The combination of empirical mode decomposition and minimum entropy deconvolution for roller bearing diagnostics in non-stationary operation

Diagnostics is based on the characterization of mechanical system condition and allows early detection of a possible fault. Signal processing is an approach widely used in diagnostics, since it allows directly characterizing the state of the system. Several types of advanced signal processing techniques have been proposed in the last decades and added to more conventional ones. Seldom, these techniques are able to consider non-stationary operations. Diagnostics of roller bearings is not an exception of this framework. In this paper, a new vibration signal processing tool, able to perform roller bearing diagnostics in whatever working condition and noise level, is developed on the basis of two data-adaptive techniques as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED), coupled by means of the mathematics related to the Hilbert transform. The effectiveness of the new signal processing tool is proven by means of experimental data measured in a test-rig that employs high power industrial size components.

Development of a new signal processing diagnostic tool for vibration signals acquired in transient conditions

The diagnostics of mechanical components operating in transient conditions is still an open issue, in both research and industrial field. Indeed, the signal processing techniques developed to analyse stationary data are not applicable or are affected by a loss of effectiveness when applied to signal acquired in transient conditions. In this paper, a suitable and original signal processing tool (named EEMED), which can be used for mechanical component diagnostics in whatever operating condition and noise level, is developed exploiting some data-adaptive techniques such as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED) and the analytical approach of the Hilbert transform. The proposed tool is able to supply diagnostic information on the basis of experimental vibrations measured in transient conditions. The tool has been originally developed in order to detect localized faults on bearings installed in high speed train traction equipments and it is more effective to detect a fault in non-stationary conditions than signal processing tools based on spectral kurtosis or envelope analysis, which represent until now the landmark for bearings diagnostics.

Effectiveness of MED for Fault Diagnosis in Roller Bearings

Diagnostics of rolling element bearings is usually performed by means of vibration signals measured by accelerometers placed in the proximity of the bearing under investigation. The aim is to monitor the integrity of the bearing components, in order to avoid catastrophic failures, or to implement condition based maintenance strategies. In particular, the trend in this field is to combine in a single algorithm different signal-enhancement and signal-analysis techniques. Among the first ones, Minimum Entropy Deconvolution (MED) has been pointed out as a key tool able to highlight the effect of a possible damage in one of the bearing components within the vibration signal. This paper presents the application of this technique to signals collected on a simple test-rig, able to test damaged industrial roller bearings in different working conditions. The effectiveness of the technique has been tested, comparing the results of one undamaged bearing with three bearings artificially damaged in different locations, namely on the inner race, outer race and rollers. Since MED performances are dependent on the filter length, the most suitable value of this parameter is defined on the basis of both the application and measured signals. This represents an original contribution of the paper.

Signal Processing Diagnostic Tool for Rolling Element Bearings Using EMD and MED

The signal processing techniques developed for the diagnostics of mechanical components operating in stationary conditions are often not applicable or are affected by a loss of effectiveness when applied to signals measured in transient conditions. In this chapter, an original signal processing tool is developed exploiting some data-adaptive techniques such as Empirical Mode Decomposition, Minimum Entropy Deconvolution and the analytical approach of the Hilbert transform. The tool has been developed to detect localized faults on bearings of traction systems of high speed trains and it is more effective to detect a fault in non-stationary conditions than signal processing tools based on envelope analysis or spectral kurtosis, which represent until now the landmark for bearings diagnostics.

Performance assessment of cascade control loopswith non-Gaussian disturbances using entropy information

Cascade control is one of the routinely used control strategies in industrial processes because it can dramatically improve the performance of single-loop control, reducing both the maximum deviation and the integral error of the disturbance response. Currently, many control performance assessment methods of cascade control loops are developed based on the assumption that all the disturbances are subject to Gaussian distribution. However, in the practical condition, several disturbance sources occur in the manipulated variable or the upstream exhibits nonlinear behaviors. In this paper, a general and effective index of the performance assessment of the cascade control system subjected to the unknown disturbance distribution is proposed. Like the minimum variance control (MVC) design, the output variances of the primary and the secondary loops are decomposed into a cascade-invariant and a cascade-dependent term, but the estimated ARMA model for the cascade control loop based on the minimum entropy, instead of the minimum mean squares error, is developed for non-Gaussian disturbances. Unlike the MVC index, an innovative control performance index is given based on the information theory and the minimum entropy criterion. The index is informative and in agreement with the expected control knowledge. To elucidate wide applicability and effectiveness of the minimum entropy cascade control index, a simulation problem and a cascade control case of an oil refinery are applied. The comparison with MVC based cascade control is also included.

Large-scale analysis of soccer matches using spatiotemporal tracking data

Although the collection of player and ball tracking data is fast becoming the norm in professional sports, large-scale mining of such spatiotemporal data has yet to surface. In this paper, given an entire season's worth of player and ball tracking data from a professional soccer league (approx 400,000,000 data points), we present a method which can conduct both individual player and team analysis. Due to the dynamic, continuous and multi-player nature of team sports like soccer, a major issue is aligning player positions over time. We present a "role-based" representation that dynamically updates each player's relative role at each frame and demonstrate how this captures the short-term context to enable both individual player and team analysis. We discover role directly from data by utilizing a minimum entropy data partitioning method and show how this can be used to accurately detect and visualize formations, as well as analyze individual player behavior.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Characterization of Schrödinger Processes with Unbounded Potentials

2000 Mathematics Subject Classification: 49L20, 60J60, 93E20

On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.

Generate disaggregated soil allocation data using a Minimum Cross Entropy Model

Montado ecosystem in the Alentejo Region, south of Portugal, has enormous agro-ecological and economics heterogeneities. A definition of homogeneous sub-units among this heterogeneous ecosystem was made, but for them is disposal only partial statistical information about soil allocation agro-forestry activities. The paper proposal is to recover the unknown soil allocation at each homogeneous sub-unit, disaggregating a complete data set for the Montado ecosystem area using incomplete information at sub-units level. The methodological framework is based on a Generalized Maximum Entropy approach, which is developed in thee steps concerning the specification of a r order Markov process, the estimates of aggregate transition probabilities and the disaggregation data to recover the unknown soil allocation at each homogeneous sub-units. The results quality is evaluated using the predicted absolute deviation (PAD) and the "Disagegation Information Gain" (DIG) and shows very acceptable estimation errors.