distribution’ is used to design a time–frequency filter for the noise reduction algorithm based on the time-variant Wiener filter for which we obtain promising results.

Bilinear phase-plane distribution functions and positivity

There is a theorem of Wigner that states that phase-plane distribution functions involving the state bilinearly and having correct marginals must take negative values for certain states. The purpose of this paper is to support the statement that these phase-plane distribution functions are for hardly any state everywhere non-negative. In particular, it is shown that for certain generalized Wigner distribution functions there are no smooth states (except the Gaussians for the Wigner distribution function itself) whose distribution function is everywhere non-negative. This class of Wigner-type distribution functions contains the Margenau–Hill distribution. Furthermore, the argument used in the proof of Wigner’s theorem is augmented to show that under mild conditions one can find for any two states f, g with non-negative distribution functions a linear combination h of f and g whose distribution function takes negative values, unless f and g are proportional.